From 9f546da17c23bbc7cecd499651adada2a1423542 Mon Sep 17 00:00:00 2001 From: Meik Hellmund Date: Fri, 12 May 2023 20:12:56 +0200 Subject: [PATCH] first commit --- .gitignore | 1 + .luarc.json | 22 + .vscode/settings.json | 22 + _quarto.yml | 129 ++ css/dark.scss | 33 + css/light.scss | 17 + css/styles.css | 210 ++ deploy.sh | 7 + ...latin-ext_latin_greek_cyrillic-regular.eot | Bin 0 -> 58390 bytes ...latin-ext_latin_greek_cyrillic-regular.svg | 306 +++ ...latin-ext_latin_greek_cyrillic-regular.ttf | Bin 0 -> 127960 bytes ...atin-ext_latin_greek_cyrillic-regular.woff | Bin 0 -> 64588 bytes ...tin-ext_latin_greek_cyrillic-regular.woff2 | Bin 0 -> 49848 bytes ...latin-ext_latin_greek_cyrillic-regular.eot | Bin 0 -> 58591 bytes ...latin-ext_latin_greek_cyrillic-regular.svg | 308 +++ ...latin-ext_latin_greek_cyrillic-regular.ttf | Bin 0 -> 129584 bytes ...atin-ext_latin_greek_cyrillic-regular.woff | Bin 0 -> 65456 bytes ...tin-ext_latin_greek_cyrillic-regular.woff2 | Bin 0 -> 50476 bytes ...-IEEE_754_Double_Floating_Point_Format.png | Bin 0 -> 9929 bytes images/Int4.aux | 3 + images/Int4.log | 386 ++++ images/Int4.pdf | Bin 0 -> 25695 bytes images/Int4.png | Bin 0 -> 25140 bytes images/Int4.tex | 57 + images/TypeTree2.pdf | Bin 0 -> 26152 bytes images/TypeTree2.png | Bin 0 -> 92282 bytes images/TypeTree2.tex | 61 + images/TypeTree2old.png | Bin 0 -> 476948 bytes images/cache.png | Bin 0 -> 106871 bytes images/favicon-32x32.png | Bin 0 -> 1093 bytes images/julia-logo-color.svg | 10 + images/julia-logo-dark.svg | 10 + images/notebook001.png | Bin 0 -> 67142 bytes images/notebook002.png | Bin 0 -> 84301 bytes images/notebook003.png | Bin 0 -> 125645 bytes images/pi1.pdf | Bin 0 -> 1441 bytes images/pi1.png | Bin 0 -> 90088 bytes images/pi1.tex | 21 + images/pi2.pdf | Bin 0 -> 43905 bytes images/pi2.png | Bin 0 -> 19864 bytes images/pi2.tex | 39 + images/twos-complement-wheel.png | Bin 0 -> 40529 bytes js/plotly-latest.min.js | 8 + macros.tex | 53 + nb/10_Strings.ipynb | 987 ++++++++ nb/5_TricksHelp.ipynb | 562 +++++ nb/6_ArraysEtcP1.ipynb | 303 +++ nb/7_ArraysP2.ipynb | 2054 +++++++++++++++++ nb/9_functs.ipynb | 1142 +++++++++ nb/Erste_Bsp.ipynb | 341 +++ nb/Pi.ipynb | 233 ++ nb/Pi2.ipynb | 313 +++ nb/ablaufsteuerung.ipynb | 83 + nb/entwicklungsumgebungen.ipynb | 167 ++ nb/example.ipynb | 146 ++ nb/first_contact.ipynb | 628 +++++ nb/first_contact.nbconvert.ipynb | 493 ++++ nb/intro.ipynb | 114 + nb/makie.ipynb | 77 + nb/numerictypes.ipynb | 1407 +++++++++++ nb/pcomplex.ipynb | 746 ++++++ nb/script1.sh | 7 + nb/summary.ipynb | 167 ++ nb/syntax.ipynb | 1185 ++++++++++ nb/types.ipynb | 178 ++ notebooks/nb-types.ipynb | 182 ++ notebooks/nb-types.ipynb.html | 615 +++++ notebooks/nb-types.md | 87 + notebooks/nb1.ipynb | 55 + 69 files changed, 13975 insertions(+) create mode 100644 .gitignore create mode 100644 .luarc.json create mode 100644 .vscode/settings.json create mode 100644 _quarto.yml create mode 100644 css/dark.scss create mode 100644 css/light.scss create mode 100644 css/styles.css create mode 100755 deploy.sh create mode 100644 fonts/roboto-condensed-v25-latin-ext_latin_greek_cyrillic-regular.eot create mode 100644 fonts/roboto-condensed-v25-latin-ext_latin_greek_cyrillic-regular.svg create mode 100644 fonts/roboto-condensed-v25-latin-ext_latin_greek_cyrillic-regular.ttf create mode 100644 fonts/roboto-condensed-v25-latin-ext_latin_greek_cyrillic-regular.woff create mode 100644 fonts/roboto-condensed-v25-latin-ext_latin_greek_cyrillic-regular.woff2 create mode 100644 fonts/roboto-v30-latin-ext_latin_greek_cyrillic-regular.eot create mode 100644 fonts/roboto-v30-latin-ext_latin_greek_cyrillic-regular.svg create mode 100644 fonts/roboto-v30-latin-ext_latin_greek_cyrillic-regular.ttf create mode 100644 fonts/roboto-v30-latin-ext_latin_greek_cyrillic-regular.woff create mode 100644 fonts/roboto-v30-latin-ext_latin_greek_cyrillic-regular.woff2 create mode 100644 images/1024px-IEEE_754_Double_Floating_Point_Format.png create mode 100644 images/Int4.aux create mode 100644 images/Int4.log create mode 100644 images/Int4.pdf create mode 100644 images/Int4.png create mode 100644 images/Int4.tex create mode 100644 images/TypeTree2.pdf create mode 100644 images/TypeTree2.png create mode 100644 images/TypeTree2.tex create mode 100644 images/TypeTree2old.png create mode 100644 images/cache.png create mode 100644 images/favicon-32x32.png create mode 100644 images/julia-logo-color.svg create mode 100644 images/julia-logo-dark.svg create mode 100644 images/notebook001.png create mode 100644 images/notebook002.png create mode 100644 images/notebook003.png create mode 100644 images/pi1.pdf create mode 100644 images/pi1.png create mode 100644 images/pi1.tex create mode 100644 images/pi2.pdf create mode 100644 images/pi2.png create mode 100644 images/pi2.tex create mode 100644 images/twos-complement-wheel.png create mode 100644 js/plotly-latest.min.js create mode 100644 macros.tex create mode 100644 nb/10_Strings.ipynb create mode 100644 nb/5_TricksHelp.ipynb create mode 100644 nb/6_ArraysEtcP1.ipynb create mode 100644 nb/7_ArraysP2.ipynb create mode 100644 nb/9_functs.ipynb create mode 100644 nb/Erste_Bsp.ipynb create mode 100644 nb/Pi.ipynb create mode 100644 nb/Pi2.ipynb create mode 100644 nb/ablaufsteuerung.ipynb create mode 100644 nb/entwicklungsumgebungen.ipynb create mode 100644 nb/example.ipynb create mode 100644 nb/first_contact.ipynb create mode 100644 nb/first_contact.nbconvert.ipynb create mode 100644 nb/intro.ipynb create mode 100644 nb/makie.ipynb create mode 100644 nb/numerictypes.ipynb create mode 100644 nb/pcomplex.ipynb create mode 100755 nb/script1.sh create mode 100644 nb/summary.ipynb create mode 100644 nb/syntax.ipynb create mode 100644 nb/types.ipynb create mode 100644 notebooks/nb-types.ipynb create mode 100644 notebooks/nb-types.ipynb.html create mode 100644 notebooks/nb-types.md create mode 100644 notebooks/nb1.ipynb diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..075b254 --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +/.quarto/ diff --git a/.luarc.json b/.luarc.json new file mode 100644 index 0000000..b0d5b85 --- /dev/null +++ b/.luarc.json @@ -0,0 +1,22 @@ +{ + "Generator": [ + "Quarto", + "This file provides type information for Lua completion and diagnostics.", + "Quarto will automatically update this file to reflect the current path", + "of your Quarto installation, and the file will also be added to .gitignore", + "since it points to the absolute path of Quarto on the local system.", + "Remove the 'Generator' key to manage this file's contents manually." + ], + "Lua.runtime.version": "Lua 5.3", + "Lua.workspace.checkThirdParty": false, + "Lua.workspace.library": [ + "/home/hellmund/W/quarto-cli/src/resources/lua-types" + ], + "Lua.runtime.plugin": "/home/hellmund/W/quarto-cli/src/resources/lua-plugin/plugin.lua", + "Lua.completion.showWord": "Disable", + "Lua.completion.keywordSnippet": "Both", + "Lua.diagnostics.disable": [ + "lowercase-global", + "trailing-space" + ] +} \ No newline at end of file diff --git a/.vscode/settings.json b/.vscode/settings.json new file mode 100644 index 0000000..b8c5d67 --- /dev/null +++ b/.vscode/settings.json @@ -0,0 +1,22 @@ +{ + "julia.environmentPath": "/home/hellmund/Julia/23", + "files.exclude": { + "**/.git": true, + "**/.svn": true, + "**/.hg": true, + "**/CVS": true, + "**/.DS_Store": true, + "**/Thumbs.db": true, + "**/*.ipynb": true, + "**/*.md": false + }, + "explorerExclude.backup": {}, + "ltex.enabled": false, + "ltex.language": "de-DE", + "ltex.markdown.nodes": { + "CodeBlock": "ignore", + "FencedCodeBlock": "ignore", + "AutoLink": "dummy", + "Code": "dummy" + } +} \ No newline at end of file diff --git a/_quarto.yml b/_quarto.yml new file mode 100644 index 0000000..ad07ef7 --- /dev/null +++ b/_quarto.yml @@ -0,0 +1,129 @@ +project: + type: book + resources: + - fonts/ + - js/ + - images/ + +lang: de +language: + title-block-published: "Updated" + title-block-author-single: "Autor" + toc-title-document: "Auf dieser Seite" + +book: + title: "Julia für Numerik" + subtitle: "Einführung in die wissenschaftliche Programmierung" + author: "Meik Hellmund" + site-url: "https://www.math.uni-leipzig.de/~hellmund/juliabook" + favicon: "images/favicon-32x32.png" + + sidebar: + logo: "images/julia-logo-color.svg" + tools: + - icon: download + href: "Julia-f%C3%BCr-Numerik.pdf" + + search: false + downloads: [pdf] + date: today + page-footer: + left: | + All content licenced under [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/). + right: | + Created with [Quarto](https://quarto.org/) + background: "#f8f9fa" + + chapters: + - index.qmd + - chapters/entwicklungsumgebungen.qmd + - chapters/first_contact.qmd + - chapters/Erste_Bsp.qmd + - chapters/syntax.qmd + - chapters/5_TricksHelp.qmd + - chapters/numerictypes.qmd + - chapters/Pi2.qmd + - chapters/types.qmd + - chapters/pcomplex.qmd + - chapters/9_functs.qmd + - chapters/6_ArraysEtcP1.qmd + - chapters/7_ArraysP2.qmd + - chapters/10_Strings.qmd + # - chapters/makie.qmd + # - chapters/ablaufsteuerung.qmd + # - chapters/example.qmd + # - chapters/intro.qmd + # - chapters/summary.qmd + + +format: + julia-html: + theme: + light: [cosmo, css/light.scss] + dark: [superhero, css/dark.scss] + css: + - css/styles.css + + highlight-style: github # arrow ????? + mainfont: "Roboto Condensed" # Ubuntu # "Atkinson Hyperlegible" # Ubuntu # Verdana #Quicksand + toc: true # change for Vorlesung + toc-depth: 3 + number-depth: 3 + email-obfuscation: javascript + smooth-scroll: false + grid: + sidebar-width: 250px + body-width: 1150px # 800 + margin-width: 250px + gutter-width: 1.5em + cap-location: bottom + + julia-pdf: + pdf-engine: xelatex + papersize: a4 + documentclass: scrreprt + classoption: [notitlepage,DIV=16,BCOR=5mm,10pt] + toc: false + number-depth: 2 + fig-cap-location: bottom + fig-pos: H + tbl-cap-location: bottom + hyperrefoptions: + - linktoc=all + colorlinks: true + linkcolor: "blue" + keep-tex: true + keep-ipynb: true + keep-md: true + code-block-bg: "#e0e0e0" + code-block-border-left: "#e0e0e0" + code-overflow: wrap + include-in-header: + - file: macros.tex + +latex-auto-install: false + + +execute: + cache: true + output: true + echo: true + warning: true + error: true + eval: true + freeze: auto + daemon: 3600 + +keep-ipynb: true +keep-tex: true +keep-md: true + + +jupyter: julia-1.8 + +filters: + - code-visibility + - julia + - latex-environment + +environments: [quote,indentb] diff --git a/css/dark.scss b/css/dark.scss new file mode 100644 index 0000000..1f384fb --- /dev/null +++ b/css/dark.scss @@ -0,0 +1,33 @@ + +/*-- scss:defaults --*/ + + +$border-radius: 0; + +/* bug in superhero theme? */ +h1,h2,h3,h4,h5,h6 {color: #f0f0f0 !important;} + +/* for output of ?help cells */ +.cell-output h1,h2,h3,h4,h5,h6 {color: #101010;} + +.cell-output code span {color: #000;} + +/*-- scss:rules --*/ +div.cell-output { background-color: #dbdbdb; } + +p code:not(.sourceCode), li code:not(sourceCode) { + background-color: #d9dbc4 !important; +} + +a code { + color: #7f36a3 !important; +} + +img.sidebar-logo { + /* display: none; */ + content: url("images/julia-logo-dark.svg"); +} +/* +img.sidebar-logo::after { + +}*/ \ No newline at end of file diff --git a/css/light.scss b/css/light.scss new file mode 100644 index 0000000..1662eff --- /dev/null +++ b/css/light.scss @@ -0,0 +1,17 @@ + +/*-- scss:defaults --*/ + +$border-radius: 0; +/* $code-block-border-left: #909090; */ +/* $code-block-bg: #f3f3f3; */ +$code-block-bg: #f7f7f7; + +/*-- scss:rules --*/ +div.cell-output { background-color: #ffffff; } +code {color: #202020;} + + +p code:not(.sourceCode), li code:not(sourceCode) { + background-color: #f3f3f3 !important; +} + \ No newline at end of file diff --git a/css/styles.css b/css/styles.css new file mode 100644 index 0000000..f83fcac --- /dev/null +++ b/css/styles.css @@ -0,0 +1,210 @@ + +/* https://google-webfonts-helper.herokuapp.com/fonts/ubuntu?subsets=cyrillic,greek,latin,latin-ext */ +/* ubuntu-regular - latin-ext_latin_greek_cyrillic */ +@font-face { + font-family: 'Ubuntu'; + font-style: normal; + font-weight: 400; + src: url('../fonts/ubuntu-v20-latin-ext_latin_greek_cyrillic-regular.eot'); /* IE9 Compat Modes */ + src: local(''), + url('../fonts/ubuntu-v20-latin-ext_latin_greek_cyrillic-regular.eot?#iefix') format('embedded-opentype'), /* IE6-IE8 */ + url('../fonts/ubuntu-v20-latin-ext_latin_greek_cyrillic-regular.woff2') format('woff2'), /* Super Modern Browsers */ + url('../fonts/ubuntu-v20-latin-ext_latin_greek_cyrillic-regular.woff') format('woff'), /* Modern Browsers */ + url('../fonts/ubuntu-v20-latin-ext_latin_greek_cyrillic-regular.ttf') format('truetype'), /* Safari, Android, iOS */ + url('../fonts/ubuntu-v20-latin-ext_latin_greek_cyrillic-regular.svg#Ubuntu') format('svg'); /* Legacy iOS */ +} + + +/* roboto-condensed-regular - latin-ext_latin_greek_cyrillic */ +@font-face { + font-family: 'Roboto Condensed'; + font-style: normal; + font-weight: 400; + src: url('../fonts/roboto-condensed-v25-latin-ext_latin_greek_cyrillic-regular.eot'); /* IE9 Compat Modes */ + src: local(''), + url('../fonts/roboto-condensed-v25-latin-ext_latin_greek_cyrillic-regular.eot?#iefix') format('embedded-opentype'), /* IE6-IE8 */ + url('../fonts/roboto-condensed-v25-latin-ext_latin_greek_cyrillic-regular.woff2') format('woff2'), /* Super Modern Browsers */ + url('../fonts/roboto-condensed-v25-latin-ext_latin_greek_cyrillic-regular.woff') format('woff'), /* Modern Browsers */ + url('../fonts/roboto-condensed-v25-latin-ext_latin_greek_cyrillic-regular.ttf') format('truetype'), /* Safari, Android, iOS */ + url('../fonts/roboto-condensed-v25-latin-ext_latin_greek_cyrillic-regular.svg#RobotoCondensed') format('svg'); /* Legacy iOS */ +} + +/* roboto-regular - latin-ext_latin_greek_cyrillic */ +@font-face { + font-family: 'Roboto'; + font-style: normal; + font-weight: 400; + src: url('../fonts/roboto-v30-latin-ext_latin_greek_cyrillic-regular.eot'); /* IE9 Compat Modes */ + src: local(''), + url('../fonts/roboto-v30-latin-ext_latin_greek_cyrillic-regular.eot?#iefix') format('embedded-opentype'), /* IE6-IE8 */ + url('../fonts/roboto-v30-latin-ext_latin_greek_cyrillic-regular.woff2') format('woff2'), /* Super Modern Browsers */ + url('../fonts/roboto-v30-latin-ext_latin_greek_cyrillic-regular.woff') format('woff'), /* Modern Browsers */ + url('../fonts/roboto-v30-latin-ext_latin_greek_cyrillic-regular.ttf') format('truetype'), /* Safari, Android, iOS */ + url('../fonts/roboto-v30-latin-ext_latin_greek_cyrillic-regular.svg#Roboto') format('svg'); /* Legacy iOS */ +} +/* quicksand-regular - latin-ext_latin */ +@font-face { + font-family: 'Quicksand'; + font-style: normal; + font-weight: 400; + src: url('../fonts/quicksand-v30-latin-ext_latin-regular.eot'); /* IE9 Compat Modes */ + src: local(''), + url('../fonts/quicksand-v30-latin-ext_latin-regular.eot?#iefix') format('embedded-opentype'), /* IE6-IE8 */ + url('../fonts/quicksand-v30-latin-ext_latin-regular.woff2') format('woff2'), /* Super Modern Browsers */ + url('../fonts/quicksand-v30-latin-ext_latin-regular.woff') format('woff'), /* Modern Browsers */ + url('../fonts/quicksand-v30-latin-ext_latin-regular.ttf') format('truetype'), /* Safari, Android, iOS */ + url('../fonts/quicksand-v30-latin-ext_latin-regular.svg#Quicksand') format('svg'); /* Legacy iOS */ +} + +/* atkinson-hyperlegible-regular - latin-ext_latin */ +@font-face { + font-family: 'Atkinson Hyperlegible'; + font-style: normal; + font-weight: 400; + src: url('../fonts/atkinson-hyperlegible-v10-latin-ext_latin-regular.eot'); /* IE9 Compat Modes */ + src: local(''), + url('../fonts/atkinson-hyperlegible-v10-latin-ext_latin-regular.eot?#iefix') format('embedded-opentype'), /* IE6-IE8 */ + url('../fonts/atkinson-hyperlegible-v10-latin-ext_latin-regular.woff2') format('woff2'), /* Super Modern Browsers */ + url('../fonts/atkinson-hyperlegible-v10-latin-ext_latin-regular.woff') format('woff'), /* Modern Browsers */ + url('../fonts/atkinson-hyperlegible-v10-latin-ext_latin-regular.ttf') format('truetype'), /* Safari, Android, iOS */ + url('../fonts/atkinson-hyperlegible-v10-latin-ext_latin-regular.svg#AtkinsonHyperlegible') format('svg'); /* Legacy iOS */ +} + + + /* https://stackoverflow.com/questions/65480036/bootstrap-5-underline-default-changed */ + /* Bootstrap 5 tweak: do not underline links unless hovered over */ + +a:not([class*="btn"]) { + text-decoration: none; +} +a:not([class*="btn"]):hover { + text-decoration: underline; +} + +/* Code cells -------------------------------------------------- */ +pre, .cell-output { + color: #202020; +} + +pre.sourceCode { + font-size: 0.90em !important; +} + +div:has(pre.sourceCode.default) { /* not-julia cells */ + margin-bottom: 1.0em; +} + +div.cell { +/* border: 2px solid #f0f0f0!important; */ + margin-bottom: 1em; + border: 1px #ccc solid; + border-left-color: green; + border-left-width: medium; +} + +div.sourceCode{ + border-radius: 0; + margin: 0; +} + +div.cell-output { + margin-bottom: 0.4em; +/* font-family: JuliaMono; */ + padding-left:0.5em; +} + +.cell-output code { + padding-left: .5em; +} + + +.cell-output pre { + margin: 0; + padding-top: 0.3em; + font-size: 0.9em !important; +} + +code { + /* color: #202020; nur in light theme*/ + font-size: 0.9em !important; + font-variant-ligatures: no-contextual; +} + +p code:not(.sourceCode), li code:not(sourceCode) { + /* background-color: #f3f3f3 !important; */ + padding: 0.05em 0.2em 0.05em 0.2em !important; +} + +/* markdown: > text ---------------------------------- */ +.blockquote { + line-height: 120%; + margin-left: 0; + font-size: 0.925rem; +} + + +/* my own environment ------------------------------- */ +.indentb { + margin-left:3.5em; + font-size:.9rem; + border-left: 3px solid #f0f0f0; + padding-left:1em; +} + +/* class for callout header with non-bold title --------------*/ +.titlenormal div.callout-header { + font-weight: 400 !important; +} + +/* nehmen wir nicht wg Farbe in dark theme +kbd { + padding: 0.05rem !important; +} +*/ + +/* Julia ?name output 'Example' ------------------*/ +div.cell-output h6 { + font-weight: bold !important; + margin-left: 1em !important; + font-size: 0.9em !important; +} + +/* code cell in callout: no border -------*/ +div.callout .cell { + border-left-width: 0 !important; + border-right-width: 0 !important; + border-top-width: 0 !important; + border-bottom-width: 0 !important; +} + +/* code cells ```julia (ohne exec) */ +:not(.cell) div.sourceCode:not(.cell-code){ + margin-bottom: 1em; +} + +/* my own div, esp. for tables*/ +div.narrow { + width: 70%; + margin-left: auto; + margin-right: auto; +} + +/* my own div for phaistos */ +div.cellmerge div.cell:first-of-type { + margin-bottom: 0; + border-bottom: 0; +} + +div.cellmerge div.cell:nth-of-type(2) { + border-top: 0; +} + + +.math.inline .MathJax { + font-size: 100% !important; +} + +.math.display .MathJax { + font-size: 104% !important; +} + diff --git a/deploy.sh b/deploy.sh new file mode 100755 index 0000000..a33d3af --- /dev/null +++ b/deploy.sh @@ -0,0 +1,7 @@ +#!/bin/bash + +# falls nicht richtig upgedated: +# rm -rf .quarto _freeze +# quarto render + +rsync -avch --delete _book/ ~/HTML/juliabook diff --git a/fonts/roboto-condensed-v25-latin-ext_latin_greek_cyrillic-regular.eot b/fonts/roboto-condensed-v25-latin-ext_latin_greek_cyrillic-regular.eot new file mode 100644 index 0000000000000000000000000000000000000000..39bbda85c3e54f7a1b5c59f0147a97d92ee7ecab GIT binary patch literal 58390 zcma%hWl$VU(B|%9i!bi(?oMEFcX!v|?pb`X;0_7y8r!C)5C$|Fj#x7GU?E_Wn=X{>R1ok7EaL0Qdr209F96 z{}4ui{(p$qe+;Mp;Zp;60h|CH03SdIAogDrUI6!hE200G|3C2o0BIcs&Hv|6|KlP6 zh1mfO!hoh$z(+#-xy!^Un{5X)Cy_p}Uh#C?LTys6Jnk!ca(o_upe=uyCQBVYErqVs 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\tkzDefShiftPoint[M](40:2){A} % polar coord rel.to M: 40deg, r=2 + \tkzDefShiftPoint[M](-40:2){C} % rel. to M: -40deg, r=2 + \tkzDefShiftPoint[M](0:2){B} % just 2 steps to the right + \tkzInterLL(A,C)(M,B) + \tkzGetPoint{N} % intersection of lines + \tkzDrawArc[delta=10,very thick](M,C)(A) % arc + \tkzDrawPoints(M,A,B,C,N) + \tkzLabelPoints[below](M,C) + \tkzLabelPoints[above right](A) + \tkzLabelPoints[right](B) + \tkzLabelPoints[below left](N) + + \tkzDrawSegment[green, very thick](A,B) + \tkzDrawSegment[green, very thick](B,C) + \tkzDrawSegment[blue, very thick](A,C) + \tkzDrawSegment[black, very thick](M,B) + \tkzDrawSegment[black, very thick](M,A) + \tkzDrawSegment[black, very thick](M,C) + + \tkzLabelSegment[above,pos=.5](M,A){$1$} + \tkzLabelSegment[above,pos=.5](M,C){$1$} + \tkzMarkRightAngle[size=.08](M,N,A) + \tkzLabelSegment[above,pos=.5](M,N){$a$} + \tkzLabelSegment[above,pos=.5](N,B){$1-a$} + \tkzLabelSegment[below right,pos=.45](A,B){$s_{2n}$} + \tkzLabelSegment[left,pos=.4](A,C){$s_{n}$} + \tkzLabelSegment[below left,pos=.3](B,C){$s_{2n}$} + +\end{tikzpicture} + +\end{document} + diff --git a/images/twos-complement-wheel.png b/images/twos-complement-wheel.png new file mode 100644 index 0000000000000000000000000000000000000000..b644026558321cab40d370a7fdb3de2d40da1fe6 GIT binary patch literal 40529 zcmbTeWmp|i)2^9>;O_3h-5r8!Ah^4`1lQp1?(Xgm!QBZG++8;AO!L0yJ2P{x`87Yd zw$Q!0dr7UTyPn#iKV`+?VQ^qRefk71DIucp>C@*e;4cpf0{CV+$a@@k`TR>kT??8nhPL z-aF*w6oJ;4JS-UEkl!$AZaMq#uA=5|9XyR-G!u-~qs;FLNz2t8bd}lW#z|yuCaD}a z1jgi9uKwG;e%n2r^;14srjS~CqH4a{OBc_#IBxsPUMY#0rd`+Lyw|+carYMucz*$)Y_IZ_UNM4JM$&G|e!EsGg0;#z0-Rf(mLl)tr{uJris zrgC4M4#RuAG;^y|++c}~zYC_QMe##Zczh-H9`c7;@mb!Hwup|8_BY0sBn)I zq;zAVHT_p)?rn$B>rH4pGD?I(j;-pQkC1^^08*T6?<^nzr7=LV(BQy?v}s1IV4oU0 zV=!Bzx8RG>_Wa}zPR9xOp0!@2-7=$e;d{il>K~Avt}#9Dh005>%7m_zKT^hh*2P^H z??I|jh(XnS5$}B70=OhiK|l)%rCOT39=nuZBjS>gk?j`B5>%n6OlOTNyj>U};0U7k 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e?e.xpx:_[0]._length/2,lt="ypx"in e?e.ypx:w[0]._length/2;if(e.pointerX=st+_[0]._offset,e.pointerY=lt+w[0]._offset,q="xval"in e?y.flat(l,e.xval):y.p2c(_,st),G="yval"in e?y.flat(l,e.yval):y.p2c(w,lt),!i(q[0])||!i(G[0]))return o.warn("Fx.hover failed",e,t),d.unhoverRaw(t,e)}var ft=1/0;function ht(t,r){for(Y=0;Yrt&&(nt.splice(0,rt),ft=nt[0].distance),m&&0!==H&&0===nt.length){et.distance=H,et.index=!1;var f=X._module.hoverPoints(et,Q,tt,"closest",{hoverLayer:c._hoverlayer});if(f&&(f=f.filter((function(t){return t.spikeDistance<=H}))),f&&f.length){var h,d=f.filter((function(t){return t.xa.showspikes&&"hovered data"!==t.xa.spikesnap}));if(d.length){var v=d[0];i(v.x0)&&i(v.y0)&&(h=dt(v),(!at.vLinePoint||at.vLinePoint.spikeDistance>h.spikeDistance)&&(at.vLinePoint=h))}var g=f.filter((function(t){return t.ya.showspikes&&"hovered data"!==t.ya.spikesnap}));if(g.length){var x=g[0];i(x.x0)&&i(x.y0)&&(h=dt(x),(!at.hLinePoint||at.hLinePoint.spikeDistance>h.spikeDistance)&&(at.hLinePoint=h))}}}}}function pt(t,e,r){for(var n,i=null,a=1/0,o=0;o0&&Math.abs(t.distance)At-1;Mt--)Ct(nt[Mt]);nt=St,mt()}var Pt=t._hoverdata,Ot=[],It=U(t),Dt=V(t);for(Z=0;Z1||nt.length>1)||"closest"===I&&ot&&nt.length>1,Yt=p.combine(c.plot_bgcolor||p.background,c.paper_bgcolor),Wt=O(nt,{gd:t,hovermode:I,rotateLabels:Zt,bgColor:Yt,container:c._hoverlayer,outerContainer:c._paper.node(),commonLabelOpts:c.hoverlabel,hoverdistance:c.hoverdistance}),Xt=Wt.hoverLabels;if(y.isUnifiedHover(I)||(function(t,e,r,n){var i,a,o,s,l,u,c,f=e?"xa":"ya",h=e?"ya":"xa",p=0,d=1,v=t.size(),g=new Array(v),y=0,m=n.minX,x=n.maxX,b=n.minY,_=n.maxY,w=function(t){return t*r._invScaleX},k=function(t){return t*r._invScaleY};function A(t){var 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0!==_&&Math.min(c,_)-Math.max(u,b)>1&&("left"===i.side?(s=i._mainLinePosition,l=r.width):l=i._mainLinePosition):void 0!==m&&void 0!==x&&Math.min(c,x)-Math.max(u,m)>1&&("top"===i.side?(s=i._mainLinePosition,l=r.height):l=i._mainLinePosition)}g[y++]=[{datum:t,traceIndex:t.trace.index,dp:0,pos:t.pos,posref:t.posref,size:t.by*(a?T:1)/2,pmin:s,pmax:l}]})),g.sort((function(t,e){return t[0].posref-e[0].posref||d*(e[0].traceIndex-t[0].traceIndex)}));!i&&p<=v;){for(p++,i=!0,s=0;s.01&&L.pmin===C.pmin&&L.pmax===C.pmax){for(l=E.length-1;l>=0;l--)E[l].dp+=a;for(S.push.apply(S,E),g.splice(s+1,1),c=0,l=S.length-1;l>=0;l--)c+=S[l].dp;for(o=c/S.length,l=S.length-1;l>=0;l--)S[l].dp-=o;i=!1}else s++}g.forEach(A)}for(s=g.length-1;s>=0;s--){var P=g[s];for(l=P.length-1;l>=0;l--){var O=P[l],I=O.datum;I.offset=O.dp,I.del=O.del}}}(Xt,Zt,c,Wt.commonLabelBoundingBox),z(Xt,Zt,c._invScaleX,c._invScaleY)),s&&s.tagName){var Jt=g.getComponentMethod("annotations","hasClickToShow")(t,Ot);f(n.select(s),Jt?"pointer":"")}s&&!a&&function(t,e,r){if(!r||r.length!==t._hoverdata.length)return!0;for(var n=r.length-1;n>=0;n--){var i=r[n],a=t._hoverdata[n];if(i.curveNumber!==a.curveNumber||String(i.pointNumber)!==String(a.pointNumber)||String(i.pointNumbers)!==String(a.pointNumbers))return!0}return!1}(t,0,Pt)&&(Pt&&t.emit("plotly_unhover",{event:e,points:Pt}),t.emit("plotly_hover",{event:e,points:t._hoverdata,xaxes:_,yaxes:w,xvals:q,yvals:G}))}(t,e,r,a,s)}))},e.loneHover=function(t,e){var r=!0;Array.isArray(t)||(r=!1,t=[t]);var i=e.gd,a=U(i),o=V(i),s=O(t.map((function(t){var r=t._x0||t.x0||t.x||0,n=t._x1||t.x1||t.x||0,s=t._y0||t.y0||t.y||0,l=t._y1||t.y1||t.y||0,u=t.eventData;if(u){var c=Math.min(r,n),f=Math.max(r,n),h=Math.min(s,l),d=Math.max(s,l),v=t.trace;if(g.traceIs(v,"gl3d")){var y=i._fullLayout[v.scene]._scene.container,m=y.offsetLeft,x=y.offsetTop;c+=m,f+=m,h+=x,d+=x}u.bbox={x0:c+o,x1:f+o,y0:h+a,y1:d+a},e.inOut_bbox&&e.inOut_bbox.push(u.bbox)}else u=!1;return{color:t.color||p.defaultLine,x0:t.x0||t.x||0,x1:t.x1||t.x||0,y0:t.y0||t.y||0,y1:t.y1||t.y||0,xLabel:t.xLabel,yLabel:t.yLabel,zLabel:t.zLabel,text:t.text,name:t.name,idealAlign:t.idealAlign,borderColor:t.borderColor,fontFamily:t.fontFamily,fontSize:t.fontSize,fontColor:t.fontColor,nameLength:t.nameLength,textAlign:t.textAlign,trace:t.trace||{index:0,hoverinfo:""},xa:{_offset:0},ya:{_offset:0},index:0,hovertemplate:t.hovertemplate||!1,hovertemplateLabels:t.hovertemplateLabels||!1,eventData:u}})),{gd:i,hovermode:"closest",rotateLabels:!1,bgColor:e.bgColor||p.background,container:n.select(e.container),outerContainer:e.outerContainer||e.container}).hoverLabels,l=0,u=0;return s.sort((function(t,e){return t.y0-e.y0})).each((function(t,r){var n=t.y0-t.by/2;t.offset=n-5([\s\S]*)<\/extra>/;function O(t,e){var r=e.gd,i=r._fullLayout,a=e.hovermode,u=e.rotateLabels,f=e.bgColor,d=e.container,v=e.outerContainer,w=e.commonLabelOpts||{};if(0===t.length)return[[]];var T=e.fontFamily||m.HOVERFONT,k=e.fontSize||m.HOVERFONTSIZE,A=t[0],E=A.xa,L=A.ya,P=a.charAt(0),O=P+"Label",D=A[O];if(void 0===D&&"multicategory"===E.type)for(var z=0;zi.width-b?(g=i.width-b,e.attr("d","M"+(b-M)+",0L"+b+","+x+M+"v"+x+(2*S+m.height)+"H-"+b+"V"+x+M+"H"+(b-2*M)+"Z")):e.attr("d","M0,0L"+M+","+x+M+"H"+b+"v"+x+(2*S+m.height)+"H-"+b+"V"+x+M+"H-"+M+"Z"),Y.minX=g-b,Y.maxX=g+b,"top"===E.side?(Y.minY=y-(2*S+m.height),Y.maxY=y-S):(Y.minY=y+S,Y.maxY=y+(2*S+m.height))}else{var _,C,P;"right"===L.side?(_="start",C=1,P="",g=E._offset+E._length):(_="end",C=-1,P="-",g=E._offset),y=L._offset+(A.y0+A.y1)/2,l.attr("text-anchor",_),e.attr("d","M0,0L"+P+M+","+M+"V"+(S+m.height/2)+"h"+P+(2*S+m.width)+"V-"+(S+m.height/2)+"H"+P+M+"V-"+M+"Z"),Y.minY=y-(S+m.height/2),Y.maxY=y+(S+m.height/2),"right"===L.side?(Y.minX=g+M,Y.maxX=g+M+(2*S+m.width)):(Y.minX=g-M-(2*S+m.width),Y.maxX=g-M);var O,I=m.height/2,z=F-m.top-I,R="clip"+i._uid+"commonlabel"+L._id;if(g=0?lt:ut+ht=0?ut:bt+ht=0?ot:st+pt=0?st:_t+pt=0,"top"!==t.idealAlign&&G||!Z?G?(O+=R/2,t.anchor="start"):t.anchor="middle":(O-=R/2,t.anchor="end"),t.crossPos=O;else{if(t.pos=O,G=P+z/2+Y<=B,Z=P-z/2-Y>=0,"left"!==t.idealAlign&&G||!Z)if(G)P+=z/2,t.anchor="start";else{t.anchor="middle";var W=Y/2,X=P+W-B,J=P-W;X>0&&(P-=X),J<0&&(P+=-J)}else P-=z/2,t.anchor="end";t.crossPos=P}w.attr("text-anchor",t.anchor),E&&A.attr("text-anchor",t.anchor),e.attr("transform",s(P,O)+(u?l(_):""))})),{hoverLabels:wt,commonLabelBoundingBox:Y}}function I(t,e,r,n,i,a){var s="",l="";void 0!==t.nameOverride&&(t.name=t.nameOverride),t.name&&(t.trace._meta&&(t.name=o.templateString(t.name,t.trace._meta)),s=N(t.name,t.nameLength));var u=r.charAt(0),c="x"===u?"y":"x";void 0!==t.zLabel?(void 0!==t.xLabel&&(l+="x: "+t.xLabel+"
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i,s,l,u,f=r.select("text.nums"),p=t.anchor,d="end"===p?-1:1,v=(u=(l=(s={start:1,end:-1,middle:0}[(i=t).anchor])*(M+S))+s*(i.txwidth+S),"middle"===i.anchor&&(l-=i.tx2width/2,u+=i.txwidth/2+S),{alignShift:s,textShiftX:l,text2ShiftX:u}),g=D(t,e),y=g.x,m=g.y,x="middle"===p;r.select("path").attr("d",x?"M-"+a(t.bx/2+t.tx2width/2)+","+o(m-t.by/2)+"h"+a(t.bx)+"v"+o(t.by)+"h-"+a(t.bx)+"Z":"M0,0L"+a(d*M+y)+","+o(M+m)+"v"+o(t.by/2-M)+"h"+a(d*t.bx)+"v-"+o(t.by)+"H"+a(d*M+y)+"V"+o(m-M)+"Z");var b=y+v.textShiftX,_=m+t.ty0-t.by/2+S,w=t.textAlign||"auto";"auto"!==w&&("left"===w&&"start"!==p?(f.attr("text-anchor","start"),b=x?-t.bx/2-t.tx2width/2+S:-t.bx-S):"right"===w&&"end"!==p&&(f.attr("text-anchor","end"),b=x?t.bx/2-t.tx2width/2-S:t.bx+S)),f.call(c.positionText,a(b),o(_)),t.tx2width&&(r.select("text.name").call(c.positionText,a(v.text2ShiftX+v.alignShift*S+y),o(m+t.ty0-t.by/2+S)),r.select("rect").call(h.setRect,a(v.text2ShiftX+(v.alignShift-1)*t.tx2width/2+y),o(m-t.by/2-1),a(t.tx2width),o(t.by+2)))}))}function R(t,e){var r=t.index,n=t.trace||{},a=t.cd[0],s=t.cd[r]||{};function l(t){return t||i(t)&&0===t}var u=Array.isArray(r)?function(t,e){var i=o.castOption(a,r,t);return l(i)?i:o.extractOption({},n,"",e)}:function(t,e){return o.extractOption(s,n,t,e)};function c(e,r,n){var i=u(r,n);l(i)&&(t[e]=i)}if(c("hoverinfo","hi","hoverinfo"),c("bgcolor","hbg","hoverlabel.bgcolor"),c("borderColor","hbc","hoverlabel.bordercolor"),c("fontFamily","htf","hoverlabel.font.family"),c("fontSize","hts","hoverlabel.font.size"),c("fontColor","htc","hoverlabel.font.color"),c("nameLength","hnl","hoverlabel.namelength"),c("textAlign","hta","hoverlabel.align"),t.posref="y"===e||"closest"===e&&"h"===n.orientation?t.xa._offset+(t.x0+t.x1)/2:t.ya._offset+(t.y0+t.y1)/2,t.x0=o.constrain(t.x0,0,t.xa._length),t.x1=o.constrain(t.x1,0,t.xa._length),t.y0=o.constrain(t.y0,0,t.ya._length),t.y1=o.constrain(t.y1,0,t.ya._length),void 0!==t.xLabelVal&&(t.xLabel="xLabel"in t?t.xLabel:v.hoverLabelText(t.xa,t.xLabelVal,n.xhoverformat),t.xVal=t.xa.c2d(t.xLabelVal)),void 0!==t.yLabelVal&&(t.yLabel="yLabel"in t?t.yLabel:v.hoverLabelText(t.ya,t.yLabelVal,n.yhoverformat),t.yVal=t.ya.c2d(t.yLabelVal)),void 0!==t.zLabelVal&&void 0===t.zLabel&&(t.zLabel=String(t.zLabelVal)),!(isNaN(t.xerr)||"log"===t.xa.type&&t.xerr<=0)){var f=v.tickText(t.xa,t.xa.c2l(t.xerr),"hover").text;void 0!==t.xerrneg?t.xLabel+=" +"+f+" / -"+v.tickText(t.xa,t.xa.c2l(t.xerrneg),"hover").text:t.xLabel+=" ± "+f,"x"===e&&(t.distance+=1)}if(!(isNaN(t.yerr)||"log"===t.ya.type&&t.yerr<=0)){var h=v.tickText(t.ya,t.ya.c2l(t.yerr),"hover").text;void 0!==t.yerrneg?t.yLabel+=" +"+h+" / -"+v.tickText(t.ya,t.ya.c2l(t.yerrneg),"hover").text:t.yLabel+=" ± "+h,"y"===e&&(t.distance+=1)}var p=t.hoverinfo||t.trace.hoverinfo;return p&&"all"!==p&&(-1===(p=Array.isArray(p)?p:p.split("+")).indexOf("x")&&(t.xLabel=void 0),-1===p.indexOf("y")&&(t.yLabel=void 0),-1===p.indexOf("z")&&(t.zLabel=void 0),-1===p.indexOf("text")&&(t.text=void 0),-1===p.indexOf("name")&&(t.name=void 0)),t}function F(t,e,r){var n,i,o=r.container,s=r.fullLayout,l=s._size,u=r.event,c=!!e.hLinePoint,f=!!e.vLinePoint;if(o.selectAll(".spikeline").remove(),f||c){var d=p.combine(s.plot_bgcolor,s.paper_bgcolor);if(c){var g,y,m=e.hLinePoint;n=m&&m.xa,"cursor"===(i=m&&m.ya).spikesnap?(g=u.pointerX,y=u.pointerY):(g=n._offset+m.x,y=i._offset+m.y);var x,b,_=a.readability(m.color,d)<1.5?p.contrast(d):m.color,w=i.spikemode,T=i.spikethickness,k=i.spikecolor||_,A=v.getPxPosition(t,i);if(-1!==w.indexOf("toaxis")||-1!==w.indexOf("across")){if(-1!==w.indexOf("toaxis")&&(x=A,b=g),-1!==w.indexOf("across")){var 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r,n,i,a=[];for(i=0;i0&&a.push(r);if(1===a.length&&a[0]===e.searchInfo&&(n=e.searchInfo.cd[0].trace).selectedpoints.length===e.pointNumbers.length){for(i=0;i1)return!1;if((n+=e.selectedpoints.length)>1)return!1}return 1===n}(s)&&(h=K(_))){for(o&&o.remove(),g=0;g=0})(i)&&i._fullLayout._deactivateShape(i),function(t){return t._fullLayout._activeSelectionIndex>=0}(i)&&i._fullLayout._deactivateSelection(i);var o=i._fullLayout._zoomlayer,s=p(r),l=v(r);if(s||l){var u,c,f=o.selectAll(".select-outline-"+n.id);f&&i._fullLayout._outlining&&(s&&(u=T(f,t)),u&&a.call("_guiRelayout",i,{shapes:u}),l&&!U(t)&&(c=k(f,t)),c&&(i._fullLayout._noEmitSelectedAtStart=!0,a.call("_guiRelayout",i,{selections:c}).then((function(){e&&A(i)}))),i._fullLayout._outlining=!1)}n.selection={},n.selection.selectionDefs=t.selectionDefs=[],n.selection.mergedPolygons=t.mergedPolygons=[]}function W(t){return t._id}function X(t,e,r,n){if(!t.calcdata)return[];var 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n.behavior.zoom().translate(e.translate()).scale(e.scale())}function f(t,e,r){var n=t.id,o=t.graphDiv,s=o.layout,l=s[n],u=o._fullLayout,c=u[n],f={},h={};function p(t,e){f[n+"."+t]=i.nestedProperty(l,t).get(),a.call("_storeDirectGUIEdit",s,u._preGUI,f);var r=i.nestedProperty(c,t);r.get()!==e&&(r.set(e),i.nestedProperty(l,t).set(e),h[n+"."+t]=e)}r(p),p("projection.scale",e.scale()/t.fitScale),p("fitbounds",!1),o.emit("plotly_relayout",h)}function h(t,e){var r=c(0,e);function i(r){var n=e.invert(t.midPt);r("center.lon",n[0]),r("center.lat",n[1])}return r.on("zoomstart",(function(){n.select(this).style(l)})).on("zoom",(function(){e.scale(n.event.scale).translate(n.event.translate),t.render(!0);var r=e.invert(t.midPt);t.graphDiv.emit("plotly_relayouting",{"geo.projection.scale":e.scale()/t.fitScale,"geo.center.lon":r[0],"geo.center.lat":r[1]})})).on("zoomend",(function(){n.select(this).style(u),f(t,e,i)})),r}function p(t,e){var r,i,a,o,s,h,p,d,v,g=c(0,e);function y(t){return 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r=0,n=0,i=t.length;nMath.abs(s)?(u.boxEnd[1]=u.boxStart[1]+Math.abs(a)*_*(s>=0?1:-1),u.boxEnd[1]l[3]&&(u.boxEnd[1]=l[3],u.boxEnd[0]=u.boxStart[0]+(l[3]-u.boxStart[1])/Math.abs(_))):(u.boxEnd[0]=u.boxStart[0]+Math.abs(s)/_*(a>=0?1:-1),u.boxEnd[0]l[2]&&(u.boxEnd[0]=l[2],u.boxEnd[1]=u.boxStart[1]+(l[2]-u.boxStart[0])*Math.abs(_)))}}else u.boxEnabled?(a=u.boxStart[0]!==u.boxEnd[0],s=u.boxStart[1]!==u.boxEnd[1],a||s?(a&&(g(0,u.boxStart[0],u.boxEnd[0]),t.xaxis.autorange=!1),s&&(g(1,u.boxStart[1],u.boxEnd[1]),t.yaxis.autorange=!1),t.relayoutCallback()):t.glplot.setDirty(),u.boxEnabled=!1,u.boxInited=!1):u.boxInited&&(u.boxInited=!1);break;case"pan":u.boxEnabled=!1,u.boxInited=!1,e?(u.panning||(u.dragStart[0]=n,u.dragStart[1]=i),Math.abs(u.dragStart[0]-n).999&&(g="turntable"):g="turntable")}else g="turntable";r("dragmode",g),r("hovermode",n.getDfltFromLayout("hovermode"))}t.exports=function(t,e,r){var i=e._basePlotModules.length>1;o(t,e,r,{type:c,attributes:l,handleDefaults:f,fullLayout:e,font:e.font,fullData:r,getDfltFromLayout:function(e){if(!i)return n.validate(t[e],l[e])?t[e]:void 0},autotypenumbersDflt:e.autotypenumbers,paper_bgcolor:e.paper_bgcolor,calendar:e.calendar})}},65500:function(t,e,r){"use strict";var n=r(77894),i=r(27670).Y,a=r(1426).extendFlat,o=r(71828).counterRegex;function 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i=r.graphDiv,a=i._fullLayout,o=r.fullSceneLayout.camera,s=o.up.x,l=o.up.y,u=o.up.z;if(u/Math.sqrt(s*s+l*l+u*u)<.999){var h=r.id+".camera.up",p={x:0,y:0,z:1},d={};d[h]=p;var v=i.layout;c.call("_storeDirectGUIEdit",v,a._preGUI,d),o.up=p,f.nestedProperty(v,h).set(p)}}else n.keyBindingMode=t;r.fullSceneLayout.hovermode=e},w.toImage=function(t){var e=this;t||(t="png"),e.staticMode&&e.container.appendChild(n),e.glplot.redraw();var r=e.glplot.gl,i=r.drawingBufferWidth,a=r.drawingBufferHeight;r.bindFramebuffer(r.FRAMEBUFFER,null);var o=new Uint8Array(i*a*4);r.readPixels(0,0,i,a,r.RGBA,r.UNSIGNED_BYTE,o),function(t,e,r){for(var n=0,i=r-1;n0)for(var s=255/o,l=0;l<3;++l)t[a+l]=Math.min(s*t[a+l],255)}}(o,i,a);var s=document.createElement("canvas");s.width=i,s.height=a;var l,u=s.getContext("2d",{willReadFrequently:!0}),c=u.createImageData(i,a);switch(c.data.set(o),u.putImageData(c,0,0),t){case"jpeg":l=s.toDataURL("image/jpeg");break;case"webp":l=s.toDataURL("image/webp");break;default:l=s.toDataURL("image/png")}return e.staticMode&&e.container.removeChild(n),l},w.setConvert=function(){for(var t=0;t<3;t++){var e=this.fullSceneLayout[k[t]];p.setConvert(e,this.fullLayout),e.setScale=f.noop}},w.make4thDimension=function(){var t=this,e=t.graphDiv._fullLayout;t._mockAxis={type:"linear",showexponent:"all",exponentformat:"B"},p.setConvert(t._mockAxis,e)},t.exports=_},90060:function(t){"use strict";t.exports=function(t,e,r,n){n=n||t.length;for(var i=new Array(n),a=0;aOpenStreetMap contributors',a=['© Carto',i].join(" "),o=['Map tiles by Stamen Design','under CC BY 3.0',"|",'Data by OpenStreetMap contributors','under ODbL'].join(" 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e,r,s=this,u=s.isSmith,c=s.gd,f=s.layers,h=t._zoomlayer,p=S.MINZOOM,d=S.OFFEDGE,v=s.radius,x=s.innerRadius,T=s.cx,k=s.cy,A=s.cxx,M=s.cyy,L=s.sectorInRad,C=s.vangles,P=s.radialAxis,O=E.clampTiny,I=E.findXYatLength,D=E.findEnclosingVertexAngles,z=S.cornerHalfWidth,R=S.cornerLen/2,F=g.makeDragger(f,"path","maindrag",!1===t.dragmode?"none":"crosshair");n.select(F).attr("d",s.pathSubplot()).attr("transform",l(T,k)),F.onmousemove=function(t){m.hover(c,t,s.id),c._fullLayout._lasthover=F,c._fullLayout._hoversubplot=s.id},F.onmouseout=function(t){c._dragging||y.unhover(c,t)};var B,N,j,U,V,H,q,G,Z,Y={element:F,gd:c,subplot:s.id,plotinfo:{id:s.id,xaxis:s.xaxis,yaxis:s.yaxis},xaxes:[s.xaxis],yaxes:[s.yaxis]};function W(t,e){return Math.sqrt(t*t+e*e)}function X(t,e){return W(t-A,e-M)}function J(t,e){return Math.atan2(M-e,t-A)}function K(t,e){return[t*Math.cos(e),t*Math.sin(-e)]}function $(t,e){if(0===t)return s.pathSector(2*z);var 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s=n(t,r([a,e])),l=s[0],u=s[1],c=n(t,r([o,e])),f=c[0],h=c[1];if(0===e)return["M"+l+","+u,"L"+f+","+h].join(" ");var p=i(t,1/Math.abs(e));return["M"+l+","+u,"A"+p+","+p+" 0 0,"+(e<0?1:0)+" "+f+","+h].join(" ")},resistanceArc:function(t,a,o,s){var l=i(t,1/(a+1)),u=n(t,r([a,o])),c=u[0],f=u[1],h=n(t,r([a,s])),p=h[0],d=h[1];if(e(o)!==e(s)){var v=n(t,r([a,0]));return["M"+c+","+f,"A"+l+","+l+" 0 0,"+(00){for(var n=[],i=0;i=c&&(h.min=0,d.min=0,g.min=0,t.aaxis&&delete t.aaxis.min,t.baxis&&delete t.baxis.min,t.caxis&&delete t.caxis.min)}function v(t,e,r,n){var i=h[e._name];function o(r,n){return a.coerce(t,e,i,r,n)}o("uirevision",n.uirevision),e.type="linear";var p=o("color"),d=p!==i.color.dflt?p:r.font.color,v=e._name.charAt(0).toUpperCase(),g="Component 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M(t,e){this.id=t.id,this.graphDiv=t.graphDiv,this.init(e),this.makeFramework(e),this.aTickLayout=null,this.bTickLayout=null,this.cTickLayout=null}t.exports=M;var S=M.prototype;S.init=function(t){this.container=t._ternarylayer,this.defs=t._defs,this.layoutId=t._uid,this.traceHash={},this.layers={}},S.plot=function(t,e){var r=this,n=e[r.id],i=e._size;r._hasClipOnAxisFalse=!1;for(var a=0;aE*b?i=(a=b)*E:a=(i=x)/E,o=y*i/x,l=m*a/b,r=e.l+e.w*v-i/2,n=e.t+e.h*(1-g)-a/2,p.x0=r,p.y0=n,p.w=i,p.h=a,p.sum=_,p.xaxis={type:"linear",range:[w+2*k-_,_-w-2*T],domain:[v-o/2,v+o/2],_id:"x"},f(p.xaxis,p.graphDiv._fullLayout),p.xaxis.setScale(),p.xaxis.isPtWithinRange=function(t){return t.a>=p.aaxis.range[0]&&t.a<=p.aaxis.range[1]&&t.b>=p.baxis.range[1]&&t.b<=p.baxis.range[0]&&t.c>=p.caxis.range[1]&&t.c<=p.caxis.range[0]},p.yaxis={type:"linear",range:[w,_-T-k],domain:[g-l/2,g+l/2],_id:"y"},f(p.yaxis,p.graphDiv._fullLayout),p.yaxis.setScale(),p.yaxis.isPtWithinRange=function(){return!0};var A=p.yaxis.domain[0],M=p.aaxis=h({},t.aaxis,{range:[w,_-T-k],side:"left",tickangle:(+t.aaxis.tickangle||0)-30,domain:[A,A+l*E],anchor:"free",position:0,_id:"y",_length:i});f(M,p.graphDiv._fullLayout),M.setScale();var S=p.baxis=h({},t.baxis,{range:[_-w-k,T],side:"bottom",domain:p.xaxis.domain,anchor:"free",position:0,_id:"x",_length:i});f(S,p.graphDiv._fullLayout),S.setScale();var L=p.caxis=h({},t.caxis,{range:[_-w-T,k],side:"right",tickangle:(+t.caxis.tickangle||0)+30,domain:[A,A+l*E],anchor:"free",position:0,_id:"y",_length:i});f(L,p.graphDiv._fullLayout),L.setScale();var C="M"+r+","+(n+a)+"h"+i+"l-"+i/2+",-"+a+"Z";p.clipDef.select("path").attr("d",C),p.layers.plotbg.select("path").attr("d",C);var P="M0,"+a+"h"+i+"l-"+i/2+",-"+a+"Z";p.clipDefRelative.select("path").attr("d",P);var O=s(r,n);p.plotContainer.selectAll(".scatterlayer,.maplayer").attr("transform",O),p.clipDefRelative.select("path").attr("transform",null);var 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A=h.select("g.dimensions").selectAll("g.dimension").data((function(t){return t.dimensions}),p);A.enter().append("g").attr("class","dimension"),A.attr("transform",(function(t){return l(t.x,0)})),A.exit().remove();var M=A.selectAll("g.category").data((function(t){return t.categories}),p),S=M.enter().append("g").attr("class","category");M.attr("transform",(function(t){return l(0,t.y)})),S.append("rect").attr("class","catrect").attr("pointer-events","none"),M.select("rect.catrect").attr("fill","none").attr("width",(function(t){return t.width})).attr("height",(function(t){return t.height})),T(S);var E=M.selectAll("rect.bandrect").data((function(t){return t.bands}),p);E.each((function(){s.raiseToTop(this)})),E.attr("fill",(function(t){return t.color}));var D=E.enter().append("rect").attr("class","bandrect").attr("stroke-opacity",0).attr("fill",(function(t){return t.color})).attr("fill-opacity",0);E.attr("fill",(function(t){return t.color})).attr("width",(function(t){return t.width})).attr("height",(function(t){return t.height})).attr("y",(function(t){return t.y})).attr("cursor",(function(t){return"fixed"===t.parcatsViewModel.arrangement?"default":"perpendicular"===t.parcatsViewModel.arrangement?"ns-resize":"move"})),k(D),E.exit().remove(),S.append("text").attr("class","catlabel").attr("pointer-events","none");var z=e._fullLayout.paper_bgcolor;M.select("text.catlabel").attr("text-anchor",(function(t){return d(t)?"start":"end"})).attr("alignment-baseline","middle").style("text-shadow",f.makeTextShadow(z)).style("fill","rgb(0, 0, 0)").attr("x",(function(t){return d(t)?t.width+5:-5})).attr("y",(function(t){return t.height/2})).text((function(t){return 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n=r(9012),i=r(27670).Y,a=r(41940),o=r(22399),s=r(5386).fF,l=r(5386).si,u=r(1426).extendFlat,c=a({editType:"plot",arrayOk:!0,colorEditType:"plot"});t.exports={labels:{valType:"data_array",editType:"calc"},label0:{valType:"number",dflt:0,editType:"calc"},dlabel:{valType:"number",dflt:1,editType:"calc"},values:{valType:"data_array",editType:"calc"},marker:{colors:{valType:"data_array",editType:"calc"},line:{color:{valType:"color",dflt:o.defaultLine,arrayOk:!0,editType:"style"},width:{valType:"number",min:0,dflt:0,arrayOk:!0,editType:"style"},editType:"calc"},editType:"calc"},text:{valType:"data_array",editType:"plot"},hovertext:{valType:"string",dflt:"",arrayOk:!0,editType:"style"},scalegroup:{valType:"string",dflt:"",editType:"calc"},textinfo:{valType:"flaglist",flags:["label","text","value","percent"],extras:["none"],editType:"calc"},hoverinfo:u({},n.hoverinfo,{flags:["label","text","value","percent","name"]}),hovertemplate:s({},{keys:["label","color","value","percent","text"]}),texttemplate:l({editType:"plot"},{keys:["label","color","value","percent","text"]}),textposition:{valType:"enumerated",values:["inside","outside","auto","none"],dflt:"auto",arrayOk:!0,editType:"plot"},textfont:u({},c,{}),insidetextorientation:{valType:"enumerated",values:["horizontal","radial","tangential","auto"],dflt:"auto",editType:"plot"},insidetextfont:u({},c,{}),outsidetextfont:u({},c,{}),automargin:{valType:"boolean",dflt:!1,editType:"plot"},title:{text:{valType:"string",dflt:"",editType:"plot"},font:u({},c,{}),position:{valType:"enumerated",values:["top 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n=r(92770),i=r(84267),a=r(7901),o={};function s(t){return function(e,r){return!!e&&!!(e=i(e)).isValid()&&(e=a.addOpacity(e,e.getAlpha()),t[r]||(t[r]=e),e)}}function l(t,e){var r,n=JSON.stringify(t),a=e[n];if(!a){for(a=t.slice(),r=0;r=0})),("funnelarea"===e.type?y:e.sort)&&a.sort((function(t,e){return e.v-t.v})),a[0]&&(a[0].vTotal=g),a},crossTraceCalc:function(t,e){var r=(e||{}).type;r||(r="pie");var n=t._fullLayout,i=t.calcdata,a=n[r+"colorway"],s=n["_"+r+"colormap"];n["extend"+r+"colors"]&&(a=l(a,o));for(var u=0,c=0;c0){s=!0;break}}s||(o=0)}return{hasLabels:r,hasValues:a,len:o}}t.exports={handleLabelsAndValues:l,supplyDefaults:function(t,e,r,n){function u(r,n){return i.coerce(t,e,a,r,n)}var c=l(u("labels"),u("values")),f=c.len;if(e._hasLabels=c.hasLabels,e._hasValues=c.hasValues,!e._hasLabels&&e._hasValues&&(u("label0"),u("dlabel")),f){e._length=f,u("marker.line.width")&&u("marker.line.color"),u("marker.colors"),u("scalegroup");var h,p=u("text"),d=u("texttemplate");if(d||(h=u("textinfo",Array.isArray(p)?"text+percent":"percent")),u("hovertext"),u("hovertemplate"),d||h&&"none"!==h){var v=u("textposition");s(t,e,n,u,v,{moduleHasSelected:!1,moduleHasUnselected:!1,moduleHasConstrain:!1,moduleHasCliponaxis:!1,moduleHasTextangle:!1,moduleHasInsideanchor:!1}),(Array.isArray(v)||"auto"===v||"outside"===v)&&u("automargin"),("inside"===v||"auto"===v||Array.isArray(v))&&u("insidetextorientation")}o(e,n,u);var g=u("hole");if(u("title.text")){var y=u("title.position",g?"middle center":"top center");g||"middle center"!==y||(e.title.position="top center"),i.coerceFont(u,"title.font",n.font)}u("sort"),u("direction"),u("rotation"),u("pull")}else e.visible=!1}}},20007:function(t,e,r){"use strict";var n=r(23469).appendArrayMultiPointValues;t.exports=function(t,e){var r={curveNumber:e.index,pointNumbers:t.pts,data:e._input,fullData:e,label:t.label,color:t.color,value:t.v,percent:t.percent,text:t.text,bbox:t.bbox,v:t.v};return 1===t.pts.length&&(r.pointNumber=r.i=t.pts[0]),n(r,e,t.pts),"funnelarea"===e.type&&(delete r.v,delete r.i),r}},53581:function(t,e,r){"use strict";var n=r(71828);function i(t){return-1!==t.indexOf("e")?t.replace(/[.]?0+e/,"e"):-1!==t.indexOf(".")?t.replace(/[.]?0+$/,""):t}e.formatPiePercent=function(t,e){var r=i((100*t).toPrecision(3));return n.numSeparate(r,e)+"%"},e.formatPieValue=function(t,e){var r=i(t.toPrecision(10));return n.numSeparate(r,e)},e.getFirstFilled=function(t,e){if(Array.isArray(t))for(var r=0;r"),name:f.hovertemplate||-1!==h.indexOf("name")?f.name:void 0,idealAlign:t.pxmid[0]<0?"left":"right",color:g.castOption(_.bgcolor,t.pts)||t.color,borderColor:g.castOption(_.bordercolor,t.pts),fontFamily:g.castOption(w.family,t.pts),fontSize:g.castOption(w.size,t.pts),fontColor:g.castOption(w.color,t.pts),nameLength:g.castOption(_.namelength,t.pts),textAlign:g.castOption(_.align,t.pts),hovertemplate:g.castOption(f.hovertemplate,t.pts),hovertemplateLabels:t,eventData:[y(t,f)]},{container:r._hoverlayer.node(),outerContainer:r._paper.node(),gd:e,inOut_bbox:T}),t.bbox=T[0],u._hasHoverLabel=!0}u._hasHoverEvent=!0,e.emit("plotly_hover",{points:[y(t,f)],event:n.event})}})),t.on("mouseout",(function(t){var r=e._fullLayout,i=e._fullData[u.index],o=n.select(this).datum();u._hasHoverEvent&&(t.originalEvent=n.event,e.emit("plotly_unhover",{points:[y(o,i)],event:n.event}),u._hasHoverEvent=!1),u._hasHoverLabel&&(a.loneUnhover(r._hoverlayer.node()),u._hasHoverLabel=!1)})),t.on("click",(function(t){var r=e._fullLayout,i=e._fullData[u.index];e._dragging||!1===r.hovermode||(e._hoverdata=[y(t,i)],a.click(e,n.event))}))}function b(t,e,r){var n=g.castOption(t.insidetextfont.color,e.pts);!n&&t._input.textfont&&(n=g.castOption(t._input.textfont.color,e.pts));var i=g.castOption(t.insidetextfont.family,e.pts)||g.castOption(t.textfont.family,e.pts)||r.family,a=g.castOption(t.insidetextfont.size,e.pts)||g.castOption(t.textfont.size,e.pts)||r.size;return{color:n||o.contrast(e.color),family:i,size:a}}function _(t,e){for(var r,n,i=0;ie&&e>n||r=-4;g-=2)y(Math.PI*g,"tan");for(g=4;g>=-4;g-=2)y(Math.PI*(g+1),"tan")}if(f||p){for(g=4;g>=-4;g-=2)y(Math.PI*(g+1.5),"rad");for(g=4;g>=-4;g-=2)y(Math.PI*(g+.5),"rad")}}if(s||d||f){var m=Math.sqrt(t.width*t.width+t.height*t.height);if((a={scale:i*n*2/m,rCenter:1-i,rotate:0}).textPosAngle=(e.startangle+e.stopangle)/2,a.scale>=1)return a;v.push(a)}(d||p)&&((a=T(t,n,o,l,u)).textPosAngle=(e.startangle+e.stopangle)/2,v.push(a)),(d||h)&&((a=k(t,n,o,l,u)).textPosAngle=(e.startangle+e.stopangle)/2,v.push(a));for(var x=0,b=0,_=0;_=1)break}return v[x]}function T(t,e,r,n,i){e=Math.max(0,e-2*v);var a=t.width/t.height,o=S(a,n,e,r);return{scale:2*o/t.height,rCenter:A(a,o/e),rotate:M(i)}}function k(t,e,r,n,i){e=Math.max(0,e-2*v);var a=t.height/t.width,o=S(a,n,e,r);return{scale:2*o/t.width,rCenter:A(a,o/e),rotate:M(i+Math.PI/2)}}function A(t,e){return Math.cos(e)-t*e}function M(t){return(180/Math.PI*t+720)%180-90}function S(t,e,r,n){var i=t+1/(2*Math.tan(e));return r*Math.min(1/(Math.sqrt(i*i+.5)+i),n/(Math.sqrt(t*t+n/2)+t))}function E(t,e){return t.v!==e.vTotal||e.trace.hole?Math.min(1/(1+1/Math.sin(t.halfangle)),t.ring/2):1}function L(t,e){var r=e.pxmid[0],n=e.pxmid[1],i=t.width/2,a=t.height/2;return r<0&&(i*=-1),n<0&&(a*=-1),{scale:1,rCenter:1,rotate:0,x:i+Math.abs(a)*(i>0?1:-1)/2,y:a/(1+r*r/(n*n)),outside:!0}}function C(t,e){var r,n,i,a=t.trace,o={x:t.cx,y:t.cy},s={tx:0,ty:0};s.ty+=a.title.font.size,i=O(a),-1!==a.title.position.indexOf("top")?(o.y-=(1+i)*t.r,s.ty-=t.titleBox.height):-1!==a.title.position.indexOf("bottom")&&(o.y+=(1+i)*t.r);var l,u=t.r/(void 0===(l=t.trace.aspectratio)?1:l),c=e.w*(a.domain.x[1]-a.domain.x[0])/2;return-1!==a.title.position.indexOf("left")?(c+=u,o.x-=(1+i)*u,s.tx+=t.titleBox.width/2):-1!==a.title.position.indexOf("center")?c*=2:-1!==a.title.position.indexOf("right")&&(c+=u,o.x+=(1+i)*u,s.tx-=t.titleBox.width/2),r=c/t.titleBox.width,n=P(t,e)/t.titleBox.height,{x:o.x,y:o.y,scale:Math.min(r,n),tx:s.tx,ty:s.ty}}function P(t,e){var r=t.trace,n=e.h*(r.domain.y[1]-r.domain.y[0]);return Math.min(t.titleBox.height,n/2)}function O(t){var e,r=t.pull;if(!r)return 0;if(Array.isArray(r))for(r=0,e=0;er&&(r=t.pull[e]);return r}function I(t,e){for(var r=[],n=0;n1?c=(u=r.r)/i.aspectratio:u=(c=r.r)*i.aspectratio,l=(u*=(1+i.baseratio)/2)*c}o=Math.min(o,l/r.vTotal)}for(n=0;n")}if(a){var x=l.castOption(i,e.i,"texttemplate");if(x){var b=function(t){return{label:t.label,value:t.v,valueLabel:g.formatPieValue(t.v,n.separators),percent:t.v/r.vTotal,percentLabel:g.formatPiePercent(t.v/r.vTotal,n.separators),color:t.color,text:t.text,customdata:l.castOption(i,t.i,"customdata")}}(e),_=g.getFirstFilled(i.text,e.pts);(m(_)||""===_)&&(b.text=_),e.text=l.texttemplateString(x,b,t._fullLayout._d3locale,b,i._meta||{})}else e.text=""}}function R(t,e){var r=t.rotate*Math.PI/180,n=Math.cos(r),i=Math.sin(r),a=(e.left+e.right)/2,o=(e.top+e.bottom)/2;t.textX=a*n-o*i,t.textY=a*i+o*n,t.noCenter=!0}t.exports={plot:function(t,e){var r=t._context.staticPlot,a=t._fullLayout,h=a._size;d("pie",a),_(e,t),I(e,h);var v=l.makeTraceGroups(a._pielayer,e,"trace").each((function(e){var d=n.select(this),v=e[0],y=v.trace;!function(t){var e,r,n,i=t[0],a=i.r,o=i.trace,s=g.getRotationAngle(o.rotation),l=2*Math.PI/i.vTotal,u="px0",c="px1";if("counterclockwise"===o.direction){for(e=0;ei.vTotal/2?1:0,r.halfangle=Math.PI*Math.min(r.v/i.vTotal,.5),r.ring=1-o.hole,r.rInscribed=E(r,i))}(e),d.attr("stroke-linejoin","round"),d.each((function(){var m=n.select(this).selectAll("g.slice").data(e);m.enter().append("g").classed("slice",!0),m.exit().remove();var _=[[[],[]],[[],[]]],T=!1;m.each((function(i,o){if(i.hidden)n.select(this).selectAll("path,g").remove();else{i.pointNumber=i.i,i.curveNumber=y.index,_[i.pxmid[1]<0?0:1][i.pxmid[0]<0?0:1].push(i);var u=v.cx,c=v.cy,h=n.select(this),d=h.selectAll("path.surface").data([i]);if(d.enter().append("path").classed("surface",!0).style({"pointer-events":r?"none":"all"}),h.call(x,t,e),y.pull){var m=+g.castOption(y.pull,i.pts)||0;m>0&&(u+=m*i.pxmid[0],c+=m*i.pxmid[1])}i.cxFinal=u,i.cyFinal=c;var k=y.hole;if(i.v===v.vTotal){var A="M"+(u+i.px0[0])+","+(c+i.px0[1])+P(i.px0,i.pxmid,!0,1)+P(i.pxmid,i.px0,!0,1)+"Z";k?d.attr("d","M"+(u+k*i.px0[0])+","+(c+k*i.px0[1])+P(i.px0,i.pxmid,!1,k)+P(i.pxmid,i.px0,!1,k)+"Z"+A):d.attr("d",A)}else{var M=P(i.px0,i.px1,!0,1);if(k){var S=1-k;d.attr("d","M"+(u+k*i.px1[0])+","+(c+k*i.px1[1])+P(i.px1,i.px0,!1,k)+"l"+S*i.px0[0]+","+S*i.px0[1]+M+"Z")}else d.attr("d","M"+u+","+c+"l"+i.px0[0]+","+i.px0[1]+M+"Z")}z(t,i,v);var E=g.castOption(y.textposition,i.pts),C=h.selectAll("g.slicetext").data(i.text&&"none"!==E?[0]:[]);C.enter().append("g").classed("slicetext",!0),C.exit().remove(),C.each((function(){var r=l.ensureSingle(n.select(this),"text","",(function(t){t.attr("data-notex",1)})),h=l.ensureUniformFontSize(t,"outside"===E?function(t,e,r){return{color:g.castOption(t.outsidetextfont.color,e.pts)||g.castOption(t.textfont.color,e.pts)||r.color,family:g.castOption(t.outsidetextfont.family,e.pts)||g.castOption(t.textfont.family,e.pts)||r.family,size:g.castOption(t.outsidetextfont.size,e.pts)||g.castOption(t.textfont.size,e.pts)||r.size}}(y,i,a.font):b(y,i,a.font));r.text(i.text).attr({class:"slicetext",transform:"","text-anchor":"middle"}).call(s.font,h).call(f.convertToTspans,t);var d,m=s.bBox(r.node());if("outside"===E)d=L(m,i);else if(d=w(m,i,v),"auto"===E&&d.scale<1){var x=l.ensureUniformFontSize(t,y.outsidetextfont);r.call(s.font,x),d=L(m=s.bBox(r.node()),i)}var _=d.textPosAngle,k=void 0===_?i.pxmid:D(v.r,_);if(d.targetX=u+k[0]*d.rCenter+(d.x||0),d.targetY=c+k[1]*d.rCenter+(d.y||0),R(d,m),d.outside){var A=d.targetY;i.yLabelMin=A-m.height/2,i.yLabelMid=A,i.yLabelMax=A+m.height/2,i.labelExtraX=0,i.labelExtraY=0,T=!0}d.fontSize=h.size,p(y.type,d,a),e[o].transform=d,l.setTransormAndDisplay(r,d)}))}function P(t,e,r,n){var a=n*(e[0]-t[0]),o=n*(e[1]-t[1]);return"a"+n*v.r+","+n*v.r+" 0 "+i.largeArc+(r?" 1 ":" 0 ")+a+","+o}}));var k=n.select(this).selectAll("g.titletext").data(y.title.text?[0]:[]);if(k.enter().append("g").classed("titletext",!0),k.exit().remove(),k.each((function(){var e,r=l.ensureSingle(n.select(this),"text","",(function(t){t.attr("data-notex",1)})),i=y.title.text;y._meta&&(i=l.templateString(i,y._meta)),r.text(i).attr({class:"titletext",transform:"","text-anchor":"middle"}).call(s.font,y.title.font).call(f.convertToTspans,t),e="middle center"===y.title.position?function(t){var e=Math.sqrt(t.titleBox.width*t.titleBox.width+t.titleBox.height*t.titleBox.height);return{x:t.cx,y:t.cy,scale:t.trace.hole*t.r*2/e,tx:0,ty:-t.titleBox.height/2+t.trace.title.font.size}}(v):C(v,h),r.attr("transform",c(e.x,e.y)+u(Math.min(1,e.scale))+c(e.tx,e.ty))})),T&&function(t,e){var r,n,i,a,o,s,l,u,c,f,h,p,d;function v(t,e){return t.pxmid[1]-e.pxmid[1]}function y(t,e){return e.pxmid[1]-t.pxmid[1]}function m(t,r){r||(r={});var i,u,c,h,p=r.labelExtraY+(n?r.yLabelMax:r.yLabelMin),d=n?t.yLabelMin:t.yLabelMax,v=n?t.yLabelMax:t.yLabelMin,y=t.cyFinal+o(t.px0[1],t.px1[1]),m=p-d;if(m*l>0&&(t.labelExtraY=m),Array.isArray(e.pull))for(u=0;u=(g.castOption(e.pull,c.pts)||0)||((t.pxmid[1]-c.pxmid[1])*l>0?(m=c.cyFinal+o(c.px0[1],c.px1[1])-d-t.labelExtraY)*l>0&&(t.labelExtraY+=m):(v+t.labelExtraY-y)*l>0&&(i=3*s*Math.abs(u-f.indexOf(t)),(h=c.cxFinal+a(c.px0[0],c.px1[0])+i-(t.cxFinal+t.pxmid[0])-t.labelExtraX)*s>0&&(t.labelExtraX+=h)))}for(n=0;n<2;n++)for(i=n?v:y,o=n?Math.max:Math.min,l=n?1:-1,r=0;r<2;r++){for(a=r?Math.max:Math.min,s=r?1:-1,(u=t[n][r]).sort(i),c=t[1-n][r],f=c.concat(u),p=[],h=0;hMath.abs(f)?s+="l"+f*t.pxmid[0]/t.pxmid[1]+","+f+"H"+(a+t.labelExtraX+u):s+="l"+t.labelExtraX+","+c+"v"+(f-c)+"h"+u}else s+="V"+(t.yLabelMid+t.labelExtraY)+"h"+u;l.ensureSingle(r,"path","textline").call(o.stroke,e.outsidetextfont.color).attr({"stroke-width":Math.min(2,e.outsidetextfont.size/8),d:s,fill:"none"})}else r.select("path.textline").remove()}))}(m,y),T&&y.automargin){var A=s.bBox(d.node()),M=y.domain,S=h.w*(M.x[1]-M.x[0]),E=h.h*(M.y[1]-M.y[0]),P=(.5*S-v.r)/h.w,O=(.5*E-v.r)/h.h;i.autoMargin(t,"pie."+y.uid+".automargin",{xl:M.x[0]-P,xr:M.x[1]+P,yb:M.y[0]-O,yt:M.y[1]+O,l:Math.max(v.cx-v.r-A.left,0),r:Math.max(A.right-(v.cx+v.r),0),b:Math.max(A.bottom-(v.cy+v.r),0),t:Math.max(v.cy-v.r-A.top,0),pad:5})}}))}));setTimeout((function(){v.selectAll("tspan").each((function(){var t=n.select(this);t.attr("dy")&&t.attr("dy",t.attr("dy"))}))}),0)},formatSliceLabel:z,transformInsideText:w,determineInsideTextFont:b,positionTitleOutside:C,prerenderTitles:_,layoutAreas:I,attachFxHandlers:x,computeTransform:R}},68357:function(t,e,r){"use strict";var n=r(39898),i=r(63463),a=r(72597).resizeText;t.exports=function(t){var e=t._fullLayout._pielayer.selectAll(".trace");a(t,e,"pie"),e.each((function(t){var e=t[0].trace,r=n.select(this);r.style({opacity:e.opacity}),r.selectAll("path.surface").each((function(t){n.select(this).call(i,t,e)}))}))}},63463:function(t,e,r){"use strict";var n=r(7901),i=r(53581).castOption;t.exports=function(t,e,r){var a=r.marker.line,o=i(a.color,e.pts)||n.defaultLine,s=i(a.width,e.pts)||0;t.style("stroke-width",s).call(n.fill,e.color).call(n.stroke,o)}},10959:function(t,e,r){"use strict";var n=r(82196);t.exports={x:n.x,y:n.y,xy:{valType:"data_array",editType:"calc"},indices:{valType:"data_array",editType:"calc"},xbounds:{valType:"data_array",editType:"calc"},ybounds:{valType:"data_array",editType:"calc"},text:n.text,marker:{color:{valType:"color",arrayOk:!1,editType:"calc"},opacity:{valType:"number",min:0,max:1,dflt:1,arrayOk:!1,editType:"calc"},blend:{valType:"boolean",dflt:null,editType:"calc"},sizemin:{valType:"number",min:.1,max:2,dflt:.5,editType:"calc"},sizemax:{valType:"number",min:.1,dflt:20,editType:"calc"},border:{color:{valType:"color",arrayOk:!1,editType:"calc"},arearatio:{valType:"number",min:0,max:1,dflt:0,editType:"calc"},editType:"calc"},editType:"calc"},transforms:void 0}},42743:function(t,e,r){"use strict";var n=r(9330).gl_pointcloud2d,i=r(78614),a=r(71739).findExtremes,o=r(34603);function s(t,e){this.scene=t,this.uid=e,this.type="pointcloud",this.pickXData=[],this.pickYData=[],this.xData=[],this.yData=[],this.textLabels=[],this.color="rgb(0, 0, 0)",this.name="",this.hoverinfo="all",this.idToIndex=new Int32Array(0),this.bounds=[0,0,0,0],this.pointcloudOptions={positions:new Float32Array(0),idToIndex:this.idToIndex,sizemin:.5,sizemax:12,color:[0,0,0,1],areaRatio:1,borderColor:[0,0,0,1]},this.pointcloud=n(t.glplot,this.pointcloudOptions),this.pointcloud._trace=this}var l=s.prototype;l.handlePick=function(t){var e=this.idToIndex[t.pointId];return{trace:this,dataCoord:t.dataCoord,traceCoord:this.pickXYData?[this.pickXYData[2*e],this.pickXYData[2*e+1]]:[this.pickXData[e],this.pickYData[e]],textLabel:Array.isArray(this.textLabels)?this.textLabels[e]:this.textLabels,color:this.color,name:this.name,pointIndex:e,hoverinfo:this.hoverinfo}},l.update=function(t){this.index=t.index,this.textLabels=t.text,this.name=t.name,this.hoverinfo=t.hoverinfo,this.bounds=[1/0,1/0,-1/0,-1/0],this.updateFast(t),this.color=o(t,{})},l.updateFast=function(t){var e,r,n,o,s,l,u=this.xData=this.pickXData=t.x,c=this.yData=this.pickYData=t.y,f=this.pickXYData=t.xy,h=t.xbounds&&t.ybounds,p=t.indices,d=this.bounds;if(f){if(n=f,e=f.length>>>1,h)d[0]=t.xbounds[0],d[2]=t.xbounds[1],d[1]=t.ybounds[0],d[3]=t.ybounds[1];else for(l=0;ld[2]&&(d[2]=o),sd[3]&&(d[3]=s);if(p)r=p;else for(r=new Int32Array(e),l=0;ld[2]&&(d[2]=o),sd[3]&&(d[3]=s);this.idToIndex=r,this.pointcloudOptions.idToIndex=r,this.pointcloudOptions.positions=n;var v=i(t.marker.color),g=i(t.marker.border.color),y=t.opacity*t.marker.opacity;v[3]*=y,this.pointcloudOptions.color=v;var m=t.marker.blend;null===m&&(m=u.length<100||c.length<100),this.pointcloudOptions.blend=m,g[3]*=y,this.pointcloudOptions.borderColor=g;var x=t.marker.sizemin,b=Math.max(t.marker.sizemax,t.marker.sizemin);this.pointcloudOptions.sizeMin=x,this.pointcloudOptions.sizeMax=b,this.pointcloudOptions.areaRatio=t.marker.border.arearatio,this.pointcloud.update(this.pointcloudOptions);var 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s(t,e,r,n){this.type="scattermapbox",this.subplot=t,this.uid=e,this.clusterEnabled=r,this.isHidden=n,this.sourceIds={fill:"source-"+e+"-fill",line:"source-"+e+"-line",circle:"source-"+e+"-circle",symbol:"source-"+e+"-symbol",cluster:"source-"+e+"-circle",clusterCount:"source-"+e+"-circle"},this.layerIds={fill:a+e+"-fill",line:a+e+"-line",circle:a+e+"-circle",symbol:a+e+"-symbol",cluster:a+e+"-cluster",clusterCount:a+e+"-cluster-count"},this.below=null}var l=s.prototype;l.addSource=function(t,e,r){var i={type:"geojson",data:e.geojson};r&&r.enabled&&n.extendFlat(i,{cluster:!0,clusterMaxZoom:r.maxzoom}),this.subplot.map.addSource(this.sourceIds[t],i)},l.setSourceData=function(t,e){this.subplot.map.getSource(this.sourceIds[t]).setData(e.geojson)},l.addLayer=function(t,e,r){var n={type:e.type,id:this.layerIds[t],source:this.sourceIds[t],layout:e.layout,paint:e.paint};e.filter&&(n.filter=e.filter),this.subplot.addLayer(n,r)},l.update=function(t){var e=t[0].trace,r=this.subplot,n=r.map,a=i(r.gd,t),s=r.belowLookup["trace-"+this.uid],l=!(!e.cluster||!e.cluster.enabled),u=!!this.clusterEnabled,c=this;function f(t){u?function(t){for(var e=o.cluster,r=e.length-1;r>=0;r--){var i=e[r];n.removeLayer(c.layerIds[i])}t||n.removeSource(c.sourceIds.circle)}(t):function(t){for(var e=o.nonCluster,r=e.length-1;r>=0;r--){var i=e[r];n.removeLayer(c.layerIds[i]),t||n.removeSource(c.sourceIds[i])}}(t)}function h(t){l?function(t){t||c.addSource("circle",a.circle,e.cluster);for(var r=o.cluster,n=0;n=0;r--){var n=e[r];t.removeLayer(this.layerIds[n]),t.removeSource(this.sourceIds[n])}},t.exports=function(t,e){var r,n,a,l=e[0].trace,u=l.cluster&&l.cluster.enabled,c=!0!==l.visible,f=new s(t,l.uid,u,c),h=i(t.gd,e),p=f.below=t.belowLookup["trace-"+l.uid];if(u)for(f.addSource("circle",h.circle,l.cluster),r=0;r")}}t.exports={hoverPoints:function(t,e,r,a){var o=n(t,e,r,a);if(o&&!1!==o[0].index){var s=o[0];if(void 0===s.index)return o;var l=t.subplot,u=s.cd[s.index],c=s.trace;if(l.isPtInside(u))return s.xLabelVal=void 0,s.yLabelVal=void 0,i(u,c,l,s),s.hovertemplate=c.hovertemplate,o}},makeHoverPointText:i}},91271:function(t,e,r){"use strict";t.exports={moduleType:"trace",name:"scatterpolar",basePlotModule:r(23580),categories:["polar","symbols","showLegend","scatter-like"],attributes:r(81245),supplyDefaults:r(22184).supplyDefaults,colorbar:r(4898),formatLabels:r(98608),calc:r(26442),plot:r(45162),style:r(16296).style,styleOnSelect:r(16296).styleOnSelect,hoverPoints:r(59150).hoverPoints,selectPoints:r(98002),meta:{}}},45162:function(t,e,r){"use strict";var n=r(32663),i=r(50606).BADNUM;t.exports=function(t,e,r){for(var a=e.layers.frontplot.select("g.scatterlayer"),o=e.xaxis,s=e.yaxis,l={xaxis:o,yaxis:s,plot:e.framework,layerClipId:e._hasClipOnAxisFalse?e.clipIds.forTraces:null},u=e.radialAxis,c=e.angularAxis,f=0;f=u&&(m.marker.cluster=d.tree),m.marker&&(m.markerSel.positions=m.markerUnsel.positions=m.marker.positions=_),m.line&&_.length>1&&l.extendFlat(m.line,s.linePositions(t,p,_)),m.text&&(l.extendFlat(m.text,{positions:_},s.textPosition(t,p,m.text,m.marker)),l.extendFlat(m.textSel,{positions:_},s.textPosition(t,p,m.text,m.markerSel)),l.extendFlat(m.textUnsel,{positions:_},s.textPosition(t,p,m.text,m.markerUnsel))),m.fill&&!h.fill2d&&(h.fill2d=!0),m.marker&&!h.scatter2d&&(h.scatter2d=!0),m.line&&!h.line2d&&(h.line2d=!0),m.text&&!h.glText&&(h.glText=!0),h.lineOptions.push(m.line),h.fillOptions.push(m.fill),h.markerOptions.push(m.marker),h.markerSelectedOptions.push(m.markerSel),h.markerUnselectedOptions.push(m.markerUnsel),h.textOptions.push(m.text),h.textSelectedOptions.push(m.textSel),h.textUnselectedOptions.push(m.textUnsel),h.selectBatch.push([]),h.unselectBatch.push([]),d.x=w,d.y=T,d.rawx=w,d.rawy=T,d.r=g,d.theta=y,d.positions=_,d._scene=h,d.index=h.count,h.count++}})),a(t,e,r)}},t.exports.reglPrecompiled={}},48300:function(t,e,r){"use 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t&&t>=0);var e=0|Math.ceil(t/26),r=t%26;this._expand(e),r>0&&e--;for(var i=0;i0&&(this.words[i]=~this.words[i]&67108863>>26-r),this.strip()},a.prototype.notn=function(t){return this.clone().inotn(t)},a.prototype.setn=function(t,e){n("number"==typeof t&&t>=0);var r=t/26|0,i=t%26;return this._expand(r+1),this.words[r]=e?this.words[r]|1<t.length?(r=this,n=t):(r=t,n=this);for(var i=0,a=0;a>>26;for(;0!==i&&a>>26;if(this.length=r.length,0!==i)this.words[this.length]=i,this.length++;else if(r!==this)for(;at.length?this.clone().iadd(t):t.clone().iadd(this)},a.prototype.isub=function(t){if(0!==t.negative){t.negative=0;var e=this.iadd(t);return t.negative=1,e._normSign()}if(0!==this.negative)return this.negative=0,this.iadd(t),this.negative=1,this._normSign();var r,n,i=this.cmp(t);if(0===i)return this.negative=0,this.length=1,this.words[0]=0,this;i>0?(r=this,n=t):(r=t,n=this);for(var 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yt=(u+(n=n+Math.imul(f,q)|0)|0)+((8191&(i=(i=i+Math.imul(f,G)|0)+Math.imul(h,q)|0))<<13)|0;u=((a=a+Math.imul(h,G)|0)+(i>>>13)|0)+(yt>>>26)|0,yt&=67108863,n=Math.imul(y,U),i=(i=Math.imul(y,V))+Math.imul(m,U)|0,a=Math.imul(m,V),n=n+Math.imul(d,q)|0,i=(i=i+Math.imul(d,G)|0)+Math.imul(v,q)|0,a=a+Math.imul(v,G)|0;var mt=(u+(n=n+Math.imul(f,Y)|0)|0)+((8191&(i=(i=i+Math.imul(f,W)|0)+Math.imul(h,Y)|0))<<13)|0;u=((a=a+Math.imul(h,W)|0)+(i>>>13)|0)+(mt>>>26)|0,mt&=67108863,n=Math.imul(b,U),i=(i=Math.imul(b,V))+Math.imul(_,U)|0,a=Math.imul(_,V),n=n+Math.imul(y,q)|0,i=(i=i+Math.imul(y,G)|0)+Math.imul(m,q)|0,a=a+Math.imul(m,G)|0,n=n+Math.imul(d,Y)|0,i=(i=i+Math.imul(d,W)|0)+Math.imul(v,Y)|0,a=a+Math.imul(v,W)|0;var xt=(u+(n=n+Math.imul(f,J)|0)|0)+((8191&(i=(i=i+Math.imul(f,K)|0)+Math.imul(h,J)|0))<<13)|0;u=((a=a+Math.imul(h,K)|0)+(i>>>13)|0)+(xt>>>26)|0,xt&=67108863,n=Math.imul(T,U),i=(i=Math.imul(T,V))+Math.imul(k,U)|0,a=Math.imul(k,V),n=n+Math.imul(b,q)|0,i=(i=i+Math.imul(b,G)|0)+Math.imul(_,q)|0,a=a+Math.imul(_,G)|0,n=n+Math.imul(y,Y)|0,i=(i=i+Math.imul(y,W)|0)+Math.imul(m,Y)|0,a=a+Math.imul(m,W)|0,n=n+Math.imul(d,J)|0,i=(i=i+Math.imul(d,K)|0)+Math.imul(v,J)|0,a=a+Math.imul(v,K)|0;var bt=(u+(n=n+Math.imul(f,Q)|0)|0)+((8191&(i=(i=i+Math.imul(f,tt)|0)+Math.imul(h,Q)|0))<<13)|0;u=((a=a+Math.imul(h,tt)|0)+(i>>>13)|0)+(bt>>>26)|0,bt&=67108863,n=Math.imul(M,U),i=(i=Math.imul(M,V))+Math.imul(S,U)|0,a=Math.imul(S,V),n=n+Math.imul(T,q)|0,i=(i=i+Math.imul(T,G)|0)+Math.imul(k,q)|0,a=a+Math.imul(k,G)|0,n=n+Math.imul(b,Y)|0,i=(i=i+Math.imul(b,W)|0)+Math.imul(_,Y)|0,a=a+Math.imul(_,W)|0,n=n+Math.imul(y,J)|0,i=(i=i+Math.imul(y,K)|0)+Math.imul(m,J)|0,a=a+Math.imul(m,K)|0,n=n+Math.imul(d,Q)|0,i=(i=i+Math.imul(d,tt)|0)+Math.imul(v,Q)|0,a=a+Math.imul(v,tt)|0;var _t=(u+(n=n+Math.imul(f,rt)|0)|0)+((8191&(i=(i=i+Math.imul(f,nt)|0)+Math.imul(h,rt)|0))<<13)|0;u=((a=a+Math.imul(h,nt)|0)+(i>>>13)|0)+(_t>>>26)|0,_t&=67108863,n=Math.imul(L,U),i=(i=Math.imul(L,V))+Math.imul(C,U)|0,a=Math.imul(C,V),n=n+Math.imul(M,q)|0,i=(i=i+Math.imul(M,G)|0)+Math.imul(S,q)|0,a=a+Math.imul(S,G)|0,n=n+Math.imul(T,Y)|0,i=(i=i+Math.imul(T,W)|0)+Math.imul(k,Y)|0,a=a+Math.imul(k,W)|0,n=n+Math.imul(b,J)|0,i=(i=i+Math.imul(b,K)|0)+Math.imul(_,J)|0,a=a+Math.imul(_,K)|0,n=n+Math.imul(y,Q)|0,i=(i=i+Math.imul(y,tt)|0)+Math.imul(m,Q)|0,a=a+Math.imul(m,tt)|0,n=n+Math.imul(d,rt)|0,i=(i=i+Math.imul(d,nt)|0)+Math.imul(v,rt)|0,a=a+Math.imul(v,nt)|0;var wt=(u+(n=n+Math.imul(f,at)|0)|0)+((8191&(i=(i=i+Math.imul(f,ot)|0)+Math.imul(h,at)|0))<<13)|0;u=((a=a+Math.imul(h,ot)|0)+(i>>>13)|0)+(wt>>>26)|0,wt&=67108863,n=Math.imul(O,U),i=(i=Math.imul(O,V))+Math.imul(I,U)|0,a=Math.imul(I,V),n=n+Math.imul(L,q)|0,i=(i=i+Math.imul(L,G)|0)+Math.imul(C,q)|0,a=a+Math.imul(C,G)|0,n=n+Math.imul(M,Y)|0,i=(i=i+Math.imul(M,W)|0)+Math.imul(S,Y)|0,a=a+Math.imul(S,W)|0,n=n+Math.imul(T,J)|0,i=(i=i+Math.imul(T,K)|0)+Math.imul(k,J)|0,a=a+Math.imul(k,K)|0,n=n+Math.imul(b,Q)|0,i=(i=i+Math.imul(b,tt)|0)+Math.imul(_,Q)|0,a=a+Math.imul(_,tt)|0,n=n+Math.imul(y,rt)|0,i=(i=i+Math.imul(y,nt)|0)+Math.imul(m,rt)|0,a=a+Math.imul(m,nt)|0,n=n+Math.imul(d,at)|0,i=(i=i+Math.imul(d,ot)|0)+Math.imul(v,at)|0,a=a+Math.imul(v,ot)|0;var Tt=(u+(n=n+Math.imul(f,lt)|0)|0)+((8191&(i=(i=i+Math.imul(f,ut)|0)+Math.imul(h,lt)|0))<<13)|0;u=((a=a+Math.imul(h,ut)|0)+(i>>>13)|0)+(Tt>>>26)|0,Tt&=67108863,n=Math.imul(z,U),i=(i=Math.imul(z,V))+Math.imul(R,U)|0,a=Math.imul(R,V),n=n+Math.imul(O,q)|0,i=(i=i+Math.imul(O,G)|0)+Math.imul(I,q)|0,a=a+Math.imul(I,G)|0,n=n+Math.imul(L,Y)|0,i=(i=i+Math.imul(L,W)|0)+Math.imul(C,Y)|0,a=a+Math.imul(C,W)|0,n=n+Math.imul(M,J)|0,i=(i=i+Math.imul(M,K)|0)+Math.imul(S,J)|0,a=a+Math.imul(S,K)|0,n=n+Math.imul(T,Q)|0,i=(i=i+Math.imul(T,tt)|0)+Math.imul(k,Q)|0,a=a+Math.imul(k,tt)|0,n=n+Math.imul(b,rt)|0,i=(i=i+Math.imul(b,nt)|0)+Math.imul(_,rt)|0,a=a+Math.imul(_,nt)|0,n=n+Math.imul(y,at)|0,i=(i=i+Math.imul(y,ot)|0)+Math.imul(m,at)|0,a=a+Math.imul(m,ot)|0,n=n+Math.imul(d,lt)|0,i=(i=i+Math.imul(d,ut)|0)+Math.imul(v,lt)|0,a=a+Math.imul(v,ut)|0;var kt=(u+(n=n+Math.imul(f,ft)|0)|0)+((8191&(i=(i=i+Math.imul(f,ht)|0)+Math.imul(h,ft)|0))<<13)|0;u=((a=a+Math.imul(h,ht)|0)+(i>>>13)|0)+(kt>>>26)|0,kt&=67108863,n=Math.imul(B,U),i=(i=Math.imul(B,V))+Math.imul(N,U)|0,a=Math.imul(N,V),n=n+Math.imul(z,q)|0,i=(i=i+Math.imul(z,G)|0)+Math.imul(R,q)|0,a=a+Math.imul(R,G)|0,n=n+Math.imul(O,Y)|0,i=(i=i+Math.imul(O,W)|0)+Math.imul(I,Y)|0,a=a+Math.imul(I,W)|0,n=n+Math.imul(L,J)|0,i=(i=i+Math.imul(L,K)|0)+Math.imul(C,J)|0,a=a+Math.imul(C,K)|0,n=n+Math.imul(M,Q)|0,i=(i=i+Math.imul(M,tt)|0)+Math.imul(S,Q)|0,a=a+Math.imul(S,tt)|0,n=n+Math.imul(T,rt)|0,i=(i=i+Math.imul(T,nt)|0)+Math.imul(k,rt)|0,a=a+Math.imul(k,nt)|0,n=n+Math.imul(b,at)|0,i=(i=i+Math.imul(b,ot)|0)+Math.imul(_,at)|0,a=a+Math.imul(_,ot)|0,n=n+Math.imul(y,lt)|0,i=(i=i+Math.imul(y,ut)|0)+Math.imul(m,lt)|0,a=a+Math.imul(m,ut)|0,n=n+Math.imul(d,ft)|0,i=(i=i+Math.imul(d,ht)|0)+Math.imul(v,ft)|0,a=a+Math.imul(v,ht)|0;var At=(u+(n=n+Math.imul(f,dt)|0)|0)+((8191&(i=(i=i+Math.imul(f,vt)|0)+Math.imul(h,dt)|0))<<13)|0;u=((a=a+Math.imul(h,vt)|0)+(i>>>13)|0)+(At>>>26)|0,At&=67108863,n=Math.imul(B,q),i=(i=Math.imul(B,G))+Math.imul(N,q)|0,a=Math.imul(N,G),n=n+Math.imul(z,Y)|0,i=(i=i+Math.imul(z,W)|0)+Math.imul(R,Y)|0,a=a+Math.imul(R,W)|0,n=n+Math.imul(O,J)|0,i=(i=i+Math.imul(O,K)|0)+Math.imul(I,J)|0,a=a+Math.imul(I,K)|0,n=n+Math.imul(L,Q)|0,i=(i=i+Math.imul(L,tt)|0)+Math.imul(C,Q)|0,a=a+Math.imul(C,tt)|0,n=n+Math.imul(M,rt)|0,i=(i=i+Math.imul(M,nt)|0)+Math.imul(S,rt)|0,a=a+Math.imul(S,nt)|0,n=n+Math.imul(T,at)|0,i=(i=i+Math.imul(T,ot)|0)+Math.imul(k,at)|0,a=a+Math.imul(k,ot)|0,n=n+Math.imul(b,lt)|0,i=(i=i+Math.imul(b,ut)|0)+Math.imul(_,lt)|0,a=a+Math.imul(_,ut)|0,n=n+Math.imul(y,ft)|0,i=(i=i+Math.imul(y,ht)|0)+Math.imul(m,ft)|0,a=a+Math.imul(m,ht)|0;var Mt=(u+(n=n+Math.imul(d,dt)|0)|0)+((8191&(i=(i=i+Math.imul(d,vt)|0)+Math.imul(v,dt)|0))<<13)|0;u=((a=a+Math.imul(v,vt)|0)+(i>>>13)|0)+(Mt>>>26)|0,Mt&=67108863,n=Math.imul(B,Y),i=(i=Math.imul(B,W))+Math.imul(N,Y)|0,a=Math.imul(N,W),n=n+Math.imul(z,J)|0,i=(i=i+Math.imul(z,K)|0)+Math.imul(R,J)|0,a=a+Math.imul(R,K)|0,n=n+Math.imul(O,Q)|0,i=(i=i+Math.imul(O,tt)|0)+Math.imul(I,Q)|0,a=a+Math.imul(I,tt)|0,n=n+Math.imul(L,rt)|0,i=(i=i+Math.imul(L,nt)|0)+Math.imul(C,rt)|0,a=a+Math.imul(C,nt)|0,n=n+Math.imul(M,at)|0,i=(i=i+Math.imul(M,ot)|0)+Math.imul(S,at)|0,a=a+Math.imul(S,ot)|0,n=n+Math.imul(T,lt)|0,i=(i=i+Math.imul(T,ut)|0)+Math.imul(k,lt)|0,a=a+Math.imul(k,ut)|0,n=n+Math.imul(b,ft)|0,i=(i=i+Math.imul(b,ht)|0)+Math.imul(_,ft)|0,a=a+Math.imul(_,ht)|0;var St=(u+(n=n+Math.imul(y,dt)|0)|0)+((8191&(i=(i=i+Math.imul(y,vt)|0)+Math.imul(m,dt)|0))<<13)|0;u=((a=a+Math.imul(m,vt)|0)+(i>>>13)|0)+(St>>>26)|0,St&=67108863,n=Math.imul(B,J),i=(i=Math.imul(B,K))+Math.imul(N,J)|0,a=Math.imul(N,K),n=n+Math.imul(z,Q)|0,i=(i=i+Math.imul(z,tt)|0)+Math.imul(R,Q)|0,a=a+Math.imul(R,tt)|0,n=n+Math.imul(O,rt)|0,i=(i=i+Math.imul(O,nt)|0)+Math.imul(I,rt)|0,a=a+Math.imul(I,nt)|0,n=n+Math.imul(L,at)|0,i=(i=i+Math.imul(L,ot)|0)+Math.imul(C,at)|0,a=a+Math.imul(C,ot)|0,n=n+Math.imul(M,lt)|0,i=(i=i+Math.imul(M,ut)|0)+Math.imul(S,lt)|0,a=a+Math.imul(S,ut)|0,n=n+Math.imul(T,ft)|0,i=(i=i+Math.imul(T,ht)|0)+Math.imul(k,ft)|0,a=a+Math.imul(k,ht)|0;var Et=(u+(n=n+Math.imul(b,dt)|0)|0)+((8191&(i=(i=i+Math.imul(b,vt)|0)+Math.imul(_,dt)|0))<<13)|0;u=((a=a+Math.imul(_,vt)|0)+(i>>>13)|0)+(Et>>>26)|0,Et&=67108863,n=Math.imul(B,Q),i=(i=Math.imul(B,tt))+Math.imul(N,Q)|0,a=Math.imul(N,tt),n=n+Math.imul(z,rt)|0,i=(i=i+Math.imul(z,nt)|0)+Math.imul(R,rt)|0,a=a+Math.imul(R,nt)|0,n=n+Math.imul(O,at)|0,i=(i=i+Math.imul(O,ot)|0)+Math.imul(I,at)|0,a=a+Math.imul(I,ot)|0,n=n+Math.imul(L,lt)|0,i=(i=i+Math.imul(L,ut)|0)+Math.imul(C,lt)|0,a=a+Math.imul(C,ut)|0,n=n+Math.imul(M,ft)|0,i=(i=i+Math.imul(M,ht)|0)+Math.imul(S,ft)|0,a=a+Math.imul(S,ht)|0;var Lt=(u+(n=n+Math.imul(T,dt)|0)|0)+((8191&(i=(i=i+Math.imul(T,vt)|0)+Math.imul(k,dt)|0))<<13)|0;u=((a=a+Math.imul(k,vt)|0)+(i>>>13)|0)+(Lt>>>26)|0,Lt&=67108863,n=Math.imul(B,rt),i=(i=Math.imul(B,nt))+Math.imul(N,rt)|0,a=Math.imul(N,nt),n=n+Math.imul(z,at)|0,i=(i=i+Math.imul(z,ot)|0)+Math.imul(R,at)|0,a=a+Math.imul(R,ot)|0,n=n+Math.imul(O,lt)|0,i=(i=i+Math.imul(O,ut)|0)+Math.imul(I,lt)|0,a=a+Math.imul(I,ut)|0,n=n+Math.imul(L,ft)|0,i=(i=i+Math.imul(L,ht)|0)+Math.imul(C,ft)|0,a=a+Math.imul(C,ht)|0;var Ct=(u+(n=n+Math.imul(M,dt)|0)|0)+((8191&(i=(i=i+Math.imul(M,vt)|0)+Math.imul(S,dt)|0))<<13)|0;u=((a=a+Math.imul(S,vt)|0)+(i>>>13)|0)+(Ct>>>26)|0,Ct&=67108863,n=Math.imul(B,at),i=(i=Math.imul(B,ot))+Math.imul(N,at)|0,a=Math.imul(N,ot),n=n+Math.imul(z,lt)|0,i=(i=i+Math.imul(z,ut)|0)+Math.imul(R,lt)|0,a=a+Math.imul(R,ut)|0,n=n+Math.imul(O,ft)|0,i=(i=i+Math.imul(O,ht)|0)+Math.imul(I,ft)|0,a=a+Math.imul(I,ht)|0;var Pt=(u+(n=n+Math.imul(L,dt)|0)|0)+((8191&(i=(i=i+Math.imul(L,vt)|0)+Math.imul(C,dt)|0))<<13)|0;u=((a=a+Math.imul(C,vt)|0)+(i>>>13)|0)+(Pt>>>26)|0,Pt&=67108863,n=Math.imul(B,lt),i=(i=Math.imul(B,ut))+Math.imul(N,lt)|0,a=Math.imul(N,ut),n=n+Math.imul(z,ft)|0,i=(i=i+Math.imul(z,ht)|0)+Math.imul(R,ft)|0,a=a+Math.imul(R,ht)|0;var Ot=(u+(n=n+Math.imul(O,dt)|0)|0)+((8191&(i=(i=i+Math.imul(O,vt)|0)+Math.imul(I,dt)|0))<<13)|0;u=((a=a+Math.imul(I,vt)|0)+(i>>>13)|0)+(Ot>>>26)|0,Ot&=67108863,n=Math.imul(B,ft),i=(i=Math.imul(B,ht))+Math.imul(N,ft)|0,a=Math.imul(N,ht);var It=(u+(n=n+Math.imul(z,dt)|0)|0)+((8191&(i=(i=i+Math.imul(z,vt)|0)+Math.imul(R,dt)|0))<<13)|0;u=((a=a+Math.imul(R,vt)|0)+(i>>>13)|0)+(It>>>26)|0,It&=67108863;var Dt=(u+(n=Math.imul(B,dt))|0)+((8191&(i=(i=Math.imul(B,vt))+Math.imul(N,dt)|0))<<13)|0;return u=((a=Math.imul(N,vt))+(i>>>13)|0)+(Dt>>>26)|0,Dt&=67108863,l[0]=gt,l[1]=yt,l[2]=mt,l[3]=xt,l[4]=bt,l[5]=_t,l[6]=wt,l[7]=Tt,l[8]=kt,l[9]=At,l[10]=Mt,l[11]=St,l[12]=Et,l[13]=Lt,l[14]=Ct,l[15]=Pt,l[16]=Ot,l[17]=It,l[18]=Dt,0!==u&&(l[19]=u,r.length++),r};function v(t,e,r){return(new g).mulp(t,e,r)}function g(t,e){this.x=t,this.y=e}Math.imul||(d=p),a.prototype.mulTo=function(t,e){var r,n=this.length+t.length;return r=10===this.length&&10===t.length?d(this,t,e):n<63?p(this,t,e):n<1024?function(t,e,r){r.negative=e.negative^t.negative,r.length=t.length+e.length;for(var n=0,i=0,a=0;a>>26)|0)>>>26,o&=67108863}r.words[a]=s,n=o,o=i}return 0!==n?r.words[a]=n:r.length--,r.strip()}(this,t,e):v(this,t,e),r},g.prototype.makeRBT=function(t){for(var e=new Array(t),r=a.prototype._countBits(t)-1,n=0;n>=1;return n},g.prototype.permute=function(t,e,r,n,i,a){for(var o=0;o>>=1)i++;return 1<>>=13,r[2*o+1]=8191&a,a>>>=13;for(o=2*e;o>=26,e+=i/67108864|0,e+=a>>>26,this.words[r]=67108863&a}return 0!==e&&(this.words[r]=e,this.length++),this},a.prototype.muln=function(t){return this.clone().imuln(t)},a.prototype.sqr=function(){return this.mul(this)},a.prototype.isqr=function(){return this.imul(this.clone())},a.prototype.pow=function(t){var e=function(t){for(var e=new Array(t.bitLength()),r=0;r>>i}return e}(t);if(0===e.length)return new a(1);for(var r=this,n=0;n=0);var e,r=t%26,i=(t-r)/26,a=67108863>>>26-r<<26-r;if(0!==r){var o=0;for(e=0;e>>26-r}o&&(this.words[e]=o,this.length++)}if(0!==i){for(e=this.length-1;e>=0;e--)this.words[e+i]=this.words[e];for(e=0;e=0),i=e?(e-e%26)/26:0;var a=t%26,o=Math.min((t-a)/26,this.length),s=67108863^67108863>>>a<o)for(this.length-=o,u=0;u=0&&(0!==c||u>=i);u--){var f=0|this.words[u];this.words[u]=c<<26-a|f>>>a,c=f&s}return l&&0!==c&&(l.words[l.length++]=c),0===this.length&&(this.words[0]=0,this.length=1),this.strip()},a.prototype.ishrn=function(t,e,r){return n(0===this.negative),this.iushrn(t,e,r)},a.prototype.shln=function(t){return this.clone().ishln(t)},a.prototype.ushln=function(t){return this.clone().iushln(t)},a.prototype.shrn=function(t){return this.clone().ishrn(t)},a.prototype.ushrn=function(t){return this.clone().iushrn(t)},a.prototype.testn=function(t){n("number"==typeof t&&t>=0);var e=t%26,r=(t-e)/26,i=1<=0);var e=t%26,r=(t-e)/26;if(n(0===this.negative,"imaskn works only with positive numbers"),this.length<=r)return this;if(0!==e&&r++,this.length=Math.min(r,this.length),0!==e){var i=67108863^67108863>>>e<=67108864;e++)this.words[e]-=67108864,e===this.length-1?this.words[e+1]=1:this.words[e+1]++;return this.length=Math.max(this.length,e+1),this},a.prototype.isubn=function(t){if(n("number"==typeof t),n(t<67108864),t<0)return this.iaddn(-t);if(0!==this.negative)return this.negative=0,this.iaddn(t),this.negative=1,this;if(this.words[0]-=t,1===this.length&&this.words[0]<0)this.words[0]=-this.words[0],this.negative=1;else for(var e=0;e>26)-(l/67108864|0),this.words[i+r]=67108863&a}for(;i>26,this.words[i+r]=67108863&a;if(0===s)return this.strip();for(n(-1===s),s=0,i=0;i>26,this.words[i]=67108863&a;return this.negative=1,this.strip()},a.prototype._wordDiv=function(t,e){var r=(this.length,t.length),n=this.clone(),i=t,o=0|i.words[i.length-1];0!=(r=26-this._countBits(o))&&(i=i.ushln(r),n.iushln(r),o=0|i.words[i.length-1]);var s,l=n.length-i.length;if("mod"!==e){(s=new a(null)).length=l+1,s.words=new Array(s.length);for(var u=0;u=0;f--){var h=67108864*(0|n.words[i.length+f])+(0|n.words[i.length+f-1]);for(h=Math.min(h/o|0,67108863),n._ishlnsubmul(i,h,f);0!==n.negative;)h--,n.negative=0,n._ishlnsubmul(i,1,f),n.isZero()||(n.negative^=1);s&&(s.words[f]=h)}return s&&s.strip(),n.strip(),"div"!==e&&0!==r&&n.iushrn(r),{div:s||null,mod:n}},a.prototype.divmod=function(t,e,r){return n(!t.isZero()),this.isZero()?{div:new a(0),mod:new a(0)}:0!==this.negative&&0===t.negative?(s=this.neg().divmod(t,e),"mod"!==e&&(i=s.div.neg()),"div"!==e&&(o=s.mod.neg(),r&&0!==o.negative&&o.iadd(t)),{div:i,mod:o}):0===this.negative&&0!==t.negative?(s=this.divmod(t.neg(),e),"mod"!==e&&(i=s.div.neg()),{div:i,mod:s.mod}):0!=(this.negative&t.negative)?(s=this.neg().divmod(t.neg(),e),"div"!==e&&(o=s.mod.neg(),r&&0!==o.negative&&o.isub(t)),{div:s.div,mod:o}):t.length>this.length||this.cmp(t)<0?{div:new a(0),mod:this}:1===t.length?"div"===e?{div:this.divn(t.words[0]),mod:null}:"mod"===e?{div:null,mod:new a(this.modn(t.words[0]))}:{div:this.divn(t.words[0]),mod:new a(this.modn(t.words[0]))}:this._wordDiv(t,e);var i,o,s},a.prototype.div=function(t){return this.divmod(t,"div",!1).div},a.prototype.mod=function(t){return this.divmod(t,"mod",!1).mod},a.prototype.umod=function(t){return this.divmod(t,"mod",!0).mod},a.prototype.divRound=function(t){var e=this.divmod(t);if(e.mod.isZero())return e.div;var r=0!==e.div.negative?e.mod.isub(t):e.mod,n=t.ushrn(1),i=t.andln(1),a=r.cmp(n);return a<0||1===i&&0===a?e.div:0!==e.div.negative?e.div.isubn(1):e.div.iaddn(1)},a.prototype.modn=function(t){n(t<=67108863);for(var e=(1<<26)%t,r=0,i=this.length-1;i>=0;i--)r=(e*r+(0|this.words[i]))%t;return r},a.prototype.idivn=function(t){n(t<=67108863);for(var e=0,r=this.length-1;r>=0;r--){var i=(0|this.words[r])+67108864*e;this.words[r]=i/t|0,e=i%t}return this.strip()},a.prototype.divn=function(t){return this.clone().idivn(t)},a.prototype.egcd=function(t){n(0===t.negative),n(!t.isZero());var e=this,r=t.clone();e=0!==e.negative?e.umod(t):e.clone();for(var i=new a(1),o=new a(0),s=new a(0),l=new a(1),u=0;e.isEven()&&r.isEven();)e.iushrn(1),r.iushrn(1),++u;for(var c=r.clone(),f=e.clone();!e.isZero();){for(var h=0,p=1;0==(e.words[0]&p)&&h<26;++h,p<<=1);if(h>0)for(e.iushrn(h);h-- >0;)(i.isOdd()||o.isOdd())&&(i.iadd(c),o.isub(f)),i.iushrn(1),o.iushrn(1);for(var d=0,v=1;0==(r.words[0]&v)&&d<26;++d,v<<=1);if(d>0)for(r.iushrn(d);d-- >0;)(s.isOdd()||l.isOdd())&&(s.iadd(c),l.isub(f)),s.iushrn(1),l.iushrn(1);e.cmp(r)>=0?(e.isub(r),i.isub(s),o.isub(l)):(r.isub(e),s.isub(i),l.isub(o))}return{a:s,b:l,gcd:r.iushln(u)}},a.prototype._invmp=function(t){n(0===t.negative),n(!t.isZero());var e=this,r=t.clone();e=0!==e.negative?e.umod(t):e.clone();for(var i,o=new a(1),s=new a(0),l=r.clone();e.cmpn(1)>0&&r.cmpn(1)>0;){for(var u=0,c=1;0==(e.words[0]&c)&&u<26;++u,c<<=1);if(u>0)for(e.iushrn(u);u-- >0;)o.isOdd()&&o.iadd(l),o.iushrn(1);for(var f=0,h=1;0==(r.words[0]&h)&&f<26;++f,h<<=1);if(f>0)for(r.iushrn(f);f-- >0;)s.isOdd()&&s.iadd(l),s.iushrn(1);e.cmp(r)>=0?(e.isub(r),o.isub(s)):(r.isub(e),s.isub(o))}return(i=0===e.cmpn(1)?o:s).cmpn(0)<0&&i.iadd(t),i},a.prototype.gcd=function(t){if(this.isZero())return t.abs();if(t.isZero())return this.abs();var e=this.clone(),r=t.clone();e.negative=0,r.negative=0;for(var n=0;e.isEven()&&r.isEven();n++)e.iushrn(1),r.iushrn(1);for(;;){for(;e.isEven();)e.iushrn(1);for(;r.isEven();)r.iushrn(1);var i=e.cmp(r);if(i<0){var a=e;e=r,r=a}else if(0===i||0===r.cmpn(1))break;e.isub(r)}return r.iushln(n)},a.prototype.invm=function(t){return this.egcd(t).a.umod(t)},a.prototype.isEven=function(){return 0==(1&this.words[0])},a.prototype.isOdd=function(){return 1==(1&this.words[0])},a.prototype.andln=function(t){return this.words[0]&t},a.prototype.bincn=function(t){n("number"==typeof t);var e=t%26,r=(t-e)/26,i=1<>>26,s&=67108863,this.words[o]=s}return 0!==a&&(this.words[o]=a,this.length++),this},a.prototype.isZero=function(){return 1===this.length&&0===this.words[0]},a.prototype.cmpn=function(t){var e,r=t<0;if(0!==this.negative&&!r)return-1;if(0===this.negative&&r)return 1;if(this.strip(),this.length>1)e=1;else{r&&(t=-t),n(t<=67108863,"Number is too big");var i=0|this.words[0];e=i===t?0:it.length)return 1;if(this.length=0;r--){var n=0|this.words[r],i=0|t.words[r];if(n!==i){ni&&(e=1);break}}return e},a.prototype.gtn=function(t){return 1===this.cmpn(t)},a.prototype.gt=function(t){return 1===this.cmp(t)},a.prototype.gten=function(t){return this.cmpn(t)>=0},a.prototype.gte=function(t){return this.cmp(t)>=0},a.prototype.ltn=function(t){return-1===this.cmpn(t)},a.prototype.lt=function(t){return-1===this.cmp(t)},a.prototype.lten=function(t){return this.cmpn(t)<=0},a.prototype.lte=function(t){return this.cmp(t)<=0},a.prototype.eqn=function(t){return 0===this.cmpn(t)},a.prototype.eq=function(t){return 0===this.cmp(t)},a.red=function(t){return new T(t)},a.prototype.toRed=function(t){return n(!this.red,"Already a number in reduction context"),n(0===this.negative,"red works only with positives"),t.convertTo(this)._forceRed(t)},a.prototype.fromRed=function(){return n(this.red,"fromRed works only with numbers in reduction context"),this.red.convertFrom(this)},a.prototype._forceRed=function(t){return this.red=t,this},a.prototype.forceRed=function(t){return n(!this.red,"Already a number in reduction context"),this._forceRed(t)},a.prototype.redAdd=function(t){return n(this.red,"redAdd works only with red numbers"),this.red.add(this,t)},a.prototype.redIAdd=function(t){return n(this.red,"redIAdd works only with red numbers"),this.red.iadd(this,t)},a.prototype.redSub=function(t){return n(this.red,"redSub works only with red numbers"),this.red.sub(this,t)},a.prototype.redISub=function(t){return n(this.red,"redISub works only with red numbers"),this.red.isub(this,t)},a.prototype.redShl=function(t){return n(this.red,"redShl works only with red numbers"),this.red.shl(this,t)},a.prototype.redMul=function(t){return n(this.red,"redMul works only with red numbers"),this.red._verify2(this,t),this.red.mul(this,t)},a.prototype.redIMul=function(t){return n(this.red,"redMul works only with red numbers"),this.red._verify2(this,t),this.red.imul(this,t)},a.prototype.redSqr=function(){return n(this.red,"redSqr works only with red numbers"),this.red._verify1(this),this.red.sqr(this)},a.prototype.redISqr=function(){return n(this.red,"redISqr works only with red numbers"),this.red._verify1(this),this.red.isqr(this)},a.prototype.redSqrt=function(){return n(this.red,"redSqrt works only with red numbers"),this.red._verify1(this),this.red.sqrt(this)},a.prototype.redInvm=function(){return n(this.red,"redInvm works only with red numbers"),this.red._verify1(this),this.red.invm(this)},a.prototype.redNeg=function(){return n(this.red,"redNeg works only with red numbers"),this.red._verify1(this),this.red.neg(this)},a.prototype.redPow=function(t){return n(this.red&&!t.red,"redPow(normalNum)"),this.red._verify1(this),this.red.pow(this,t)};var y={k256:null,p224:null,p192:null,p25519:null};function m(t,e){this.name=t,this.p=new a(e,16),this.n=this.p.bitLength(),this.k=new a(1).iushln(this.n).isub(this.p),this.tmp=this._tmp()}function x(){m.call(this,"k256","ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f")}function b(){m.call(this,"p224","ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001")}function _(){m.call(this,"p192","ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff")}function w(){m.call(this,"25519","7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed")}function T(t){if("string"==typeof t){var e=a._prime(t);this.m=e.p,this.prime=e}else n(t.gtn(1),"modulus must be greater than 1"),this.m=t,this.prime=null}function k(t){T.call(this,t),this.shift=this.m.bitLength(),this.shift%26!=0&&(this.shift+=26-this.shift%26),this.r=new a(1).iushln(this.shift),this.r2=this.imod(this.r.sqr()),this.rinv=this.r._invmp(this.m),this.minv=this.rinv.mul(this.r).isubn(1).div(this.m),this.minv=this.minv.umod(this.r),this.minv=this.r.sub(this.minv)}m.prototype._tmp=function(){var t=new a(null);return t.words=new Array(Math.ceil(this.n/13)),t},m.prototype.ireduce=function(t){var 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v=l("labels");l("labelFont")&&(v=!0),o("labelEnable"),a("labelSize"),a("labelPad"),u("labelColor"),o("lineEnable"),o("lineMirror"),a("lineWidth"),u("lineColor"),o("lineTickEnable"),o("lineTickMirror"),a("lineTickLength"),a("lineTickWidth"),u("lineTickColor"),o("gridEnable"),a("gridWidth"),u("gridColor"),o("zeroEnable"),u("zeroLineColor"),a("zeroLineWidth"),o("backgroundEnable"),u("backgroundColor"),this._text?this._text&&(v||c)&&this._text.update(this.bounds,this.labels,this.labelFont,this.ticks,this.tickFont):this._text=n(this.gl,this.bounds,this.labels,this.labelFont,this.ticks,this.tickFont),this._lines&&c&&(this._lines.dispose(),this._lines=null),this._lines||(this._lines=i(this.gl,this.bounds,this.ticks))};var p=[new h,new h,new h];function d(t,e,r,n,i){for(var a=t.primalOffset,o=t.primalMinor,s=t.mirrorOffset,l=t.mirrorMinor,u=n[e],c=0;c<3;++c)if(e!==c){var f=a,h=s,p=o,d=l;u&1<0?(p[c]=-1,d[c]=0):(p[c]=0,d[c]=1)}}var v=[0,0,0],g={model:l,view:l,projection:l,_ortho:!1};f.isOpaque=function(){return!0},f.isTransparent=function(){return!1},f.drawTransparent=function(t){};var y=[0,0,0],m=[0,0,0],x=[0,0,0];f.draw=function(t){t=t||g;for(var e=this.gl,r=t.model||l,n=t.view||l,i=t.projection||l,a=this.bounds,s=t._ortho||!1,c=o(r,n,i,a,s),f=c.cubeEdges,h=c.axis,b=n[12],_=n[13],w=n[14],T=n[15],k=(s?2:1)*this.pixelRatio*(i[3]*b+i[7]*_+i[11]*w+i[15]*T)/e.drawingBufferHeight,A=0;A<3;++A)this.lastCubeProps.cubeEdges[A]=f[A],this.lastCubeProps.axis[A]=h[A];var M=p;for(A=0;A<3;++A)d(p[A],A,this.bounds,f,h);e=this.gl;var S,E,L,C=v;for(A=0;A<3;++A)this.backgroundEnable[A]?C[A]=h[A]:C[A]=0;for(this._background.draw(r,n,i,a,C,this.backgroundColor),this._lines.bind(r,n,i,this),A=0;A<3;++A){var P=[0,0,0];h[A]>0?P[A]=a[1][A]:P[A]=a[0][A];for(var O=0;O<2;++O){var I=(A+1+O)%3,D=(A+1+(1^O))%3;this.gridEnable[I]&&this._lines.drawGrid(I,D,this.bounds,P,this.gridColor[I],this.gridWidth[I]*this.pixelRatio)}for(O=0;O<2;++O)I=(A+1+O)%3,D=(A+1+(1^O))%3,this.zeroEnable[D]&&Math.min(a[0][D],a[1][D])<=0&&Math.max(a[0][D],a[1][D])>=0&&this._lines.drawZero(I,D,this.bounds,P,this.zeroLineColor[D],this.zeroLineWidth[D]*this.pixelRatio)}for(A=0;A<3;++A){this.lineEnable[A]&&this._lines.drawAxisLine(A,this.bounds,M[A].primalOffset,this.lineColor[A],this.lineWidth[A]*this.pixelRatio),this.lineMirror[A]&&this._lines.drawAxisLine(A,this.bounds,M[A].mirrorOffset,this.lineColor[A],this.lineWidth[A]*this.pixelRatio);var z=u(y,M[A].primalMinor),R=u(m,M[A].mirrorMinor),F=this.lineTickLength;for(O=0;O<3;++O){var B=k/r[5*O];z[O]*=F[O]*B,R[O]*=F[O]*B}this.lineTickEnable[A]&&this._lines.drawAxisTicks(A,M[A].primalOffset,z,this.lineTickColor[A],this.lineTickWidth[A]*this.pixelRatio),this.lineTickMirror[A]&&this._lines.drawAxisTicks(A,M[A].mirrorOffset,R,this.lineTickColor[A],this.lineTickWidth[A]*this.pixelRatio)}function N(t){(L=[0,0,0])[t]=1}function j(t,e,r){var n=(t+1)%3,i=(t+2)%3,a=e[n],o=e[i],s=r[n],l=r[i];a>0&&l>0||a>0&&l<0||a<0&&l>0||a<0&&l<0?N(n):(o>0&&s>0||o>0&&s<0||o<0&&s>0||o<0&&s<0)&&N(i)}for(this._lines.unbind(),this._text.bind(r,n,i,this.pixelRatio),A=0;A<3;++A){var U=M[A].primalMinor,V=M[A].mirrorMinor,H=u(x,M[A].primalOffset);for(O=0;O<3;++O)this.lineTickEnable[A]&&(H[O]+=k*U[O]*Math.max(this.lineTickLength[O],0)/r[5*O]);var q=[0,0,0];if(q[A]=1,this.tickEnable[A]){for(-3600===this.tickAngle[A]?(this.tickAngle[A]=0,this.tickAlign[A]="auto"):this.tickAlign[A]=-1,E=1,"auto"===(S=[this.tickAlign[A],.5,E])[0]?S[0]=0:S[0]=parseInt(""+S[0]),L=[0,0,0],j(A,U,V),O=0;O<3;++O)H[O]+=k*U[O]*this.tickPad[O]/r[5*O];this._text.drawTicks(A,this.tickSize[A],this.tickAngle[A],H,this.tickColor[A],q,L,S)}if(this.labelEnable[A]){for(E=0,L=[0,0,0],this.labels[A].length>4&&(N(A),E=1),"auto"===(S=[this.labelAlign[A],.5,E])[0]?S[0]=0:S[0]=parseInt(""+S[0]),O=0;O<3;++O)H[O]+=k*U[O]*this.labelPad[O]/r[5*O];H[A]+=.5*(a[0][A]+a[1][A]),this._text.drawLabel(A,this.labelSize[A],this.labelAngle[A],H,this.labelColor[A],[0,0,0],L,S)}}this._text.unbind()},f.dispose=function(){this._text.dispose(),this._lines.dispose(),this._background.dispose(),this._lines=null,this._text=null,this._background=null,this.gl=null}},1011:function(t,e,r){"use strict";t.exports=function(t){for(var e=[],r=[],s=0,l=0;l<3;++l)for(var u=(l+1)%3,c=(l+2)%3,f=[0,0,0],h=[0,0,0],p=-1;p<=1;p+=2){r.push(s,s+2,s+1,s+1,s+2,s+3),f[l]=p,h[l]=p;for(var d=-1;d<=1;d+=2){f[u]=d;for(var v=-1;v<=1;v+=2)f[c]=v,e.push(f[0],f[1],f[2],h[0],h[1],h[2]),s+=1}var g=u;u=c,c=g}var y=n(t,new Float32Array(e)),m=n(t,new Uint16Array(r),t.ELEMENT_ARRAY_BUFFER),x=i(t,[{buffer:y,type:t.FLOAT,size:3,offset:0,stride:24},{buffer:y,type:t.FLOAT,size:3,offset:12,stride:24}],m),b=a(t);return b.attributes.position.location=0,b.attributes.normal.location=1,new o(t,y,x,b)};var n=r(5827),i=r(2944),a=r(1943).bg;function o(t,e,r,n){this.gl=t,this.buffer=e,this.vao=r,this.shader=n}var s=o.prototype;s.draw=function(t,e,r,n,i,a){for(var o=!1,s=0;s<3;++s)o=o||i[s];if(o){var l=this.gl;l.enable(l.POLYGON_OFFSET_FILL),l.polygonOffset(1,2),this.shader.bind(),this.shader.uniforms={model:t,view:e,projection:r,bounds:n,enable:i,colors:a},this.vao.bind(),this.vao.draw(this.gl.TRIANGLES,36),this.vao.unbind(),l.disable(l.POLYGON_OFFSET_FILL)}},s.dispose=function(){this.vao.dispose(),this.buffer.dispose(),this.shader.dispose()}},2864:function(t,e,r){"use strict";t.exports=function(t,e,r,a,p){i(s,e,t),i(s,r,s);for(var m=0,x=0;x<2;++x){c[2]=a[x][2];for(var b=0;b<2;++b){c[1]=a[b][1];for(var _=0;_<2;++_)c[0]=a[_][0],h(l[m],c,s),m+=1}}var w=-1;for(x=0;x<8;++x){for(var T=l[x][3],k=0;k<3;++k)u[x][k]=l[x][k]/T;p&&(u[x][2]*=-1),T<0&&(w<0||u[x][2]E&&(w|=1<E&&(w|=1<u[x][1])&&(R=x);var F=-1;for(x=0;x<3;++x)(N=R^1<u[B][0]&&(B=N))}var j=v;j[0]=j[1]=j[2]=0,j[n.log2(F^R)]=R&F,j[n.log2(R^B)]=R&B;var U=7^B;U===w||U===z?(U=7^F,j[n.log2(B^U)]=U&B):j[n.log2(F^U)]=U&F;var V=g,H=w;for(A=0;A<3;++A)V[A]=H&1< HALF_PI) && (b <= ONE_AND_HALF_PI)) ?\n b - PI :\n b;\n}\n\nfloat look_horizontal_or_vertical(float a, float ratio) {\n // ratio controls the ratio between being horizontal to (vertical + horizontal)\n // if ratio is set to 0.5 then it is 50%, 50%.\n // when using a higher ratio e.g. 0.75 the result would\n // likely be more horizontal than vertical.\n\n float b = positive_angle(a);\n\n return\n (b < ( ratio) * HALF_PI) ? 0.0 :\n (b < (2.0 - ratio) * HALF_PI) ? -HALF_PI :\n (b < (2.0 + ratio) * HALF_PI) ? 0.0 :\n (b < (4.0 - ratio) * HALF_PI) ? HALF_PI :\n 0.0;\n}\n\nfloat roundTo(float a, float b) {\n return float(b * floor((a + 0.5 * b) / b));\n}\n\nfloat look_round_n_directions(float a, int n) {\n float b = positive_angle(a);\n float div = TWO_PI / float(n);\n float c = roundTo(b, div);\n return look_upwards(c);\n}\n\nfloat applyAlignOption(float rawAngle, float delta) {\n return\n (option > 2) ? look_round_n_directions(rawAngle + delta, option) : // option 3-n: round to n directions\n (option == 2) ? look_horizontal_or_vertical(rawAngle + delta, hv_ratio) : // horizontal or vertical\n (option == 1) ? rawAngle + delta : // use free angle, and flip to align with one direction of the axis\n (option == 0) ? look_upwards(rawAngle) : // use free angle, and stay upwards\n (option ==-1) ? 0.0 : // useful for backward compatibility, all texts remains horizontal\n rawAngle; // otherwise return back raw input angle\n}\n\nbool isAxisTitle = (axis.x == 0.0) &&\n (axis.y == 0.0) &&\n (axis.z == 0.0);\n\nvoid main() {\n //Compute world offset\n float axisDistance = position.z;\n vec3 dataPosition = axisDistance * axis + offset;\n\n float beta = angle; // i.e. user defined attributes for each tick\n\n float axisAngle;\n float clipAngle;\n float flip;\n\n if (enableAlign) {\n axisAngle = (isAxisTitle) ? HALF_PI :\n computeViewAngle(dataPosition, dataPosition + axis);\n clipAngle = computeViewAngle(dataPosition, dataPosition + alignDir);\n\n axisAngle += (sin(axisAngle) < 0.0) ? PI : 0.0;\n clipAngle += (sin(clipAngle) < 0.0) ? PI : 0.0;\n\n flip = (dot(vec2(cos(axisAngle), sin(axisAngle)),\n vec2(sin(clipAngle),-cos(clipAngle))) > 0.0) ? 1.0 : 0.0;\n\n beta += applyAlignOption(clipAngle, flip * PI);\n }\n\n //Compute plane offset\n vec2 planeCoord = position.xy * pixelScale;\n\n mat2 planeXform = scale * mat2(\n cos(beta), sin(beta),\n -sin(beta), cos(beta)\n );\n\n vec2 viewOffset = 2.0 * planeXform * planeCoord / resolution;\n\n //Compute clip position\n vec3 clipPosition = project(dataPosition);\n\n //Apply text offset in clip coordinates\n clipPosition += vec3(viewOffset, 0.0);\n\n //Done\n gl_Position = vec4(clipPosition, 1.0);\n}"]),l=n(["precision highp float;\n#define GLSLIFY 1\n\nuniform vec4 color;\nvoid main() {\n gl_FragColor = color;\n}"]);e.f=function(t){return i(t,s,l,null,[{name:"position",type:"vec3"}])};var u=n(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec3 position;\nattribute vec3 normal;\n\nuniform mat4 model, view, projection;\nuniform vec3 enable;\nuniform vec3 bounds[2];\n\nvarying vec3 colorChannel;\n\nvoid main() {\n\n vec3 signAxis = sign(bounds[1] - bounds[0]);\n\n vec3 realNormal = signAxis * normal;\n\n if(dot(realNormal, enable) > 0.0) {\n vec3 minRange = min(bounds[0], bounds[1]);\n vec3 maxRange = max(bounds[0], bounds[1]);\n vec3 nPosition = mix(minRange, maxRange, 0.5 * (position + 1.0));\n gl_Position = projection * view * model * vec4(nPosition, 1.0);\n } else {\n gl_Position = vec4(0,0,0,0);\n }\n\n colorChannel = abs(realNormal);\n}"]),c=n(["precision highp float;\n#define GLSLIFY 1\n\nuniform vec4 colors[3];\n\nvarying vec3 colorChannel;\n\nvoid main() {\n gl_FragColor = colorChannel.x * colors[0] +\n colorChannel.y * colors[1] +\n colorChannel.z * colors[2];\n}"]);e.bg=function(t){return i(t,u,c,null,[{name:"position",type:"vec3"},{name:"normal",type:"vec3"}])}},9557:function(t,e,r){"use strict";t.exports=function(t,e,r,i,o,l){var u=n(t),f=a(t,[{buffer:u,size:3}]),h=s(t);h.attributes.position.location=0;var p=new c(t,h,u,f);return p.update(e,r,i,o,l),p};var n=r(5827),a=r(2944),o=r(875),s=r(1943).f,l=window||i.global||{},u=l.__TEXT_CACHE||{};function c(t,e,r,n){this.gl=t,this.shader=e,this.buffer=r,this.vao=n,this.tickOffset=this.tickCount=this.labelOffset=this.labelCount=null}l.__TEXT_CACHE={};var f=c.prototype,h=[0,0];f.bind=function(t,e,r,n){this.vao.bind(),this.shader.bind();var i=this.shader.uniforms;i.model=t,i.view=e,i.projection=r,i.pixelScale=n,h[0]=this.gl.drawingBufferWidth,h[1]=this.gl.drawingBufferHeight,this.shader.uniforms.resolution=h},f.unbind=function(){this.vao.unbind()},f.update=function(t,e,r,n,i){var a=[];function s(t,e,r,n,i,s){var l=u[r];l||(l=u[r]={});var c=l[e];c||(c=l[e]=function(t,e){try{return o(t,e)}catch(e){return console.warn('error vectorizing text:"'+t+'" error:',e),{cells:[],positions:[]}}}(e,{triangles:!0,font:r,textAlign:"center",textBaseline:"middle",lineSpacing:i,styletags:s}));for(var f=(n||12)/12,h=c.positions,p=c.cells,d=0,v=p.length;d=0;--y){var m=h[g[y]];a.push(f*m[0],-f*m[1],t)}}for(var l=[0,0,0],c=[0,0,0],f=[0,0,0],h=[0,0,0],p={breaklines:!0,bolds:!0,italics:!0,subscripts:!0,superscripts:!0},d=0;d<3;++d){f[d]=a.length/3|0,s(.5*(t[0][d]+t[1][d]),e[d],r[d],12,1.25,p),h[d]=(a.length/3|0)-f[d],l[d]=a.length/3|0;for(var v=0;v=0&&(i=r.length-n-1);var a=Math.pow(10,i),o=Math.round(t*e*a),s=o+"";if(s.indexOf("e")>=0)return s;var l=o/a,u=o%a;o<0?(l=0|-Math.ceil(l),u=0|-u):(l=0|Math.floor(l),u|=0);var c=""+l;if(o<0&&(c="-"+c),i){for(var f=""+u;f.length=t[0][i];--o)a.push({x:o*e[i],text:r(e[i],o)});n.push(a)}return n},e.equal=function(t,e){for(var r=0;r<3;++r){if(t[r].length!==e[r].length)return!1;for(var n=0;nr)throw new Error("gl-buffer: If resizing buffer, must not specify offset");return t.bufferSubData(e,a,i),r}function c(t,e){for(var r=n.malloc(t.length,e),i=t.length,a=0;a=0;--n){if(e[n]!==r)return!1;r*=t[n]}return!0}(t.shape,t.stride))0===t.offset&&t.data.length===t.shape[0]?this.length=u(this.gl,this.type,this.length,this.usage,t.data,e):this.length=u(this.gl,this.type,this.length,this.usage,t.data.subarray(t.offset,t.shape[0]),e);else{var s=n.malloc(t.size,r),l=a(s,t.shape);i.assign(l,t),this.length=u(this.gl,this.type,this.length,this.usage,e<0?s:s.subarray(0,t.size),e),n.free(s)}}else if(Array.isArray(t)){var f;f=this.type===this.gl.ELEMENT_ARRAY_BUFFER?c(t,"uint16"):c(t,"float32"),this.length=u(this.gl,this.type,this.length,this.usage,e<0?f:f.subarray(0,t.length),e),n.free(f)}else if("object"==typeof t&&"number"==typeof t.length)this.length=u(this.gl,this.type,this.length,this.usage,t,e);else{if("number"!=typeof t&&void 0!==t)throw new Error("gl-buffer: Invalid data type");if(e>=0)throw new Error("gl-buffer: Cannot specify offset when resizing buffer");(t|=0)<=0&&(t=1),this.gl.bufferData(this.type,0|t,this.usage),this.length=t}},t.exports=function(t,e,r,n){if(r=r||t.ARRAY_BUFFER,n=n||t.DYNAMIC_DRAW,r!==t.ARRAY_BUFFER&&r!==t.ELEMENT_ARRAY_BUFFER)throw new Error("gl-buffer: Invalid type for webgl buffer, must be either gl.ARRAY_BUFFER or gl.ELEMENT_ARRAY_BUFFER");if(n!==t.DYNAMIC_DRAW&&n!==t.STATIC_DRAW&&n!==t.STREAM_DRAW)throw new Error("gl-buffer: Invalid usage for buffer, must be either gl.DYNAMIC_DRAW, gl.STATIC_DRAW or gl.STREAM_DRAW");var i=t.createBuffer(),a=new s(t,r,i,0,n);return a.update(e),a}},1140:function(t,e,r){"use strict";var n=r(2858);t.exports=function(t,e){var r=t.positions,i=t.vectors,a={positions:[],vertexIntensity:[],vertexIntensityBounds:t.vertexIntensityBounds,vectors:[],cells:[],coneOffset:t.coneOffset,colormap:t.colormap};if(0===t.positions.length)return e&&(e[0]=[0,0,0],e[1]=[0,0,0]),a;for(var o=0,s=1/0,l=-1/0,u=1/0,c=-1/0,f=1/0,h=-1/0,p=null,d=null,v=[],g=1/0,y=!1,m=0;mo&&(o=n.length(b)),m){var _=2*n.distance(p,x)/(n.length(d)+n.length(b));_?(g=Math.min(g,_),y=!1):y=!0}y||(p=x,d=b),v.push(b)}var w=[s,u,f],T=[l,c,h];e&&(e[0]=w,e[1]=T),0===o&&(o=1);var k=1/o;isFinite(g)||(g=1),a.vectorScale=g;var A=t.coneSize||.5;t.absoluteConeSize&&(A=t.absoluteConeSize*k),a.coneScale=A,m=0;for(var M=0;m=1},p.isTransparent=function(){return this.opacity<1},p.pickSlots=1,p.setPickBase=function(t){this.pickId=t},p.update=function(t){t=t||{};var e=this.gl;this.dirty=!0,"lightPosition"in t&&(this.lightPosition=t.lightPosition),"opacity"in t&&(this.opacity=t.opacity),"ambient"in t&&(this.ambientLight=t.ambient),"diffuse"in t&&(this.diffuseLight=t.diffuse),"specular"in t&&(this.specularLight=t.specular),"roughness"in t&&(this.roughness=t.roughness),"fresnel"in t&&(this.fresnel=t.fresnel),void 0!==t.tubeScale&&(this.tubeScale=t.tubeScale),void 0!==t.vectorScale&&(this.vectorScale=t.vectorScale),void 0!==t.coneScale&&(this.coneScale=t.coneScale),void 0!==t.coneOffset&&(this.coneOffset=t.coneOffset),t.colormap&&(this.texture.shape=[256,256],this.texture.minFilter=e.LINEAR_MIPMAP_LINEAR,this.texture.magFilter=e.LINEAR,this.texture.setPixels(function(t){for(var e=c({colormap:t,nshades:256,format:"rgba"}),r=new Uint8Array(1024),n=0;n<256;++n){for(var i=e[n],a=0;a<3;++a)r[4*n+a]=i[a];r[4*n+3]=255*i[3]}return u(r,[256,256,4],[4,0,1])}(t.colormap)),this.texture.generateMipmap());var r=t.cells,n=t.positions,i=t.vectors;if(n&&r&&i){var a=[],o=[],s=[],l=[],f=[];this.cells=r,this.positions=n,this.vectors=i;var h=t.meshColor||[1,1,1,1],p=t.vertexIntensity,d=1/0,v=-1/0;if(p)if(t.vertexIntensityBounds)d=+t.vertexIntensityBounds[0],v=+t.vertexIntensityBounds[1];else for(var g=0;g0){var v=this.triShader;v.bind(),v.uniforms=u,this.triangleVAO.bind(),e.drawArrays(e.TRIANGLES,0,3*this.triangleCount),this.triangleVAO.unbind()}},p.drawPick=function(t){t=t||{};for(var e=this.gl,r=t.model||f,n=t.view||f,i=t.projection||f,a=[[-1e6,-1e6,-1e6],[1e6,1e6,1e6]],o=0;o<3;++o)a[0][o]=Math.max(a[0][o],this.clipBounds[0][o]),a[1][o]=Math.min(a[1][o],this.clipBounds[1][o]);this._model=[].slice.call(r),this._view=[].slice.call(n),this._projection=[].slice.call(i),this._resolution=[e.drawingBufferWidth,e.drawingBufferHeight];var s={model:r,view:n,projection:i,clipBounds:a,tubeScale:this.tubeScale,vectorScale:this.vectorScale,coneScale:this.coneScale,coneOffset:this.coneOffset,pickId:this.pickId/255},l=this.pickShader;l.bind(),l.uniforms=s,this.triangleCount>0&&(this.triangleVAO.bind(),e.drawArrays(e.TRIANGLES,0,3*this.triangleCount),this.triangleVAO.unbind())},p.pick=function(t){if(!t)return null;if(t.id!==this.pickId)return null;var e=t.value[0]+256*t.value[1]+65536*t.value[2],r=this.cells[e],n=this.positions[r[1]].slice(0,3),i={position:n,dataCoordinate:n,index:Math.floor(r[1]/48)};return"cone"===this.traceType?i.index=Math.floor(r[1]/48):"streamtube"===this.traceType&&(i.intensity=this.intensity[r[1]],i.velocity=this.vectors[r[1]].slice(0,3),i.divergence=this.vectors[r[1]][3],i.index=e),i},p.dispose=function(){this.texture.dispose(),this.triShader.dispose(),this.pickShader.dispose(),this.triangleVAO.dispose(),this.trianglePositions.dispose(),this.triangleVectors.dispose(),this.triangleColors.dispose(),this.triangleUVs.dispose(),this.triangleIds.dispose()},t.exports=function(t,e,r){var n=r.shaders;1===arguments.length&&(t=(e=t).gl);var s=d(t,n),l=v(t,n),c=o(t,u(new Uint8Array([255,255,255,255]),[1,1,4]));c.generateMipmap(),c.minFilter=t.LINEAR_MIPMAP_LINEAR,c.magFilter=t.LINEAR;var f=i(t),p=i(t),g=i(t),y=i(t),m=i(t),x=a(t,[{buffer:f,type:t.FLOAT,size:4},{buffer:m,type:t.UNSIGNED_BYTE,size:4,normalized:!0},{buffer:g,type:t.FLOAT,size:4},{buffer:y,type:t.FLOAT,size:2},{buffer:p,type:t.FLOAT,size:4}]),b=new h(t,c,s,l,f,p,m,g,y,x,r.traceType||"cone");return b.update(e),b}},7234:function(t,e,r){var n=r(6832),i=n(["precision highp float;\n\nprecision highp float;\n#define GLSLIFY 1\n\nvec3 getOrthogonalVector(vec3 v) {\n // Return up-vector for only-z vector.\n // Return ax + by + cz = 0, a point that lies on the plane that has v as a normal and that isn't (0,0,0).\n // From the above if-statement we have ||a|| > 0 U ||b|| > 0.\n // Assign z = 0, x = -b, y = a:\n // a*-b + b*a + c*0 = -ba + ba + 0 = 0\n if (v.x*v.x > v.z*v.z || v.y*v.y > v.z*v.z) {\n return normalize(vec3(-v.y, v.x, 0.0));\n } else {\n return normalize(vec3(0.0, v.z, -v.y));\n }\n}\n\n// Calculate the cone vertex and normal at the given index.\n//\n// The returned vertex is for a cone with its top at origin and height of 1.0,\n// pointing in the direction of the vector attribute.\n//\n// Each cone is made up of a top vertex, a center base vertex and base perimeter vertices.\n// These vertices are used to make up the triangles of the cone by the following:\n// segment + 0 top vertex\n// segment + 1 perimeter vertex a+1\n// segment + 2 perimeter vertex a\n// segment + 3 center base vertex\n// segment + 4 perimeter vertex a\n// segment + 5 perimeter vertex a+1\n// Where segment is the number of the radial segment * 6 and a is the angle at that radial segment.\n// To go from index to segment, floor(index / 6)\n// To go from segment to angle, 2*pi * (segment/segmentCount)\n// To go from index to segment index, index - (segment*6)\n//\nvec3 getConePosition(vec3 d, float rawIndex, float coneOffset, out vec3 normal) {\n\n const float segmentCount = 8.0;\n\n float index = rawIndex - floor(rawIndex /\n (segmentCount * 6.0)) *\n (segmentCount * 6.0);\n\n float segment = floor(0.001 + index/6.0);\n float segmentIndex = index - (segment*6.0);\n\n normal = -normalize(d);\n\n if (segmentIndex > 2.99 && segmentIndex < 3.01) {\n return mix(vec3(0.0), -d, coneOffset);\n }\n\n float nextAngle = (\n (segmentIndex > 0.99 && segmentIndex < 1.01) ||\n (segmentIndex > 4.99 && segmentIndex < 5.01)\n ) ? 1.0 : 0.0;\n float angle = 2.0 * 3.14159 * ((segment + nextAngle) / segmentCount);\n\n vec3 v1 = mix(d, vec3(0.0), coneOffset);\n vec3 v2 = v1 - d;\n\n vec3 u = getOrthogonalVector(d);\n vec3 v = normalize(cross(u, d));\n\n vec3 x = u * cos(angle) * length(d)*0.25;\n vec3 y = v * sin(angle) * length(d)*0.25;\n vec3 v3 = v2 + x + y;\n if (segmentIndex < 3.0) {\n vec3 tx = u * sin(angle);\n vec3 ty = v * -cos(angle);\n vec3 tangent = tx + ty;\n normal = normalize(cross(v3 - v1, tangent));\n }\n\n if (segmentIndex == 0.0) {\n return mix(d, vec3(0.0), coneOffset);\n }\n return v3;\n}\n\nattribute vec3 vector;\nattribute vec4 color, position;\nattribute vec2 uv;\n\nuniform float vectorScale, coneScale, coneOffset;\nuniform mat4 model, view, projection, inverseModel;\nuniform vec3 eyePosition, lightPosition;\n\nvarying vec3 f_normal, f_lightDirection, f_eyeDirection, f_data, f_position;\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n // Scale the vector magnitude to stay constant with\n // model & view changes.\n vec3 normal;\n vec3 XYZ = getConePosition(mat3(model) * ((vectorScale * coneScale) * vector), position.w, coneOffset, normal);\n vec4 conePosition = model * vec4(position.xyz, 1.0) + vec4(XYZ, 0.0);\n\n //Lighting geometry parameters\n vec4 cameraCoordinate = view * conePosition;\n cameraCoordinate.xyz /= cameraCoordinate.w;\n f_lightDirection = lightPosition - cameraCoordinate.xyz;\n f_eyeDirection = eyePosition - cameraCoordinate.xyz;\n f_normal = normalize((vec4(normal, 0.0) * inverseModel).xyz);\n\n // vec4 m_position = model * vec4(conePosition, 1.0);\n vec4 t_position = view * conePosition;\n gl_Position = projection * t_position;\n\n f_color = color;\n f_data = conePosition.xyz;\n f_position = position.xyz;\n f_uv = uv;\n}\n"]),a=n(["#extension GL_OES_standard_derivatives : enable\n\nprecision highp float;\n#define GLSLIFY 1\n\nfloat beckmannDistribution(float x, float roughness) {\n float NdotH = max(x, 0.0001);\n float cos2Alpha = NdotH * NdotH;\n float tan2Alpha = (cos2Alpha - 1.0) / cos2Alpha;\n float roughness2 = roughness * roughness;\n float denom = 3.141592653589793 * roughness2 * cos2Alpha * cos2Alpha;\n return exp(tan2Alpha / roughness2) / denom;\n}\n\nfloat cookTorranceSpecular(\n vec3 lightDirection,\n vec3 viewDirection,\n vec3 surfaceNormal,\n float roughness,\n float fresnel) {\n\n float VdotN = max(dot(viewDirection, surfaceNormal), 0.0);\n float LdotN = max(dot(lightDirection, surfaceNormal), 0.0);\n\n //Half angle vector\n vec3 H = normalize(lightDirection + viewDirection);\n\n //Geometric term\n float NdotH = max(dot(surfaceNormal, H), 0.0);\n float VdotH = max(dot(viewDirection, H), 0.000001);\n float LdotH = max(dot(lightDirection, H), 0.000001);\n float G1 = (2.0 * NdotH * VdotN) / VdotH;\n float G2 = (2.0 * NdotH * LdotN) / LdotH;\n float G = min(1.0, min(G1, G2));\n \n //Distribution term\n float D = beckmannDistribution(NdotH, roughness);\n\n //Fresnel term\n float F = pow(1.0 - VdotN, fresnel);\n\n //Multiply terms and done\n return G * F * D / max(3.14159265 * VdotN, 0.000001);\n}\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform float roughness, fresnel, kambient, kdiffuse, kspecular, opacity;\nuniform sampler2D texture;\n\nvarying vec3 f_normal, f_lightDirection, f_eyeDirection, f_data, f_position;\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], f_position)) discard;\n vec3 N = normalize(f_normal);\n vec3 L = normalize(f_lightDirection);\n vec3 V = normalize(f_eyeDirection);\n\n if(gl_FrontFacing) {\n N = -N;\n }\n\n float specular = min(1.0, max(0.0, cookTorranceSpecular(L, V, N, roughness, fresnel)));\n float diffuse = min(kambient + kdiffuse * max(dot(N, L), 0.0), 1.0);\n\n vec4 surfaceColor = f_color * texture2D(texture, f_uv);\n vec4 litColor = surfaceColor.a * vec4(diffuse * surfaceColor.rgb + kspecular * vec3(1,1,1) * specular, 1.0);\n\n gl_FragColor = litColor * opacity;\n}\n"]),o=n(["precision highp float;\n\nprecision highp float;\n#define GLSLIFY 1\n\nvec3 getOrthogonalVector(vec3 v) {\n // Return up-vector for only-z vector.\n // Return ax + by + cz = 0, a point that lies on the plane that has v as a normal and that isn't (0,0,0).\n // From the above if-statement we have ||a|| > 0 U ||b|| > 0.\n // Assign z = 0, x = -b, y = a:\n // a*-b + b*a + c*0 = -ba + ba + 0 = 0\n if (v.x*v.x > v.z*v.z || v.y*v.y > v.z*v.z) {\n return normalize(vec3(-v.y, v.x, 0.0));\n } else {\n return normalize(vec3(0.0, v.z, -v.y));\n }\n}\n\n// Calculate the cone vertex and normal at the given index.\n//\n// The returned vertex is for a cone with its top at origin and height of 1.0,\n// pointing in the direction of the vector attribute.\n//\n// Each cone is made up of a top vertex, a center base vertex and base perimeter vertices.\n// These vertices are used to make up the triangles of the cone by the following:\n// segment + 0 top vertex\n// segment + 1 perimeter vertex a+1\n// segment + 2 perimeter vertex a\n// segment + 3 center base vertex\n// segment + 4 perimeter vertex a\n// segment + 5 perimeter vertex a+1\n// Where segment is the number of the radial segment * 6 and a is the angle at that radial segment.\n// To go from index to segment, floor(index / 6)\n// To go from segment to angle, 2*pi * (segment/segmentCount)\n// To go from index to segment index, index - (segment*6)\n//\nvec3 getConePosition(vec3 d, float rawIndex, float coneOffset, out vec3 normal) {\n\n const float segmentCount = 8.0;\n\n float index = rawIndex - floor(rawIndex /\n (segmentCount * 6.0)) *\n (segmentCount * 6.0);\n\n float segment = floor(0.001 + index/6.0);\n float segmentIndex = index - (segment*6.0);\n\n normal = -normalize(d);\n\n if (segmentIndex > 2.99 && segmentIndex < 3.01) {\n return mix(vec3(0.0), -d, coneOffset);\n }\n\n float nextAngle = (\n (segmentIndex > 0.99 && segmentIndex < 1.01) ||\n (segmentIndex > 4.99 && segmentIndex < 5.01)\n ) ? 1.0 : 0.0;\n float angle = 2.0 * 3.14159 * ((segment + nextAngle) / segmentCount);\n\n vec3 v1 = mix(d, vec3(0.0), coneOffset);\n vec3 v2 = v1 - d;\n\n vec3 u = getOrthogonalVector(d);\n vec3 v = normalize(cross(u, d));\n\n vec3 x = u * cos(angle) * length(d)*0.25;\n vec3 y = v * sin(angle) * length(d)*0.25;\n vec3 v3 = v2 + x + y;\n if (segmentIndex < 3.0) {\n vec3 tx = u * sin(angle);\n vec3 ty = v * -cos(angle);\n vec3 tangent = tx + ty;\n normal = normalize(cross(v3 - v1, tangent));\n }\n\n if (segmentIndex == 0.0) {\n return mix(d, vec3(0.0), coneOffset);\n }\n return v3;\n}\n\nattribute vec4 vector;\nattribute vec4 position;\nattribute vec4 id;\n\nuniform mat4 model, view, projection;\nuniform float vectorScale, coneScale, coneOffset;\n\nvarying vec3 f_position;\nvarying vec4 f_id;\n\nvoid main() {\n vec3 normal;\n vec3 XYZ = getConePosition(mat3(model) * ((vectorScale * coneScale) * vector.xyz), position.w, coneOffset, normal);\n vec4 conePosition = model * vec4(position.xyz, 1.0) + vec4(XYZ, 0.0);\n gl_Position = projection * view * conePosition;\n f_id = id;\n f_position = position.xyz;\n}\n"]),s=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform float pickId;\n\nvarying vec3 f_position;\nvarying vec4 f_id;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], f_position)) discard;\n\n gl_FragColor = vec4(pickId, f_id.xyz);\n}"]);e.meshShader={vertex:i,fragment:a,attributes:[{name:"position",type:"vec4"},{name:"color",type:"vec4"},{name:"uv",type:"vec2"},{name:"vector",type:"vec3"}]},e.pickShader={vertex:o,fragment:s,attributes:[{name:"position",type:"vec4"},{name:"id",type:"vec4"},{name:"vector",type:"vec3"}]}},1950:function(t){t.exports={0:"NONE",1:"ONE",2:"LINE_LOOP",3:"LINE_STRIP",4:"TRIANGLES",5:"TRIANGLE_STRIP",6:"TRIANGLE_FAN",256:"DEPTH_BUFFER_BIT",512:"NEVER",513:"LESS",514:"EQUAL",515:"LEQUAL",516:"GREATER",517:"NOTEQUAL",518:"GEQUAL",519:"ALWAYS",768:"SRC_COLOR",769:"ONE_MINUS_SRC_COLOR",770:"SRC_ALPHA",771:"ONE_MINUS_SRC_ALPHA",772:"DST_ALPHA",773:"ONE_MINUS_DST_ALPHA",774:"DST_COLOR",775:"ONE_MINUS_DST_COLOR",776:"SRC_ALPHA_SATURATE",1024:"STENCIL_BUFFER_BIT",1028:"FRONT",1029:"BACK",1032:"FRONT_AND_BACK",1280:"INVALID_ENUM",1281:"INVALID_VALUE",1282:"INVALID_OPERATION",1285:"OUT_OF_MEMORY",1286:"INVALID_FRAMEBUFFER_OPERATION",2304:"CW",2305:"CCW",2849:"LINE_WIDTH",2884:"CULL_FACE",2885:"CULL_FACE_MODE",2886:"FRONT_FACE",2928:"DEPTH_RANGE",2929:"DEPTH_TEST",2930:"DEPTH_WRITEMASK",2931:"DEPTH_CLEAR_VALUE",2932:"DEPTH_FUNC",2960:"STENCIL_TEST",2961:"STENCIL_CLEAR_VALUE",2962:"STENCIL_FUNC",2963:"STENCIL_VALUE_MASK",2964:"STENCIL_FAIL",2965:"STENCIL_PASS_DEPTH_FAIL",2966:"STENCIL_PASS_DEPTH_PASS",2967:"STENCIL_REF",2968:"STENCIL_WRITEMASK",2978:"VIEWPORT",3024:"DITHER",3042:"BLEND",3088:"SCISSOR_BOX",3089:"SCISSOR_TEST",3106:"COLOR_CLEAR_VALUE",3107:"COLOR_WRITEMASK",3317:"UNPACK_ALIGNMENT",3333:"PACK_ALIGNMENT",3379:"MAX_TEXTURE_SIZE",3386:"MAX_VIEWPORT_DIMS",3408:"SUBPIXEL_BITS",3410:"RED_BITS",3411:"GREEN_BITS",3412:"BLUE_BITS",3413:"ALPHA_BITS",3414:"DEPTH_BITS",3415:"STENCIL_BITS",3553:"TEXTURE_2D",4352:"DONT_CARE",4353:"FASTEST",4354:"NICEST",5120:"BYTE",5121:"UNSIGNED_BYTE",5122:"SHORT",5123:"UNSIGNED_SHORT",5124:"INT",5125:"UNSIGNED_INT",5126:"FLOAT",5386:"INVERT",5890:"TEXTURE",6401:"STENCIL_INDEX",6402:"DEPTH_COMPONENT",6406:"ALPHA",6407:"RGB",6408:"RGBA",6409:"LUMINANCE",6410:"LUMINANCE_ALPHA",7680:"KEEP",7681:"REPLACE",7682:"INCR",7683:"DECR",7936:"VENDOR",7937:"RENDERER",7938:"VERSION",9728:"NEAREST",9729:"LINEAR",9984:"NEAREST_MIPMAP_NEAREST",9985:"LINEAR_MIPMAP_NEAREST",9986:"NEAREST_MIPMAP_LINEAR",9987:"LINEAR_MIPMAP_LINEAR",10240:"TEXTURE_MAG_FILTER",10241:"TEXTURE_MIN_FILTER",10242:"TEXTURE_WRAP_S",10243:"TEXTURE_WRAP_T",10497:"REPEAT",10752:"POLYGON_OFFSET_UNITS",16384:"COLOR_BUFFER_BIT",32769:"CONSTANT_COLOR",32770:"ONE_MINUS_CONSTANT_COLOR",32771:"CONSTANT_ALPHA",32772:"ONE_MINUS_CONSTANT_ALPHA",32773:"BLEND_COLOR",32774:"FUNC_ADD",32777:"BLEND_EQUATION_RGB",32778:"FUNC_SUBTRACT",32779:"FUNC_REVERSE_SUBTRACT",32819:"UNSIGNED_SHORT_4_4_4_4",32820:"UNSIGNED_SHORT_5_5_5_1",32823:"POLYGON_OFFSET_FILL",32824:"POLYGON_OFFSET_FACTOR",32854:"RGBA4",32855:"RGB5_A1",32873:"TEXTURE_BINDING_2D",32926:"SAMPLE_ALPHA_TO_COVERAGE",32928:"SAMPLE_COVERAGE",32936:"SAMPLE_BUFFERS",32937:"SAMPLES",32938:"SAMPLE_COVERAGE_VALUE",32939:"SAMPLE_COVERAGE_INVERT",32968:"BLEND_DST_RGB",32969:"BLEND_SRC_RGB",32970:"BLEND_DST_ALPHA",32971:"BLEND_SRC_ALPHA",33071:"CLAMP_TO_EDGE",33170:"GENERATE_MIPMAP_HINT",33189:"DEPTH_COMPONENT16",33306:"DEPTH_STENCIL_ATTACHMENT",33635:"UNSIGNED_SHORT_5_6_5",33648:"MIRRORED_REPEAT",33901:"ALIASED_POINT_SIZE_RANGE",33902:"ALIASED_LINE_WIDTH_RANGE",33984:"TEXTURE0",33985:"TEXTURE1",33986:"TEXTURE2",33987:"TEXTURE3",33988:"TEXTURE4",33989:"TEXTURE5",33990:"TEXTURE6",33991:"TEXTURE7",33992:"TEXTURE8",33993:"TEXTURE9",33994:"TEXTURE10",33995:"TEXTURE11",33996:"TEXTURE12",33997:"TEXTURE13",33998:"TEXTURE14",33999:"TEXTURE15",34e3:"TEXTURE16",34001:"TEXTURE17",34002:"TEXTURE18",34003:"TEXTURE19",34004:"TEXTURE20",34005:"TEXTURE21",34006:"TEXTURE22",34007:"TEXTURE23",34008:"TEXTURE24",34009:"TEXTURE25",34010:"TEXTURE26",34011:"TEXTURE27",34012:"TEXTURE28",34013:"TEXTURE29",34014:"TEXTURE30",34015:"TEXTURE31",34016:"ACTIVE_TEXTURE",34024:"MAX_RENDERBUFFER_SIZE",34041:"DEPTH_STENCIL",34055:"INCR_WRAP",34056:"DECR_WRAP",34067:"TEXTURE_CUBE_MAP",34068:"TEXTURE_BINDING_CUBE_MAP",34069:"TEXTURE_CUBE_MAP_POSITIVE_X",34070:"TEXTURE_CUBE_MAP_NEGATIVE_X",34071:"TEXTURE_CUBE_MAP_POSITIVE_Y",34072:"TEXTURE_CUBE_MAP_NEGATIVE_Y",34073:"TEXTURE_CUBE_MAP_POSITIVE_Z",34074:"TEXTURE_CUBE_MAP_NEGATIVE_Z",34076:"MAX_CUBE_MAP_TEXTURE_SIZE",34338:"VERTEX_ATTRIB_ARRAY_ENABLED",34339:"VERTEX_ATTRIB_ARRAY_SIZE",34340:"VERTEX_ATTRIB_ARRAY_STRIDE",34341:"VERTEX_ATTRIB_ARRAY_TYPE",34342:"CURRENT_VERTEX_ATTRIB",34373:"VERTEX_ATTRIB_ARRAY_POINTER",34466:"NUM_COMPRESSED_TEXTURE_FORMATS",34467:"COMPRESSED_TEXTURE_FORMATS",34660:"BUFFER_SIZE",34661:"BUFFER_USAGE",34816:"STENCIL_BACK_FUNC",34817:"STENCIL_BACK_FAIL",34818:"STENCIL_BACK_PASS_DEPTH_FAIL",34819:"STENCIL_BACK_PASS_DEPTH_PASS",34877:"BLEND_EQUATION_ALPHA",34921:"MAX_VERTEX_ATTRIBS",34922:"VERTEX_ATTRIB_ARRAY_NORMALIZED",34930:"MAX_TEXTURE_IMAGE_UNITS",34962:"ARRAY_BUFFER",34963:"ELEMENT_ARRAY_BUFFER",34964:"ARRAY_BUFFER_BINDING",34965:"ELEMENT_ARRAY_BUFFER_BINDING",34975:"VERTEX_ATTRIB_ARRAY_BUFFER_BINDING",35040:"STREAM_DRAW",35044:"STATIC_DRAW",35048:"DYNAMIC_DRAW",35632:"FRAGMENT_SHADER",35633:"VERTEX_SHADER",35660:"MAX_VERTEX_TEXTURE_IMAGE_UNITS",35661:"MAX_COMBINED_TEXTURE_IMAGE_UNITS",35663:"SHADER_TYPE",35664:"FLOAT_VEC2",35665:"FLOAT_VEC3",35666:"FLOAT_VEC4",35667:"INT_VEC2",35668:"INT_VEC3",35669:"INT_VEC4",35670:"BOOL",35671:"BOOL_VEC2",35672:"BOOL_VEC3",35673:"BOOL_VEC4",35674:"FLOAT_MAT2",35675:"FLOAT_MAT3",35676:"FLOAT_MAT4",35678:"SAMPLER_2D",35680:"SAMPLER_CUBE",35712:"DELETE_STATUS",35713:"COMPILE_STATUS",35714:"LINK_STATUS",35715:"VALIDATE_STATUS",35716:"INFO_LOG_LENGTH",35717:"ATTACHED_SHADERS",35718:"ACTIVE_UNIFORMS",35719:"ACTIVE_UNIFORM_MAX_LENGTH",35720:"SHADER_SOURCE_LENGTH",35721:"ACTIVE_ATTRIBUTES",35722:"ACTIVE_ATTRIBUTE_MAX_LENGTH",35724:"SHADING_LANGUAGE_VERSION",35725:"CURRENT_PROGRAM",36003:"STENCIL_BACK_REF",36004:"STENCIL_BACK_VALUE_MASK",36005:"STENCIL_BACK_WRITEMASK",36006:"FRAMEBUFFER_BINDING",36007:"RENDERBUFFER_BINDING",36048:"FRAMEBUFFER_ATTACHMENT_OBJECT_TYPE",36049:"FRAMEBUFFER_ATTACHMENT_OBJECT_NAME",36050:"FRAMEBUFFER_ATTACHMENT_TEXTURE_LEVEL",36051:"FRAMEBUFFER_ATTACHMENT_TEXTURE_CUBE_MAP_FACE",36053:"FRAMEBUFFER_COMPLETE",36054:"FRAMEBUFFER_INCOMPLETE_ATTACHMENT",36055:"FRAMEBUFFER_INCOMPLETE_MISSING_ATTACHMENT",36057:"FRAMEBUFFER_INCOMPLETE_DIMENSIONS",36061:"FRAMEBUFFER_UNSUPPORTED",36064:"COLOR_ATTACHMENT0",36096:"DEPTH_ATTACHMENT",36128:"STENCIL_ATTACHMENT",36160:"FRAMEBUFFER",36161:"RENDERBUFFER",36162:"RENDERBUFFER_WIDTH",36163:"RENDERBUFFER_HEIGHT",36164:"RENDERBUFFER_INTERNAL_FORMAT",36168:"STENCIL_INDEX8",36176:"RENDERBUFFER_RED_SIZE",36177:"RENDERBUFFER_GREEN_SIZE",36178:"RENDERBUFFER_BLUE_SIZE",36179:"RENDERBUFFER_ALPHA_SIZE",36180:"RENDERBUFFER_DEPTH_SIZE",36181:"RENDERBUFFER_STENCIL_SIZE",36194:"RGB565",36336:"LOW_FLOAT",36337:"MEDIUM_FLOAT",36338:"HIGH_FLOAT",36339:"LOW_INT",36340:"MEDIUM_INT",36341:"HIGH_INT",36346:"SHADER_COMPILER",36347:"MAX_VERTEX_UNIFORM_VECTORS",36348:"MAX_VARYING_VECTORS",36349:"MAX_FRAGMENT_UNIFORM_VECTORS",37440:"UNPACK_FLIP_Y_WEBGL",37441:"UNPACK_PREMULTIPLY_ALPHA_WEBGL",37442:"CONTEXT_LOST_WEBGL",37443:"UNPACK_COLORSPACE_CONVERSION_WEBGL",37444:"BROWSER_DEFAULT_WEBGL"}},6603:function(t,e,r){var n=r(1950);t.exports=function(t){return n[t]}},3110:function(t,e,r){"use strict";t.exports=function(t){var e=t.gl,r=n(e),o=i(e,[{buffer:r,type:e.FLOAT,size:3,offset:0,stride:40},{buffer:r,type:e.FLOAT,size:4,offset:12,stride:40},{buffer:r,type:e.FLOAT,size:3,offset:28,stride:40}]),l=a(e);l.attributes.position.location=0,l.attributes.color.location=1,l.attributes.offset.location=2;var u=new s(e,r,o,l);return u.update(t),u};var n=r(5827),i=r(2944),a=r(7667),o=[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1];function s(t,e,r,n){this.gl=t,this.shader=n,this.buffer=e,this.vao=r,this.pixelRatio=1,this.bounds=[[1/0,1/0,1/0],[-1/0,-1/0,-1/0]],this.clipBounds=[[-1/0,-1/0,-1/0],[1/0,1/0,1/0]],this.lineWidth=[1,1,1],this.capSize=[10,10,10],this.lineCount=[0,0,0],this.lineOffset=[0,0,0],this.opacity=1,this.hasAlpha=!1}var l=s.prototype;function u(t,e){for(var r=0;r<3;++r)t[0][r]=Math.min(t[0][r],e[r]),t[1][r]=Math.max(t[1][r],e[r])}l.isOpaque=function(){return!this.hasAlpha},l.isTransparent=function(){return this.hasAlpha},l.drawTransparent=l.draw=function(t){var e=this.gl,r=this.shader.uniforms;this.shader.bind();var n=r.view=t.view||o,i=r.projection=t.projection||o;r.model=t.model||o,r.clipBounds=this.clipBounds,r.opacity=this.opacity;var a=n[12],s=n[13],l=n[14],u=n[15],c=(t._ortho?2:1)*this.pixelRatio*(i[3]*a+i[7]*s+i[11]*l+i[15]*u)/e.drawingBufferHeight;this.vao.bind();for(var f=0;f<3;++f)e.lineWidth(this.lineWidth[f]*this.pixelRatio),r.capSize=this.capSize[f]*c,this.lineCount[f]&&e.drawArrays(e.LINES,this.lineOffset[f],this.lineCount[f]);this.vao.unbind()};var c=function(){for(var t=new Array(3),e=0;e<3;++e){for(var r=[],n=1;n<=2;++n)for(var i=-1;i<=1;i+=2){var a=[0,0,0];a[(n+e)%3]=i,r.push(a)}t[e]=r}return t}();function f(t,e,r,n){for(var i=c[n],a=0;a0&&((p=c.slice())[s]+=d[1][s],i.push(c[0],c[1],c[2],v[0],v[1],v[2],v[3],0,0,0,p[0],p[1],p[2],v[0],v[1],v[2],v[3],0,0,0),u(this.bounds,p),o+=2+f(i,p,v,s)))}this.lineCount[s]=o-this.lineOffset[s]}this.buffer.update(i)}},l.dispose=function(){this.shader.dispose(),this.buffer.dispose(),this.vao.dispose()}},7667:function(t,e,r){"use strict";var n=r(6832),i=r(5158),a=n(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec3 position, offset;\nattribute vec4 color;\nuniform mat4 model, view, projection;\nuniform float capSize;\nvarying vec4 fragColor;\nvarying vec3 fragPosition;\n\nvoid main() {\n vec4 worldPosition = model * vec4(position, 1.0);\n worldPosition = (worldPosition / worldPosition.w) + vec4(capSize * offset, 0.0);\n gl_Position = projection * view * worldPosition;\n fragColor = color;\n fragPosition = position;\n}"]),o=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform float opacity;\nvarying vec3 fragPosition;\nvarying vec4 fragColor;\n\nvoid main() {\n if (\n outOfRange(clipBounds[0], clipBounds[1], fragPosition) ||\n fragColor.a * opacity == 0.\n ) discard;\n\n gl_FragColor = opacity * fragColor;\n}"]);t.exports=function(t){return i(t,a,o,null,[{name:"position",type:"vec3"},{name:"color",type:"vec4"},{name:"offset",type:"vec3"}])}},4234:function(t,e,r){"use strict";var n=r(8931);t.exports=function(t,e,r,n){i||(i=t.FRAMEBUFFER_UNSUPPORTED,a=t.FRAMEBUFFER_INCOMPLETE_ATTACHMENT,o=t.FRAMEBUFFER_INCOMPLETE_DIMENSIONS,s=t.FRAMEBUFFER_INCOMPLETE_MISSING_ATTACHMENT);var u=t.getExtension("WEBGL_draw_buffers");if(!l&&u&&function(t,e){var r=t.getParameter(e.MAX_COLOR_ATTACHMENTS_WEBGL);l=new Array(r+1);for(var n=0;n<=r;++n){for(var i=new Array(r),a=0;ac||r<0||r>c)throw new Error("gl-fbo: Parameters are too large for FBO");var f=1;if("color"in(n=n||{})){if((f=Math.max(0|n.color,0))<0)throw new Error("gl-fbo: Must specify a nonnegative number of colors");if(f>1){if(!u)throw new Error("gl-fbo: Multiple draw buffer extension not supported");if(f>t.getParameter(u.MAX_COLOR_ATTACHMENTS_WEBGL))throw new Error("gl-fbo: Context does not support "+f+" draw buffers")}}var h=t.UNSIGNED_BYTE,p=t.getExtension("OES_texture_float");if(n.float&&f>0){if(!p)throw new Error("gl-fbo: Context does not support floating point textures");h=t.FLOAT}else n.preferFloat&&f>0&&p&&(h=t.FLOAT);var v=!0;"depth"in n&&(v=!!n.depth);var g=!1;return"stencil"in n&&(g=!!n.stencil),new d(t,e,r,h,f,v,g,u)};var i,a,o,s,l=null;function u(t){return[t.getParameter(t.FRAMEBUFFER_BINDING),t.getParameter(t.RENDERBUFFER_BINDING),t.getParameter(t.TEXTURE_BINDING_2D)]}function c(t,e){t.bindFramebuffer(t.FRAMEBUFFER,e[0]),t.bindRenderbuffer(t.RENDERBUFFER,e[1]),t.bindTexture(t.TEXTURE_2D,e[2])}function f(t){switch(t){case i:throw new Error("gl-fbo: Framebuffer unsupported");case a:throw new Error("gl-fbo: Framebuffer incomplete attachment");case o:throw new Error("gl-fbo: Framebuffer incomplete dimensions");case s:throw new Error("gl-fbo: Framebuffer incomplete missing attachment");default:throw new Error("gl-fbo: Framebuffer failed for unspecified reason")}}function h(t,e,r,i,a,o){if(!i)return null;var s=n(t,e,r,a,i);return s.magFilter=t.NEAREST,s.minFilter=t.NEAREST,s.mipSamples=1,s.bind(),t.framebufferTexture2D(t.FRAMEBUFFER,o,t.TEXTURE_2D,s.handle,0),s}function p(t,e,r,n,i){var a=t.createRenderbuffer();return t.bindRenderbuffer(t.RENDERBUFFER,a),t.renderbufferStorage(t.RENDERBUFFER,n,e,r),t.framebufferRenderbuffer(t.FRAMEBUFFER,i,t.RENDERBUFFER,a),a}function d(t,e,r,n,i,a,o,s){this.gl=t,this._shape=[0|e,0|r],this._destroyed=!1,this._ext=s,this.color=new Array(i);for(var d=0;d1&&s.drawBuffersWEBGL(l[o]);var m=r.getExtension("WEBGL_depth_texture");m?d?t.depth=h(r,i,a,m.UNSIGNED_INT_24_8_WEBGL,r.DEPTH_STENCIL,r.DEPTH_STENCIL_ATTACHMENT):v&&(t.depth=h(r,i,a,r.UNSIGNED_SHORT,r.DEPTH_COMPONENT,r.DEPTH_ATTACHMENT)):v&&d?t._depth_rb=p(r,i,a,r.DEPTH_STENCIL,r.DEPTH_STENCIL_ATTACHMENT):v?t._depth_rb=p(r,i,a,r.DEPTH_COMPONENT16,r.DEPTH_ATTACHMENT):d&&(t._depth_rb=p(r,i,a,r.STENCIL_INDEX,r.STENCIL_ATTACHMENT));var x=r.checkFramebufferStatus(r.FRAMEBUFFER);if(x!==r.FRAMEBUFFER_COMPLETE){for(t._destroyed=!0,r.bindFramebuffer(r.FRAMEBUFFER,null),r.deleteFramebuffer(t.handle),t.handle=null,t.depth&&(t.depth.dispose(),t.depth=null),t._depth_rb&&(r.deleteRenderbuffer(t._depth_rb),t._depth_rb=null),y=0;yi||r<0||r>i)throw new Error("gl-fbo: Can't resize FBO, invalid dimensions");t._shape[0]=e,t._shape[1]=r;for(var a=u(n),o=0;o>8*p&255;this.pickOffset=r,i.bind();var d=i.uniforms;d.viewTransform=t,d.pickOffset=e,d.shape=this.shape;var v=i.attributes;return this.positionBuffer.bind(),v.position.pointer(),this.weightBuffer.bind(),v.weight.pointer(s.UNSIGNED_BYTE,!1),this.idBuffer.bind(),v.pickId.pointer(s.UNSIGNED_BYTE,!1),s.drawArrays(s.TRIANGLES,0,o),r+this.shape[0]*this.shape[1]}}}(),f.pick=function(t,e,r){var n=this.pickOffset,i=this.shape[0]*this.shape[1];if(r=n+i)return null;var a=r-n,o=this.xData,s=this.yData;return{object:this,pointId:a,dataCoord:[o[a%this.shape[0]],s[a/this.shape[0]|0]]}},f.update=function(t){var e=(t=t||{}).shape||[0,0],r=t.x||i(e[0]),o=t.y||i(e[1]),s=t.z||new Float32Array(e[0]*e[1]),l=!1!==t.zsmooth;this.xData=r,this.yData=o;var u,c,f,p,d=t.colorLevels||[0],v=t.colorValues||[0,0,0,1],g=d.length,y=this.bounds;l?(u=y[0]=r[0],c=y[1]=o[0],f=y[2]=r[r.length-1],p=y[3]=o[o.length-1]):(u=y[0]=r[0]+(r[1]-r[0])/2,c=y[1]=o[0]+(o[1]-o[0])/2,f=y[2]=r[r.length-1]+(r[r.length-1]-r[r.length-2])/2,p=y[3]=o[o.length-1]+(o[o.length-1]-o[o.length-2])/2);var m=1/(f-u),x=1/(p-c),b=e[0],_=e[1];this.shape=[b,_];var w=(l?(b-1)*(_-1):b*_)*(h.length>>>1);this.numVertices=w;for(var T=a.mallocUint8(4*w),k=a.mallocFloat32(2*w),A=a.mallocUint8(2*w),M=a.mallocUint32(w),S=0,E=l?b-1:b,L=l?_-1:_,C=0;C max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform sampler2D dashTexture;\nuniform float dashScale;\nuniform float opacity;\n\nvarying vec3 worldPosition;\nvarying float pixelArcLength;\nvarying vec4 fragColor;\n\nvoid main() {\n if (\n outOfRange(clipBounds[0], clipBounds[1], worldPosition) ||\n fragColor.a * opacity == 0.\n ) discard;\n\n float dashWeight = texture2D(dashTexture, vec2(dashScale * pixelArcLength, 0)).r;\n if(dashWeight < 0.5) {\n discard;\n }\n gl_FragColor = fragColor * opacity;\n}\n"]),s=n(["precision highp float;\n#define GLSLIFY 1\n\n#define FLOAT_MAX 1.70141184e38\n#define FLOAT_MIN 1.17549435e-38\n\n// https://github.com/mikolalysenko/glsl-read-float/blob/master/index.glsl\nvec4 packFloat(float v) {\n float av = abs(v);\n\n //Handle special cases\n if(av < FLOAT_MIN) {\n return vec4(0.0, 0.0, 0.0, 0.0);\n } else if(v > FLOAT_MAX) {\n return vec4(127.0, 128.0, 0.0, 0.0) / 255.0;\n } else if(v < -FLOAT_MAX) {\n return vec4(255.0, 128.0, 0.0, 0.0) / 255.0;\n }\n\n vec4 c = vec4(0,0,0,0);\n\n //Compute exponent and mantissa\n float e = floor(log2(av));\n float m = av * pow(2.0, -e) - 1.0;\n\n //Unpack mantissa\n c[1] = floor(128.0 * m);\n m -= c[1] / 128.0;\n c[2] = floor(32768.0 * m);\n m -= c[2] / 32768.0;\n c[3] = floor(8388608.0 * m);\n\n //Unpack exponent\n float ebias = e + 127.0;\n c[0] = floor(ebias / 2.0);\n ebias -= c[0] * 2.0;\n c[1] += floor(ebias) * 128.0;\n\n //Unpack sign bit\n c[0] += 128.0 * step(0.0, -v);\n\n //Scale back to range\n return c / 255.0;\n}\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform float pickId;\nuniform vec3 clipBounds[2];\n\nvarying vec3 worldPosition;\nvarying float pixelArcLength;\nvarying vec4 fragColor;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], worldPosition)) discard;\n\n gl_FragColor = vec4(pickId/255.0, packFloat(pixelArcLength).xyz);\n}"]),l=[{name:"position",type:"vec3"},{name:"nextPosition",type:"vec3"},{name:"arcLength",type:"float"},{name:"lineWidth",type:"float"},{name:"color",type:"vec4"}];e.createShader=function(t){return i(t,a,o,null,l)},e.createPickShader=function(t){return i(t,a,s,null,l)}},6086:function(t,e,r){"use strict";t.exports=function(t){var e=t.gl||t.scene&&t.scene.gl,r=f(e);r.attributes.position.location=0,r.attributes.nextPosition.location=1,r.attributes.arcLength.location=2,r.attributes.lineWidth.location=3,r.attributes.color.location=4;var o=h(e);o.attributes.position.location=0,o.attributes.nextPosition.location=1,o.attributes.arcLength.location=2,o.attributes.lineWidth.location=3,o.attributes.color.location=4;for(var s=n(e),l=i(e,[{buffer:s,size:3,offset:0,stride:48},{buffer:s,size:3,offset:12,stride:48},{buffer:s,size:1,offset:24,stride:48},{buffer:s,size:1,offset:28,stride:48},{buffer:s,size:4,offset:32,stride:48}]),c=u(new Array(1024),[256,1,4]),p=0;p<1024;++p)c.data[p]=255;var d=a(e,c);d.wrap=e.REPEAT;var v=new y(e,r,o,s,l,d);return v.update(t),v};var n=r(5827),i=r(2944),a=r(8931),o=new Uint8Array(4),s=new Float32Array(o.buffer),l=r(5070),u=r(5050),c=r(248),f=c.createShader,h=c.createPickShader,p=[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1];function d(t,e){for(var r=0,n=0;n<3;++n){var i=t[n]-e[n];r+=i*i}return Math.sqrt(r)}function v(t){for(var e=[[-1e6,-1e6,-1e6],[1e6,1e6,1e6]],r=0;r<3;++r)e[0][r]=Math.max(t[0][r],e[0][r]),e[1][r]=Math.min(t[1][r],e[1][r]);return e}function g(t,e,r,n){this.arcLength=t,this.position=e,this.index=r,this.dataCoordinate=n}function y(t,e,r,n,i,a){this.gl=t,this.shader=e,this.pickShader=r,this.buffer=n,this.vao=i,this.clipBounds=[[-1/0,-1/0,-1/0],[1/0,1/0,1/0]],this.points=[],this.arcLength=[],this.vertexCount=0,this.bounds=[[0,0,0],[0,0,0]],this.pickId=0,this.lineWidth=1,this.texture=a,this.dashScale=1,this.opacity=1,this.hasAlpha=!1,this.dirty=!0,this.pixelRatio=1}var m=y.prototype;m.isTransparent=function(){return this.hasAlpha},m.isOpaque=function(){return!this.hasAlpha},m.pickSlots=1,m.setPickBase=function(t){this.pickId=t},m.drawTransparent=m.draw=function(t){if(this.vertexCount){var e=this.gl,r=this.shader,n=this.vao;r.bind(),r.uniforms={model:t.model||p,view:t.view||p,projection:t.projection||p,clipBounds:v(this.clipBounds),dashTexture:this.texture.bind(),dashScale:this.dashScale/this.arcLength[this.arcLength.length-1],opacity:this.opacity,screenShape:[e.drawingBufferWidth,e.drawingBufferHeight],pixelRatio:this.pixelRatio},n.bind(),n.draw(e.TRIANGLE_STRIP,this.vertexCount),n.unbind()}},m.drawPick=function(t){if(this.vertexCount){var e=this.gl,r=this.pickShader,n=this.vao;r.bind(),r.uniforms={model:t.model||p,view:t.view||p,projection:t.projection||p,pickId:this.pickId,clipBounds:v(this.clipBounds),screenShape:[e.drawingBufferWidth,e.drawingBufferHeight],pixelRatio:this.pixelRatio},n.bind(),n.draw(e.TRIANGLE_STRIP,this.vertexCount),n.unbind()}},m.update=function(t){var e,r;this.dirty=!0;var n=!!t.connectGaps;"dashScale"in t&&(this.dashScale=t.dashScale),this.hasAlpha=!1,"opacity"in t&&(this.opacity=+t.opacity,this.opacity<1&&(this.hasAlpha=!0));var i=[],a=[],o=[],s=0,c=0,f=[[1/0,1/0,1/0],[-1/0,-1/0,-1/0]],h=t.position||t.positions;if(h){var p=t.color||t.colors||[0,0,0,1],v=t.lineWidth||1,g=!1;t:for(e=1;e0){for(var w=0;w<24;++w)i.push(i[i.length-12]);c+=2,g=!0}continue t}f[0][r]=Math.min(f[0][r],b[r],_[r]),f[1][r]=Math.max(f[1][r],b[r],_[r])}Array.isArray(p[0])?(y=p.length>e-1?p[e-1]:p.length>0?p[p.length-1]:[0,0,0,1],m=p.length>e?p[e]:p.length>0?p[p.length-1]:[0,0,0,1]):y=m=p,3===y.length&&(y=[y[0],y[1],y[2],1]),3===m.length&&(m=[m[0],m[1],m[2],1]),!this.hasAlpha&&y[3]<1&&(this.hasAlpha=!0),x=Array.isArray(v)?v.length>e-1?v[e-1]:v.length>0?v[v.length-1]:[0,0,0,1]:v;var T=s;if(s+=d(b,_),g){for(r=0;r<2;++r)i.push(b[0],b[1],b[2],_[0],_[1],_[2],T,x,y[0],y[1],y[2],y[3]);c+=2,g=!1}i.push(b[0],b[1],b[2],_[0],_[1],_[2],T,x,y[0],y[1],y[2],y[3],b[0],b[1],b[2],_[0],_[1],_[2],T,-x,y[0],y[1],y[2],y[3],_[0],_[1],_[2],b[0],b[1],b[2],s,-x,m[0],m[1],m[2],m[3],_[0],_[1],_[2],b[0],b[1],b[2],s,x,m[0],m[1],m[2],m[3]),c+=4}}if(this.buffer.update(i),a.push(s),o.push(h[h.length-1].slice()),this.bounds=f,this.vertexCount=c,this.points=o,this.arcLength=a,"dashes"in t){var k=t.dashes.slice();for(k.unshift(0),e=1;e1.0001)return null;y+=g[f]}return Math.abs(y-1)>.001?null:[h,s(t,g),g]}},2056:function(t,e,r){var n=r(6832),i=n(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec3 position, normal;\nattribute vec4 color;\nattribute vec2 uv;\n\nuniform mat4 model\n , view\n , projection\n , inverseModel;\nuniform vec3 eyePosition\n , lightPosition;\n\nvarying vec3 f_normal\n , f_lightDirection\n , f_eyeDirection\n , f_data;\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvec4 project(vec3 p) {\n return projection * view * model * vec4(p, 1.0);\n}\n\nvoid main() {\n gl_Position = project(position);\n\n //Lighting geometry parameters\n vec4 cameraCoordinate = view * vec4(position , 1.0);\n cameraCoordinate.xyz /= cameraCoordinate.w;\n f_lightDirection = lightPosition - cameraCoordinate.xyz;\n f_eyeDirection = eyePosition - cameraCoordinate.xyz;\n f_normal = normalize((vec4(normal, 0.0) * inverseModel).xyz);\n\n f_color = color;\n f_data = position;\n f_uv = uv;\n}\n"]),a=n(["#extension GL_OES_standard_derivatives : enable\n\nprecision highp float;\n#define GLSLIFY 1\n\nfloat beckmannDistribution(float x, float roughness) {\n float NdotH = max(x, 0.0001);\n float cos2Alpha = NdotH * NdotH;\n float tan2Alpha = (cos2Alpha - 1.0) / cos2Alpha;\n float roughness2 = roughness * roughness;\n float denom = 3.141592653589793 * roughness2 * cos2Alpha * cos2Alpha;\n return exp(tan2Alpha / roughness2) / denom;\n}\n\nfloat cookTorranceSpecular(\n vec3 lightDirection,\n vec3 viewDirection,\n vec3 surfaceNormal,\n float roughness,\n float fresnel) {\n\n float VdotN = max(dot(viewDirection, surfaceNormal), 0.0);\n float LdotN = max(dot(lightDirection, surfaceNormal), 0.0);\n\n //Half angle vector\n vec3 H = normalize(lightDirection + viewDirection);\n\n //Geometric term\n float NdotH = max(dot(surfaceNormal, H), 0.0);\n float VdotH = max(dot(viewDirection, H), 0.000001);\n float LdotH = max(dot(lightDirection, H), 0.000001);\n float G1 = (2.0 * NdotH * VdotN) / VdotH;\n float G2 = (2.0 * NdotH * LdotN) / LdotH;\n float G = min(1.0, min(G1, G2));\n \n //Distribution term\n float D = beckmannDistribution(NdotH, roughness);\n\n //Fresnel term\n float F = pow(1.0 - VdotN, fresnel);\n\n //Multiply terms and done\n return G * F * D / max(3.14159265 * VdotN, 0.000001);\n}\n\n//#pragma glslify: beckmann = require(glsl-specular-beckmann) // used in gl-surface3d\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform float roughness\n , fresnel\n , kambient\n , kdiffuse\n , kspecular;\nuniform sampler2D texture;\n\nvarying vec3 f_normal\n , f_lightDirection\n , f_eyeDirection\n , f_data;\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n if (f_color.a == 0.0 ||\n outOfRange(clipBounds[0], clipBounds[1], f_data)\n ) discard;\n\n vec3 N = normalize(f_normal);\n vec3 L = normalize(f_lightDirection);\n vec3 V = normalize(f_eyeDirection);\n\n if(gl_FrontFacing) {\n N = -N;\n }\n\n float specular = min(1.0, max(0.0, cookTorranceSpecular(L, V, N, roughness, fresnel)));\n //float specular = max(0.0, beckmann(L, V, N, roughness)); // used in gl-surface3d\n\n float diffuse = min(kambient + kdiffuse * max(dot(N, L), 0.0), 1.0);\n\n vec4 surfaceColor = vec4(f_color.rgb, 1.0) * texture2D(texture, f_uv);\n vec4 litColor = surfaceColor.a * vec4(diffuse * surfaceColor.rgb + kspecular * vec3(1,1,1) * specular, 1.0);\n\n gl_FragColor = litColor * f_color.a;\n}\n"]),o=n(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec3 position;\nattribute vec4 color;\nattribute vec2 uv;\n\nuniform mat4 model, view, projection;\n\nvarying vec4 f_color;\nvarying vec3 f_data;\nvarying vec2 f_uv;\n\nvoid main() {\n gl_Position = projection * view * model * vec4(position, 1.0);\n f_color = color;\n f_data = position;\n f_uv = uv;\n}"]),s=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform sampler2D texture;\nuniform float opacity;\n\nvarying vec4 f_color;\nvarying vec3 f_data;\nvarying vec2 f_uv;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], f_data)) discard;\n\n gl_FragColor = f_color * texture2D(texture, f_uv) * opacity;\n}"]),l=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nattribute vec3 position;\nattribute vec4 color;\nattribute vec2 uv;\nattribute float pointSize;\n\nuniform mat4 model, view, projection;\nuniform vec3 clipBounds[2];\n\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], position)) {\n\n gl_Position = vec4(0.0, 0.0 ,0.0 ,0.0);\n } else {\n gl_Position = projection * view * model * vec4(position, 1.0);\n }\n gl_PointSize = pointSize;\n f_color = color;\n f_uv = uv;\n}"]),u=n(["precision highp float;\n#define GLSLIFY 1\n\nuniform sampler2D texture;\nuniform float opacity;\n\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n vec2 pointR = gl_PointCoord.xy - vec2(0.5, 0.5);\n if(dot(pointR, pointR) > 0.25) {\n discard;\n }\n gl_FragColor = f_color * texture2D(texture, f_uv) * opacity;\n}"]),c=n(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec3 position;\nattribute vec4 id;\n\nuniform mat4 model, view, projection;\n\nvarying vec3 f_position;\nvarying vec4 f_id;\n\nvoid main() {\n gl_Position = projection * view * model * vec4(position, 1.0);\n f_id = id;\n f_position = position;\n}"]),f=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform float pickId;\n\nvarying vec3 f_position;\nvarying vec4 f_id;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], f_position)) discard;\n\n gl_FragColor = vec4(pickId, f_id.xyz);\n}"]),h=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nattribute vec3 position;\nattribute float pointSize;\nattribute vec4 id;\n\nuniform mat4 model, view, projection;\nuniform vec3 clipBounds[2];\n\nvarying vec3 f_position;\nvarying vec4 f_id;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], position)) {\n\n gl_Position = vec4(0.0, 0.0, 0.0, 0.0);\n } else {\n gl_Position = projection * view * model * vec4(position, 1.0);\n gl_PointSize = pointSize;\n }\n f_id = id;\n f_position = position;\n}"]),p=n(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec3 position;\n\nuniform mat4 model, view, projection;\n\nvoid main() {\n gl_Position = projection * view * model * vec4(position, 1.0);\n}"]),d=n(["precision highp float;\n#define GLSLIFY 1\n\nuniform vec3 contourColor;\n\nvoid main() {\n gl_FragColor = vec4(contourColor, 1.0);\n}\n"]);e.meshShader={vertex:i,fragment:a,attributes:[{name:"position",type:"vec3"},{name:"normal",type:"vec3"},{name:"color",type:"vec4"},{name:"uv",type:"vec2"}]},e.wireShader={vertex:o,fragment:s,attributes:[{name:"position",type:"vec3"},{name:"color",type:"vec4"},{name:"uv",type:"vec2"}]},e.pointShader={vertex:l,fragment:u,attributes:[{name:"position",type:"vec3"},{name:"color",type:"vec4"},{name:"uv",type:"vec2"},{name:"pointSize",type:"float"}]},e.pickShader={vertex:c,fragment:f,attributes:[{name:"position",type:"vec3"},{name:"id",type:"vec4"}]},e.pointPickShader={vertex:h,fragment:f,attributes:[{name:"position",type:"vec3"},{name:"pointSize",type:"float"},{name:"id",type:"vec4"}]},e.contourShader={vertex:p,fragment:d,attributes:[{name:"position",type:"vec3"}]}},8116:function(t,e,r){"use strict";var n=r(5158),i=r(5827),a=r(2944),o=r(8931),s=r(115),l=r(104),u=r(7437),c=r(5050),f=r(9156),h=r(7212),p=r(5306),d=r(2056),v=r(4340),g=d.meshShader,y=d.wireShader,m=d.pointShader,x=d.pickShader,b=d.pointPickShader,_=d.contourShader,w=[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1];function T(t,e,r,n,i,a,o,s,l,u,c,f,h,p,d,v,g,y,m,x,b,_,T,k,A,M,S){this.gl=t,this.pixelRatio=1,this.cells=[],this.positions=[],this.intensity=[],this.texture=e,this.dirty=!0,this.triShader=r,this.lineShader=n,this.pointShader=i,this.pickShader=a,this.pointPickShader=o,this.contourShader=s,this.trianglePositions=l,this.triangleColors=c,this.triangleNormals=h,this.triangleUVs=f,this.triangleIds=u,this.triangleVAO=p,this.triangleCount=0,this.lineWidth=1,this.edgePositions=d,this.edgeColors=g,this.edgeUVs=y,this.edgeIds=v,this.edgeVAO=m,this.edgeCount=0,this.pointPositions=x,this.pointColors=_,this.pointUVs=T,this.pointSizes=k,this.pointIds=b,this.pointVAO=A,this.pointCount=0,this.contourLineWidth=1,this.contourPositions=M,this.contourVAO=S,this.contourCount=0,this.contourColor=[0,0,0],this.contourEnable=!0,this.pickVertex=!0,this.pickId=1,this.bounds=[[1/0,1/0,1/0],[-1/0,-1/0,-1/0]],this.clipBounds=[[-1/0,-1/0,-1/0],[1/0,1/0,1/0]],this.lightPosition=[1e5,1e5,0],this.ambientLight=.8,this.diffuseLight=.8,this.specularLight=2,this.roughness=.5,this.fresnel=1.5,this.opacity=1,this.hasAlpha=!1,this.opacityscale=!1,this._model=w,this._view=w,this._projection=w,this._resolution=[1,1]}var k=T.prototype;function A(t,e){if(!e)return 1;if(!e.length)return 1;for(var r=0;rt&&r>0){var n=(e[r][0]-t)/(e[r][0]-e[r-1][0]);return e[r][1]*(1-n)+n*e[r-1][1]}}return 1}function M(t){var e=n(t,g.vertex,g.fragment);return e.attributes.position.location=0,e.attributes.color.location=2,e.attributes.uv.location=3,e.attributes.normal.location=4,e}function S(t){var e=n(t,y.vertex,y.fragment);return e.attributes.position.location=0,e.attributes.color.location=2,e.attributes.uv.location=3,e}function E(t){var e=n(t,m.vertex,m.fragment);return e.attributes.position.location=0,e.attributes.color.location=2,e.attributes.uv.location=3,e.attributes.pointSize.location=4,e}function L(t){var e=n(t,x.vertex,x.fragment);return e.attributes.position.location=0,e.attributes.id.location=1,e}function C(t){var e=n(t,b.vertex,b.fragment);return e.attributes.position.location=0,e.attributes.id.location=1,e.attributes.pointSize.location=4,e}function P(t){var e=n(t,_.vertex,_.fragment);return e.attributes.position.location=0,e}k.isOpaque=function(){return!this.hasAlpha},k.isTransparent=function(){return this.hasAlpha},k.pickSlots=1,k.setPickBase=function(t){this.pickId=t},k.highlight=function(t){if(t&&this.contourEnable){for(var e=h(this.cells,this.intensity,t.intensity),r=e.cells,n=e.vertexIds,i=e.vertexWeights,a=r.length,o=p.mallocFloat32(6*a),s=0,l=0;l0&&((f=this.triShader).bind(),f.uniforms=s,this.triangleVAO.bind(),e.drawArrays(e.TRIANGLES,0,3*this.triangleCount),this.triangleVAO.unbind()),this.edgeCount>0&&this.lineWidth>0&&((f=this.lineShader).bind(),f.uniforms=s,this.edgeVAO.bind(),e.lineWidth(this.lineWidth*this.pixelRatio),e.drawArrays(e.LINES,0,2*this.edgeCount),this.edgeVAO.unbind()),this.pointCount>0&&((f=this.pointShader).bind(),f.uniforms=s,this.pointVAO.bind(),e.drawArrays(e.POINTS,0,this.pointCount),this.pointVAO.unbind()),this.contourEnable&&this.contourCount>0&&this.contourLineWidth>0&&((f=this.contourShader).bind(),f.uniforms=s,this.contourVAO.bind(),e.drawArrays(e.LINES,0,this.contourCount),this.contourVAO.unbind())},k.drawPick=function(t){t=t||{};for(var e=this.gl,r=t.model||w,n=t.view||w,i=t.projection||w,a=[[-1e6,-1e6,-1e6],[1e6,1e6,1e6]],o=0;o<3;++o)a[0][o]=Math.max(a[0][o],this.clipBounds[0][o]),a[1][o]=Math.min(a[1][o],this.clipBounds[1][o]);this._model=[].slice.call(r),this._view=[].slice.call(n),this._projection=[].slice.call(i),this._resolution=[e.drawingBufferWidth,e.drawingBufferHeight];var s,l={model:r,view:n,projection:i,clipBounds:a,pickId:this.pickId/255};(s=this.pickShader).bind(),s.uniforms=l,this.triangleCount>0&&(this.triangleVAO.bind(),e.drawArrays(e.TRIANGLES,0,3*this.triangleCount),this.triangleVAO.unbind()),this.edgeCount>0&&(this.edgeVAO.bind(),e.lineWidth(this.lineWidth*this.pixelRatio),e.drawArrays(e.LINES,0,2*this.edgeCount),this.edgeVAO.unbind()),this.pointCount>0&&((s=this.pointPickShader).bind(),s.uniforms=l,this.pointVAO.bind(),e.drawArrays(e.POINTS,0,this.pointCount),this.pointVAO.unbind())},k.pick=function(t){if(!t)return null;if(t.id!==this.pickId)return null;for(var e=t.value[0]+256*t.value[1]+65536*t.value[2],r=this.cells[e],n=this.positions,i=new Array(r.length),a=0;ai[k]&&(r.uniforms.dataAxis=u,r.uniforms.screenOffset=c,r.uniforms.color=g[t],r.uniforms.angle=y[t],a.drawArrays(a.TRIANGLES,i[k],i[A]-i[k]))),m[t]&&T&&(c[1^t]-=M*p*x[t],r.uniforms.dataAxis=f,r.uniforms.screenOffset=c,r.uniforms.color=b[t],r.uniforms.angle=_[t],a.drawArrays(a.TRIANGLES,w,T)),c[1^t]=M*s[2+(1^t)]-1,d[t+2]&&(c[1^t]+=M*p*v[t+2],ki[k]&&(r.uniforms.dataAxis=u,r.uniforms.screenOffset=c,r.uniforms.color=g[t+2],r.uniforms.angle=y[t+2],a.drawArrays(a.TRIANGLES,i[k],i[A]-i[k]))),m[t+2]&&T&&(c[1^t]+=M*p*x[t+2],r.uniforms.dataAxis=f,r.uniforms.screenOffset=c,r.uniforms.color=b[t+2],r.uniforms.angle=_[t+2],a.drawArrays(a.TRIANGLES,w,T))}),v.drawTitle=function(){var t=[0,0],e=[0,0];return function(){var r=this.plot,n=this.shader,i=r.gl,a=r.screenBox,o=r.titleCenter,s=r.titleAngle,l=r.titleColor,u=r.pixelRatio;if(this.titleCount){for(var c=0;c<2;++c)e[c]=2*(o[c]*u-a[c])/(a[2+c]-a[c])-1;n.bind(),n.uniforms.dataAxis=t,n.uniforms.screenOffset=e,n.uniforms.angle=s,n.uniforms.color=l,i.drawArrays(i.TRIANGLES,this.titleOffset,this.titleCount)}}}(),v.bind=(h=[0,0],p=[0,0],d=[0,0],function(){var t=this.plot,e=this.shader,r=t._tickBounds,n=t.dataBox,i=t.screenBox,a=t.viewBox;e.bind();for(var o=0;o<2;++o){var s=r[o],l=r[o+2]-s,u=.5*(n[o+2]+n[o]),c=n[o+2]-n[o],f=a[o],v=a[o+2]-f,g=i[o],y=i[o+2]-g;p[o]=2*l/c*v/y,h[o]=2*(s-u)/c*v/y}d[1]=2*t.pixelRatio/(i[3]-i[1]),d[0]=d[1]*(i[3]-i[1])/(i[2]-i[0]),e.uniforms.dataScale=p,e.uniforms.dataShift=h,e.uniforms.textScale=d,this.vbo.bind(),e.attributes.textCoordinate.pointer()}),v.update=function(t){var e,r,n,i,o,s=[],l=t.ticks,u=t.bounds;for(o=0;o<2;++o){var c=[Math.floor(s.length/3)],f=[-1/0],h=l[o];for(e=0;e=0){var v=e[d]-n[d]*(e[d+2]-e[d])/(n[d+2]-n[d]);0===d?o.drawLine(v,e[1],v,e[3],p[d],h[d]):o.drawLine(e[0],v,e[2],v,p[d],h[d])}}for(d=0;d=0;--t)this.objects[t].dispose();for(this.objects.length=0,t=this.overlays.length-1;t>=0;--t)this.overlays[t].dispose();this.overlays.length=0,this.gl=null},u.addObject=function(t){this.objects.indexOf(t)<0&&(this.objects.push(t),this.setDirty())},u.removeObject=function(t){for(var e=this.objects,r=0;rMath.abs(e))u.rotate(a,0,0,-t*r*Math.PI*d.rotateSpeed/window.innerWidth);else if(!d._ortho){var o=-d.zoomSpeed*i*e/window.innerHeight*(a-u.lastT())/20;u.pan(a,0,0,f*(Math.exp(o)-1))}}}),!0)},d.enableMouseListeners(),d};var n=r(8161),i=r(1152),a=r(6145),o=r(6475),s=r(2565),l=r(5233)},8245:function(t,e,r){var n=r(6832),i=r(5158),a=n(["precision mediump float;\n#define GLSLIFY 1\nattribute vec2 position;\nvarying vec2 uv;\nvoid main() {\n uv = position;\n gl_Position = vec4(position, 0, 1);\n}"]),o=n(["precision mediump float;\n#define GLSLIFY 1\n\nuniform sampler2D accumBuffer;\nvarying vec2 uv;\n\nvoid main() {\n vec4 accum = texture2D(accumBuffer, 0.5 * (uv + 1.0));\n gl_FragColor = min(vec4(1,1,1,1), accum);\n}"]);t.exports=function(t){return i(t,a,o,null,[{name:"position",type:"vec2"}])}},1059:function(t,e,r){"use strict";var n=r(4296),i=r(7453),a=r(2771),o=r(6496),s=r(2611),l=r(4234),u=r(8126),c=r(6145),f=r(1120),h=r(5268),p=r(8245),d=r(2321)({tablet:!0,featureDetect:!0});function v(){this.mouse=[-1,-1],this.screen=null,this.distance=1/0,this.index=null,this.dataCoordinate=null,this.dataPosition=null,this.object=null,this.data=null}function g(t){var e=Math.round(Math.log(Math.abs(t))/Math.log(10));if(e<0){var r=Math.round(Math.pow(10,-e));return Math.ceil(t*r)/r}return e>0?(r=Math.round(Math.pow(10,e)),Math.ceil(t/r)*r):Math.ceil(t)}function y(t){return"boolean"!=typeof t||t}t.exports={createScene:function(t){(t=t||{}).camera=t.camera||{};var e=t.canvas;e||(e=document.createElement("canvas"),t.container?t.container.appendChild(e):document.body.appendChild(e));var r=t.gl;if(r||(t.glOptions&&(d=!!t.glOptions.preserveDrawingBuffer),r=function(t,e){var r=null;try{(r=t.getContext("webgl",e))||(r=t.getContext("experimental-webgl",e))}catch(t){return null}return r}(e,t.glOptions||{premultipliedAlpha:!0,antialias:!0,preserveDrawingBuffer:d})),!r)throw new Error("webgl not supported");var m=t.bounds||[[-10,-10,-10],[10,10,10]],x=new v,b=l(r,r.drawingBufferWidth,r.drawingBufferHeight,{preferFloat:!d}),_=p(r),w=t.cameraObject&&!0===t.cameraObject._ortho||t.camera.projection&&"orthographic"===t.camera.projection.type||!1,T={eye:t.camera.eye||[2,0,0],center:t.camera.center||[0,0,0],up:t.camera.up||[0,1,0],zoomMin:t.camera.zoomMax||.1,zoomMax:t.camera.zoomMin||100,mode:t.camera.mode||"turntable",_ortho:w},k=t.axes||{},A=i(r,k);A.enable=!k.disable;var M=t.spikes||{},S=o(r,M),E=[],L=[],C=[],P=[],O=!0,I=!0,D={view:null,projection:new Array(16),model:new Array(16),_ortho:!1},z=(I=!0,[r.drawingBufferWidth,r.drawingBufferHeight]),R=t.cameraObject||n(e,T),F={gl:r,contextLost:!1,pixelRatio:t.pixelRatio||1,canvas:e,selection:x,camera:R,axes:A,axesPixels:null,spikes:S,bounds:m,objects:E,shape:z,aspect:t.aspectRatio||[1,1,1],pickRadius:t.pickRadius||10,zNear:t.zNear||.01,zFar:t.zFar||1e3,fovy:t.fovy||Math.PI/4,clearColor:t.clearColor||[0,0,0,0],autoResize:y(t.autoResize),autoBounds:y(t.autoBounds),autoScale:!!t.autoScale,autoCenter:y(t.autoCenter),clipToBounds:y(t.clipToBounds),snapToData:!!t.snapToData,onselect:t.onselect||null,onrender:t.onrender||null,onclick:t.onclick||null,cameraParams:D,oncontextloss:null,mouseListener:null,_stopped:!1,getAspectratio:function(){return{x:this.aspect[0],y:this.aspect[1],z:this.aspect[2]}},setAspectratio:function(t){this.aspect[0]=t.x,this.aspect[1]=t.y,this.aspect[2]=t.z,I=!0},setBounds:function(t,e){this.bounds[0][t]=e.min,this.bounds[1][t]=e.max},setClearColor:function(t){this.clearColor=t},clearRGBA:function(){this.gl.clearColor(this.clearColor[0],this.clearColor[1],this.clearColor[2],this.clearColor[3]),this.gl.clear(this.gl.COLOR_BUFFER_BIT|this.gl.DEPTH_BUFFER_BIT)}},B=[r.drawingBufferWidth/F.pixelRatio|0,r.drawingBufferHeight/F.pixelRatio|0];function N(){if(!F._stopped&&F.autoResize){var t=e.parentNode,r=1,n=1;t&&t!==document.body?(r=t.clientWidth,n=t.clientHeight):(r=window.innerWidth,n=window.innerHeight);var i=0|Math.ceil(r*F.pixelRatio),a=0|Math.ceil(n*F.pixelRatio);if(i!==e.width||a!==e.height){e.width=i,e.height=a;var o=e.style;o.position=o.position||"absolute",o.left="0px",o.top="0px",o.width=r+"px",o.height=n+"px",O=!0}}}function j(){for(var t=E.length,e=P.length,n=0;n0&&0===C[e-1];)C.pop(),P.pop().dispose()}function U(){if(F.contextLost)return!0;r.isContextLost()&&(F.contextLost=!0,F.mouseListener.enabled=!1,F.selection.object=null,F.oncontextloss&&F.oncontextloss())}F.autoResize&&N(),window.addEventListener("resize",N),F.update=function(t){F._stopped||(t=t||{},O=!0,I=!0)},F.add=function(t){F._stopped||(t.axes=A,E.push(t),L.push(-1),O=!0,I=!0,j())},F.remove=function(t){if(!F._stopped){var e=E.indexOf(t);e<0||(E.splice(e,1),L.pop(),O=!0,I=!0,j())}},F.dispose=function(){if(!F._stopped&&(F._stopped=!0,window.removeEventListener("resize",N),e.removeEventListener("webglcontextlost",U),F.mouseListener.enabled=!1,!F.contextLost)){A.dispose(),S.dispose();for(var t=0;tx.distance)continue;for(var u=0;u 1.0) {\n discard;\n }\n baseColor = mix(borderColor, color, step(radius, centerFraction));\n gl_FragColor = vec4(baseColor.rgb * baseColor.a, baseColor.a);\n }\n}\n"]),e.pickVertex=n(["precision mediump float;\n#define GLSLIFY 1\n\nattribute vec2 position;\nattribute vec4 pickId;\n\nuniform mat3 matrix;\nuniform float pointSize;\nuniform vec4 pickOffset;\n\nvarying vec4 fragId;\n\nvoid main() {\n vec3 hgPosition = matrix * vec3(position, 1);\n gl_Position = vec4(hgPosition.xy, 0, hgPosition.z);\n gl_PointSize = pointSize;\n\n vec4 id = pickId + pickOffset;\n id.y += floor(id.x / 256.0);\n id.x -= floor(id.x / 256.0) * 256.0;\n\n id.z += floor(id.y / 256.0);\n id.y -= floor(id.y / 256.0) * 256.0;\n\n id.w += floor(id.z / 256.0);\n id.z -= floor(id.z / 256.0) * 256.0;\n\n fragId = id;\n}\n"]),e.pickFragment=n(["precision mediump float;\n#define GLSLIFY 1\n\nvarying vec4 fragId;\n\nvoid main() {\n float radius = length(2.0 * gl_PointCoord.xy - 1.0);\n if(radius > 1.0) {\n discard;\n }\n gl_FragColor = fragId / 255.0;\n}\n"])},8271:function(t,e,r){"use strict";var n=r(5158),i=r(5827),a=r(5306),o=r(8023);function s(t,e,r,n,i){this.plot=t,this.offsetBuffer=e,this.pickBuffer=r,this.shader=n,this.pickShader=i,this.sizeMin=.5,this.sizeMinCap=2,this.sizeMax=20,this.areaRatio=1,this.pointCount=0,this.color=[1,0,0,1],this.borderColor=[0,0,0,1],this.blend=!1,this.pickOffset=0,this.points=null}t.exports=function(t,e){var r=t.gl,a=new s(t,i(r),i(r),n(r,o.pointVertex,o.pointFragment),n(r,o.pickVertex,o.pickFragment));return a.update(e),t.addObject(a),a};var l,u,c=s.prototype;c.dispose=function(){this.shader.dispose(),this.pickShader.dispose(),this.offsetBuffer.dispose(),this.pickBuffer.dispose(),this.plot.removeObject(this)},c.update=function(t){var e;function r(e,r){return e in t?t[e]:r}t=t||{},this.sizeMin=r("sizeMin",.5),this.sizeMax=r("sizeMax",20),this.color=r("color",[1,0,0,1]).slice(),this.areaRatio=r("areaRatio",1),this.borderColor=r("borderColor",[0,0,0,1]).slice(),this.blend=r("blend",!1);var n=t.positions.length>>>1,i=t.positions instanceof Float32Array,o=t.idToIndex instanceof Int32Array&&t.idToIndex.length>=n,s=t.positions,l=i?s:a.mallocFloat32(s.length),u=o?t.idToIndex:a.mallocInt32(n);if(i||l.set(s),!o)for(l.set(s),e=0;e>>1;for(r=0;r=e[0]&&a<=e[2]&&o>=e[1]&&o<=e[3]&&n++}return n}(this.points,i),c=this.plot.pickPixelRatio*Math.max(Math.min(this.sizeMinCap,this.sizeMin),Math.min(this.sizeMax,this.sizeMax/Math.pow(s,.33333)));l[0]=2/a,l[4]=2/o,l[6]=-2*i[0]/a-1,l[7]=-2*i[1]/o-1,this.offsetBuffer.bind(),r.bind(),r.attributes.position.pointer(),r.uniforms.matrix=l,r.uniforms.color=this.color,r.uniforms.borderColor=this.borderColor,r.uniforms.pointCloud=c<5,r.uniforms.pointSize=c,r.uniforms.centerFraction=Math.min(1,Math.max(0,Math.sqrt(1-this.areaRatio))),e&&(u[0]=255&t,u[1]=t>>8&255,u[2]=t>>16&255,u[3]=t>>24&255,this.pickBuffer.bind(),r.attributes.pickId.pointer(n.UNSIGNED_BYTE),r.uniforms.pickOffset=u,this.pickOffset=t);var f=n.getParameter(n.BLEND),h=n.getParameter(n.DITHER);return f&&!this.blend&&n.disable(n.BLEND),h&&n.disable(n.DITHER),n.drawArrays(n.POINTS,0,this.pointCount),f&&!this.blend&&n.enable(n.BLEND),h&&n.enable(n.DITHER),t+this.pointCount}),c.draw=c.unifiedDraw,c.drawPick=c.unifiedDraw,c.pick=function(t,e,r){var n=this.pickOffset,i=this.pointCount;if(r=n+i)return null;var a=r-n,o=this.points;return{object:this,pointId:a,dataCoord:[o[2*a],o[2*a+1]]}}},6093:function(t){t.exports=function(t,e,r,n){var i,a,o,s,l,u=e[0],c=e[1],f=e[2],h=e[3],p=r[0],d=r[1],v=r[2],g=r[3];return(a=u*p+c*d+f*v+h*g)<0&&(a=-a,p=-p,d=-d,v=-v,g=-g),1-a>1e-6?(i=Math.acos(a),o=Math.sin(i),s=Math.sin((1-n)*i)/o,l=Math.sin(n*i)/o):(s=1-n,l=n),t[0]=s*u+l*p,t[1]=s*c+l*d,t[2]=s*f+l*v,t[3]=s*h+l*g,t}},8240:function(t){"use strict";t.exports=function(t){return t||0===t?t.toString():""}},4123:function(t,e,r){"use strict";var n=r(875);t.exports=function(t,e,r){var a=i[e];if(a||(a=i[e]={}),t in a)return a[t];var o={textAlign:"center",textBaseline:"middle",lineHeight:1,font:e,lineSpacing:1.25,styletags:{breaklines:!0,bolds:!0,italics:!0,subscripts:!0,superscripts:!0},triangles:!0},s=n(t,o);o.triangles=!1;var l,u,c=n(t,o);if(r&&1!==r){for(l=0;l max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nattribute vec3 position;\nattribute vec4 color;\nattribute vec2 glyph;\nattribute vec4 id;\n\nuniform vec4 highlightId;\nuniform float highlightScale;\nuniform mat4 model, view, projection;\nuniform vec3 clipBounds[2];\n\nvarying vec4 interpColor;\nvarying vec4 pickId;\nvarying vec3 dataCoordinate;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], position)) {\n\n gl_Position = vec4(0,0,0,0);\n } else {\n float scale = 1.0;\n if(distance(highlightId, id) < 0.0001) {\n scale = highlightScale;\n }\n\n vec4 worldPosition = model * vec4(position, 1);\n vec4 viewPosition = view * worldPosition;\n viewPosition = viewPosition / viewPosition.w;\n vec4 clipPosition = projection * (viewPosition + scale * vec4(glyph.x, -glyph.y, 0, 0));\n\n gl_Position = clipPosition;\n interpColor = color;\n pickId = id;\n dataCoordinate = position;\n }\n}"]),o=i(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nattribute vec3 position;\nattribute vec4 color;\nattribute vec2 glyph;\nattribute vec4 id;\n\nuniform mat4 model, view, projection;\nuniform vec2 screenSize;\nuniform vec3 clipBounds[2];\nuniform float highlightScale, pixelRatio;\nuniform vec4 highlightId;\n\nvarying vec4 interpColor;\nvarying vec4 pickId;\nvarying vec3 dataCoordinate;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], position)) {\n\n gl_Position = vec4(0,0,0,0);\n } else {\n float scale = pixelRatio;\n if(distance(highlightId.bgr, id.bgr) < 0.001) {\n scale *= highlightScale;\n }\n\n vec4 worldPosition = model * vec4(position, 1.0);\n vec4 viewPosition = view * worldPosition;\n vec4 clipPosition = projection * viewPosition;\n clipPosition /= clipPosition.w;\n\n gl_Position = clipPosition + vec4(screenSize * scale * vec2(glyph.x, -glyph.y), 0.0, 0.0);\n interpColor = color;\n pickId = id;\n dataCoordinate = position;\n }\n}"]),s=i(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nattribute vec3 position;\nattribute vec4 color;\nattribute vec2 glyph;\nattribute vec4 id;\n\nuniform float highlightScale;\nuniform vec4 highlightId;\nuniform vec3 axes[2];\nuniform mat4 model, view, projection;\nuniform vec2 screenSize;\nuniform vec3 clipBounds[2];\nuniform float scale, pixelRatio;\n\nvarying vec4 interpColor;\nvarying vec4 pickId;\nvarying vec3 dataCoordinate;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], position)) {\n\n gl_Position = vec4(0,0,0,0);\n } else {\n float lscale = pixelRatio * scale;\n if(distance(highlightId, id) < 0.0001) {\n lscale *= highlightScale;\n }\n\n vec4 clipCenter = projection * view * model * vec4(position, 1);\n vec3 dataPosition = position + 0.5*lscale*(axes[0] * glyph.x + axes[1] * glyph.y) * clipCenter.w * screenSize.y;\n vec4 clipPosition = projection * view * model * vec4(dataPosition, 1);\n\n gl_Position = clipPosition;\n interpColor = color;\n pickId = id;\n dataCoordinate = dataPosition;\n }\n}\n"]),l=i(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 fragClipBounds[2];\nuniform float opacity;\n\nvarying vec4 interpColor;\nvarying vec3 dataCoordinate;\n\nvoid main() {\n if (\n outOfRange(fragClipBounds[0], fragClipBounds[1], dataCoordinate) ||\n interpColor.a * opacity == 0.\n ) discard;\n gl_FragColor = interpColor * opacity;\n}\n"]),u=i(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 fragClipBounds[2];\nuniform float pickGroup;\n\nvarying vec4 pickId;\nvarying vec3 dataCoordinate;\n\nvoid main() {\n if (outOfRange(fragClipBounds[0], fragClipBounds[1], dataCoordinate)) discard;\n\n gl_FragColor = vec4(pickGroup, pickId.bgr);\n}"]),c=[{name:"position",type:"vec3"},{name:"color",type:"vec4"},{name:"glyph",type:"vec2"},{name:"id",type:"vec4"}],f={vertex:a,fragment:l,attributes:c},h={vertex:o,fragment:l,attributes:c},p={vertex:s,fragment:l,attributes:c},d={vertex:a,fragment:u,attributes:c},v={vertex:o,fragment:u,attributes:c},g={vertex:s,fragment:u,attributes:c};function y(t,e){var r=n(t,e),i=r.attributes;return i.position.location=0,i.color.location=1,i.glyph.location=2,i.id.location=3,r}e.createPerspective=function(t){return y(t,f)},e.createOrtho=function(t){return y(t,h)},e.createProject=function(t){return y(t,p)},e.createPickPerspective=function(t){return y(t,d)},e.createPickOrtho=function(t){return y(t,v)},e.createPickProject=function(t){return y(t,g)}},2182:function(t,e,r){"use strict";var n=r(3596),i=r(5827),a=r(2944),o=r(5306),s=r(104),l=r(9282),u=r(4123),c=r(8240),f=[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1];function h(t,e){var r=t[0],n=t[1],i=t[2],a=t[3];return t[0]=e[0]*r+e[4]*n+e[8]*i+e[12]*a,t[1]=e[1]*r+e[5]*n+e[9]*i+e[13]*a,t[2]=e[2]*r+e[6]*n+e[10]*i+e[14]*a,t[3]=e[3]*r+e[7]*n+e[11]*i+e[15]*a,t}function p(t,e,r,n){return h(n,n),h(n,n),h(n,n)}function d(t,e){this.index=t,this.dataCoordinate=this.position=e}function v(t){return!0===t||t>1?1:t}function g(t,e,r,n,i,a,o,s,l,u,c,f){this.gl=t,this.pixelRatio=1,this.shader=e,this.orthoShader=r,this.projectShader=n,this.pointBuffer=i,this.colorBuffer=a,this.glyphBuffer=o,this.idBuffer=s,this.vao=l,this.vertexCount=0,this.lineVertexCount=0,this.opacity=1,this.hasAlpha=!1,this.lineWidth=0,this.projectScale=[2/3,2/3,2/3],this.projectOpacity=[1,1,1],this.projectHasAlpha=!1,this.pickId=0,this.pickPerspectiveShader=u,this.pickOrthoShader=c,this.pickProjectShader=f,this.points=[],this._selectResult=new d(0,[0,0,0]),this.useOrtho=!0,this.bounds=[[1/0,1/0,1/0],[-1/0,-1/0,-1/0]],this.axesProject=[!0,!0,!0],this.axesBounds=[[-1/0,-1/0,-1/0],[1/0,1/0,1/0]],this.highlightId=[1,1,1,1],this.highlightScale=2,this.clipBounds=[[-1/0,-1/0,-1/0],[1/0,1/0,1/0]],this.dirty=!0}t.exports=function(t){var e=t.gl,r=l.createPerspective(e),n=l.createOrtho(e),o=l.createProject(e),s=l.createPickPerspective(e),u=l.createPickOrtho(e),c=l.createPickProject(e),f=i(e),h=i(e),p=i(e),d=i(e),v=new g(e,r,n,o,f,h,p,d,a(e,[{buffer:f,size:3,type:e.FLOAT},{buffer:h,size:4,type:e.FLOAT},{buffer:p,size:2,type:e.FLOAT},{buffer:d,size:4,type:e.UNSIGNED_BYTE,normalized:!0}]),s,u,c);return v.update(t),v};var y=g.prototype;y.pickSlots=1,y.setPickBase=function(t){this.pickId=t},y.isTransparent=function(){if(this.hasAlpha)return!0;for(var t=0;t<3;++t)if(this.axesProject[t]&&this.projectHasAlpha)return!0;return!1},y.isOpaque=function(){if(!this.hasAlpha)return!0;for(var t=0;t<3;++t)if(this.axesProject[t]&&!this.projectHasAlpha)return!0;return!1};var m=[0,0],x=[0,0,0],b=[0,0,0],_=[0,0,0,1],w=[0,0,0,1],T=f.slice(),k=[0,0,0],A=[[0,0,0],[0,0,0]];function M(t){return t[0]=t[1]=t[2]=0,t}function S(t,e){return t[0]=e[0],t[1]=e[1],t[2]=e[2],t[3]=1,t}function E(t,e,r,n){return t[0]=e[0],t[1]=e[1],t[2]=e[2],t[r]=n,t}var L=[[-1e8,-1e8,-1e8],[1e8,1e8,1e8]];function C(t,e,r,n,i,a,o){var l=r.gl;if((a===r.projectHasAlpha||o)&&function(t,e,r,n){var i,a=e.axesProject,o=e.gl,l=t.uniforms,u=r.model||f,c=r.view||f,h=r.projection||f,d=e.axesBounds,v=function(t){for(var e=A,r=0;r<2;++r)for(var n=0;n<3;++n)e[r][n]=Math.max(Math.min(t[r][n],1e8),-1e8);return e}(e.clipBounds);i=e.axes&&e.axes.lastCubeProps?e.axes.lastCubeProps.axis:[1,1,1],m[0]=2/o.drawingBufferWidth,m[1]=2/o.drawingBufferHeight,t.bind(),l.view=c,l.projection=h,l.screenSize=m,l.highlightId=e.highlightId,l.highlightScale=e.highlightScale,l.clipBounds=v,l.pickGroup=e.pickId/255,l.pixelRatio=n;for(var g=0;g<3;++g)if(a[g]){l.scale=e.projectScale[g],l.opacity=e.projectOpacity[g];for(var y=T,L=0;L<16;++L)y[L]=0;for(L=0;L<4;++L)y[5*L]=1;y[5*g]=0,i[g]<0?y[12+g]=d[0][g]:y[12+g]=d[1][g],s(y,u,y),l.model=y;var C=(g+1)%3,P=(g+2)%3,O=M(x),I=M(b);O[C]=1,I[P]=1;var D=p(0,0,0,S(_,O)),z=p(0,0,0,S(w,I));if(Math.abs(D[1])>Math.abs(z[1])){var R=D;D=z,z=R,R=O,O=I,I=R;var F=C;C=P,P=F}D[0]<0&&(O[C]=-1),z[1]>0&&(I[P]=-1);var B=0,N=0;for(L=0;L<4;++L)B+=Math.pow(u[4*C+L],2),N+=Math.pow(u[4*P+L],2);O[C]/=Math.sqrt(B),I[P]/=Math.sqrt(N),l.axes[0]=O,l.axes[1]=I,l.fragClipBounds[0]=E(k,v[0],g,-1e8),l.fragClipBounds[1]=E(k,v[1],g,1e8),e.vao.bind(),e.vao.draw(o.TRIANGLES,e.vertexCount),e.lineWidth>0&&(o.lineWidth(e.lineWidth*n),e.vao.draw(o.LINES,e.lineVertexCount,e.vertexCount)),e.vao.unbind()}}(e,r,n,i),a===r.hasAlpha||o){t.bind();var u=t.uniforms;u.model=n.model||f,u.view=n.view||f,u.projection=n.projection||f,m[0]=2/l.drawingBufferWidth,m[1]=2/l.drawingBufferHeight,u.screenSize=m,u.highlightId=r.highlightId,u.highlightScale=r.highlightScale,u.fragClipBounds=L,u.clipBounds=r.axes.bounds,u.opacity=r.opacity,u.pickGroup=r.pickId/255,u.pixelRatio=i,r.vao.bind(),r.vao.draw(l.TRIANGLES,r.vertexCount),r.lineWidth>0&&(l.lineWidth(r.lineWidth*i),r.vao.draw(l.LINES,r.lineVertexCount,r.vertexCount)),r.vao.unbind()}}function P(t,e,r,i){var a;a=Array.isArray(t)?e=this.pointCount||e<0)return null;var r=this.points[e],n=this._selectResult;n.index=e;for(var i=0;i<3;++i)n.position[i]=n.dataCoordinate[i]=r[i];return n},y.highlight=function(t){if(t){var e=t.index,r=255&e,n=e>>8&255,i=e>>16&255;this.highlightId=[r/255,n/255,i/255,0]}else this.highlightId=[1,1,1,1]},y.update=function(t){if("perspective"in(t=t||{})&&(this.useOrtho=!t.perspective),"orthographic"in t&&(this.useOrtho=!!t.orthographic),"lineWidth"in t&&(this.lineWidth=t.lineWidth),"project"in t)if(Array.isArray(t.project))this.axesProject=t.project;else{var e=!!t.project;this.axesProject=[e,e,e]}if("projectScale"in t)if(Array.isArray(t.projectScale))this.projectScale=t.projectScale.slice();else{var r=+t.projectScale;this.projectScale=[r,r,r]}if(this.projectHasAlpha=!1,"projectOpacity"in t){Array.isArray(t.projectOpacity)?this.projectOpacity=t.projectOpacity.slice():(r=+t.projectOpacity,this.projectOpacity=[r,r,r]);for(var n=0;n<3;++n)this.projectOpacity[n]=v(this.projectOpacity[n]),this.projectOpacity[n]<1&&(this.projectHasAlpha=!0)}this.hasAlpha=!1,"opacity"in t&&(this.opacity=v(t.opacity),this.opacity<1&&(this.hasAlpha=!0)),this.dirty=!0;var i,a,s=t.position,l=t.font||"normal",u=t.alignment||[0,0];if(2===u.length)i=u[0],a=u[1];else for(i=[],a=[],n=0;n0){var I=0,D=x,z=[0,0,0,1],R=[0,0,0,1],F=Array.isArray(p)&&Array.isArray(p[0]),B=Array.isArray(y)&&Array.isArray(y[0]);t:for(n=0;n<_;++n){for(m+=1,w=s[n],T=0;T<3;++T){if(isNaN(w[T])||!isFinite(w[T]))continue t;f[T]=Math.max(f[T],w[T]),c[T]=Math.min(c[T],w[T])}k=(N=P(h,n,l,this.pixelRatio)).mesh,A=N.lines,M=N.bounds;var N,j=N.visible;if(j)if(Array.isArray(p)){if(3===(U=F?n0?1-M[0][0]:Z<0?1+M[1][0]:1,Y*=Y>0?1-M[0][1]:Y<0?1+M[1][1]:1],X=k.cells||[],J=k.positions||[];for(T=0;T0){var y=r*c;o.drawBox(f-y,h-y,p+y,h+y,a),o.drawBox(f-y,d-y,p+y,d+y,a),o.drawBox(f-y,h-y,f+y,d+y,a),o.drawBox(p-y,h-y,p+y,d+y,a)}}}},s.update=function(t){t=t||{},this.innerFill=!!t.innerFill,this.outerFill=!!t.outerFill,this.innerColor=(t.innerColor||[0,0,0,.5]).slice(),this.outerColor=(t.outerColor||[0,0,0,.5]).slice(),this.borderColor=(t.borderColor||[0,0,0,1]).slice(),this.borderWidth=t.borderWidth||0,this.selectBox=(t.selectBox||this.selectBox).slice()},s.dispose=function(){this.boxBuffer.dispose(),this.boxShader.dispose(),this.plot.removeOverlay(this)}},2611:function(t,e,r){"use strict";t.exports=function(t,e){var r=e[0],a=e[1];return new l(t,n(t,r,a,{}),i.mallocUint8(r*a*4))};var n=r(4234),i=r(5306),a=r(5050),o=r(2288).nextPow2;function s(t,e,r,n,i){this.coord=[t,e],this.id=r,this.value=n,this.distance=i}function l(t,e,r){this.gl=t,this.fbo=e,this.buffer=r,this._readTimeout=null;var 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a};var n=r(9068);function i(t,e,r,n,i,a){this._gl=t,this._wrapper=e,this._index=r,this._locations=n,this._dimension=i,this._constFunc=a}var a=i.prototype;a.pointer=function(t,e,r,n){var i=this,a=i._gl,o=i._locations[i._index];a.vertexAttribPointer(o,i._dimension,t||a.FLOAT,!!e,r||0,n||0),a.enableVertexAttribArray(o)},a.set=function(t,e,r,n){return this._constFunc(this._locations[this._index],t,e,r,n)},Object.defineProperty(a,"location",{get:function(){return this._locations[this._index]},set:function(t){return t!==this._locations[this._index]&&(this._locations[this._index]=0|t,this._wrapper.program=null),0|t}});var o=[function(t,e,r){return void 0===r.length?t.vertexAttrib1f(e,r):t.vertexAttrib1fv(e,r)},function(t,e,r,n){return void 0===r.length?t.vertexAttrib2f(e,r,n):t.vertexAttrib2fv(e,r)},function(t,e,r,n,i){return void 0===r.length?t.vertexAttrib3f(e,r,n,i):t.vertexAttrib3fv(e,r)},function(t,e,r,n,i,a){return void 0===r.length?t.vertexAttrib4f(e,r,n,i,a):t.vertexAttrib4fv(e,r)}];function s(t,e,r,n,a,s,l){var u=o[a],c=new i(t,e,r,n,a,u);Object.defineProperty(s,l,{set:function(e){return t.disableVertexAttribArray(n[r]),u(t,n[r],e),e},get:function(){return c},enumerable:!0})}function l(t,e,r,n,i,a,o){for(var l=new Array(i),u=new Array(i),c=0;c4)throw new i("","Invalid uniform dimension type for matrix "+name+": "+m);t["uniformMatrix"+y+"fv"](s[f],!1,h);break}throw new i("","Unknown uniform data type for "+name+": "+m)}if((y=m.charCodeAt(m.length-1)-48)<2||y>4)throw new i("","Invalid data type");switch(m.charAt(0)){case"b":case"i":t["uniform"+y+"iv"](s[f],h);break;case"v":t["uniform"+y+"fv"](s[f],h);break;default:throw new i("","Unrecognized data type for vector "+name+": "+m)}}}}}}function u(t,e){if("object"!=typeof e)return[[t,e]];var r=[];for(var n in e){var i=e[n],a=t;parseInt(n)+""===n?a+="["+n+"]":a+="."+n,"object"==typeof i?r.push.apply(r,u(a,i)):r.push([a,i])}return r}function c(t,e,n){if("object"==typeof n){var u=f(n);Object.defineProperty(t,e,{get:a(u),set:l(n),enumerable:!0,configurable:!1})}else s[n]?Object.defineProperty(t,e,{get:(c=n,function(t,e,r){return t.getUniform(e.program,r[c])}),set:l(n),enumerable:!0,configurable:!1}):t[e]=function(t){switch(t){case"bool":return!1;case"int":case"sampler2D":case"samplerCube":case"float":return 0;default:var e=t.indexOf("vec");if(0<=e&&e<=1&&t.length===4+e){if((r=t.charCodeAt(t.length-1)-48)<2||r>4)throw new i("","Invalid data type");return"b"===t.charAt(0)?o(r,!1):o(r,0)}if(0===t.indexOf("mat")&&4===t.length){var r;if((r=t.charCodeAt(t.length-1)-48)<2||r>4)throw new i("","Invalid uniform dimension type for matrix "+name+": "+t);return o(r*r,0)}throw new i("","Unknown uniform data type for "+name+": "+t)}}(r[n].type);var c}function f(t){var e;if(Array.isArray(t)){e=new Array(t.length);for(var r=0;r1){s[0]in a||(a[s[0]]=[]),a=a[s[0]];for(var l=1;l1)for(var l=0;l 0 U ||b|| > 0.\n // Assign z = 0, x = -b, y = a:\n // a*-b + b*a + c*0 = -ba + ba + 0 = 0\n if (v.x*v.x > v.z*v.z || v.y*v.y > v.z*v.z) {\n return normalize(vec3(-v.y, v.x, 0.0));\n } else {\n return normalize(vec3(0.0, v.z, -v.y));\n }\n}\n\n// Calculate the tube vertex and normal at the given index.\n//\n// The returned vertex is for a tube ring with its center at origin, radius of length(d), pointing in the direction of d.\n//\n// Each tube segment is made up of a ring of vertices.\n// These vertices are used to make up the triangles of the tube by connecting them together in the vertex array.\n// The indexes of tube segments run from 0 to 8.\n//\nvec3 getTubePosition(vec3 d, float index, out vec3 normal) {\n float segmentCount = 8.0;\n\n float angle = 2.0 * 3.14159 * (index / segmentCount);\n\n vec3 u = getOrthogonalVector(d);\n vec3 v = normalize(cross(u, d));\n\n vec3 x = u * cos(angle) * length(d);\n vec3 y = v * sin(angle) * length(d);\n vec3 v3 = x + y;\n\n normal = normalize(v3);\n\n return v3;\n}\n\nattribute vec4 vector;\nattribute vec4 color, position;\nattribute vec2 uv;\n\nuniform float vectorScale, tubeScale;\nuniform mat4 model, view, projection, inverseModel;\nuniform vec3 eyePosition, lightPosition;\n\nvarying vec3 f_normal, f_lightDirection, f_eyeDirection, f_data, f_position;\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n // Scale the vector magnitude to stay constant with\n // model & view changes.\n vec3 normal;\n vec3 XYZ = getTubePosition(mat3(model) * (tubeScale * vector.w * normalize(vector.xyz)), position.w, normal);\n vec4 tubePosition = model * vec4(position.xyz, 1.0) + vec4(XYZ, 0.0);\n\n //Lighting geometry parameters\n vec4 cameraCoordinate = view * tubePosition;\n cameraCoordinate.xyz /= cameraCoordinate.w;\n f_lightDirection = lightPosition - cameraCoordinate.xyz;\n f_eyeDirection = eyePosition - cameraCoordinate.xyz;\n f_normal = normalize((vec4(normal, 0.0) * inverseModel).xyz);\n\n // vec4 m_position = model * vec4(tubePosition, 1.0);\n vec4 t_position = view * tubePosition;\n gl_Position = projection * t_position;\n\n f_color = color;\n f_data = tubePosition.xyz;\n f_position = position.xyz;\n f_uv = uv;\n}\n"]),a=n(["#extension GL_OES_standard_derivatives : enable\n\nprecision highp float;\n#define GLSLIFY 1\n\nfloat beckmannDistribution(float x, float roughness) {\n float NdotH = max(x, 0.0001);\n float cos2Alpha = NdotH * NdotH;\n float tan2Alpha = (cos2Alpha - 1.0) / cos2Alpha;\n float roughness2 = roughness * roughness;\n float denom = 3.141592653589793 * roughness2 * cos2Alpha * cos2Alpha;\n return exp(tan2Alpha / roughness2) / denom;\n}\n\nfloat cookTorranceSpecular(\n vec3 lightDirection,\n vec3 viewDirection,\n vec3 surfaceNormal,\n float roughness,\n float fresnel) {\n\n float VdotN = max(dot(viewDirection, surfaceNormal), 0.0);\n float LdotN = max(dot(lightDirection, surfaceNormal), 0.0);\n\n //Half angle vector\n vec3 H = normalize(lightDirection + viewDirection);\n\n //Geometric term\n float NdotH = max(dot(surfaceNormal, H), 0.0);\n float VdotH = max(dot(viewDirection, H), 0.000001);\n float LdotH = max(dot(lightDirection, H), 0.000001);\n float G1 = (2.0 * NdotH * VdotN) / VdotH;\n float G2 = (2.0 * NdotH * LdotN) / LdotH;\n float G = min(1.0, min(G1, G2));\n \n //Distribution term\n float D = beckmannDistribution(NdotH, roughness);\n\n //Fresnel term\n float F = pow(1.0 - VdotN, fresnel);\n\n //Multiply terms and done\n return G * F * D / max(3.14159265 * VdotN, 0.000001);\n}\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform float roughness, fresnel, kambient, kdiffuse, kspecular, opacity;\nuniform sampler2D texture;\n\nvarying vec3 f_normal, f_lightDirection, f_eyeDirection, f_data, f_position;\nvarying vec4 f_color;\nvarying vec2 f_uv;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], f_position)) discard;\n vec3 N = normalize(f_normal);\n vec3 L = normalize(f_lightDirection);\n vec3 V = normalize(f_eyeDirection);\n\n if(gl_FrontFacing) {\n N = -N;\n }\n\n float specular = min(1.0, max(0.0, cookTorranceSpecular(L, V, N, roughness, fresnel)));\n float diffuse = min(kambient + kdiffuse * max(dot(N, L), 0.0), 1.0);\n\n vec4 surfaceColor = f_color * texture2D(texture, f_uv);\n vec4 litColor = surfaceColor.a * vec4(diffuse * surfaceColor.rgb + kspecular * vec3(1,1,1) * specular, 1.0);\n\n gl_FragColor = litColor * opacity;\n}\n"]),o=n(["precision highp float;\n\nprecision highp float;\n#define GLSLIFY 1\n\nvec3 getOrthogonalVector(vec3 v) {\n // Return up-vector for only-z vector.\n // Return ax + by + cz = 0, a point that lies on the plane that has v as a normal and that isn't (0,0,0).\n // From the above if-statement we have ||a|| > 0 U ||b|| > 0.\n // Assign z = 0, x = -b, y = a:\n // a*-b + b*a + c*0 = -ba + ba + 0 = 0\n if (v.x*v.x > v.z*v.z || v.y*v.y > v.z*v.z) {\n return normalize(vec3(-v.y, v.x, 0.0));\n } else {\n return normalize(vec3(0.0, v.z, -v.y));\n }\n}\n\n// Calculate the tube vertex and normal at the given index.\n//\n// The returned vertex is for a tube ring with its center at origin, radius of length(d), pointing in the direction of d.\n//\n// Each tube segment is made up of a ring of vertices.\n// These vertices are used to make up the triangles of the tube by connecting them together in the vertex array.\n// The indexes of tube segments run from 0 to 8.\n//\nvec3 getTubePosition(vec3 d, float index, out vec3 normal) {\n float segmentCount = 8.0;\n\n float angle = 2.0 * 3.14159 * (index / segmentCount);\n\n vec3 u = getOrthogonalVector(d);\n vec3 v = normalize(cross(u, d));\n\n vec3 x = u * cos(angle) * length(d);\n vec3 y = v * sin(angle) * length(d);\n vec3 v3 = x + y;\n\n normal = normalize(v3);\n\n return v3;\n}\n\nattribute vec4 vector;\nattribute vec4 position;\nattribute vec4 id;\n\nuniform mat4 model, view, projection;\nuniform float tubeScale;\n\nvarying vec3 f_position;\nvarying vec4 f_id;\n\nvoid main() {\n vec3 normal;\n vec3 XYZ = getTubePosition(mat3(model) * (tubeScale * vector.w * normalize(vector.xyz)), position.w, normal);\n vec4 tubePosition = model * vec4(position.xyz, 1.0) + vec4(XYZ, 0.0);\n\n gl_Position = projection * view * tubePosition;\n f_id = id;\n f_position = position.xyz;\n}\n"]),s=n(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 clipBounds[2];\nuniform float pickId;\n\nvarying vec3 f_position;\nvarying vec4 f_id;\n\nvoid main() {\n if (outOfRange(clipBounds[0], clipBounds[1], f_position)) discard;\n\n gl_FragColor = vec4(pickId, f_id.xyz);\n}"]);e.meshShader={vertex:i,fragment:a,attributes:[{name:"position",type:"vec4"},{name:"color",type:"vec4"},{name:"uv",type:"vec2"},{name:"vector",type:"vec4"}]},e.pickShader={vertex:o,fragment:s,attributes:[{name:"position",type:"vec4"},{name:"id",type:"vec4"},{name:"vector",type:"vec4"}]}},7307:function(t,e,r){"use strict";var n=r(2858),i=r(4020),a=["xyz","xzy","yxz","yzx","zxy","zyx"],o=function(t,e){var r,n=t.length;for(r=0;re)return r-1}return r},s=function(t,e,r){return tr?r:t},l=function(t){var e=1/0;t.sort((function(t,e){return t-e}));for(var r=t.length,n=1;nf-1||m>h-1||x>p-1)return n.create();var b,_,w,T,k,A,M=a[0][d],S=a[0][y],E=a[1][v],L=a[1][m],C=a[2][g],P=(l-M)/(S-M),O=(u-E)/(L-E),I=(c-C)/(a[2][x]-C);switch(isFinite(P)||(P=.5),isFinite(O)||(O=.5),isFinite(I)||(I=.5),r.reversedX&&(d=f-1-d,y=f-1-y),r.reversedY&&(v=h-1-v,m=h-1-m),r.reversedZ&&(g=p-1-g,x=p-1-x),r.filled){case 5:k=g,A=x,w=v*p,T=m*p,b=d*p*h,_=y*p*h;break;case 4:k=g,A=x,b=d*p,_=y*p,w=v*p*f,T=m*p*f;break;case 3:w=v,T=m,k=g*h,A=x*h,b=d*h*p,_=y*h*p;break;case 2:w=v,T=m,b=d*h,_=y*h,k=g*h*f,A=x*h*f;break;case 1:b=d,_=y,k=g*f,A=x*f,w=v*f*p,T=m*f*p;break;default:b=d,_=y,w=v*f,T=m*f,k=g*f*h,A=x*f*h}var D=i[b+w+k],z=i[b+w+A],R=i[b+T+k],F=i[b+T+A],B=i[_+w+k],N=i[_+w+A],j=i[_+T+k],U=i[_+T+A],V=n.create(),H=n.create(),q=n.create(),G=n.create();n.lerp(V,D,B,P),n.lerp(H,z,N,P),n.lerp(q,R,j,P),n.lerp(G,F,U,P);var Z=n.create(),Y=n.create();n.lerp(Z,V,q,O),n.lerp(Y,H,G,O);var W=n.create();return n.lerp(W,Z,Y,I),W}(e,t,p)},v=t.getDivergence||function(t,e){var r=n.create(),i=1e-4;n.add(r,t,[i,0,0]);var a=d(r);n.subtract(a,a,e),n.scale(a,a,1/i),n.add(r,t,[0,i,0]);var o=d(r);n.subtract(o,o,e),n.scale(o,o,1/i),n.add(r,t,[0,0,i]);var s=d(r);return n.subtract(s,s,e),n.scale(s,s,1/i),n.add(r,a,o),n.add(r,r,s),r},g=[],y=e[0][0],m=e[0][1],x=e[0][2],b=e[1][0],_=e[1][1],w=e[1][2],T=function(t){var e=t[0],r=t[1],n=t[2];return!(eb||r_||nw)},k=10*n.distance(e[0],e[1])/u,A=k*k,M=1,S=0,E=r.length;E>1&&(M=function(t){for(var e=[],r=[],n=[],i={},a={},o={},s=t.length,u=0;uS&&(S=F),z.push(F),g.push({points:P,velocities:O,divergences:z});for(var B=0;B<100*u&&P.lengthA&&n.scale(N,N,k/Math.sqrt(j)),n.add(N,N,C),I=d(N),n.squaredDistance(D,N)-A>-1e-4*A&&(P.push(N),D=N,O.push(I),R=v(N,I),F=n.length(R),isFinite(F)&&F>S&&(S=F),z.push(F)),C=N}}var U=function(t,e,r,a){for(var o=0,s=0;s0)for(T=0;T<8;T++){var k=(T+1)%8;u.push(h[T],p[T],p[k],p[k],h[k],h[T]),f.push(m,y,y,y,m,m),d.push(v,g,g,g,v,v);var A=u.length;c.push([A-6,A-5,A-4],[A-3,A-2,A-1])}var M=h;h=p,p=M;var S=m;m=y,y=S;var E=v;v=g,g=E}return{positions:u,cells:c,vectors:f,vertexIntensity:d}}(t,r,a,o)})),f=[],h=[],p=[],d=[];for(s=0;s max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec3 lowerBound, upperBound;\nuniform float contourTint;\nuniform vec4 contourColor;\nuniform sampler2D colormap;\nuniform vec3 clipBounds[2];\nuniform float roughness, fresnel, kambient, kdiffuse, kspecular, opacity;\nuniform float vertexColor;\n\nvarying float value, kill;\nvarying vec3 worldCoordinate;\nvarying vec3 lightDirection, eyeDirection, surfaceNormal;\nvarying vec4 vColor;\n\nvoid main() {\n if (\n kill > 0.0 ||\n vColor.a == 0.0 ||\n outOfRange(clipBounds[0], clipBounds[1], worldCoordinate)\n ) discard;\n\n vec3 N = normalize(surfaceNormal);\n vec3 V = normalize(eyeDirection);\n vec3 L = normalize(lightDirection);\n\n if(gl_FrontFacing) {\n N = -N;\n }\n\n float specular = max(beckmannSpecular(L, V, N, roughness), 0.);\n float diffuse = min(kambient + kdiffuse * max(dot(N, L), 0.0), 1.0);\n\n //decide how to interpolate color — in vertex or in fragment\n vec4 surfaceColor =\n step(vertexColor, .5) * texture2D(colormap, vec2(value, value)) +\n step(.5, vertexColor) * vColor;\n\n vec4 litColor = surfaceColor.a * vec4(diffuse * surfaceColor.rgb + kspecular * vec3(1,1,1) * specular, 1.0);\n\n gl_FragColor = mix(litColor, contourColor, contourTint) * opacity;\n}\n"]),s=i(["precision highp float;\n#define GLSLIFY 1\n\nattribute vec4 uv;\nattribute float f;\n\nuniform vec3 objectOffset;\nuniform mat3 permutation;\nuniform mat4 model, view, projection;\nuniform float height, zOffset;\nuniform sampler2D colormap;\n\nvarying float value, kill;\nvarying vec3 worldCoordinate;\nvarying vec2 planeCoordinate;\nvarying vec3 lightDirection, eyeDirection, surfaceNormal;\nvarying vec4 vColor;\n\nvoid main() {\n vec3 dataCoordinate = permutation * vec3(uv.xy, height);\n worldCoordinate = objectOffset + dataCoordinate;\n vec4 worldPosition = model * vec4(worldCoordinate, 1.0);\n\n vec4 clipPosition = projection * view * worldPosition;\n clipPosition.z += zOffset;\n\n gl_Position = clipPosition;\n value = f + objectOffset.z;\n kill = -1.0;\n planeCoordinate = uv.zw;\n\n vColor = texture2D(colormap, vec2(value, value));\n\n //Don't do lighting for contours\n surfaceNormal = vec3(1,0,0);\n eyeDirection = vec3(0,1,0);\n lightDirection = vec3(0,0,1);\n}\n"]),l=i(["precision highp float;\n#define GLSLIFY 1\n\nbool outOfRange(float a, float b, float p) {\n return ((p > max(a, b)) || \n (p < min(a, b)));\n}\n\nbool outOfRange(vec2 a, vec2 b, vec2 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y));\n}\n\nbool outOfRange(vec3 a, vec3 b, vec3 p) {\n return (outOfRange(a.x, b.x, p.x) ||\n outOfRange(a.y, b.y, p.y) ||\n outOfRange(a.z, b.z, p.z));\n}\n\nbool outOfRange(vec4 a, vec4 b, vec4 p) {\n return outOfRange(a.xyz, b.xyz, p.xyz);\n}\n\nuniform vec2 shape;\nuniform vec3 clipBounds[2];\nuniform float pickId;\n\nvarying float value, kill;\nvarying vec3 worldCoordinate;\nvarying vec2 planeCoordinate;\nvarying vec3 surfaceNormal;\n\nvec2 splitFloat(float v) {\n float vh = 255.0 * v;\n float upper = floor(vh);\n float lower = fract(vh);\n return vec2(upper / 255.0, floor(lower * 16.0) / 16.0);\n}\n\nvoid main() {\n if ((kill > 0.0) ||\n (outOfRange(clipBounds[0], clipBounds[1], worldCoordinate))) discard;\n\n vec2 ux = splitFloat(planeCoordinate.x / shape.x);\n vec2 uy = splitFloat(planeCoordinate.y / shape.y);\n gl_FragColor = vec4(pickId, ux.x, uy.x, ux.y + (uy.y/16.0));\n}\n"]);e.createShader=function(t){var e=n(t,a,o,null,[{name:"uv",type:"vec4"},{name:"f",type:"vec3"},{name:"normal",type:"vec3"}]);return e.attributes.uv.location=0,e.attributes.f.location=1,e.attributes.normal.location=2,e},e.createPickShader=function(t){var e=n(t,a,l,null,[{name:"uv",type:"vec4"},{name:"f",type:"vec3"},{name:"normal",type:"vec3"}]);return e.attributes.uv.location=0,e.attributes.f.location=1,e.attributes.normal.location=2,e},e.createContourShader=function(t){var e=n(t,s,o,null,[{name:"uv",type:"vec4"},{name:"f",type:"float"}]);return e.attributes.uv.location=0,e.attributes.f.location=1,e},e.createPickContourShader=function(t){var e=n(t,s,l,null,[{name:"uv",type:"vec4"},{name:"f",type:"float"}]);return e.attributes.uv.location=0,e.attributes.f.location=1,e}},3754:function(t,e,r){"use strict";t.exports=function(t){var e=t.gl,r=m(e),n=b(e),s=x(e),l=_(e),u=i(e),c=a(e,[{buffer:u,size:4,stride:40,offset:0},{buffer:u,size:3,stride:40,offset:16},{buffer:u,size:3,stride:40,offset:28}]),f=i(e),h=a(e,[{buffer:f,size:4,stride:20,offset:0},{buffer:f,size:1,stride:20,offset:16}]),p=i(e),d=a(e,[{buffer:p,size:2,type:e.FLOAT}]),v=o(e,1,256,e.RGBA,e.UNSIGNED_BYTE);v.minFilter=e.LINEAR,v.magFilter=e.LINEAR;var g=new M(e,[0,0],[[0,0,0],[0,0,0]],r,n,u,c,v,s,l,f,h,p,d,[0,0,0]),y={levels:[[],[],[]]};for(var w in t)y[w]=t[w];return y.colormap=y.colormap||"jet",g.update(y),g};var n=r(2288),i=r(5827),a=r(2944),o=r(8931),s=r(5306),l=r(9156),u=r(7498),c=r(7382),f=r(5050),h=r(4162),p=r(104),d=r(7437),v=r(5070),g=r(9144),y=r(9054),m=y.createShader,x=y.createContourShader,b=y.createPickShader,_=y.createPickContourShader,w=[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1],T=[[0,0],[0,1],[1,0],[1,1],[1,0],[0,1]],k=[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]];function A(t,e,r,n,i){this.position=t,this.index=e,this.uv=r,this.level=n,this.dataCoordinate=i}function M(t,e,r,n,i,a,o,l,u,c,h,p,d,v,g){this.gl=t,this.shape=e,this.bounds=r,this.objectOffset=g,this.intensityBounds=[],this._shader=n,this._pickShader=i,this._coordinateBuffer=a,this._vao=o,this._colorMap=l,this._contourShader=u,this._contourPickShader=c,this._contourBuffer=h,this._contourVAO=p,this._contourOffsets=[[],[],[]],this._contourCounts=[[],[],[]],this._vertexCount=0,this._pickResult=new A([0,0,0],[0,0],[0,0],[0,0,0],[0,0,0]),this._dynamicBuffer=d,this._dynamicVAO=v,this._dynamicOffsets=[0,0,0],this._dynamicCounts=[0,0,0],this.contourWidth=[1,1,1],this.contourLevels=[[1],[1],[1]],this.contourTint=[0,0,0],this.contourColor=[[.5,.5,.5,1],[.5,.5,.5,1],[.5,.5,.5,1]],this.showContour=!0,this.showSurface=!0,this.enableHighlight=[!0,!0,!0],this.highlightColor=[[0,0,0,1],[0,0,0,1],[0,0,0,1]],this.highlightTint=[1,1,1],this.highlightLevel=[-1,-1,-1],this.enableDynamic=[!0,!0,!0],this.dynamicLevel=[NaN,NaN,NaN],this.dynamicColor=[[0,0,0,1],[0,0,0,1],[0,0,0,1]],this.dynamicTint=[1,1,1],this.dynamicWidth=[1,1,1],this.axesBounds=[[1/0,1/0,1/0],[-1/0,-1/0,-1/0]],this.surfaceProject=[!1,!1,!1],this.contourProject=[[!1,!1,!1],[!1,!1,!1],[!1,!1,!1]],this.colorBounds=[!1,!1],this._field=[f(s.mallocFloat(1024),[0,0]),f(s.mallocFloat(1024),[0,0]),f(s.mallocFloat(1024),[0,0])],this.pickId=1,this.clipBounds=[[-1/0,-1/0,-1/0],[1/0,1/0,1/0]],this.snapToData=!1,this.pixelRatio=1,this.opacity=1,this.lightPosition=[10,1e4,0],this.ambientLight=.8,this.diffuseLight=.8,this.specularLight=2,this.roughness=.5,this.fresnel=1.5,this.vertexColor=0,this.dirty=!0}!function(){for(var t=0;t<3;++t){var e=k[t],r=(t+2)%3;e[(t+1)%3+0]=1,e[r+3]=1,e[t+6]=1}}();var S=M.prototype;S.genColormap=function(t,e){var r=!1,n=c([l({colormap:t,nshades:256,format:"rgba"}).map((function(t,n){var i=e?function(t,e){if(!e)return 1;if(!e.length)return 1;for(var r=0;rt&&r>0){var n=(e[r][0]-t)/(e[r][0]-e[r-1][0]);return e[r][1]*(1-n)+n*e[r-1][1]}}return 1}(n/255,e):t[3];return i<1&&(r=!0),[t[0],t[1],t[2],255*i]}))]);return u.divseq(n,255),this.hasAlphaScale=r,n},S.isTransparent=function(){return this.opacity<1||this.hasAlphaScale},S.isOpaque=function(){return!this.isTransparent()},S.pickSlots=1,S.setPickBase=function(t){this.pickId=t};var E=[0,0,0],L={showSurface:!1,showContour:!1,projections:[w.slice(),w.slice(),w.slice()],clipBounds:[[[0,0,0],[0,0,0]],[[0,0,0],[0,0,0]],[[0,0,0],[0,0,0]]]};function C(t,e){var r,n,i,a=e.axes&&e.axes.lastCubeProps.axis||E,o=e.showSurface,s=e.showContour;for(r=0;r<3;++r)for(o=o||e.surfaceProject[r],n=0;n<3;++n)s=s||e.contourProject[r][n];for(r=0;r<3;++r){var l=L.projections[r];for(n=0;n<16;++n)l[n]=0;for(n=0;n<4;++n)l[5*n]=1;l[5*r]=0,l[12+r]=e.axesBounds[+(a[r]>0)][r],p(l,t.model,l);var u=L.clipBounds[r];for(i=0;i<2;++i)for(n=0;n<3;++n)u[i][n]=t.clipBounds[i][n];u[0][r]=-1e8,u[1][r]=1e8}return L.showSurface=o,L.showContour=s,L}var P={model:w,view:w,projection:w,inverseModel:w.slice(),lowerBound:[0,0,0],upperBound:[0,0,0],colorMap:0,clipBounds:[[0,0,0],[0,0,0]],height:0,contourTint:0,contourColor:[0,0,0,1],permutation:[1,0,0,0,1,0,0,0,1],zOffset:-1e-4,objectOffset:[0,0,0],kambient:1,kdiffuse:1,kspecular:1,lightPosition:[1e3,1e3,1e3],eyePosition:[0,0,0],roughness:1,fresnel:1,opacity:1,vertexColor:0},O=w.slice(),I=[1,0,0,0,1,0,0,0,1];function D(t,e){t=t||{};var r=this.gl;r.disable(r.CULL_FACE),this._colorMap.bind(0);var n=P;n.model=t.model||w,n.view=t.view||w,n.projection=t.projection||w,n.lowerBound=[this.bounds[0][0],this.bounds[0][1],this.colorBounds[0]||this.bounds[0][2]],n.upperBound=[this.bounds[1][0],this.bounds[1][1],this.colorBounds[1]||this.bounds[1][2]],n.objectOffset=this.objectOffset,n.contourColor=this.contourColor[0],n.inverseModel=d(n.inverseModel,n.model);for(var i=0;i<2;++i)for(var a=n.clipBounds[i],o=0;o<3;++o)a[o]=Math.min(Math.max(this.clipBounds[i][o],-1e8),1e8);n.kambient=this.ambientLight,n.kdiffuse=this.diffuseLight,n.kspecular=this.specularLight,n.roughness=this.roughness,n.fresnel=this.fresnel,n.opacity=this.opacity,n.height=0,n.permutation=I,n.vertexColor=this.vertexColor;var s=O;for(p(s,n.view,n.model),p(s,n.projection,s),d(s,s),i=0;i<3;++i)n.eyePosition[i]=s[12+i]/s[15];var l=s[15];for(i=0;i<3;++i)l+=this.lightPosition[i]*s[4*i+3];for(i=0;i<3;++i){var u=s[12+i];for(o=0;o<3;++o)u+=s[4*o+i]*this.lightPosition[o];n.lightPosition[i]=u/l}var c=C(n,this);if(c.showSurface){for(this._shader.bind(),this._shader.uniforms=n,this._vao.bind(),this.showSurface&&this._vertexCount&&this._vao.draw(r.TRIANGLES,this._vertexCount),i=0;i<3;++i)this.surfaceProject[i]&&this.vertexCount&&(this._shader.uniforms.model=c.projections[i],this._shader.uniforms.clipBounds=c.clipBounds[i],this._vao.draw(r.TRIANGLES,this._vertexCount));this._vao.unbind()}if(c.showContour){var f=this._contourShader;n.kambient=1,n.kdiffuse=0,n.kspecular=0,n.opacity=1,f.bind(),f.uniforms=n;var h=this._contourVAO;for(h.bind(),i=0;i<3;++i)for(f.uniforms.permutation=k[i],r.lineWidth(this.contourWidth[i]*this.pixelRatio),o=0;o>4)/16)/255,i=Math.floor(n),a=n-i,o=e[1]*(t.value[1]+(15&t.value[2])/16)/255,s=Math.floor(o),l=o-s;i+=1,s+=1;var u=r.position;u[0]=u[1]=u[2]=0;for(var c=0;c<2;++c)for(var f=c?a:1-a,h=0;h<2;++h)for(var p=i+c,d=s+h,g=f*(h?l:1-l),y=0;y<3;++y)u[y]+=this._field[y].get(p,d)*g;for(var m=this._pickResult.level,x=0;x<3;++x)if(m[x]=v.le(this.contourLevels[x],u[x]),m[x]<0)this.contourLevels[x].length>0&&(m[x]=0);else if(m[x]Math.abs(_-u[x])&&(m[x]+=1)}for(r.index[0]=a<.5?i:i+1,r.index[1]=l<.5?s:s+1,r.uv[0]=n/e[0],r.uv[1]=o/e[1],y=0;y<3;++y)r.dataCoordinate[y]=this._field[y].get(r.index[0],r.index[1]);return r},S.padField=function(t,e){var r=e.shape.slice(),n=t.shape.slice();u.assign(t.lo(1,1).hi(r[0],r[1]),e),u.assign(t.lo(1).hi(r[0],1),e.hi(r[0],1)),u.assign(t.lo(1,n[1]-1).hi(r[0],1),e.lo(0,r[1]-1).hi(r[0],1)),u.assign(t.lo(0,1).hi(1,r[1]),e.hi(1)),u.assign(t.lo(n[0]-1,1).hi(1,r[1]),e.lo(r[0]-1)),t.set(0,0,e.get(0,0)),t.set(0,n[1]-1,e.get(0,r[1]-1)),t.set(n[0]-1,0,e.get(r[0]-1,0)),t.set(n[0]-1,n[1]-1,e.get(r[0]-1,r[1]-1))},S.update=function(t){t=t||{},this.objectOffset=t.objectOffset||this.objectOffset,this.dirty=!0,"contourWidth"in t&&(this.contourWidth=R(t.contourWidth,Number)),"showContour"in t&&(this.showContour=R(t.showContour,Boolean)),"showSurface"in t&&(this.showSurface=!!t.showSurface),"contourTint"in t&&(this.contourTint=R(t.contourTint,Boolean)),"contourColor"in t&&(this.contourColor=B(t.contourColor)),"contourProject"in t&&(this.contourProject=R(t.contourProject,(function(t){return R(t,Boolean)}))),"surfaceProject"in t&&(this.surfaceProject=t.surfaceProject),"dynamicColor"in t&&(this.dynamicColor=B(t.dynamicColor)),"dynamicTint"in t&&(this.dynamicTint=R(t.dynamicTint,Number)),"dynamicWidth"in t&&(this.dynamicWidth=R(t.dynamicWidth,Number)),"opacity"in t&&(this.opacity=t.opacity),"opacityscale"in t&&(this.opacityscale=t.opacityscale),"colorBounds"in t&&(this.colorBounds=t.colorBounds),"vertexColor"in t&&(this.vertexColor=t.vertexColor?1:0),"colormap"in t&&this._colorMap.setPixels(this.genColormap(t.colormap,this.opacityscale));var e=t.field||t.coords&&t.coords[2]||null,r=!1;if(e||(e=this._field[2].shape[0]||this._field[2].shape[2]?this._field[2].lo(1,1).hi(this._field[2].shape[0]-2,this._field[2].shape[1]-2):this._field[2].hi(0,0)),"field"in t||"coords"in t){var i=(e.shape[0]+2)*(e.shape[1]+2);i>this._field[2].data.length&&(s.freeFloat(this._field[2].data),this._field[2].data=s.mallocFloat(n.nextPow2(i))),this._field[2]=f(this._field[2].data,[e.shape[0]+2,e.shape[1]+2]),this.padField(this._field[2],e),this.shape=e.shape.slice();for(var a=this.shape,o=0;o<2;++o)this._field[2].size>this._field[o].data.length&&(s.freeFloat(this._field[o].data),this._field[o].data=s.mallocFloat(this._field[2].size)),this._field[o]=f(this._field[o].data,[a[0]+2,a[1]+2]);if(t.coords){var l=t.coords;if(!Array.isArray(l)||3!==l.length)throw new Error("gl-surface: invalid coordinates for x/y");for(o=0;o<2;++o){var u=l[o];for(y=0;y<2;++y)if(u.shape[y]!==a[y])throw new Error("gl-surface: coords have incorrect shape");this.padField(this._field[o],u)}}else if(t.ticks){var c=t.ticks;if(!Array.isArray(c)||2!==c.length)throw new Error("gl-surface: invalid ticks");for(o=0;o<2;++o){var p=c[o];if((Array.isArray(p)||p.length)&&(p=f(p)),p.shape[0]!==a[o])throw new Error("gl-surface: invalid tick length");var d=f(p.data,a);d.stride[o]=p.stride[0],d.stride[1^o]=0,this.padField(this._field[o],d)}}else{for(o=0;o<2;++o){var v=[0,0];v[o]=1,this._field[o]=f(this._field[o].data,[a[0]+2,a[1]+2],v,0)}this._field[0].set(0,0,0);for(var y=0;y0){for(var xt=0;xt<5;++xt)$.pop();U-=1}continue t}$.push(nt[0],nt[1],ot[0],ot[1],nt[2]),U+=1}}rt.push(U)}this._contourOffsets[Q]=et,this._contourCounts[Q]=rt}var bt=s.mallocFloat($.length);for(o=0;o<$.length;++o)bt[o]=$[o];this._contourBuffer.update(bt),s.freeFloat(bt)}},S.dispose=function(){this._shader.dispose(),this._vao.dispose(),this._coordinateBuffer.dispose(),this._colorMap.dispose(),this._contourBuffer.dispose(),this._contourVAO.dispose(),this._contourShader.dispose(),this._contourPickShader.dispose(),this._dynamicBuffer.dispose(),this._dynamicVAO.dispose();for(var t=0;t<3;++t)s.freeFloat(this._field[t].data)},S.highlight=function(t){var e,r;if(!t)return this._dynamicCounts=[0,0,0],this.dyanamicLevel=[NaN,NaN,NaN],void(this.highlightLevel=[-1,-1,-1]);for(e=0;e<3;++e)this.enableHighlight[e]?this.highlightLevel[e]=t.level[e]:this.highlightLevel[e]=-1;for(r=this.snapToData?t.dataCoordinate:t.position,e=0;e<3;++e)r[e]-=this.objectOffset[e];if(this.enableDynamic[0]&&r[0]!==this.dynamicLevel[0]||this.enableDynamic[1]&&r[1]!==this.dynamicLevel[1]||this.enableDynamic[2]&&r[2]!==this.dynamicLevel[2]){for(var n=0,i=this.shape,a=s.mallocFloat(12*i[0]*i[1]),o=0;o<3;++o)if(this.enableDynamic[o]){this.dynamicLevel[o]=r[o];var l=(o+1)%3,u=(o+2)%3,c=this._field[o],f=this._field[l],p=this._field[u],d=h(c,r[o]),v=d.cells,g=d.positions;for(this._dynamicOffsets[o]=n,e=0;ei||r<0||r>i)throw new Error("gl-texture2d: Invalid texture size");return t._shape=[e,r],t.bind(),n.texImage2D(n.TEXTURE_2D,0,t.format,e,r,0,t.format,t.type,null),t._mipLevels=[0],t}function p(t,e,r,n,i,a){this.gl=t,this.handle=e,this.format=i,this.type=a,this._shape=[r,n],this._mipLevels=[0],this._magFilter=t.NEAREST,this._minFilter=t.NEAREST,this._wrapS=t.CLAMP_TO_EDGE,this._wrapT=t.CLAMP_TO_EDGE,this._anisoSamples=1;var o=this,s=[this._wrapS,this._wrapT];Object.defineProperties(s,[{get:function(){return o._wrapS},set:function(t){return o.wrapS=t}},{get:function(){return o._wrapT},set:function(t){return o.wrapT=t}}]),this._wrapVector=s;var l=[this._shape[0],this._shape[1]];Object.defineProperties(l,[{get:function(){return o._shape[0]},set:function(t){return o.width=t}},{get:function(){return o._shape[1]},set:function(t){return o.height=t}}]),this._shapeVector=l}var d=p.prototype;function v(t,e){return 3===t.length?1===e[2]&&e[1]===t[0]*t[2]&&e[0]===t[2]:1===e[0]&&e[1]===t[0]}function g(t){var e=t.createTexture();return t.bindTexture(t.TEXTURE_2D,e),t.texParameteri(t.TEXTURE_2D,t.TEXTURE_MIN_FILTER,t.NEAREST),t.texParameteri(t.TEXTURE_2D,t.TEXTURE_MAG_FILTER,t.NEAREST),t.texParameteri(t.TEXTURE_2D,t.TEXTURE_WRAP_S,t.CLAMP_TO_EDGE),t.texParameteri(t.TEXTURE_2D,t.TEXTURE_WRAP_T,t.CLAMP_TO_EDGE),e}function y(t,e,r,n,i){var a=t.getParameter(t.MAX_TEXTURE_SIZE);if(e<0||e>a||r<0||r>a)throw new Error("gl-texture2d: Invalid texture shape");if(i===t.FLOAT&&!t.getExtension("OES_texture_float"))throw new Error("gl-texture2d: Floating point textures not supported on this platform");var o=g(t);return t.texImage2D(t.TEXTURE_2D,0,n,e,r,0,n,i,null),new p(t,o,e,r,n,i)}function m(t,e,r,n,i,a){var o=g(t);return t.texImage2D(t.TEXTURE_2D,0,i,i,a,e),new p(t,o,r,n,i,a)}function x(t,e){var r=e.dtype,o=e.shape.slice(),s=t.getParameter(t.MAX_TEXTURE_SIZE);if(o[0]<0||o[0]>s||o[1]<0||o[1]>s)throw new Error("gl-texture2d: Invalid texture size");var l=v(o,e.stride.slice()),u=0;"float32"===r?u=t.FLOAT:"float64"===r?(u=t.FLOAT,l=!1,r="float32"):"uint8"===r?u=t.UNSIGNED_BYTE:(u=t.UNSIGNED_BYTE,l=!1,r="uint8");var c,h,d=0;if(2===o.length)d=t.LUMINANCE,o=[o[0],o[1],1],e=n(e.data,o,[e.stride[0],e.stride[1],1],e.offset);else{if(3!==o.length)throw new Error("gl-texture2d: Invalid shape for texture");if(1===o[2])d=t.ALPHA;else if(2===o[2])d=t.LUMINANCE_ALPHA;else if(3===o[2])d=t.RGB;else{if(4!==o[2])throw new Error("gl-texture2d: Invalid shape for pixel coords");d=t.RGBA}}u!==t.FLOAT||t.getExtension("OES_texture_float")||(u=t.UNSIGNED_BYTE,l=!1);var y=e.size;if(l)c=0===e.offset&&e.data.length===y?e.data:e.data.subarray(e.offset,e.offset+y);else{var m=[o[2],o[2]*o[0],1];h=a.malloc(y,r);var x=n(h,o,m,0);"float32"!==r&&"float64"!==r||u!==t.UNSIGNED_BYTE?i.assign(x,e):f(x,e),c=h.subarray(0,y)}var b=g(t);return t.texImage2D(t.TEXTURE_2D,0,d,o[0],o[1],0,d,u,c),l||a.free(h),new p(t,b,o[0],o[1],d,u)}Object.defineProperties(d,{minFilter:{get:function(){return this._minFilter},set:function(t){this.bind();var e=this.gl;if(this.type===e.FLOAT&&o.indexOf(t)>=0&&(e.getExtension("OES_texture_float_linear")||(t=e.NEAREST)),s.indexOf(t)<0)throw new Error("gl-texture2d: Unknown filter mode "+t);return e.texParameteri(e.TEXTURE_2D,e.TEXTURE_MIN_FILTER,t),this._minFilter=t}},magFilter:{get:function(){return this._magFilter},set:function(t){this.bind();var e=this.gl;if(this.type===e.FLOAT&&o.indexOf(t)>=0&&(e.getExtension("OES_texture_float_linear")||(t=e.NEAREST)),s.indexOf(t)<0)throw new Error("gl-texture2d: Unknown filter mode "+t);return e.texParameteri(e.TEXTURE_2D,e.TEXTURE_MAG_FILTER,t),this._magFilter=t}},mipSamples:{get:function(){return this._anisoSamples},set:function(t){var e=this._anisoSamples;if(this._anisoSamples=0|Math.max(t,1),e!==this._anisoSamples){var r=this.gl.getExtension("EXT_texture_filter_anisotropic");r&&this.gl.texParameterf(this.gl.TEXTURE_2D,r.TEXTURE_MAX_ANISOTROPY_EXT,this._anisoSamples)}return this._anisoSamples}},wrapS:{get:function(){return this._wrapS},set:function(t){if(this.bind(),l.indexOf(t)<0)throw new Error("gl-texture2d: Unknown wrap mode "+t);return this.gl.texParameteri(this.gl.TEXTURE_2D,this.gl.TEXTURE_WRAP_S,t),this._wrapS=t}},wrapT:{get:function(){return this._wrapT},set:function(t){if(this.bind(),l.indexOf(t)<0)throw new Error("gl-texture2d: Unknown wrap mode "+t);return this.gl.texParameteri(this.gl.TEXTURE_2D,this.gl.TEXTURE_WRAP_T,t),this._wrapT=t}},wrap:{get:function(){return this._wrapVector},set:function(t){if(Array.isArray(t)||(t=[t,t]),2!==t.length)throw new Error("gl-texture2d: Must specify wrap mode for rows and columns");for(var e=0;e<2;++e)if(l.indexOf(t[e])<0)throw new Error("gl-texture2d: Unknown wrap mode "+t);this._wrapS=t[0],this._wrapT=t[1];var r=this.gl;return this.bind(),r.texParameteri(r.TEXTURE_2D,r.TEXTURE_WRAP_S,this._wrapS),r.texParameteri(r.TEXTURE_2D,r.TEXTURE_WRAP_T,this._wrapT),t}},shape:{get:function(){return this._shapeVector},set:function(t){if(Array.isArray(t)){if(2!==t.length)throw new Error("gl-texture2d: Invalid texture shape")}else t=[0|t,0|t];return h(this,0|t[0],0|t[1]),[0|t[0],0|t[1]]}},width:{get:function(){return this._shape[0]},set:function(t){return h(this,t|=0,this._shape[1]),t}},height:{get:function(){return this._shape[1]},set:function(t){return t|=0,h(this,this._shape[0],t),t}}}),d.bind=function(t){var e=this.gl;return void 0!==t&&e.activeTexture(e.TEXTURE0+(0|t)),e.bindTexture(e.TEXTURE_2D,this.handle),void 0!==t?0|t:e.getParameter(e.ACTIVE_TEXTURE)-e.TEXTURE0},d.dispose=function(){this.gl.deleteTexture(this.handle)},d.generateMipmap=function(){this.bind(),this.gl.generateMipmap(this.gl.TEXTURE_2D);for(var t=Math.min(this._shape[0],this._shape[1]),e=0;t>0;++e,t>>>=1)this._mipLevels.indexOf(e)<0&&this._mipLevels.push(e)},d.setPixels=function(t,e,r,o){var s=this.gl;this.bind(),Array.isArray(e)?(o=r,r=0|e[1],e=0|e[0]):(e=e||0,r=r||0),o=o||0;var l=c(t)?t:t.raw;if(l)this._mipLevels.indexOf(o)<0?(s.texImage2D(s.TEXTURE_2D,0,this.format,this.format,this.type,l),this._mipLevels.push(o)):s.texSubImage2D(s.TEXTURE_2D,o,e,r,this.format,this.type,l);else{if(!(t.shape&&t.stride&&t.data))throw new Error("gl-texture2d: Unsupported data type");if(t.shape.length<2||e+t.shape[1]>this._shape[1]>>>o||r+t.shape[0]>this._shape[0]>>>o||e<0||r<0)throw new Error("gl-texture2d: Texture dimensions are out of bounds");!function(t,e,r,o,s,l,u,c){var h=c.dtype,p=c.shape.slice();if(p.length<2||p.length>3)throw new Error("gl-texture2d: Invalid ndarray, must be 2d or 3d");var d=0,g=0,y=v(p,c.stride.slice());if("float32"===h?d=t.FLOAT:"float64"===h?(d=t.FLOAT,y=!1,h="float32"):"uint8"===h?d=t.UNSIGNED_BYTE:(d=t.UNSIGNED_BYTE,y=!1,h="uint8"),2===p.length)g=t.LUMINANCE,p=[p[0],p[1],1],c=n(c.data,p,[c.stride[0],c.stride[1],1],c.offset);else{if(3!==p.length)throw new Error("gl-texture2d: Invalid shape for texture");if(1===p[2])g=t.ALPHA;else if(2===p[2])g=t.LUMINANCE_ALPHA;else if(3===p[2])g=t.RGB;else{if(4!==p[2])throw new Error("gl-texture2d: Invalid shape for pixel coords");g=t.RGBA}p[2]}if(g!==t.LUMINANCE&&g!==t.ALPHA||s!==t.LUMINANCE&&s!==t.ALPHA||(g=s),g!==s)throw new Error("gl-texture2d: Incompatible texture format for setPixels");var m=c.size,x=u.indexOf(o)<0;if(x&&u.push(o),d===l&&y)0===c.offset&&c.data.length===m?x?t.texImage2D(t.TEXTURE_2D,o,s,p[0],p[1],0,s,l,c.data):t.texSubImage2D(t.TEXTURE_2D,o,e,r,p[0],p[1],s,l,c.data):x?t.texImage2D(t.TEXTURE_2D,o,s,p[0],p[1],0,s,l,c.data.subarray(c.offset,c.offset+m)):t.texSubImage2D(t.TEXTURE_2D,o,e,r,p[0],p[1],s,l,c.data.subarray(c.offset,c.offset+m));else{var b;b=l===t.FLOAT?a.mallocFloat32(m):a.mallocUint8(m);var _=n(b,p,[p[2],p[2]*p[0],1]);d===t.FLOAT&&l===t.UNSIGNED_BYTE?f(_,c):i.assign(_,c),x?t.texImage2D(t.TEXTURE_2D,o,s,p[0],p[1],0,s,l,b.subarray(0,m)):t.texSubImage2D(t.TEXTURE_2D,o,e,r,p[0],p[1],s,l,b.subarray(0,m)),l===t.FLOAT?a.freeFloat32(b):a.freeUint8(b)}}(s,e,r,o,this.format,this.type,this._mipLevels,t)}}},3056:function(t){"use strict";t.exports=function(t,e,r){e?e.bind():t.bindBuffer(t.ELEMENT_ARRAY_BUFFER,null);var n=0|t.getParameter(t.MAX_VERTEX_ATTRIBS);if(r){if(r.length>n)throw new Error("gl-vao: Too many vertex attributes");for(var 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i=t.expression.evaluate(e,null,{},r,n);return this._calculate(i,i,i,e)}return this._calculate(t.expression.evaluate(new Si(Math.floor(e.zoom-1),e)),t.expression.evaluate(new Si(Math.floor(e.zoom),e)),t.expression.evaluate(new Si(Math.floor(e.zoom+1),e)),e)}},Ni.prototype._calculate=function(t,e,r,n){return n.zoom>n.zoomHistory.lastIntegerZoom?{from:t,to:e}:{from:r,to:e}},Ni.prototype.interpolate=function(t){return t};var ji=function(t){this.specification=t};ji.prototype.possiblyEvaluate=function(t,e,r,n){return!!t.expression.evaluate(e,null,{},r,n)},ji.prototype.interpolate=function(){return!1};var Ui=function(t){for(var e in this.properties=t,this.defaultPropertyValues={},this.defaultTransitionablePropertyValues={},this.defaultTransitioningPropertyValues={},this.defaultPossiblyEvaluatedValues={},this.overridableProperties=[],t){var r=t[e];r.specification.overridable&&this.overridableProperties.push(e);var n=this.defaultPropertyValues[e]=new Ei(r,void 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this._transitionablePaint.setTransition(t.slice(0,-Vi.length),e||void 0),!1;var i=this._transitionablePaint._values[t],a="cross-faded-data-driven"===i.property.specification["property-type"],o=i.value.isDataDriven(),s=i.value;this._transitionablePaint.setValue(t,e),this._handleSpecialPaintPropertyUpdate(t);var l=this._transitionablePaint._values[t].value;return l.isDataDriven()||o||a||this._handleOverridablePaintPropertyUpdate(t,s,l)},e.prototype._handleSpecialPaintPropertyUpdate=function(t){},e.prototype._handleOverridablePaintPropertyUpdate=function(t,e,r){return!1},e.prototype.isHidden=function(t){return!!(this.minzoom&&t=this.maxzoom)||"none"===this.visibility},e.prototype.updateTransitions=function(t){this._transitioningPaint=this._transitionablePaint.transitioned(t,this._transitioningPaint)},e.prototype.hasTransition=function(){return this._transitioningPaint.hasTransition()},e.prototype.recalculate=function(t,e){t.getCrossfadeParameters&&(this._crossfadeParameters=t.getCrossfadeParameters()),this._unevaluatedLayout&&(this.layout=this._unevaluatedLayout.possiblyEvaluate(t,void 0,e)),this.paint=this._transitioningPaint.possiblyEvaluate(t,void 0,e)},e.prototype.serialize=function(){var t={id:this.id,type:this.type,source:this.source,"source-layer":this.sourceLayer,metadata:this.metadata,minzoom:this.minzoom,maxzoom:this.maxzoom,filter:this.filter,layout:this._unevaluatedLayout&&this._unevaluatedLayout.serialize(),paint:this._transitionablePaint&&this._transitionablePaint.serialize()};return this.visibility&&(t.layout=t.layout||{},t.layout.visibility=this.visibility),x(t,(function(t,e){return!(void 0===t||"layout"===e&&!Object.keys(t).length||"paint"===e&&!Object.keys(t).length)}))},e.prototype._validate=function(t,e,r,n,i){return void 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ArrayBuffer(this.capacity*this.bytesPerElement);var e=this.uint8;this._refreshViews(),e&&this.uint8.set(e)}},Zi.prototype._refreshViews=function(){throw new Error("_refreshViews() must be implemented by each concrete StructArray layout")};var Xi=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.int16=new Int16Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t,e){var r=this.length;return this.resize(r+1),this.emplace(r,t,e)},e.prototype.emplace=function(t,e,r){var n=2*t;return this.int16[n+0]=e,this.int16[n+1]=r,t},e}(Zi);Xi.prototype.bytesPerElement=4,Qn("StructArrayLayout2i4",Xi);var Ji=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new 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this.int16[s+0]=e,this.int16[s+1]=r,this.int16[s+2]=n,this.int16[s+3]=i,this.int16[s+4]=a,this.int16[s+5]=o,t},e}(Zi);Ki.prototype.bytesPerElement=12,Qn("StructArrayLayout2i4i12",Ki);var $i=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.int16=new Int16Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t,e,r,n,i,a){var o=this.length;return this.resize(o+1),this.emplace(o,t,e,r,n,i,a)},e.prototype.emplace=function(t,e,r,n,i,a,o){var s=4*t,l=8*t;return this.int16[s+0]=e,this.int16[s+1]=r,this.uint8[l+4]=n,this.uint8[l+5]=i,this.uint8[l+6]=a,this.uint8[l+7]=o,t},e}(Zi);$i.prototype.bytesPerElement=8,Qn("StructArrayLayout2i4ub8",$i);var Qi=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.uint16=new Uint16Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t,e,r,n,i,a,o,s,l,u){var c=this.length;return this.resize(c+1),this.emplace(c,t,e,r,n,i,a,o,s,l,u)},e.prototype.emplace=function(t,e,r,n,i,a,o,s,l,u,c){var f=9*t,h=18*t;return this.uint16[f+0]=e,this.uint16[f+1]=r,this.uint16[f+2]=n,this.uint16[f+3]=i,this.uint16[f+4]=a,this.uint16[f+5]=o,this.uint16[f+6]=s,this.uint16[f+7]=l,this.uint8[h+16]=u,this.uint8[h+17]=c,t},e}(Zi);Qi.prototype.bytesPerElement=18,Qn("StructArrayLayout8ui2ub18",Qi);var ta=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.int16=new Int16Array(this.arrayBuffer),this.uint16=new 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t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.float32=new Float32Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t,e,r,n){var i=this.length;return this.resize(i+1),this.emplace(i,t,e,r,n)},e.prototype.emplace=function(t,e,r,n,i){var a=12*t,o=3*t;return this.uint8[a+0]=e,this.uint8[a+1]=r,this.float32[o+1]=n,this.float32[o+2]=i,t},e}(Zi);oa.prototype.bytesPerElement=12,Qn("StructArrayLayout2ub2f12",oa);var sa=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.uint16=new Uint16Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t,e,r){var n=this.length;return this.resize(n+1),this.emplace(n,t,e,r)},e.prototype.emplace=function(t,e,r,n){var i=3*t;return this.uint16[i+0]=e,this.uint16[i+1]=r,this.uint16[i+2]=n,t},e}(Zi);sa.prototype.bytesPerElement=6,Qn("StructArrayLayout3ui6",sa);var la=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.int16=new Int16Array(this.arrayBuffer),this.uint16=new Uint16Array(this.arrayBuffer),this.uint32=new Uint32Array(this.arrayBuffer),this.float32=new Float32Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t,e,r,n,i,a,o,s,l,u,c,f,h,p,d,v,g){var y=this.length;return this.resize(y+1),this.emplace(y,t,e,r,n,i,a,o,s,l,u,c,f,h,p,d,v,g)},e.prototype.emplace=function(t,e,r,n,i,a,o,s,l,u,c,f,h,p,d,v,g,y){var m=24*t,x=12*t,b=48*t;return this.int16[m+0]=e,this.int16[m+1]=r,this.uint16[m+2]=n,this.uint16[m+3]=i,this.uint32[x+2]=a,this.uint32[x+3]=o,this.uint32[x+4]=s,this.uint16[m+10]=l,this.uint16[m+11]=u,this.uint16[m+12]=c,this.float32[x+7]=f,this.float32[x+8]=h,this.uint8[b+36]=p,this.uint8[b+37]=d,this.uint8[b+38]=v,this.uint32[x+10]=g,this.int16[m+22]=y,t},e}(Zi);la.prototype.bytesPerElement=48,Qn("StructArrayLayout2i2ui3ul3ui2f3ub1ul1i48",la);var ua=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.int16=new Int16Array(this.arrayBuffer),this.uint16=new Uint16Array(this.arrayBuffer),this.uint32=new Uint32Array(this.arrayBuffer),this.float32=new Float32Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t,e,r,n,i,a,o,s,l,u,c,f,h,p,d,v,g,y,m,x,b,_,w,T,k,A,M,S){var E=this.length;return this.resize(E+1),this.emplace(E,t,e,r,n,i,a,o,s,l,u,c,f,h,p,d,v,g,y,m,x,b,_,w,T,k,A,M,S)},e.prototype.emplace=function(t,e,r,n,i,a,o,s,l,u,c,f,h,p,d,v,g,y,m,x,b,_,w,T,k,A,M,S,E){var L=34*t,C=17*t;return this.int16[L+0]=e,this.int16[L+1]=r,this.int16[L+2]=n,this.int16[L+3]=i,this.int16[L+4]=a,this.int16[L+5]=o,this.int16[L+6]=s,this.int16[L+7]=l,this.uint16[L+8]=u,this.uint16[L+9]=c,this.uint16[L+10]=f,this.uint16[L+11]=h,this.uint16[L+12]=p,this.uint16[L+13]=d,this.uint16[L+14]=v,this.uint16[L+15]=g,this.uint16[L+16]=y,this.uint16[L+17]=m,this.uint16[L+18]=x,this.uint16[L+19]=b,this.uint16[L+20]=_,this.uint16[L+21]=w,this.uint16[L+22]=T,this.uint32[C+12]=k,this.float32[C+13]=A,this.float32[C+14]=M,this.float32[C+15]=S,this.float32[C+16]=E,t},e}(Zi);ua.prototype.bytesPerElement=68,Qn("StructArrayLayout8i15ui1ul4f68",ua);var ca=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.float32=new Float32Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t){var e=this.length;return this.resize(e+1),this.emplace(e,t)},e.prototype.emplace=function(t,e){var r=1*t;return this.float32[r+0]=e,t},e}(Zi);ca.prototype.bytesPerElement=4,Qn("StructArrayLayout1f4",ca);var fa=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.int16=new Int16Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t,e,r){var n=this.length;return this.resize(n+1),this.emplace(n,t,e,r)},e.prototype.emplace=function(t,e,r,n){var i=3*t;return this.int16[i+0]=e,this.int16[i+1]=r,this.int16[i+2]=n,t},e}(Zi);fa.prototype.bytesPerElement=6,Qn("StructArrayLayout3i6",fa);var ha=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.uint32=new Uint32Array(this.arrayBuffer),this.uint16=new Uint16Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t,e,r){var n=this.length;return this.resize(n+1),this.emplace(n,t,e,r)},e.prototype.emplace=function(t,e,r,n){var i=2*t,a=4*t;return this.uint32[i+0]=e,this.uint16[a+2]=r,this.uint16[a+3]=n,t},e}(Zi);ha.prototype.bytesPerElement=8,Qn("StructArrayLayout1ul2ui8",ha);var pa=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.uint16=new Uint16Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t,e){var r=this.length;return this.resize(r+1),this.emplace(r,t,e)},e.prototype.emplace=function(t,e,r){var n=2*t;return this.uint16[n+0]=e,this.uint16[n+1]=r,t},e}(Zi);pa.prototype.bytesPerElement=4,Qn("StructArrayLayout2ui4",pa);var da=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.uint16=new Uint16Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t){var e=this.length;return this.resize(e+1),this.emplace(e,t)},e.prototype.emplace=function(t,e){var r=1*t;return this.uint16[r+0]=e,t},e}(Zi);da.prototype.bytesPerElement=2,Qn("StructArrayLayout1ui2",da);var va=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.float32=new Float32Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t,e){var r=this.length;return this.resize(r+1),this.emplace(r,t,e)},e.prototype.emplace=function(t,e,r){var n=2*t;return this.float32[n+0]=e,this.float32[n+1]=r,t},e}(Zi);va.prototype.bytesPerElement=8,Qn("StructArrayLayout2f8",va);var ga=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype._refreshViews=function(){this.uint8=new Uint8Array(this.arrayBuffer),this.float32=new Float32Array(this.arrayBuffer)},e.prototype.emplaceBack=function(t,e,r,n){var i=this.length;return this.resize(i+1),this.emplace(i,t,e,r,n)},e.prototype.emplace=function(t,e,r,n,i){var a=4*t;return this.float32[a+0]=e,this.float32[a+1]=r,this.float32[a+2]=n,this.float32[a+3]=i,t},e}(Zi);ga.prototype.bytesPerElement=16,Qn("StructArrayLayout4f16",ga);var ya=function(t){function e(){t.apply(this,arguments)}t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e;var r={anchorPointX:{configurable:!0},anchorPointY:{configurable:!0},x1:{configurable:!0},y1:{configurable:!0},x2:{configurable:!0},y2:{configurable:!0},featureIndex:{configurable:!0},sourceLayerIndex:{configurable:!0},bucketIndex:{configurable:!0},anchorPoint:{configurable:!0}};return r.anchorPointX.get=function(){return this._structArray.int16[this._pos2+0]},r.anchorPointY.get=function(){return this._structArray.int16[this._pos2+1]},r.x1.get=function(){return this._structArray.int16[this._pos2+2]},r.y1.get=function(){return this._structArray.int16[this._pos2+3]},r.x2.get=function(){return this._structArray.int16[this._pos2+4]},r.y2.get=function(){return this._structArray.int16[this._pos2+5]},r.featureIndex.get=function(){return this._structArray.uint32[this._pos4+3]},r.sourceLayerIndex.get=function(){return this._structArray.uint16[this._pos2+8]},r.bucketIndex.get=function(){return this._structArray.uint16[this._pos2+9]},r.anchorPoint.get=function(){return new a(this.anchorPointX,this.anchorPointY)},Object.defineProperties(e.prototype,r),e}(Gi);ya.prototype.size=20;var ma=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype.get=function(t){return new ya(this,t)},e}(na);Qn("CollisionBoxArray",ma);var xa=function(t){function e(){t.apply(this,arguments)}t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e;var r={anchorX:{configurable:!0},anchorY:{configurable:!0},glyphStartIndex:{configurable:!0},numGlyphs:{configurable:!0},vertexStartIndex:{configurable:!0},lineStartIndex:{configurable:!0},lineLength:{configurable:!0},segment:{configurable:!0},lowerSize:{configurable:!0},upperSize:{configurable:!0},lineOffsetX:{configurable:!0},lineOffsetY:{configurable:!0},writingMode:{configurable:!0},placedOrientation:{configurable:!0},hidden:{configurable:!0},crossTileID:{configurable:!0},associatedIconIndex:{configurable:!0}};return r.anchorX.get=function(){return this._structArray.int16[this._pos2+0]},r.anchorY.get=function(){return this._structArray.int16[this._pos2+1]},r.glyphStartIndex.get=function(){return this._structArray.uint16[this._pos2+2]},r.numGlyphs.get=function(){return this._structArray.uint16[this._pos2+3]},r.vertexStartIndex.get=function(){return this._structArray.uint32[this._pos4+2]},r.lineStartIndex.get=function(){return this._structArray.uint32[this._pos4+3]},r.lineLength.get=function(){return this._structArray.uint32[this._pos4+4]},r.segment.get=function(){return this._structArray.uint16[this._pos2+10]},r.lowerSize.get=function(){return this._structArray.uint16[this._pos2+11]},r.upperSize.get=function(){return this._structArray.uint16[this._pos2+12]},r.lineOffsetX.get=function(){return this._structArray.float32[this._pos4+7]},r.lineOffsetY.get=function(){return this._structArray.float32[this._pos4+8]},r.writingMode.get=function(){return this._structArray.uint8[this._pos1+36]},r.placedOrientation.get=function(){return this._structArray.uint8[this._pos1+37]},r.placedOrientation.set=function(t){this._structArray.uint8[this._pos1+37]=t},r.hidden.get=function(){return this._structArray.uint8[this._pos1+38]},r.hidden.set=function(t){this._structArray.uint8[this._pos1+38]=t},r.crossTileID.get=function(){return this._structArray.uint32[this._pos4+10]},r.crossTileID.set=function(t){this._structArray.uint32[this._pos4+10]=t},r.associatedIconIndex.get=function(){return this._structArray.int16[this._pos2+22]},Object.defineProperties(e.prototype,r),e}(Gi);xa.prototype.size=48;var ba=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype.get=function(t){return new xa(this,t)},e}(la);Qn("PlacedSymbolArray",ba);var _a=function(t){function e(){t.apply(this,arguments)}t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e;var r={anchorX:{configurable:!0},anchorY:{configurable:!0},rightJustifiedTextSymbolIndex:{configurable:!0},centerJustifiedTextSymbolIndex:{configurable:!0},leftJustifiedTextSymbolIndex:{configurable:!0},verticalPlacedTextSymbolIndex:{configurable:!0},placedIconSymbolIndex:{configurable:!0},verticalPlacedIconSymbolIndex:{configurable:!0},key:{configurable:!0},textBoxStartIndex:{configurable:!0},textBoxEndIndex:{configurable:!0},verticalTextBoxStartIndex:{configurable:!0},verticalTextBoxEndIndex:{configurable:!0},iconBoxStartIndex:{configurable:!0},iconBoxEndIndex:{configurable:!0},verticalIconBoxStartIndex:{configurable:!0},verticalIconBoxEndIndex:{configurable:!0},featureIndex:{configurable:!0},numHorizontalGlyphVertices:{configurable:!0},numVerticalGlyphVertices:{configurable:!0},numIconVertices:{configurable:!0},numVerticalIconVertices:{configurable:!0},useRuntimeCollisionCircles:{configurable:!0},crossTileID:{configurable:!0},textBoxScale:{configurable:!0},textOffset0:{configurable:!0},textOffset1:{configurable:!0},collisionCircleDiameter:{configurable:!0}};return r.anchorX.get=function(){return this._structArray.int16[this._pos2+0]},r.anchorY.get=function(){return this._structArray.int16[this._pos2+1]},r.rightJustifiedTextSymbolIndex.get=function(){return this._structArray.int16[this._pos2+2]},r.centerJustifiedTextSymbolIndex.get=function(){return this._structArray.int16[this._pos2+3]},r.leftJustifiedTextSymbolIndex.get=function(){return this._structArray.int16[this._pos2+4]},r.verticalPlacedTextSymbolIndex.get=function(){return this._structArray.int16[this._pos2+5]},r.placedIconSymbolIndex.get=function(){return this._structArray.int16[this._pos2+6]},r.verticalPlacedIconSymbolIndex.get=function(){return this._structArray.int16[this._pos2+7]},r.key.get=function(){return this._structArray.uint16[this._pos2+8]},r.textBoxStartIndex.get=function(){return this._structArray.uint16[this._pos2+9]},r.textBoxEndIndex.get=function(){return this._structArray.uint16[this._pos2+10]},r.verticalTextBoxStartIndex.get=function(){return this._structArray.uint16[this._pos2+11]},r.verticalTextBoxEndIndex.get=function(){return this._structArray.uint16[this._pos2+12]},r.iconBoxStartIndex.get=function(){return this._structArray.uint16[this._pos2+13]},r.iconBoxEndIndex.get=function(){return this._structArray.uint16[this._pos2+14]},r.verticalIconBoxStartIndex.get=function(){return this._structArray.uint16[this._pos2+15]},r.verticalIconBoxEndIndex.get=function(){return this._structArray.uint16[this._pos2+16]},r.featureIndex.get=function(){return this._structArray.uint16[this._pos2+17]},r.numHorizontalGlyphVertices.get=function(){return this._structArray.uint16[this._pos2+18]},r.numVerticalGlyphVertices.get=function(){return this._structArray.uint16[this._pos2+19]},r.numIconVertices.get=function(){return this._structArray.uint16[this._pos2+20]},r.numVerticalIconVertices.get=function(){return this._structArray.uint16[this._pos2+21]},r.useRuntimeCollisionCircles.get=function(){return this._structArray.uint16[this._pos2+22]},r.crossTileID.get=function(){return this._structArray.uint32[this._pos4+12]},r.crossTileID.set=function(t){this._structArray.uint32[this._pos4+12]=t},r.textBoxScale.get=function(){return this._structArray.float32[this._pos4+13]},r.textOffset0.get=function(){return this._structArray.float32[this._pos4+14]},r.textOffset1.get=function(){return this._structArray.float32[this._pos4+15]},r.collisionCircleDiameter.get=function(){return this._structArray.float32[this._pos4+16]},Object.defineProperties(e.prototype,r),e}(Gi);_a.prototype.size=68;var wa=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype.get=function(t){return new _a(this,t)},e}(ua);Qn("SymbolInstanceArray",wa);var Ta=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype.getoffsetX=function(t){return this.float32[1*t+0]},e}(ca);Qn("GlyphOffsetArray",Ta);var ka=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype.getx=function(t){return this.int16[3*t+0]},e.prototype.gety=function(t){return this.int16[3*t+1]},e.prototype.gettileUnitDistanceFromAnchor=function(t){return this.int16[3*t+2]},e}(fa);Qn("SymbolLineVertexArray",ka);var Aa=function(t){function e(){t.apply(this,arguments)}t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e;var r={featureIndex:{configurable:!0},sourceLayerIndex:{configurable:!0},bucketIndex:{configurable:!0}};return r.featureIndex.get=function(){return this._structArray.uint32[this._pos4+0]},r.sourceLayerIndex.get=function(){return this._structArray.uint16[this._pos2+2]},r.bucketIndex.get=function(){return this._structArray.uint16[this._pos2+3]},Object.defineProperties(e.prototype,r),e}(Gi);Aa.prototype.size=8;var Ma=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype.get=function(t){return new Aa(this,t)},e}(ha);Qn("FeatureIndexArray",Ma);var Sa=Yi([{name:"a_pos",components:2,type:"Int16"}],4).members,Ea=function(t){void 0===t&&(t=[]),this.segments=t};function La(t,e){return 256*(t=u(Math.floor(t),0,255))+u(Math.floor(e),0,255)}Ea.prototype.prepareSegment=function(t,e,r,n){var i=this.segments[this.segments.length-1];return t>Ea.MAX_VERTEX_ARRAY_LENGTH&&w("Max vertices per segment is "+Ea.MAX_VERTEX_ARRAY_LENGTH+": bucket requested "+t),(!i||i.vertexLength+t>Ea.MAX_VERTEX_ARRAY_LENGTH||i.sortKey!==n)&&(i={vertexOffset:e.length,primitiveOffset:r.length,vertexLength:0,primitiveLength:0},void 0!==n&&(i.sortKey=n),this.segments.push(i)),i},Ea.prototype.get=function(){return this.segments},Ea.prototype.destroy=function(){for(var t=0,e=this.segments;t>>16)*o&65535)<<16)&4294967295)<<15|l>>>17))*s+(((l>>>16)*s&65535)<<16)&4294967295)<<13|i>>>19))+((5*(i>>>16)&65535)<<16)&4294967295))+((58964+(a>>>16)&65535)<<16);switch(l=0,r){case 3:l^=(255&t.charCodeAt(u+2))<<16;case 2:l^=(255&t.charCodeAt(u+1))<<8;case 1:i^=l=(65535&(l=(l=(65535&(l^=255&t.charCodeAt(u)))*o+(((l>>>16)*o&65535)<<16)&4294967295)<<15|l>>>17))*s+(((l>>>16)*s&65535)<<16)&4294967295}return i^=t.length,i=2246822507*(65535&(i^=i>>>16))+((2246822507*(i>>>16)&65535)<<16)&4294967295,i=3266489909*(65535&(i^=i>>>13))+((3266489909*(i>>>16)&65535)<<16)&4294967295,(i^=i>>>16)>>>0}})),Oa=e((function(t){t.exports=function(t,e){for(var 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t.id}))};function Ks(t,e){return t.x===e.x&&(t.x<0||t.x>oo)||t.y===e.y&&(t.y<0||t.y>oo)}Js.prototype.populate=function(t,e,r){this.features=[],this.hasPattern=Ps("fill-extrusion",this.layers,e);for(var n=0,i=t;noo}))||O.every((function(t){return t.y<0}))||O.every((function(t){return t.y>oo}))))for(var v=0,g=0;g=1){var m=d[g-1];if(!Ks(y,m)){f.vertexLength+4>Ea.MAX_VERTEX_ARRAY_LENGTH&&(f=this.segments.prepareSegment(4,this.layoutVertexArray,this.indexArray));var x=y.sub(m)._perp()._unit(),b=m.dist(y);v+b>32768&&(v=0),Xs(this.layoutVertexArray,y.x,y.y,x.x,x.y,0,0,v),Xs(this.layoutVertexArray,y.x,y.y,x.x,x.y,0,1,v),v+=b,Xs(this.layoutVertexArray,m.x,m.y,x.x,x.y,0,0,v),Xs(this.layoutVertexArray,m.x,m.y,x.x,x.y,0,1,v);var 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c=o.vertexLength++;this.e1>=0&&this.e2>=0&&(this.indexArray.emplaceBack(this.e1,this.e2,c),o.primitiveLength++),i?this.e2=c:this.e1=c},ol.prototype.updateScaledDistance=function(){this.scaledDistance=this.totalDistance>0?(this.clipStart+(this.clipEnd-this.clipStart)*this.distance/this.totalDistance)*(al-1):this.distance},ol.prototype.updateDistance=function(t,e){this.distance+=t.dist(e),this.updateScaledDistance()},Qn("LineBucket",ol,{omit:["layers","patternFeatures"]});var sl=new Ui({"line-cap":new Ri(It.layout_line["line-cap"]),"line-join":new Fi(It.layout_line["line-join"]),"line-miter-limit":new Ri(It.layout_line["line-miter-limit"]),"line-round-limit":new Ri(It.layout_line["line-round-limit"]),"line-sort-key":new Fi(It.layout_line["line-sort-key"])}),ll={paint:new Ui({"line-opacity":new Fi(It.paint_line["line-opacity"]),"line-color":new Fi(It.paint_line["line-color"]),"line-translate":new Ri(It.paint_line["line-translate"]),"line-translate-anchor":new 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l=Mo(t,this.paint.get("line-translate"),this.paint.get("line-translate-anchor"),o.angle,s),u=s/2*hl(this.paint.get("line-width").evaluate(e,r),this.paint.get("line-gap-width").evaluate(e,r)),c=this.paint.get("line-offset").evaluate(e,r);return c&&(n=function(t,e){for(var r=[],n=new a(0,0),i=0;i=3)for(var a=0;a0?e+2*t:t}var 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t.sections.forEach((function(t){t.text=function(t,e,r){var 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i=t-1>>1,a=e[i];if(r(n,a)>=0)break;e[t]=a,t=i}e[t]=n},Ou.prototype._down=function(t){for(var e=this.data,r=this.compare,n=this.length>>1,i=e[t];t=0)break;e[t]=o,t=a}e[t]=i};var Fu=Number.POSITIVE_INFINITY;function Bu(t,e){return e[1]!==Fu?function(t,e,r){var n=0,i=0;switch(e=Math.abs(e),r=Math.abs(r),t){case"top-right":case"top-left":case"top":i=r-7;break;case"bottom-right":case"bottom-left":case"bottom":i=7-r}switch(t){case"top-right":case"bottom-right":case"right":n=-e;break;case"top-left":case"bottom-left":case"left":n=e}return[n,i]}(t,e[0],e[1]):function(t,e){var r=0,n=0;e<0&&(e=0);var i=e/Math.sqrt(2);switch(t){case"top-right":case"top-left":n=i-7;break;case"bottom-right":case"bottom-left":n=7-i;break;case"bottom":n=7-e;break;case"top":n=e-7}switch(t){case"top-right":case"bottom-right":r=-i;break;case"top-left":case"bottom-left":r=i;break;case"left":r=e;break;case"right":r=-e}return[r,n]}(t,e[0])}function 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r=0,n=this.symbolInstanceIndexes;r=0&&n.indexOf(t)===r&&e.addIndicesForPlacedSymbol(e.text,t)})),a.verticalPlacedTextSymbolIndex>=0&&this.addIndicesForPlacedSymbol(this.text,a.verticalPlacedTextSymbolIndex),a.placedIconSymbolIndex>=0&&this.addIndicesForPlacedSymbol(this.icon,a.placedIconSymbolIndex),a.verticalPlacedIconSymbolIndex>=0&&this.addIndicesForPlacedSymbol(this.icon,a.verticalPlacedIconSymbolIndex)}this.text.indexBuffer&&this.text.indexBuffer.updateData(this.text.indexArray),this.icon.indexBuffer&&this.icon.indexBuffer.updateData(this.icon.indexArray)}},Qn("SymbolBucket",Ku,{omit:["layers","collisionBoxArray","features","compareText"]}),Ku.MAX_GLYPHS=65535,Ku.addDynamicAttributes=Yu;var $u=new Ui({"symbol-placement":new Ri(It.layout_symbol["symbol-placement"]),"symbol-spacing":new Ri(It.layout_symbol["symbol-spacing"]),"symbol-avoid-edges":new Ri(It.layout_symbol["symbol-avoid-edges"]),"symbol-sort-key":new Fi(It.layout_symbol["symbol-sort-key"]),"symbol-z-order":new Ri(It.layout_symbol["symbol-z-order"]),"icon-allow-overlap":new Ri(It.layout_symbol["icon-allow-overlap"]),"icon-ignore-placement":new Ri(It.layout_symbol["icon-ignore-placement"]),"icon-optional":new Ri(It.layout_symbol["icon-optional"]),"icon-rotation-alignment":new Ri(It.layout_symbol["icon-rotation-alignment"]),"icon-size":new Fi(It.layout_symbol["icon-size"]),"icon-text-fit":new Ri(It.layout_symbol["icon-text-fit"]),"icon-text-fit-padding":new Ri(It.layout_symbol["icon-text-fit-padding"]),"icon-image":new Fi(It.layout_symbol["icon-image"]),"icon-rotate":new Fi(It.layout_symbol["icon-rotate"]),"icon-padding":new Ri(It.layout_symbol["icon-padding"]),"icon-keep-upright":new Ri(It.layout_symbol["icon-keep-upright"]),"icon-offset":new Fi(It.layout_symbol["icon-offset"]),"icon-anchor":new Fi(It.layout_symbol["icon-anchor"]),"icon-pitch-alignment":new Ri(It.layout_symbol["icon-pitch-alignment"]),"text-pitch-alignment":new Ri(It.layout_symbol["text-pitch-alignment"]),"text-rotation-alignment":new Ri(It.layout_symbol["text-rotation-alignment"]),"text-field":new Fi(It.layout_symbol["text-field"]),"text-font":new Fi(It.layout_symbol["text-font"]),"text-size":new Fi(It.layout_symbol["text-size"]),"text-max-width":new Fi(It.layout_symbol["text-max-width"]),"text-line-height":new Ri(It.layout_symbol["text-line-height"]),"text-letter-spacing":new Fi(It.layout_symbol["text-letter-spacing"]),"text-justify":new Fi(It.layout_symbol["text-justify"]),"text-radial-offset":new Fi(It.layout_symbol["text-radial-offset"]),"text-variable-anchor":new Ri(It.layout_symbol["text-variable-anchor"]),"text-anchor":new Fi(It.layout_symbol["text-anchor"]),"text-max-angle":new Ri(It.layout_symbol["text-max-angle"]),"text-writing-mode":new Ri(It.layout_symbol["text-writing-mode"]),"text-rotate":new Fi(It.layout_symbol["text-rotate"]),"text-padding":new Ri(It.layout_symbol["text-padding"]),"text-keep-upright":new Ri(It.layout_symbol["text-keep-upright"]),"text-transform":new Fi(It.layout_symbol["text-transform"]),"text-offset":new Fi(It.layout_symbol["text-offset"]),"text-allow-overlap":new Ri(It.layout_symbol["text-allow-overlap"]),"text-ignore-placement":new Ri(It.layout_symbol["text-ignore-placement"]),"text-optional":new Ri(It.layout_symbol["text-optional"])}),Qu={paint:new Ui({"icon-opacity":new Fi(It.paint_symbol["icon-opacity"]),"icon-color":new Fi(It.paint_symbol["icon-color"]),"icon-halo-color":new Fi(It.paint_symbol["icon-halo-color"]),"icon-halo-width":new Fi(It.paint_symbol["icon-halo-width"]),"icon-halo-blur":new Fi(It.paint_symbol["icon-halo-blur"]),"icon-translate":new Ri(It.paint_symbol["icon-translate"]),"icon-translate-anchor":new Ri(It.paint_symbol["icon-translate-anchor"]),"text-opacity":new Fi(It.paint_symbol["text-opacity"]),"text-color":new Fi(It.paint_symbol["text-color"],{runtimeType:Gt,getOverride:function(t){return t.textColor},hasOverride:function(t){return!!t.textColor}}),"text-halo-color":new Fi(It.paint_symbol["text-halo-color"]),"text-halo-width":new Fi(It.paint_symbol["text-halo-width"]),"text-halo-blur":new Fi(It.paint_symbol["text-halo-blur"]),"text-translate":new Ri(It.paint_symbol["text-translate"]),"text-translate-anchor":new Ri(It.paint_symbol["text-translate-anchor"])}),layout:$u},tc=function(t){this.type=t.property.overrides?t.property.overrides.runtimeType:Ut,this.defaultValue=t};tc.prototype.evaluate=function(t){if(t.formattedSection){var e=this.defaultValue.property.overrides;if(e&&e.hasOverride(t.formattedSection))return e.getOverride(t.formattedSection)}return t.feature&&t.featureState?this.defaultValue.evaluate(t.feature,t.featureState):this.defaultValue.property.specification.default},tc.prototype.eachChild=function(t){this.defaultValue.isConstant()||t(this.defaultValue.value._styleExpression.expression)},tc.prototype.outputDefined=function(){return!1},tc.prototype.serialize=function(){return null},Qn("FormatSectionOverride",tc,{omit:["defaultValue"]});var ec=function(t){function e(e){t.call(this,e,Qu)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype.recalculate=function(e,r){if(t.prototype.recalculate.call(this,e,r),"auto"===this.layout.get("icon-rotation-alignment")&&("point"!==this.layout.get("symbol-placement")?this.layout._values["icon-rotation-alignment"]="map":this.layout._values["icon-rotation-alignment"]="viewport"),"auto"===this.layout.get("text-rotation-alignment")&&("point"!==this.layout.get("symbol-placement")?this.layout._values["text-rotation-alignment"]="map":this.layout._values["text-rotation-alignment"]="viewport"),"auto"===this.layout.get("text-pitch-alignment")&&(this.layout._values["text-pitch-alignment"]=this.layout.get("text-rotation-alignment")),"auto"===this.layout.get("icon-pitch-alignment")&&(this.layout._values["icon-pitch-alignment"]=this.layout.get("icon-rotation-alignment")),"point"===this.layout.get("symbol-placement")){var n=this.layout.get("text-writing-mode");if(n){for(var i=[],a=0,o=n;a",targetMapId:n,sourceMapId:a.mapId})}}},vc.prototype.receive=function(t){var e=t.data,r=e.id;if(r&&(!e.targetMapId||this.mapId===e.targetMapId))if(""===e.type){delete this.tasks[r];var n=this.cancelCallbacks[r];delete this.cancelCallbacks[r],n&&n()}else A()||e.mustQueue?(this.tasks[r]=e,this.taskQueue.push(r),this.invoker.trigger()):this.processTask(r,e)},vc.prototype.process=function(){if(this.taskQueue.length){var t=this.taskQueue.shift(),e=this.tasks[t];delete this.tasks[t],this.taskQueue.length&&this.invoker.trigger(),e&&this.processTask(t,e)}},vc.prototype.processTask=function(t,e){var r=this;if(""===e.type){var n=this.callbacks[t];delete this.callbacks[t],n&&(e.error?n(ii(e.error)):n(null,ii(e.data)))}else{var i=!1,a=E(this.globalScope)?void 0:[],o=e.hasCallback?function(e,n){i=!0,delete r.cancelCallbacks[t],r.target.postMessage({id:t,type:"",sourceMapId:r.mapId,error:e?ni(e):null,data:ni(n,a)},a)}:function(t){i=!0},s=null,l=ii(e.data);if(this.parent[e.type])s=this.parent[e.type](e.sourceMapId,l,o);else if(this.parent.getWorkerSource){var u=e.type.split(".");s=this.parent.getWorkerSource(e.sourceMapId,u[0],l.source)[u[1]](l,o)}else o(new Error("Could not find function "+e.type));!i&&s&&s.cancel&&(this.cancelCallbacks[t]=s.cancel)}},vc.prototype.remove=function(){this.invoker.remove(),this.target.removeEventListener("message",this.receive,!1)};var yc=function(t,e){t&&(e?this.setSouthWest(t).setNorthEast(e):4===t.length?this.setSouthWest([t[0],t[1]]).setNorthEast([t[2],t[3]]):this.setSouthWest(t[0]).setNorthEast(t[1]))};yc.prototype.setNorthEast=function(t){return this._ne=t instanceof xc?new xc(t.lng,t.lat):xc.convert(t),this},yc.prototype.setSouthWest=function(t){return this._sw=t instanceof xc?new xc(t.lng,t.lat):xc.convert(t),this},yc.prototype.extend=function(t){var e,r,n=this._sw,i=this._ne;if(t instanceof xc)e=t,r=t;else{if(!(t instanceof yc)){if(Array.isArray(t)){if(4===t.length||t.every(Array.isArray)){var a=t;return this.extend(yc.convert(a))}var o=t;return this.extend(xc.convert(o))}return this}if(e=t._sw,r=t._ne,!e||!r)return this}return n||i?(n.lng=Math.min(e.lng,n.lng),n.lat=Math.min(e.lat,n.lat),i.lng=Math.max(r.lng,i.lng),i.lat=Math.max(r.lat,i.lat)):(this._sw=new xc(e.lng,e.lat),this._ne=new xc(r.lng,r.lat)),this},yc.prototype.getCenter=function(){return new xc((this._sw.lng+this._ne.lng)/2,(this._sw.lat+this._ne.lat)/2)},yc.prototype.getSouthWest=function(){return this._sw},yc.prototype.getNorthEast=function(){return this._ne},yc.prototype.getNorthWest=function(){return new xc(this.getWest(),this.getNorth())},yc.prototype.getSouthEast=function(){return new xc(this.getEast(),this.getSouth())},yc.prototype.getWest=function(){return this._sw.lng},yc.prototype.getSouth=function(){return this._sw.lat},yc.prototype.getEast=function(){return this._ne.lng},yc.prototype.getNorth=function(){return this._ne.lat},yc.prototype.toArray=function(){return[this._sw.toArray(),this._ne.toArray()]},yc.prototype.toString=function(){return"LngLatBounds("+this._sw.toString()+", "+this._ne.toString()+")"},yc.prototype.isEmpty=function(){return!(this._sw&&this._ne)},yc.prototype.contains=function(t){var e=xc.convert(t),r=e.lng,n=e.lat,i=this._sw.lat<=n&&n<=this._ne.lat,a=this._sw.lng<=r&&r<=this._ne.lng;return this._sw.lng>this._ne.lng&&(a=this._sw.lng>=r&&r>=this._ne.lng),i&&a},yc.convert=function(t){return!t||t instanceof yc?t:new yc(t)};var mc=6371008.8,xc=function(t,e){if(isNaN(t)||isNaN(e))throw new Error("Invalid LngLat object: ("+t+", "+e+")");if(this.lng=+t,this.lat=+e,this.lat>90||this.lat<-90)throw new Error("Invalid LngLat latitude value: must be between -90 and 90")};xc.prototype.wrap=function(){return new xc(c(this.lng,-180,180),this.lat)},xc.prototype.toArray=function(){return[this.lng,this.lat]},xc.prototype.toString=function(){return"LngLat("+this.lng+", "+this.lat+")"},xc.prototype.distanceTo=function(t){var e=Math.PI/180,r=this.lat*e,n=t.lat*e,i=Math.sin(r)*Math.sin(n)+Math.cos(r)*Math.cos(n)*Math.cos((t.lng-this.lng)*e);return mc*Math.acos(Math.min(i,1))},xc.prototype.toBounds=function(t){void 0===t&&(t=0);var e=360*t/40075017,r=e/Math.cos(Math.PI/180*this.lat);return new yc(new xc(this.lng-r,this.lat-e),new xc(this.lng+r,this.lat+e))},xc.convert=function(t){if(t instanceof xc)return t;if(Array.isArray(t)&&(2===t.length||3===t.length))return new xc(Number(t[0]),Number(t[1]));if(!Array.isArray(t)&&"object"==typeof t&&null!==t)return new xc(Number("lng"in t?t.lng:t.lon),Number(t.lat));throw new Error("`LngLatLike` argument must be specified as a LngLat instance, an object {lng: , lat: }, an object {lon: , lat: }, or an array of [, ]")};var bc=2*Math.PI*mc;function _c(t){return bc*Math.cos(t*Math.PI/180)}function wc(t){return(180+t)/360}function Tc(t){return(180-180/Math.PI*Math.log(Math.tan(Math.PI/4+t*Math.PI/360)))/360}function kc(t,e){return t/_c(e)}function Ac(t){var e=180-360*t;return 360/Math.PI*Math.atan(Math.exp(e*Math.PI/180))-90}var Mc=function(t,e,r){void 0===r&&(r=0),this.x=+t,this.y=+e,this.z=+r};Mc.fromLngLat=function(t,e){void 0===e&&(e=0);var r=xc.convert(t);return new Mc(wc(r.lng),Tc(r.lat),kc(e,r.lat))},Mc.prototype.toLngLat=function(){return new xc(360*this.x-180,Ac(this.y))},Mc.prototype.toAltitude=function(){return t=this.z,e=this.y,t*_c(Ac(e));var t,e},Mc.prototype.meterInMercatorCoordinateUnits=function(){return 1/bc*(t=Ac(this.y),1/Math.cos(t*Math.PI/180));var t};var Sc=function(t,e,r){this.z=t,this.x=e,this.y=r,this.key=Cc(0,t,t,e,r)};Sc.prototype.equals=function(t){return this.z===t.z&&this.x===t.x&&this.y===t.y},Sc.prototype.url=function(t,e){var r,n,i,a,o,s=(r=this.x,n=this.y,i=this.z,a=gc(256*r,256*(n=Math.pow(2,i)-n-1),i),o=gc(256*(r+1),256*(n+1),i),a[0]+","+a[1]+","+o[0]+","+o[1]),l=function(t,e,r){for(var n,i="",a=t;a>0;a--)i+=(e&(n=1<this.canonical.z?new Lc(t,this.wrap,this.canonical.z,this.canonical.x,this.canonical.y):new Lc(t,this.wrap,t,this.canonical.x>>e,this.canonical.y>>e)},Lc.prototype.calculateScaledKey=function(t,e){var r=this.canonical.z-t;return t>this.canonical.z?Cc(this.wrap*+e,t,this.canonical.z,this.canonical.x,this.canonical.y):Cc(this.wrap*+e,t,t,this.canonical.x>>r,this.canonical.y>>r)},Lc.prototype.isChildOf=function(t){if(t.wrap!==this.wrap)return!1;var e=this.canonical.z-t.canonical.z;return 0===t.overscaledZ||t.overscaledZ>e&&t.canonical.y===this.canonical.y>>e},Lc.prototype.children=function(t){if(this.overscaledZ>=t)return[new Lc(this.overscaledZ+1,this.wrap,this.canonical.z,this.canonical.x,this.canonical.y)];var e=this.canonical.z+1,r=2*this.canonical.x,n=2*this.canonical.y;return[new Lc(e,this.wrap,e,r,n),new Lc(e,this.wrap,e,r+1,n),new Lc(e,this.wrap,e,r,n+1),new Lc(e,this.wrap,e,r+1,n+1)]},Lc.prototype.isLessThan=function(t){return this.wrapt.wrap)&&(this.overscaledZt.overscaledZ)&&(this.canonical.xt.canonical.x)&&this.canonical.y=this.dim+1||e<-1||e>=this.dim+1)throw new RangeError("out of range source coordinates for DEM data");return(e+1)*this.stride+(t+1)},Pc.prototype._unpackMapbox=function(t,e,r){return(256*t*256+256*e+r)/10-1e4},Pc.prototype._unpackTerrarium=function(t,e,r){return 256*t+e+r/256-32768},Pc.prototype.getPixels=function(){return new qo({width:this.stride,height:this.stride},new Uint8Array(this.data.buffer))},Pc.prototype.backfillBorder=function(t,e,r){if(this.dim!==t.dim)throw new Error("dem dimension mismatch");var n=e*this.dim,i=e*this.dim+this.dim,a=r*this.dim,o=r*this.dim+this.dim;switch(e){case-1:n=i-1;break;case 1:i=n+1}switch(r){case-1:a=o-1;break;case 1:o=a+1}for(var s=-e*this.dim,l=-r*this.dim,u=a;u=0&&c[3]>=0&&s.insert(o,c[0],c[1],c[2],c[3])}},Rc.prototype.loadVTLayers=function(){return this.vtLayers||(this.vtLayers=new Zs.VectorTile(new Tl(this.rawTileData)).layers,this.sourceLayerCoder=new Oc(this.vtLayers?Object.keys(this.vtLayers).sort():["_geojsonTileLayer"])),this.vtLayers},Rc.prototype.query=function(t,e,r,n){var i=this;this.loadVTLayers();for(var o=t.params||{},s=oo/t.tileSize/t.scale,l=xn(o.filter),u=t.queryGeometry,c=t.queryPadding*s,f=Bc(u),h=this.grid.query(f.minX-c,f.minY-c,f.maxX+c,f.maxY+c),p=Bc(t.cameraQueryGeometry),d=0,v=this.grid3D.query(p.minX-c,p.minY-c,p.maxX+c,p.maxY+c,(function(e,r,n,i){return function(t,e,r,n,i){for(var o=0,s=t;o=l.x&&i>=l.y)return!0}var u=[new a(e,r),new a(e,i),new a(n,i),new a(n,r)];if(t.length>2)for(var c=0,f=u;c=0)return!0;return!1}(a,f)){var h=this.sourceLayerCoder.decode(r),p=this.vtLayers[h].feature(n);if(i.filter(new Si(this.tileID.overscaledZ),p))for(var d=this.getId(p,h),v=0;vn)i=!1;else if(e)if(this.expirationTimect&&(t.getActor().send("enforceCacheSizeLimit",ut),gt=0)},t.clamp=u,t.clearTileCache=function(t){var e=self.caches.delete(lt);t&&e.catch(t).then((function(){return t()}))},t.clipLine=Au,t.clone=function(t){var e=new Lo(16);return e[0]=t[0],e[1]=t[1],e[2]=t[2],e[3]=t[3],e[4]=t[4],e[5]=t[5],e[6]=t[6],e[7]=t[7],e[8]=t[8],e[9]=t[9],e[10]=t[10],e[11]=t[11],e[12]=t[12],e[13]=t[13],e[14]=t[14],e[15]=t[15],e},t.clone$1=b,t.clone$2=function(t){var e=new Lo(3);return e[0]=t[0],e[1]=t[1],e[2]=t[2],e},t.collisionCircleLayout=yl,t.config=B,t.create=function(){var t=new Lo(16);return Lo!=Float32Array&&(t[1]=0,t[2]=0,t[3]=0,t[4]=0,t[6]=0,t[7]=0,t[8]=0,t[9]=0,t[11]=0,t[12]=0,t[13]=0,t[14]=0),t[0]=1,t[5]=1,t[10]=1,t[15]=1,t},t.create$1=function(){var t=new Lo(9);return Lo!=Float32Array&&(t[1]=0,t[2]=0,t[3]=0,t[5]=0,t[6]=0,t[7]=0),t[0]=1,t[4]=1,t[8]=1,t},t.create$2=function(){var t=new Lo(4);return Lo!=Float32Array&&(t[1]=0,t[2]=0),t[0]=1,t[3]=1,t},t.createCommonjsModule=e,t.createExpression=an,t.createLayout=Yi,t.createStyleLayer=function(t){return"custom"===t.type?new oc(t):new sc[t.type](t)},t.cross=function(t,e,r){var n=e[0],i=e[1],a=e[2],o=r[0],s=r[1],l=r[2];return t[0]=i*l-a*s,t[1]=a*o-n*l,t[2]=n*s-i*o,t},t.deepEqual=function t(e,r){if(Array.isArray(e)){if(!Array.isArray(r)||e.length!==r.length)return!1;for(var n=0;n0&&(a=1/Math.sqrt(a)),t[0]=e[0]*a,t[1]=e[1]*a,t[2]=e[2]*a,t},t.number=Ke,t.offscreenCanvasSupported=yt,t.ortho=function(t,e,r,n,i,a,o){var s=1/(e-r),l=1/(n-i),u=1/(a-o);return t[0]=-2*s,t[1]=0,t[2]=0,t[3]=0,t[4]=0,t[5]=-2*l,t[6]=0,t[7]=0,t[8]=0,t[9]=0,t[10]=2*u,t[11]=0,t[12]=(e+r)*s,t[13]=(i+n)*l,t[14]=(o+a)*u,t[15]=1,t},t.parseGlyphPBF=function(t){return new Tl(t).readFields(Hl,[])},t.pbf=Tl,t.performSymbolLayout=function(t,e,r,n,i,a,o){t.createArrays();var s=512*t.overscaling;t.tilePixelRatio=oo/s,t.compareText={},t.iconsNeedLinear=!1;var l=t.layers[0].layout,u=t.layers[0]._unevaluatedLayout._values,c={};if("composite"===t.textSizeData.kind){var f=t.textSizeData,h=f.minZoom,p=f.maxZoom;c.compositeTextSizes=[u["text-size"].possiblyEvaluate(new Si(h),o),u["text-size"].possiblyEvaluate(new Si(p),o)]}if("composite"===t.iconSizeData.kind){var d=t.iconSizeData,v=d.minZoom,g=d.maxZoom;c.compositeIconSizes=[u["icon-size"].possiblyEvaluate(new Si(v),o),u["icon-size"].possiblyEvaluate(new Si(g),o)]}c.layoutTextSize=u["text-size"].possiblyEvaluate(new Si(t.zoom+1),o),c.layoutIconSize=u["icon-size"].possiblyEvaluate(new Si(t.zoom+1),o),c.textMaxSize=u["text-size"].possiblyEvaluate(new Si(18));for(var y=l.get("text-line-height")*bl,m="map"===l.get("text-rotation-alignment")&&"point"!==l.get("symbol-placement"),x=l.get("text-keep-upright"),b=l.get("text-size"),_=function(){var a=k[T],s=l.get("text-font").evaluate(a,{},o).join(","),u=b.evaluate(a,{},o),f=c.layoutTextSize.evaluate(a,{},o),h=c.layoutIconSize.evaluate(a,{},o),p={horizontal:{},vertical:void 0},d=a.text,v=[0,0];if(d){var g=d.toString(),_=l.get("text-letter-spacing").evaluate(a,{},o)*bl,A=function(t){for(var e=0,r=t;e=oo||f.y<0||f.y>=oo||function(t,e,r,n,i,a,o,s,l,u,c,f,h,p,d,v,g,y,m,x,b,_,T,k,A){var M,S,E,L,C,P=t.addToLineVertexArray(e,r),O=0,I=0,D=0,z=0,R=-1,F=-1,B={},N=Ia(""),j=0,U=0;if(void 0===s._unevaluatedLayout.getValue("text-radial-offset")?(j=(M=s.layout.get("text-offset").evaluate(b,{},k).map((function(t){return t*bl})))[0],U=M[1]):(j=s.layout.get("text-radial-offset").evaluate(b,{},k)*bl,U=Fu),t.allowVerticalPlacement&&n.vertical){var V=s.layout.get("text-rotate").evaluate(b,{},k)+90,H=n.vertical;L=new Pu(l,e,u,c,f,H,h,p,d,V),o&&(C=new Pu(l,e,u,c,f,o,g,y,d,V))}if(i){var q=s.layout.get("icon-rotate").evaluate(b,{}),G="none"!==s.layout.get("icon-text-fit"),Z=Mu(i,q,T,G),Y=o?Mu(o,q,T,G):void 0;E=new Pu(l,e,u,c,f,i,g,y,!1,q),O=4*Z.length;var W=t.iconSizeData,X=null;"source"===W.kind?(X=[pu*s.layout.get("icon-size").evaluate(b,{})])[0]>ju&&w(t.layerIds[0]+': Value for "icon-size" is >= '+'255. 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r=this.loading,n=t.uid;r&&r[n]&&r[n].abort&&(r[n].abort(),delete r[n]),e()},l.prototype.removeTile=function(t,e){var r=this.loaded,n=t.uid;r&&r[n]&&delete r[n],e()};var u=t.window.ImageBitmap,c=function(){this.loaded={}};c.prototype.loadTile=function(e,r){var n=e.uid,i=e.encoding,a=e.rawImageData,o=u&&a instanceof u?this.getImageData(a):a,s=new t.DEMData(n,o,i);this.loaded=this.loaded||{},this.loaded[n]=s,r(null,s)},c.prototype.getImageData=function(e){this.offscreenCanvas&&this.offscreenCanvasContext||(this.offscreenCanvas=new OffscreenCanvas(e.width,e.height),this.offscreenCanvasContext=this.offscreenCanvas.getContext("2d")),this.offscreenCanvas.width=e.width,this.offscreenCanvas.height=e.height,this.offscreenCanvasContext.drawImage(e,0,0,e.width,e.height);var r=this.offscreenCanvasContext.getImageData(-1,-1,e.width+2,e.height+2);return this.offscreenCanvasContext.clearRect(0,0,this.offscreenCanvas.width,this.offscreenCanvas.height),new 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r(t,r,n,i){e.call(this,t,r,n,At),i&&(this.loadGeoJSON=i)}return e&&(r.__proto__=e),r.prototype=Object.create(e&&e.prototype),r.prototype.constructor=r,r.prototype.loadData=function(t,e){this._pendingCallback&&this._pendingCallback(null,{abandoned:!0}),this._pendingCallback=e,this._pendingLoadDataParams=t,this._state&&"Idle"!==this._state?this._state="NeedsLoadData":(this._state="Coalescing",this._loadData())},r.prototype._loadData=function(){var e=this;if(this._pendingCallback&&this._pendingLoadDataParams){var r=this._pendingCallback,n=this._pendingLoadDataParams;delete this._pendingCallback,delete this._pendingLoadDataParams;var i=!!(n&&n.request&&n.request.collectResourceTiming)&&new t.RequestPerformance(n.request);this.loadGeoJSON(n,(function(a,o){if(a||!o)return r(a);if("object"!=typeof o)return r(new Error("Input data given to '"+n.source+"' is not a valid GeoJSON object."));f(o,!0);try{e._geoJSONIndex=n.cluster?new V(function(e){var r=e.superclusterOptions,n=e.clusterProperties;if(!n||!r)return r;for(var i={},a={},o={accumulated:null,zoom:0},s={properties:null},l=Object.keys(n),u=0,c=l;u=0?0:e.button},r.remove=function(t){t.parentNode&&t.parentNode.removeChild(t)};var h=function(e){function r(){e.call(this),this.images={},this.updatedImages={},this.callbackDispatchedThisFrame={},this.loaded=!1,this.requestors=[],this.patterns={},this.atlasImage=new t.RGBAImage({width:1,height:1}),this.dirty=!0}return e&&(r.__proto__=e),r.prototype=Object.create(e&&e.prototype),r.prototype.constructor=r,r.prototype.isLoaded=function(){return this.loaded},r.prototype.setLoaded=function(t){if(this.loaded!==t&&(this.loaded=t,t)){for(var e=0,r=this.requestors;e=0?1.2:1))}function y(t,e,r,n,i,a,o){for(var s=0;s65535)e(new Error("glyphs > 65535 not supported"));else if(a.ranges[s])e(null,{stack:r,id:i,glyph:o});else{var l=a.requests[s];l||(l=a.requests[s]=[],x.loadGlyphRange(r,s,n.url,n.requestManager,(function(t,e){if(e){for(var r in e)n._doesCharSupportLocalGlyph(+r)||(a.glyphs[+r]=e[+r]);a.ranges[s]=!0}for(var i=0,o=l;i1&&(l=t[++s]);var c=Math.abs(u-l.left),f=Math.abs(u-l.right),h=Math.min(c,f),p=void 0,d=i/r*(n+1);if(l.isDash){var v=n-Math.abs(d);p=Math.sqrt(h*h+v*v)}else p=n-Math.sqrt(h*h+d*d);this.data[o+u]=Math.max(0,Math.min(255,p+128))}},k.prototype.addRegularDash=function(t){for(var e=t.length-1;e>=0;--e){var r=t[e],n=t[e+1];r.zeroLength?t.splice(e,1):n&&n.isDash===r.isDash&&(n.left=r.left,t.splice(e,1))}var i=t[0],a=t[t.length-1];i.isDash===a.isDash&&(i.left=a.left-this.width,a.right=i.right+this.width);for(var o=this.width*this.nextRow,s=0,l=t[s],u=0;u1&&(l=t[++s]);var c=Math.abs(u-l.left),f=Math.abs(u-l.right),h=Math.min(c,f),p=l.isDash?h:-h;this.data[o+u]=Math.max(0,Math.min(255,p+128))}},k.prototype.addDash=function(e,r){var n=r?7:0,i=2*n+1;if(this.nextRow+i>this.height)return t.warnOnce("LineAtlas out of space"),null;for(var a=0,o=0;o=n&&e.x=i&&e.y0&&(l[new t.OverscaledTileID(e.overscaledZ,a,r.z,i,r.y-1).key]={backfilled:!1},l[new t.OverscaledTileID(e.overscaledZ,e.wrap,r.z,r.x,r.y-1).key]={backfilled:!1},l[new t.OverscaledTileID(e.overscaledZ,s,r.z,o,r.y-1).key]={backfilled:!1}),r.y+10&&(n.resourceTiming=e._resourceTiming,e._resourceTiming=[]),e.fire(new t.Event("data",n))}}))},r.prototype.onAdd=function(t){this.map=t,this.load()},r.prototype.setData=function(e){var r=this;return this._data=e,this.fire(new t.Event("dataloading",{dataType:"source"})),this._updateWorkerData((function(e){if(e)r.fire(new t.ErrorEvent(e));else{var n={dataType:"source",sourceDataType:"content"};r._collectResourceTiming&&r._resourceTiming&&r._resourceTiming.length>0&&(n.resourceTiming=r._resourceTiming,r._resourceTiming=[]),r.fire(new t.Event("data",n))}})),this},r.prototype.getClusterExpansionZoom=function(t,e){return this.actor.send("geojson.getClusterExpansionZoom",{clusterId:t,source:this.id},e),this},r.prototype.getClusterChildren=function(t,e){return this.actor.send("geojson.getClusterChildren",{clusterId:t,source:this.id},e),this},r.prototype.getClusterLeaves=function(t,e,r,n){return this.actor.send("geojson.getClusterLeaves",{source:this.id,clusterId:t,limit:e,offset:r},n),this},r.prototype._updateWorkerData=function(e){var r=this;this._loaded=!1;var n=t.extend({},this.workerOptions),i=this._data;"string"==typeof i?(n.request=this.map._requestManager.transformRequest(t.browser.resolveURL(i),t.ResourceType.Source),n.request.collectResourceTiming=this._collectResourceTiming):n.data=JSON.stringify(i),this.actor.send(this.type+".loadData",n,(function(t,i){r._removed||i&&i.abandoned||(r._loaded=!0,i&&i.resourceTiming&&i.resourceTiming[r.id]&&(r._resourceTiming=i.resourceTiming[r.id].slice(0)),r.actor.send(r.type+".coalesce",{source:n.source},null),e(t))}))},r.prototype.loaded=function(){return this._loaded},r.prototype.loadTile=function(e,r){var n=this,i=e.actor?"reloadTile":"loadTile";e.actor=this.actor;var a={type:this.type,uid:e.uid,tileID:e.tileID,zoom:e.tileID.overscaledZ,maxZoom:this.maxzoom,tileSize:this.tileSize,source:this.id,pixelRatio:t.browser.devicePixelRatio,showCollisionBoxes:this.map.showCollisionBoxes,promoteId:this.promoteId};e.request=this.actor.send(i,a,(function(t,a){return delete e.request,e.unloadVectorData(),e.aborted?r(null):t?r(t):(e.loadVectorData(a,n.map.painter,"reloadTile"===i),r(null))}))},r.prototype.abortTile=function(t){t.request&&(t.request.cancel(),delete t.request),t.aborted=!0},r.prototype.unloadTile=function(t){t.unloadVectorData(),this.actor.send("removeTile",{uid:t.uid,type:this.type,source:this.id})},r.prototype.onRemove=function(){this._removed=!0,this.actor.send("removeSource",{type:this.type,source:this.id})},r.prototype.serialize=function(){return t.extend({},this._options,{type:this.type,data:this._data})},r.prototype.hasTransition=function(){return!1},r}(t.Evented),O=t.createLayout([{name:"a_pos",type:"Int16",components:2},{name:"a_texture_pos",type:"Int16",components:2}]),I=function(e){function r(t,r,n,i){e.call(this),this.id=t,this.dispatcher=n,this.coordinates=r.coordinates,this.type="image",this.minzoom=0,this.maxzoom=22,this.tileSize=512,this.tiles={},this._loaded=!1,this.setEventedParent(i),this.options=r}return e&&(r.__proto__=e),r.prototype=Object.create(e&&e.prototype),r.prototype.constructor=r,r.prototype.load=function(e,r){var n=this;this._loaded=!1,this.fire(new t.Event("dataloading",{dataType:"source"})),this.url=this.options.url,t.getImage(this.map._requestManager.transformRequest(this.url,t.ResourceType.Image),(function(i,a){n._loaded=!0,i?n.fire(new t.ErrorEvent(i)):a&&(n.image=a,e&&(n.coordinates=e),r&&r(),n._finishLoading())}))},r.prototype.loaded=function(){return this._loaded},r.prototype.updateImage=function(t){var e=this;return this.image&&t.url?(this.options.url=t.url,this.load(t.coordinates,(function(){e.texture=null})),this):this},r.prototype._finishLoading=function(){this.map&&(this.setCoordinates(this.coordinates),this.fire(new t.Event("data",{dataType:"source",sourceDataType:"metadata"})))},r.prototype.onAdd=function(t){this.map=t,this.load()},r.prototype.setCoordinates=function(e){var r=this;this.coordinates=e;var n=e.map(t.MercatorCoordinate.fromLngLat);this.tileID=function(e){for(var r=1/0,n=1/0,i=-1/0,a=-1/0,o=0,s=e;or.end(0)?this.fire(new t.ErrorEvent(new t.ValidationError("sources."+this.id,null,"Playback for this video can be set only between the "+r.start(0)+" and "+r.end(0)+"-second mark."))):this.video.currentTime=e}},r.prototype.getVideo=function(){return this.video},r.prototype.onAdd=function(t){this.map||(this.map=t,this.load(),this.video&&(this.video.play(),this.setCoordinates(this.coordinates)))},r.prototype.prepare=function(){if(!(0===Object.keys(this.tiles).length||this.video.readyState<2)){var e=this.map.painter.context,r=e.gl;for(var n in this.boundsBuffer||(this.boundsBuffer=e.createVertexBuffer(this._boundsArray,O.members)),this.boundsSegments||(this.boundsSegments=t.SegmentVector.simpleSegment(0,0,4,2)),this.texture?this.video.paused||(this.texture.bind(r.LINEAR,r.CLAMP_TO_EDGE),r.texSubImage2D(r.TEXTURE_2D,0,0,0,r.RGBA,r.UNSIGNED_BYTE,this.video)):(this.texture=new t.Texture(e,this.video,r.RGBA),this.texture.bind(r.LINEAR,r.CLAMP_TO_EDGE)),this.tiles){var i=this.tiles[n];"loaded"!==i.state&&(i.state="loaded",i.texture=this.texture)}}},r.prototype.serialize=function(){return{type:"video",urls:this.urls,coordinates:this.coordinates}},r.prototype.hasTransition=function(){return this.video&&!this.video.paused},r}(I),z=function(e){function r(r,n,i,a){e.call(this,r,n,i,a),n.coordinates?Array.isArray(n.coordinates)&&4===n.coordinates.length&&!n.coordinates.some((function(t){return!Array.isArray(t)||2!==t.length||t.some((function(t){return"number"!=typeof t}))}))||this.fire(new t.ErrorEvent(new t.ValidationError("sources."+r,null,'"coordinates" property must be an array of 4 longitude/latitude array pairs'))):this.fire(new t.ErrorEvent(new t.ValidationError("sources."+r,null,'missing required property "coordinates"'))),n.animate&&"boolean"!=typeof n.animate&&this.fire(new t.ErrorEvent(new t.ValidationError("sources."+r,null,'optional "animate" property must be a boolean value'))),n.canvas?"string"==typeof n.canvas||n.canvas instanceof t.window.HTMLCanvasElement||this.fire(new t.ErrorEvent(new t.ValidationError("sources."+r,null,'"canvas" must be either a string representing the ID of the canvas element from which to read, or an HTMLCanvasElement instance'))):this.fire(new t.ErrorEvent(new t.ValidationError("sources."+r,null,'missing required property "canvas"'))),this.options=n,this.animate=void 0===n.animate||n.animate}return e&&(r.__proto__=e),r.prototype=Object.create(e&&e.prototype),r.prototype.constructor=r,r.prototype.load=function(){this._loaded=!0,this.canvas||(this.canvas=this.options.canvas instanceof t.window.HTMLCanvasElement?this.options.canvas:t.window.document.getElementById(this.options.canvas)),this.width=this.canvas.width,this.height=this.canvas.height,this._hasInvalidDimensions()?this.fire(new t.ErrorEvent(new Error("Canvas dimensions cannot be less than or equal to zero."))):(this.play=function(){this._playing=!0,this.map.triggerRepaint()},this.pause=function(){this._playing&&(this.prepare(),this._playing=!1)},this._finishLoading())},r.prototype.getCanvas=function(){return this.canvas},r.prototype.onAdd=function(t){this.map=t,this.load(),this.canvas&&this.animate&&this.play()},r.prototype.onRemove=function(){this.pause()},r.prototype.prepare=function(){var e=!1;if(this.canvas.width!==this.width&&(this.width=this.canvas.width,e=!0),this.canvas.height!==this.height&&(this.height=this.canvas.height,e=!0),!this._hasInvalidDimensions()&&0!==Object.keys(this.tiles).length){var r=this.map.painter.context,n=r.gl;for(var i in this.boundsBuffer||(this.boundsBuffer=r.createVertexBuffer(this._boundsArray,O.members)),this.boundsSegments||(this.boundsSegments=t.SegmentVector.simpleSegment(0,0,4,2)),this.texture?(e||this._playing)&&this.texture.update(this.canvas,{premultiply:!0}):this.texture=new t.Texture(r,this.canvas,n.RGBA,{premultiply:!0}),this.tiles){var a=this.tiles[i];"loaded"!==a.state&&(a.state="loaded",a.texture=this.texture)}}},r.prototype.serialize=function(){return{type:"canvas",coordinates:this.coordinates}},r.prototype.hasTransition=function(){return this._playing},r.prototype._hasInvalidDimensions=function(){for(var t=0,e=[this.canvas.width,this.canvas.height];tthis.max){var o=this._getAndRemoveByKey(this.order[0]);o&&this.onRemove(o)}return this},j.prototype.has=function(t){return t.wrapped().key in this.data},j.prototype.getAndRemove=function(t){return this.has(t)?this._getAndRemoveByKey(t.wrapped().key):null},j.prototype._getAndRemoveByKey=function(t){var e=this.data[t].shift();return e.timeout&&clearTimeout(e.timeout),0===this.data[t].length&&delete this.data[t],this.order.splice(this.order.indexOf(t),1),e.value},j.prototype.getByKey=function(t){var e=this.data[t];return e?e[0].value:null},j.prototype.get=function(t){return this.has(t)?this.data[t.wrapped().key][0].value:null},j.prototype.remove=function(t,e){if(!this.has(t))return this;var r=t.wrapped().key,n=void 0===e?0:this.data[r].indexOf(e),i=this.data[r][n];return this.data[r].splice(n,1),i.timeout&&clearTimeout(i.timeout),0===this.data[r].length&&delete this.data[r],this.onRemove(i.value),this.order.splice(this.order.indexOf(r),1),this},j.prototype.setMaxSize=function(t){for(this.max=t;this.order.length>this.max;){var e=this._getAndRemoveByKey(this.order[0]);e&&this.onRemove(e)}return this},j.prototype.filter=function(t){var e=[];for(var r in this.data)for(var n=0,i=this.data[r];n1||(Math.abs(r)>1&&(1===Math.abs(r+i)?r+=i:1===Math.abs(r-i)&&(r-=i)),e.dem&&t.dem&&(t.dem.backfillBorder(e.dem,r,n),t.neighboringTiles&&t.neighboringTiles[a]&&(t.neighboringTiles[a].backfilled=!0)))}},r.prototype.getTile=function(t){return this.getTileByID(t.key)},r.prototype.getTileByID=function(t){return this._tiles[t]},r.prototype._retainLoadedChildren=function(t,e,r,n){for(var i in this._tiles){var a=this._tiles[i];if(!(n[i]||!a.hasData()||a.tileID.overscaledZ<=e||a.tileID.overscaledZ>r)){for(var o=a.tileID;a&&a.tileID.overscaledZ>e+1;){var s=a.tileID.scaledTo(a.tileID.overscaledZ-1);(a=this._tiles[s.key])&&a.hasData()&&(o=s)}for(var l=o;l.overscaledZ>e;)if(t[(l=l.scaledTo(l.overscaledZ-1)).key]){n[o.key]=o;break}}}},r.prototype.findLoadedParent=function(t,e){if(t.key in this._loadedParentTiles){var r=this._loadedParentTiles[t.key];return r&&r.tileID.overscaledZ>=e?r:null}for(var n=t.overscaledZ-1;n>=e;n--){var i=t.scaledTo(n),a=this._getLoadedTile(i);if(a)return a}},r.prototype._getLoadedTile=function(t){var e=this._tiles[t.key];return e&&e.hasData()?e:this._cache.getByKey(t.wrapped().key)},r.prototype.updateCacheSize=function(t){var e=(Math.ceil(t.width/this._source.tileSize)+1)*(Math.ceil(t.height/this._source.tileSize)+1),r=Math.floor(5*e),n="number"==typeof this._maxTileCacheSize?Math.min(this._maxTileCacheSize,r):r;this._cache.setMaxSize(n)},r.prototype.handleWrapJump=function(t){var e=(t-(void 0===this._prevLng?t:this._prevLng))/360,r=Math.round(e);if(this._prevLng=t,r){var n={};for(var i in this._tiles){var a=this._tiles[i];a.tileID=a.tileID.unwrapTo(a.tileID.wrap+r),n[a.tileID.key]=a}for(var o in this._tiles=n,this._timers)clearTimeout(this._timers[o]),delete this._timers[o];for(var s in this._tiles){var l=this._tiles[s];this._setTileReloadTimer(s,l)}}},r.prototype.update=function(e){var n=this;if(this.transform=e,this._sourceLoaded&&!this._paused){var i;this.updateCacheSize(e),this.handleWrapJump(this.transform.center.lng),this._coveredTiles={},this.used?this._source.tileID?i=e.getVisibleUnwrappedCoordinates(this._source.tileID).map((function(e){return new t.OverscaledTileID(e.canonical.z,e.wrap,e.canonical.z,e.canonical.x,e.canonical.y)})):(i=e.coveringTiles({tileSize:this._source.tileSize,minzoom:this._source.minzoom,maxzoom:this._source.maxzoom,roundZoom:this._source.roundZoom,reparseOverscaled:this._source.reparseOverscaled}),this._source.hasTile&&(i=i.filter((function(t){return n._source.hasTile(t)})))):i=[];var a=e.coveringZoomLevel(this._source),o=Math.max(a-r.maxOverzooming,this._source.minzoom),s=Math.max(a+r.maxUnderzooming,this._source.minzoom),l=this._updateRetainedTiles(i,a);if(Dt(this._source.type)){for(var u={},c={},f=0,h=Object.keys(l);fthis._source.maxzoom){var g=d.children(this._source.maxzoom)[0],y=this.getTile(g);if(y&&y.hasData()){n[g.key]=g;continue}}else{var m=d.children(this._source.maxzoom);if(n[m[0].key]&&n[m[1].key]&&n[m[2].key]&&n[m[3].key])continue}for(var x=v.wasRequested(),b=d.overscaledZ-1;b>=a;--b){var _=d.scaledTo(b);if(i[_.key])break;if(i[_.key]=!0,!(v=this.getTile(_))&&x&&(v=this._addTile(_)),v&&(n[_.key]=_,x=v.wasRequested(),v.hasData()))break}}}return n},r.prototype._updateLoadedParentTileCache=function(){for(var t in this._loadedParentTiles={},this._tiles){for(var e=[],r=void 0,n=this._tiles[t].tileID;n.overscaledZ>0;){if(n.key in this._loadedParentTiles){r=this._loadedParentTiles[n.key];break}e.push(n.key);var i=n.scaledTo(n.overscaledZ-1);if(r=this._getLoadedTile(i))break;n=i}for(var a=0,o=e;a0||(e.hasData()&&"reloading"!==e.state?this._cache.add(e.tileID,e,e.getExpiryTimeout()):(e.aborted=!0,this._abortTile(e),this._unloadTile(e))))},r.prototype.clearTiles=function(){for(var t in this._shouldReloadOnResume=!1,this._paused=!1,this._tiles)this._removeTile(t);this._cache.reset()},r.prototype.tilesIn=function(e,r,n){var i=this,a=[],o=this.transform;if(!o)return a;for(var s=n?o.getCameraQueryGeometry(e):e,l=e.map((function(t){return o.pointCoordinate(t)})),u=s.map((function(t){return o.pointCoordinate(t)})),c=this.getIds(),f=1/0,h=1/0,p=-1/0,d=-1/0,v=0,g=u;v=0&&y[1].y+g>=0){var m=l.map((function(t){return s.getTilePoint(t)})),x=u.map((function(t){return s.getTilePoint(t)}));a.push({tile:n,tileID:s,queryGeometry:m,cameraQueryGeometry:x,scale:v})}}},x=0;x=t.browser.now())return!0}return!1},r.prototype.setFeatureState=function(t,e,r){t=t||"_geojsonTileLayer",this._state.updateState(t,e,r)},r.prototype.removeFeatureState=function(t,e,r){t=t||"_geojsonTileLayer",this._state.removeFeatureState(t,e,r)},r.prototype.getFeatureState=function(t,e){return t=t||"_geojsonTileLayer",this._state.getState(t,e)},r.prototype.setDependencies=function(t,e,r){var n=this._tiles[t];n&&n.setDependencies(e,r)},r.prototype.reloadTilesForDependencies=function(t,e){for(var r in this._tiles)this._tiles[r].hasDependency(t,e)&&this._reloadTile(r,"reloading");this._cache.filter((function(r){return!r.hasDependency(t,e)}))},r}(t.Evented);function It(t,e){var r=Math.abs(2*t.wrap)-+(t.wrap<0),n=Math.abs(2*e.wrap)-+(e.wrap<0);return t.overscaledZ-e.overscaledZ||n-r||e.canonical.y-t.canonical.y||e.canonical.x-t.canonical.x}function Dt(t){return"raster"===t||"image"===t||"video"===t}function zt(){return new t.window.Worker(ta.workerUrl)}Ot.maxOverzooming=10,Ot.maxUnderzooming=3;var Rt="mapboxgl_preloaded_worker_pool",Ft=function(){this.active={}};Ft.prototype.acquire=function(t){if(!this.workers)for(this.workers=[];this.workers.length0?(i-o)/s:0;return this.points[a].mult(1-l).add(this.points[r].mult(l))};var Qt=function(t,e,r){var n=this.boxCells=[],i=this.circleCells=[];this.xCellCount=Math.ceil(t/r),this.yCellCount=Math.ceil(e/r);for(var a=0;a=-e[0]&&r<=e[0]&&n>=-e[1]&&n<=e[1]}function ae(e,r,n,i,a,o,s,l){var u=i?e.textSizeData:e.iconSizeData,c=t.evaluateSizeForZoom(u,n.transform.zoom),f=[256/n.width*2+1,256/n.height*2+1],h=i?e.text.dynamicLayoutVertexArray:e.icon.dynamicLayoutVertexArray;h.clear();for(var p=e.lineVertexArray,d=i?e.text.placedSymbolArray:e.icon.placedSymbolArray,v=n.transform.width/n.transform.height,g=!1,y=0;yMath.abs(n.x-r.x)*i?{useVertical:!0}:(e===t.WritingMode.vertical?r.yn.x)?{needsFlipping:!0}:null}function le(e,r,n,i,a,o,s,l,u,c,f,h,p,d){var v,g=r/24,y=e.lineOffsetX*g,m=e.lineOffsetY*g;if(e.numGlyphs>1){var x=e.glyphStartIndex+e.numGlyphs,b=e.lineStartIndex,_=e.lineStartIndex+e.lineLength,w=oe(g,l,y,m,n,f,h,e,u,o,p);if(!w)return{notEnoughRoom:!0};var T=re(w.first.point,s).point,k=re(w.last.point,s).point;if(i&&!n){var A=se(e.writingMode,T,k,d);if(A)return A}v=[w.first];for(var M=e.glyphStartIndex+1;M0?C.point:ue(h,L,S,1,a),O=se(e.writingMode,S,P,d);if(O)return O}var I=ce(g*l.getoffsetX(e.glyphStartIndex),y,m,n,f,h,e.segment,e.lineStartIndex,e.lineStartIndex+e.lineLength,u,o,p);if(!I)return{notEnoughRoom:!0};v=[I]}for(var D=0,z=v;D0?1:-1,v=0;i&&(d*=-1,v=Math.PI),d<0&&(v+=Math.PI);for(var g=d>0?l+s:l+s+1,y=a,m=a,x=0,b=0,_=Math.abs(p),w=[];x+b<=_;){if((g+=d)=u)return null;if(m=y,w.push(y),void 0===(y=h[g])){var T=new t.Point(c.getx(g),c.gety(g)),k=re(T,f);if(k.signedDistanceFromCamera>0)y=h[g]=k.point;else{var A=g-d;y=ue(0===x?o:new t.Point(c.getx(A),c.gety(A)),T,m,_-x+1,f)}}x+=b,b=m.dist(y)}var M=(_-x)/b,S=y.sub(m),E=S.mult(M)._add(m);E._add(S._unit()._perp()._mult(n*d));var L=v+Math.atan2(y.y-m.y,y.x-m.x);return w.push(E),{point:E,angle:L,path:w}}Qt.prototype.keysLength=function(){return this.boxKeys.length+this.circleKeys.length},Qt.prototype.insert=function(t,e,r,n,i){this._forEachCell(e,r,n,i,this._insertBoxCell,this.boxUid++),this.boxKeys.push(t),this.bboxes.push(e),this.bboxes.push(r),this.bboxes.push(n),this.bboxes.push(i)},Qt.prototype.insertCircle=function(t,e,r,n){this._forEachCell(e-n,r-n,e+n,r+n,this._insertCircleCell,this.circleUid++),this.circleKeys.push(t),this.circles.push(e),this.circles.push(r),this.circles.push(n)},Qt.prototype._insertBoxCell=function(t,e,r,n,i,a){this.boxCells[i].push(a)},Qt.prototype._insertCircleCell=function(t,e,r,n,i,a){this.circleCells[i].push(a)},Qt.prototype._query=function(t,e,r,n,i,a){if(r<0||t>this.width||n<0||e>this.height)return!i&&[];var o=[];if(t<=0&&e<=0&&this.width<=r&&this.height<=n){if(i)return!0;for(var s=0;s0:o},Qt.prototype._queryCircle=function(t,e,r,n,i){var a=t-r,o=t+r,s=e-r,l=e+r;if(o<0||a>this.width||l<0||s>this.height)return!n&&[];var u=[],c={hitTest:n,circle:{x:t,y:e,radius:r},seenUids:{box:{},circle:{}}};return this._forEachCell(a,s,o,l,this._queryCellCircle,u,c,i),n?u.length>0:u},Qt.prototype.query=function(t,e,r,n,i){return this._query(t,e,r,n,!1,i)},Qt.prototype.hitTest=function(t,e,r,n,i){return this._query(t,e,r,n,!0,i)},Qt.prototype.hitTestCircle=function(t,e,r,n){return this._queryCircle(t,e,r,!0,n)},Qt.prototype._queryCell=function(t,e,r,n,i,a,o,s){var l=o.seenUids,u=this.boxCells[i];if(null!==u)for(var c=this.bboxes,f=0,h=u;f=c[d+0]&&n>=c[d+1]&&(!s||s(this.boxKeys[p]))){if(o.hitTest)return a.push(!0),!0;a.push({key:this.boxKeys[p],x1:c[d],y1:c[d+1],x2:c[d+2],y2:c[d+3]})}}}var v=this.circleCells[i];if(null!==v)for(var g=this.circles,y=0,m=v;yo*o+s*s},Qt.prototype._circleAndRectCollide=function(t,e,r,n,i,a,o){var s=(a-n)/2,l=Math.abs(t-(n+s));if(l>s+r)return!1;var u=(o-i)/2,c=Math.abs(e-(i+u));if(c>u+r)return!1;if(l<=s||c<=u)return!0;var f=l-s,h=c-u;return f*f+h*h<=r*r};var fe=new Float32Array([-1/0,-1/0,0,-1/0,-1/0,0,-1/0,-1/0,0,-1/0,-1/0,0]);function he(t,e){for(var r=0;r=1;P--)C.push(E.path[P]);for(var O=1;O0){for(var R=C[0].clone(),F=C[0].clone(),B=1;B=A.x&&F.x<=M.x&&R.y>=A.y&&F.y<=M.y?[C]:F.xM.x||F.yM.y?[]:t.clipLine([C],A.x,A.y,M.x,M.y)}for(var N=0,j=z;N=this.screenRightBoundary||nthis.screenBottomBoundary},ve.prototype.isInsideGrid=function(t,e,r,n){return r>=0&&t=0&&e0?(this.prevPlacement&&this.prevPlacement.variableOffsets[f.crossTileID]&&this.prevPlacement.placements[f.crossTileID]&&this.prevPlacement.placements[f.crossTileID].text&&(v=this.prevPlacement.variableOffsets[f.crossTileID].anchor),this.variableOffsets[f.crossTileID]={textOffset:g,width:r,height:n,anchor:t,textBoxScale:i,prevAnchor:v},this.markUsedJustification(h,t,f,p),h.allowVerticalPlacement&&(this.markUsedOrientation(h,p,f),this.placedOrientations[f.crossTileID]=p),{shift:y,placedGlyphBoxes:m}):void 0},Ae.prototype.placeLayerBucketPart=function(e,r,n){var i=this,a=e.parameters,o=a.bucket,s=a.layout,l=a.posMatrix,u=a.textLabelPlaneMatrix,c=a.labelToScreenMatrix,f=a.textPixelRatio,h=a.holdingForFade,p=a.collisionBoxArray,d=a.partiallyEvaluatedTextSize,v=a.collisionGroup,g=s.get("text-optional"),y=s.get("icon-optional"),m=s.get("text-allow-overlap"),x=s.get("icon-allow-overlap"),b="map"===s.get("text-rotation-alignment"),_="map"===s.get("text-pitch-alignment"),w="none"!==s.get("icon-text-fit"),T="viewport-y"===s.get("symbol-z-order"),k=m&&(x||!o.hasIconData()||y),A=x&&(m||!o.hasTextData()||g);!o.collisionArrays&&p&&o.deserializeCollisionBoxes(p);var M=function(e,a){if(!r[e.crossTileID])if(h)i.placements[e.crossTileID]=new xe(!1,!1,!1);else{var p,T=!1,M=!1,S=!0,E=null,L={box:null,offscreen:null},C={box:null,offscreen:null},P=null,O=null,I=0,D=0,z=0;a.textFeatureIndex?I=a.textFeatureIndex:e.useRuntimeCollisionCircles&&(I=e.featureIndex),a.verticalTextFeatureIndex&&(D=a.verticalTextFeatureIndex);var R=a.textBox;if(R){var F=function(r){var n=t.WritingMode.horizontal;if(o.allowVerticalPlacement&&!r&&i.prevPlacement){var a=i.prevPlacement.placedOrientations[e.crossTileID];a&&(i.placedOrientations[e.crossTileID]=a,n=a,i.markUsedOrientation(o,n,e))}return n},B=function(r,n){if(o.allowVerticalPlacement&&e.numVerticalGlyphVertices>0&&a.verticalTextBox)for(var i=0,s=o.writingModes;i0&&(N=N.filter((function(t){return t!==j.anchor}))).unshift(j.anchor)}var U=function(t,r,n){for(var a=t.x2-t.x1,s=t.y2-t.y1,u=e.textBoxScale,c=w&&!x?r:null,h={box:[],offscreen:!1},p=m?2*N.length:N.length,d=0;d=N.length,k=i.attemptAnchorPlacement(g,t,a,s,u,b,_,f,l,v,y,e,o,n,c);if(k&&(h=k.placedGlyphBoxes)&&h.box&&h.box.length){T=!0,E=k.shift;break}}return h};B((function(){return U(R,a.iconBox,t.WritingMode.horizontal)}),(function(){var r=a.verticalTextBox,n=L&&L.box&&L.box.length;return o.allowVerticalPlacement&&!n&&e.numVerticalGlyphVertices>0&&r?U(r,a.verticalIconBox,t.WritingMode.vertical):{box:null,offscreen:null}})),L&&(T=L.box,S=L.offscreen);var V=F(L&&L.box);if(!T&&i.prevPlacement){var H=i.prevPlacement.variableOffsets[e.crossTileID];H&&(i.variableOffsets[e.crossTileID]=H,i.markUsedJustification(o,H.anchor,e,V))}}else{var q=function(t,r){var n=i.collisionIndex.placeCollisionBox(t,m,f,l,v.predicate);return n&&n.box&&n.box.length&&(i.markUsedOrientation(o,r,e),i.placedOrientations[e.crossTileID]=r),n};B((function(){return q(R,t.WritingMode.horizontal)}),(function(){var r=a.verticalTextBox;return o.allowVerticalPlacement&&e.numVerticalGlyphVertices>0&&r?q(r,t.WritingMode.vertical):{box:null,offscreen:null}})),F(L&&L.box&&L.box.length)}}if(T=(p=L)&&p.box&&p.box.length>0,S=p&&p.offscreen,e.useRuntimeCollisionCircles){var G=o.text.placedSymbolArray.get(e.centerJustifiedTextSymbolIndex),Z=t.evaluateSizeForFeature(o.textSizeData,d,G),Y=s.get("text-padding"),W=e.collisionCircleDiameter;P=i.collisionIndex.placeCollisionCircles(m,G,o.lineVertexArray,o.glyphOffsetArray,Z,l,u,c,n,_,v.predicate,W,Y),T=m||P.circles.length>0&&!P.collisionDetected,S=S&&P.offscreen}if(a.iconFeatureIndex&&(z=a.iconFeatureIndex),a.iconBox){var X=function(t){var e=w&&E?ke(t,E.x,E.y,b,_,i.transform.angle):t;return i.collisionIndex.placeCollisionBox(e,x,f,l,v.predicate)};M=C&&C.box&&C.box.length&&a.verticalIconBox?(O=X(a.verticalIconBox)).box.length>0:(O=X(a.iconBox)).box.length>0,S=S&&O.offscreen}var J=g||0===e.numHorizontalGlyphVertices&&0===e.numVerticalGlyphVertices,K=y||0===e.numIconVertices;if(J||K?K?J||(M=M&&T):T=M&&T:M=T=M&&T,T&&p&&p.box&&(C&&C.box&&D?i.collisionIndex.insertCollisionBox(p.box,s.get("text-ignore-placement"),o.bucketInstanceId,D,v.ID):i.collisionIndex.insertCollisionBox(p.box,s.get("text-ignore-placement"),o.bucketInstanceId,I,v.ID)),M&&O&&i.collisionIndex.insertCollisionBox(O.box,s.get("icon-ignore-placement"),o.bucketInstanceId,z,v.ID),P&&(T&&i.collisionIndex.insertCollisionCircles(P.circles,s.get("text-ignore-placement"),o.bucketInstanceId,I,v.ID),n)){var $=o.bucketInstanceId,Q=i.collisionCircleArrays[$];void 0===Q&&(Q=i.collisionCircleArrays[$]=new be);for(var tt=0;tt=0;--E){var L=S[E];M(o.symbolInstances.get(L),o.collisionArrays[L])}else for(var C=e.symbolInstanceStart;C=0&&(e.text.placedSymbolArray.get(u).crossTileID=a>=0&&u!==a?0:n.crossTileID)}},Ae.prototype.markUsedOrientation=function(e,r,n){for(var i=r===t.WritingMode.horizontal||r===t.WritingMode.horizontalOnly?r:0,a=r===t.WritingMode.vertical?r:0,o=0,s=[n.leftJustifiedTextSymbolIndex,n.centerJustifiedTextSymbolIndex,n.rightJustifiedTextSymbolIndex];o0||l>0,x=a.numIconVertices>0,b=i.placedOrientations[a.crossTileID],_=b===t.WritingMode.vertical,w=b===t.WritingMode.horizontal||b===t.WritingMode.horizontalOnly;if(m){var T=De(y.text),k=_?ze:T;d(e.text,s,k);var A=w?ze:T;d(e.text,l,A);var M=y.text.isHidden();[a.rightJustifiedTextSymbolIndex,a.centerJustifiedTextSymbolIndex,a.leftJustifiedTextSymbolIndex].forEach((function(t){t>=0&&(e.text.placedSymbolArray.get(t).hidden=M||_?1:0)})),a.verticalPlacedTextSymbolIndex>=0&&(e.text.placedSymbolArray.get(a.verticalPlacedTextSymbolIndex).hidden=M||w?1:0);var S=i.variableOffsets[a.crossTileID];S&&i.markUsedJustification(e,S.anchor,a,b);var E=i.placedOrientations[a.crossTileID];E&&(i.markUsedJustification(e,"left",a,E),i.markUsedOrientation(e,E,a))}if(x){var L=De(y.icon),C=!(h&&a.verticalPlacedIconSymbolIndex&&_);if(a.placedIconSymbolIndex>=0){var P=C?L:ze;d(e.icon,a.numIconVertices,P),e.icon.placedSymbolArray.get(a.placedIconSymbolIndex).hidden=y.icon.isHidden()}if(a.verticalPlacedIconSymbolIndex>=0){var O=C?ze:L;d(e.icon,a.numVerticalIconVertices,O),e.icon.placedSymbolArray.get(a.verticalPlacedIconSymbolIndex).hidden=y.icon.isHidden()}}if(e.hasIconCollisionBoxData()||e.hasTextCollisionBoxData()){var I=e.collisionArrays[n];if(I){var D=new t.Point(0,0);if(I.textBox||I.verticalTextBox){var z=!0;if(u){var R=i.variableOffsets[v];R?(D=Te(R.anchor,R.width,R.height,R.textOffset,R.textBoxScale),c&&D._rotate(f?i.transform.angle:-i.transform.angle)):z=!1}I.textBox&&Me(e.textCollisionBox.collisionVertexArray,y.text.placed,!z||_,D.x,D.y),I.verticalTextBox&&Me(e.textCollisionBox.collisionVertexArray,y.text.placed,!z||w,D.x,D.y)}var F=Boolean(!w&&I.verticalIconBox);I.iconBox&&Me(e.iconCollisionBox.collisionVertexArray,y.icon.placed,F,h?D.x:0,h?D.y:0),I.verticalIconBox&&Me(e.iconCollisionBox.collisionVertexArray,y.icon.placed,!F,h?D.x:0,h?D.y:0)}}},g=0;gt},Ae.prototype.setStale=function(){this.stale=!0};var Se=Math.pow(2,25),Ee=Math.pow(2,24),Le=Math.pow(2,17),Ce=Math.pow(2,16),Pe=Math.pow(2,9),Oe=Math.pow(2,8),Ie=Math.pow(2,1);function De(t){if(0===t.opacity&&!t.placed)return 0;if(1===t.opacity&&t.placed)return 4294967295;var e=t.placed?1:0,r=Math.floor(127*t.opacity);return r*Se+e*Ee+r*Le+e*Ce+r*Pe+e*Oe+r*Ie+e}var ze=0,Re=function(t){this._sortAcrossTiles="viewport-y"!==t.layout.get("symbol-z-order")&&void 0!==t.layout.get("symbol-sort-key").constantOr(1),this._currentTileIndex=0,this._currentPartIndex=0,this._seenCrossTileIDs={},this._bucketParts=[]};Re.prototype.continuePlacement=function(t,e,r,n,i){for(var a=this._bucketParts;this._currentTileIndex2};this._currentPlacementIndex>=0;){var s=r[e[this._currentPlacementIndex]],l=this.placement.collisionIndex.transform.zoom;if("symbol"===s.type&&(!s.minzoom||s.minzoom<=l)&&(!s.maxzoom||s.maxzoom>l)){if(this._inProgressLayer||(this._inProgressLayer=new Re(s)),this._inProgressLayer.continuePlacement(n[s.source],this.placement,this._showCollisionBoxes,s,o))return;delete this._inProgressLayer}this._currentPlacementIndex--}this._done=!0},Fe.prototype.commit=function(t){return this.placement.commit(t),this.placement};var Be=512/t.EXTENT/2,Ne=function(t,e,r){this.tileID=t,this.indexedSymbolInstances={},this.bucketInstanceId=r;for(var n=0;nt.overscaledZ)for(var s in o){var l=o[s];l.tileID.isChildOf(t)&&l.findMatches(e.symbolInstances,t,i)}else{var u=o[t.scaledTo(Number(a)).key];u&&u.findMatches(e.symbolInstances,t,i)}}for(var c=0;c1?"@2x":"",l=t.getJSON(r.transformRequest(r.normalizeSpriteURL(e,s,".json"),t.ResourceType.SpriteJSON),(function(t,e){l=null,o||(o=t,i=e,c())})),u=t.getImage(r.transformRequest(r.normalizeSpriteURL(e,s,".png"),t.ResourceType.SpriteImage),(function(t,e){u=null,o||(o=t,a=e,c())}));function c(){if(o)n(o);else if(i&&a){var e=t.browser.getImageData(a),r={};for(var s in i){var l=i[s],u=l.width,c=l.height,f=l.x,h=l.y,p=l.sdf,d=l.pixelRatio,v=l.stretchX,g=l.stretchY,y=l.content,m=new t.RGBAImage({width:u,height:c});t.RGBAImage.copy(e,m,{x:f,y:h},{x:0,y:0},{width:u,height:c}),r[s]={data:m,pixelRatio:d,sdf:p,stretchX:v,stretchY:g,content:y}}n(null,r)}}return{cancel:function(){l&&(l.cancel(),l=null),u&&(u.cancel(),u=null)}}}(e,this.map._requestManager,(function(e,n){if(r._spriteRequest=null,e)r.fire(new t.ErrorEvent(e));else if(n)for(var i in n)r.imageManager.addImage(i,n[i]);r.imageManager.setLoaded(!0),r._availableImages=r.imageManager.listImages(),r.dispatcher.broadcast("setImages",r._availableImages),r.fire(new t.Event("data",{dataType:"style"}))}))},r.prototype._validateLayer=function(e){var r=this.sourceCaches[e.source];if(r){var n=e.sourceLayer;if(n){var i=r.getSource();("geojson"===i.type||i.vectorLayerIds&&-1===i.vectorLayerIds.indexOf(n))&&this.fire(new t.ErrorEvent(new Error('Source layer "'+n+'" does not exist on source "'+i.id+'" as specified by style layer "'+e.id+'"')))}}},r.prototype.loaded=function(){if(!this._loaded)return!1;if(Object.keys(this._updatedSources).length)return!1;for(var t in this.sourceCaches)if(!this.sourceCaches[t].loaded())return!1;return!!this.imageManager.isLoaded()},r.prototype._serializeLayers=function(t){for(var e=[],r=0,n=t;r0)throw new Error("Unimplemented: "+i.map((function(t){return t.command})).join(", ")+".");return n.forEach((function(t){"setTransition"!==t.command&&r[t.command].apply(r,t.args)})),this.stylesheet=e,!0},r.prototype.addImage=function(e,r){if(this.getImage(e))return this.fire(new t.ErrorEvent(new Error("An image with this name already exists.")));this.imageManager.addImage(e,r),this._availableImages=this.imageManager.listImages(),this._changedImages[e]=!0,this._changed=!0,this.fire(new t.Event("data",{dataType:"style"}))},r.prototype.updateImage=function(t,e){this.imageManager.updateImage(t,e)},r.prototype.getImage=function(t){return this.imageManager.getImage(t)},r.prototype.removeImage=function(e){if(!this.getImage(e))return this.fire(new t.ErrorEvent(new Error("No image with this name exists.")));this.imageManager.removeImage(e),this._availableImages=this.imageManager.listImages(),this._changedImages[e]=!0,this._changed=!0,this.fire(new t.Event("data",{dataType:"style"}))},r.prototype.listImages=function(){return this._checkLoaded(),this.imageManager.listImages()},r.prototype.addSource=function(e,r,n){var i=this;if(void 0===n&&(n={}),this._checkLoaded(),void 0!==this.sourceCaches[e])throw new Error("There is already a source with this ID");if(!r.type)throw new Error("The type property must be defined, but the only the following properties were given: "+Object.keys(r).join(", ")+".");if(!(["vector","raster","geojson","video","image"].indexOf(r.type)>=0&&this._validate(t.validateStyle.source,"sources."+e,r,null,n))){this.map&&this.map._collectResourceTiming&&(r.collectResourceTiming=!0);var a=this.sourceCaches[e]=new Ot(e,r,this.dispatcher);a.style=this,a.setEventedParent(this,(function(){return{isSourceLoaded:i.loaded(),source:a.serialize(),sourceId:e}})),a.onAdd(this.map),this._changed=!0}},r.prototype.removeSource=function(e){if(this._checkLoaded(),void 0===this.sourceCaches[e])throw new Error("There is no source with this ID");for(var r in this._layers)if(this._layers[r].source===e)return this.fire(new t.ErrorEvent(new Error('Source "'+e+'" cannot be removed while layer "'+r+'" is using it.')));var n=this.sourceCaches[e];delete this.sourceCaches[e],delete this._updatedSources[e],n.fire(new t.Event("data",{sourceDataType:"metadata",dataType:"source",sourceId:e})),n.setEventedParent(null),n.clearTiles(),n.onRemove&&n.onRemove(this.map),this._changed=!0},r.prototype.setGeoJSONSourceData=function(t,e){this._checkLoaded(),this.sourceCaches[t].getSource().setData(e),this._changed=!0},r.prototype.getSource=function(t){return this.sourceCaches[t]&&this.sourceCaches[t].getSource()},r.prototype.addLayer=function(e,r,n){void 0===n&&(n={}),this._checkLoaded();var i=e.id;if(this.getLayer(i))this.fire(new t.ErrorEvent(new Error('Layer with id "'+i+'" already exists on this map')));else{var a;if("custom"===e.type){if(He(this,t.validateCustomStyleLayer(e)))return;a=t.createStyleLayer(e)}else{if("object"==typeof e.source&&(this.addSource(i,e.source),e=t.clone$1(e),e=t.extend(e,{source:i})),this._validate(t.validateStyle.layer,"layers."+i,e,{arrayIndex:-1},n))return;a=t.createStyleLayer(e),this._validateLayer(a),a.setEventedParent(this,{layer:{id:i}}),this._serializedLayers[a.id]=a.serialize()}var o=r?this._order.indexOf(r):this._order.length;if(r&&-1===o)this.fire(new t.ErrorEvent(new Error('Layer with id "'+r+'" does not exist on this map.')));else{if(this._order.splice(o,0,i),this._layerOrderChanged=!0,this._layers[i]=a,this._removedLayers[i]&&a.source&&"custom"!==a.type){var s=this._removedLayers[i];delete this._removedLayers[i],s.type!==a.type?this._updatedSources[a.source]="clear":(this._updatedSources[a.source]="reload",this.sourceCaches[a.source].pause())}this._updateLayer(a),a.onAdd&&a.onAdd(this.map)}}},r.prototype.moveLayer=function(e,r){if(this._checkLoaded(),this._changed=!0,this._layers[e]){if(e!==r){var n=this._order.indexOf(e);this._order.splice(n,1);var i=r?this._order.indexOf(r):this._order.length;r&&-1===i?this.fire(new t.ErrorEvent(new Error('Layer with id "'+r+'" does not exist on this map.'))):(this._order.splice(i,0,e),this._layerOrderChanged=!0)}}else this.fire(new t.ErrorEvent(new Error("The layer '"+e+"' does not exist in the map's style and cannot be moved.")))},r.prototype.removeLayer=function(e){this._checkLoaded();var r=this._layers[e];if(r){r.setEventedParent(null);var n=this._order.indexOf(e);this._order.splice(n,1),this._layerOrderChanged=!0,this._changed=!0,this._removedLayers[e]=r,delete this._layers[e],delete this._serializedLayers[e],delete this._updatedLayers[e],delete this._updatedPaintProps[e],r.onRemove&&r.onRemove(this.map)}else this.fire(new t.ErrorEvent(new Error("The layer '"+e+"' does not exist in the map's style and cannot be removed.")))},r.prototype.getLayer=function(t){return this._layers[t]},r.prototype.hasLayer=function(t){return t in this._layers},r.prototype.setLayerZoomRange=function(e,r,n){this._checkLoaded();var i=this.getLayer(e);i?i.minzoom===r&&i.maxzoom===n||(null!=r&&(i.minzoom=r),null!=n&&(i.maxzoom=n),this._updateLayer(i)):this.fire(new t.ErrorEvent(new Error("The layer '"+e+"' does not exist in the map's style and cannot have zoom extent.")))},r.prototype.setFilter=function(e,r,n){void 0===n&&(n={}),this._checkLoaded();var i=this.getLayer(e);if(i){if(!t.deepEqual(i.filter,r))return null==r?(i.filter=void 0,void this._updateLayer(i)):void(this._validate(t.validateStyle.filter,"layers."+i.id+".filter",r,null,n)||(i.filter=t.clone$1(r),this._updateLayer(i)))}else this.fire(new t.ErrorEvent(new Error("The layer '"+e+"' does not exist in the map's style and cannot be filtered.")))},r.prototype.getFilter=function(e){return t.clone$1(this.getLayer(e).filter)},r.prototype.setLayoutProperty=function(e,r,n,i){void 0===i&&(i={}),this._checkLoaded();var a=this.getLayer(e);a?t.deepEqual(a.getLayoutProperty(r),n)||(a.setLayoutProperty(r,n,i),this._updateLayer(a)):this.fire(new t.ErrorEvent(new Error("The layer '"+e+"' does not exist in the map's style and cannot be styled.")))},r.prototype.getLayoutProperty=function(e,r){var n=this.getLayer(e);if(n)return n.getLayoutProperty(r);this.fire(new t.ErrorEvent(new Error("The layer '"+e+"' does not exist in the map's style.")))},r.prototype.setPaintProperty=function(e,r,n,i){void 0===i&&(i={}),this._checkLoaded();var a=this.getLayer(e);a?t.deepEqual(a.getPaintProperty(r),n)||(a.setPaintProperty(r,n,i)&&this._updateLayer(a),this._changed=!0,this._updatedPaintProps[e]=!0):this.fire(new t.ErrorEvent(new Error("The layer '"+e+"' does not exist in the map's style and cannot be styled.")))},r.prototype.getPaintProperty=function(t,e){return this.getLayer(t).getPaintProperty(e)},r.prototype.setFeatureState=function(e,r){this._checkLoaded();var n=e.source,i=e.sourceLayer,a=this.sourceCaches[n];if(void 0!==a){var o=a.getSource().type;"geojson"===o&&i?this.fire(new t.ErrorEvent(new Error("GeoJSON sources cannot have a sourceLayer parameter."))):"vector"!==o||i?(void 0===e.id&&this.fire(new t.ErrorEvent(new Error("The feature id parameter must be provided."))),a.setFeatureState(i,e.id,r)):this.fire(new t.ErrorEvent(new Error("The sourceLayer parameter must be provided for vector source types.")))}else this.fire(new t.ErrorEvent(new Error("The source '"+n+"' does not exist in the map's style.")))},r.prototype.removeFeatureState=function(e,r){this._checkLoaded();var n=e.source,i=this.sourceCaches[n];if(void 0!==i){var a=i.getSource().type,o="vector"===a?e.sourceLayer:void 0;"vector"!==a||o?r&&"string"!=typeof e.id&&"number"!=typeof e.id?this.fire(new t.ErrorEvent(new Error("A feature id is requred to remove its specific state property."))):i.removeFeatureState(o,e.id,r):this.fire(new t.ErrorEvent(new Error("The sourceLayer parameter must be provided for vector source types.")))}else this.fire(new t.ErrorEvent(new Error("The source '"+n+"' does not exist in the map's style.")))},r.prototype.getFeatureState=function(e){this._checkLoaded();var r=e.source,n=e.sourceLayer,i=this.sourceCaches[r];if(void 0!==i){if("vector"!==i.getSource().type||n)return void 0===e.id&&this.fire(new t.ErrorEvent(new Error("The feature id parameter must be provided."))),i.getFeatureState(n,e.id);this.fire(new t.ErrorEvent(new Error("The sourceLayer parameter must be provided for vector source types.")))}else this.fire(new t.ErrorEvent(new Error("The source '"+r+"' does not exist in the map's style.")))},r.prototype.getTransition=function(){return t.extend({duration:300,delay:0},this.stylesheet&&this.stylesheet.transition)},r.prototype.serialize=function(){return t.filterObject({version:this.stylesheet.version,name:this.stylesheet.name,metadata:this.stylesheet.metadata,light:this.stylesheet.light,center:this.stylesheet.center,zoom:this.stylesheet.zoom,bearing:this.stylesheet.bearing,pitch:this.stylesheet.pitch,sprite:this.stylesheet.sprite,glyphs:this.stylesheet.glyphs,transition:this.stylesheet.transition,sources:t.mapObject(this.sourceCaches,(function(t){return t.serialize()})),layers:this._serializeLayers(this._order)},(function(t){return void 0!==t}))},r.prototype._updateLayer=function(t){this._updatedLayers[t.id]=!0,t.source&&!this._updatedSources[t.source]&&"raster"!==this.sourceCaches[t.source].getSource().type&&(this._updatedSources[t.source]="reload",this.sourceCaches[t.source].pause()),this._changed=!0},r.prototype._flattenAndSortRenderedFeatures=function(t){for(var e=this,r=function(t){return"fill-extrusion"===e._layers[t].type},n={},i=[],a=this._order.length-1;a>=0;a--){var o=this._order[a];if(r(o)){n[o]=a;for(var s=0,l=t;s=0;d--){var v=this._order[d];if(r(v))for(var g=i.length-1;g>=0;g--){var y=i[g].feature;if(n[y.layer.id] 0.5) {gl_FragColor=vec4(0.0,0.0,1.0,0.5)*alpha;}if (v_notUsed > 0.5) {gl_FragColor*=.1;}}","attribute vec2 a_pos;attribute vec2 a_anchor_pos;attribute vec2 a_extrude;attribute vec2 a_placed;attribute vec2 a_shift;uniform mat4 u_matrix;uniform vec2 u_extrude_scale;uniform float u_camera_to_center_distance;varying float v_placed;varying float v_notUsed;void main() {vec4 projectedPoint=u_matrix*vec4(a_anchor_pos,0,1);highp float camera_to_anchor_distance=projectedPoint.w;highp float collision_perspective_ratio=clamp(0.5+0.5*(u_camera_to_center_distance/camera_to_anchor_distance),0.0,4.0);gl_Position=u_matrix*vec4(a_pos,0.0,1.0);gl_Position.xy+=(a_extrude+a_shift)*u_extrude_scale*gl_Position.w*collision_perspective_ratio;v_placed=a_placed.x;v_notUsed=a_placed.y;}"),nr=_r("varying float v_radius;varying vec2 v_extrude;varying float v_perspective_ratio;varying float v_collision;void main() {float alpha=0.5*min(v_perspective_ratio,1.0);float stroke_radius=0.9*max(v_perspective_ratio,1.0);float distance_to_center=length(v_extrude);float distance_to_edge=abs(distance_to_center-v_radius);float opacity_t=smoothstep(-stroke_radius,0.0,-distance_to_edge);vec4 color=mix(vec4(0.0,0.0,1.0,0.5),vec4(1.0,0.0,0.0,1.0),v_collision);gl_FragColor=color*alpha*opacity_t;}","attribute vec2 a_pos;attribute float a_radius;attribute vec2 a_flags;uniform mat4 u_matrix;uniform mat4 u_inv_matrix;uniform vec2 u_viewport_size;uniform float u_camera_to_center_distance;varying float v_radius;varying vec2 v_extrude;varying float v_perspective_ratio;varying float v_collision;vec3 toTilePosition(vec2 screenPos) {vec4 rayStart=u_inv_matrix*vec4(screenPos,-1.0,1.0);vec4 rayEnd =u_inv_matrix*vec4(screenPos, 1.0,1.0);rayStart.xyz/=rayStart.w;rayEnd.xyz /=rayEnd.w;highp float t=(0.0-rayStart.z)/(rayEnd.z-rayStart.z);return mix(rayStart.xyz,rayEnd.xyz,t);}void main() {vec2 quadCenterPos=a_pos;float radius=a_radius;float collision=a_flags.x;float vertexIdx=a_flags.y;vec2 quadVertexOffset=vec2(mix(-1.0,1.0,float(vertexIdx >=2.0)),mix(-1.0,1.0,float(vertexIdx >=1.0 && vertexIdx <=2.0)));vec2 quadVertexExtent=quadVertexOffset*radius;vec3 tilePos=toTilePosition(quadCenterPos);vec4 clipPos=u_matrix*vec4(tilePos,1.0);highp float camera_to_anchor_distance=clipPos.w;highp float collision_perspective_ratio=clamp(0.5+0.5*(u_camera_to_center_distance/camera_to_anchor_distance),0.0,4.0);float padding_factor=1.2;v_radius=radius;v_extrude=quadVertexExtent*padding_factor;v_perspective_ratio=collision_perspective_ratio;v_collision=collision;gl_Position=vec4(clipPos.xyz/clipPos.w,1.0)+vec4(quadVertexExtent*padding_factor/u_viewport_size*2.0,0.0,0.0);}"),ir=_r("uniform highp vec4 u_color;uniform sampler2D u_overlay;varying vec2 v_uv;void main() {vec4 overlay_color=texture2D(u_overlay,v_uv);gl_FragColor=mix(u_color,overlay_color,overlay_color.a);}","attribute vec2 a_pos;varying vec2 v_uv;uniform mat4 u_matrix;uniform float u_overlay_scale;void main() {v_uv=a_pos/8192.0;gl_Position=u_matrix*vec4(a_pos*u_overlay_scale,0,1);}"),ar=_r("#pragma mapbox: define highp vec4 color\n#pragma mapbox: define lowp float opacity\nvoid main() {\n#pragma mapbox: initialize highp vec4 color\n#pragma mapbox: initialize lowp float opacity\ngl_FragColor=color*opacity;\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","attribute vec2 a_pos;uniform mat4 u_matrix;\n#pragma mapbox: define highp vec4 color\n#pragma mapbox: define lowp float opacity\nvoid main() {\n#pragma mapbox: initialize highp vec4 color\n#pragma mapbox: initialize lowp float opacity\ngl_Position=u_matrix*vec4(a_pos,0,1);}"),or=_r("varying vec2 v_pos;\n#pragma mapbox: define highp vec4 outline_color\n#pragma mapbox: define lowp float opacity\nvoid main() {\n#pragma mapbox: initialize highp vec4 outline_color\n#pragma mapbox: initialize lowp float opacity\nfloat dist=length(v_pos-gl_FragCoord.xy);float alpha=1.0-smoothstep(0.0,1.0,dist);gl_FragColor=outline_color*(alpha*opacity);\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","attribute vec2 a_pos;uniform mat4 u_matrix;uniform vec2 u_world;varying vec2 v_pos;\n#pragma mapbox: define highp vec4 outline_color\n#pragma mapbox: define lowp float opacity\nvoid main() {\n#pragma mapbox: initialize highp vec4 outline_color\n#pragma mapbox: initialize lowp float opacity\ngl_Position=u_matrix*vec4(a_pos,0,1);v_pos=(gl_Position.xy/gl_Position.w+1.0)/2.0*u_world;}"),sr=_r("uniform vec2 u_texsize;uniform sampler2D u_image;uniform float u_fade;varying vec2 v_pos_a;varying vec2 v_pos_b;varying vec2 v_pos;\n#pragma mapbox: define lowp float opacity\n#pragma mapbox: define lowp vec4 pattern_from\n#pragma mapbox: define lowp vec4 pattern_to\nvoid main() {\n#pragma mapbox: initialize lowp float opacity\n#pragma mapbox: initialize mediump vec4 pattern_from\n#pragma mapbox: initialize mediump vec4 pattern_to\nvec2 pattern_tl_a=pattern_from.xy;vec2 pattern_br_a=pattern_from.zw;vec2 pattern_tl_b=pattern_to.xy;vec2 pattern_br_b=pattern_to.zw;vec2 imagecoord=mod(v_pos_a,1.0);vec2 pos=mix(pattern_tl_a/u_texsize,pattern_br_a/u_texsize,imagecoord);vec4 color1=texture2D(u_image,pos);vec2 imagecoord_b=mod(v_pos_b,1.0);vec2 pos2=mix(pattern_tl_b/u_texsize,pattern_br_b/u_texsize,imagecoord_b);vec4 color2=texture2D(u_image,pos2);float dist=length(v_pos-gl_FragCoord.xy);float alpha=1.0-smoothstep(0.0,1.0,dist);gl_FragColor=mix(color1,color2,u_fade)*alpha*opacity;\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","uniform mat4 u_matrix;uniform vec2 u_world;uniform vec2 u_pixel_coord_upper;uniform vec2 u_pixel_coord_lower;uniform vec3 u_scale;attribute vec2 a_pos;varying vec2 v_pos_a;varying vec2 v_pos_b;varying vec2 v_pos;\n#pragma mapbox: define lowp float opacity\n#pragma mapbox: define lowp vec4 pattern_from\n#pragma mapbox: define lowp vec4 pattern_to\n#pragma mapbox: define lowp float pixel_ratio_from\n#pragma mapbox: define lowp float pixel_ratio_to\nvoid main() {\n#pragma mapbox: initialize lowp float opacity\n#pragma mapbox: initialize mediump vec4 pattern_from\n#pragma mapbox: initialize mediump vec4 pattern_to\n#pragma mapbox: initialize lowp float pixel_ratio_from\n#pragma mapbox: initialize lowp float pixel_ratio_to\nvec2 pattern_tl_a=pattern_from.xy;vec2 pattern_br_a=pattern_from.zw;vec2 pattern_tl_b=pattern_to.xy;vec2 pattern_br_b=pattern_to.zw;float tileRatio=u_scale.x;float fromScale=u_scale.y;float toScale=u_scale.z;gl_Position=u_matrix*vec4(a_pos,0,1);vec2 display_size_a=(pattern_br_a-pattern_tl_a)/pixel_ratio_from;vec2 display_size_b=(pattern_br_b-pattern_tl_b)/pixel_ratio_to;v_pos_a=get_pattern_pos(u_pixel_coord_upper,u_pixel_coord_lower,fromScale*display_size_a,tileRatio,a_pos);v_pos_b=get_pattern_pos(u_pixel_coord_upper,u_pixel_coord_lower,toScale*display_size_b,tileRatio,a_pos);v_pos=(gl_Position.xy/gl_Position.w+1.0)/2.0*u_world;}"),lr=_r("uniform vec2 u_texsize;uniform float u_fade;uniform sampler2D u_image;varying vec2 v_pos_a;varying vec2 v_pos_b;\n#pragma mapbox: define lowp float opacity\n#pragma mapbox: define lowp vec4 pattern_from\n#pragma mapbox: define lowp vec4 pattern_to\nvoid main() {\n#pragma mapbox: initialize lowp float opacity\n#pragma mapbox: initialize mediump vec4 pattern_from\n#pragma mapbox: initialize mediump vec4 pattern_to\nvec2 pattern_tl_a=pattern_from.xy;vec2 pattern_br_a=pattern_from.zw;vec2 pattern_tl_b=pattern_to.xy;vec2 pattern_br_b=pattern_to.zw;vec2 imagecoord=mod(v_pos_a,1.0);vec2 pos=mix(pattern_tl_a/u_texsize,pattern_br_a/u_texsize,imagecoord);vec4 color1=texture2D(u_image,pos);vec2 imagecoord_b=mod(v_pos_b,1.0);vec2 pos2=mix(pattern_tl_b/u_texsize,pattern_br_b/u_texsize,imagecoord_b);vec4 color2=texture2D(u_image,pos2);gl_FragColor=mix(color1,color2,u_fade)*opacity;\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","uniform mat4 u_matrix;uniform vec2 u_pixel_coord_upper;uniform vec2 u_pixel_coord_lower;uniform vec3 u_scale;attribute vec2 a_pos;varying vec2 v_pos_a;varying vec2 v_pos_b;\n#pragma mapbox: define lowp float opacity\n#pragma mapbox: define lowp vec4 pattern_from\n#pragma mapbox: define lowp vec4 pattern_to\n#pragma mapbox: define lowp float pixel_ratio_from\n#pragma mapbox: define lowp float pixel_ratio_to\nvoid main() {\n#pragma mapbox: initialize lowp float opacity\n#pragma mapbox: initialize mediump vec4 pattern_from\n#pragma mapbox: initialize mediump vec4 pattern_to\n#pragma mapbox: initialize lowp float pixel_ratio_from\n#pragma mapbox: initialize lowp float pixel_ratio_to\nvec2 pattern_tl_a=pattern_from.xy;vec2 pattern_br_a=pattern_from.zw;vec2 pattern_tl_b=pattern_to.xy;vec2 pattern_br_b=pattern_to.zw;float tileZoomRatio=u_scale.x;float fromScale=u_scale.y;float toScale=u_scale.z;vec2 display_size_a=(pattern_br_a-pattern_tl_a)/pixel_ratio_from;vec2 display_size_b=(pattern_br_b-pattern_tl_b)/pixel_ratio_to;gl_Position=u_matrix*vec4(a_pos,0,1);v_pos_a=get_pattern_pos(u_pixel_coord_upper,u_pixel_coord_lower,fromScale*display_size_a,tileZoomRatio,a_pos);v_pos_b=get_pattern_pos(u_pixel_coord_upper,u_pixel_coord_lower,toScale*display_size_b,tileZoomRatio,a_pos);}"),ur=_r("varying vec4 v_color;void main() {gl_FragColor=v_color;\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","uniform mat4 u_matrix;uniform vec3 u_lightcolor;uniform lowp vec3 u_lightpos;uniform lowp float u_lightintensity;uniform float u_vertical_gradient;uniform lowp float u_opacity;attribute vec2 a_pos;attribute vec4 a_normal_ed;varying vec4 v_color;\n#pragma mapbox: define highp float base\n#pragma mapbox: define highp float height\n#pragma mapbox: define highp vec4 color\nvoid main() {\n#pragma mapbox: initialize highp float base\n#pragma mapbox: initialize highp float height\n#pragma mapbox: initialize highp vec4 color\nvec3 normal=a_normal_ed.xyz;base=max(0.0,base);height=max(0.0,height);float t=mod(normal.x,2.0);gl_Position=u_matrix*vec4(a_pos,t > 0.0 ? height : base,1);float colorvalue=color.r*0.2126+color.g*0.7152+color.b*0.0722;v_color=vec4(0.0,0.0,0.0,1.0);vec4 ambientlight=vec4(0.03,0.03,0.03,1.0);color+=ambientlight;float directional=clamp(dot(normal/16384.0,u_lightpos),0.0,1.0);directional=mix((1.0-u_lightintensity),max((1.0-colorvalue+u_lightintensity),1.0),directional);if (normal.y !=0.0) {directional*=((1.0-u_vertical_gradient)+(u_vertical_gradient*clamp((t+base)*pow(height/150.0,0.5),mix(0.7,0.98,1.0-u_lightintensity),1.0)));}v_color.r+=clamp(color.r*directional*u_lightcolor.r,mix(0.0,0.3,1.0-u_lightcolor.r),1.0);v_color.g+=clamp(color.g*directional*u_lightcolor.g,mix(0.0,0.3,1.0-u_lightcolor.g),1.0);v_color.b+=clamp(color.b*directional*u_lightcolor.b,mix(0.0,0.3,1.0-u_lightcolor.b),1.0);v_color*=u_opacity;}"),cr=_r("uniform vec2 u_texsize;uniform float u_fade;uniform sampler2D u_image;varying vec2 v_pos_a;varying vec2 v_pos_b;varying vec4 v_lighting;\n#pragma mapbox: define lowp float base\n#pragma mapbox: define lowp float height\n#pragma mapbox: define lowp vec4 pattern_from\n#pragma mapbox: define lowp vec4 pattern_to\n#pragma mapbox: define lowp float pixel_ratio_from\n#pragma mapbox: define lowp float pixel_ratio_to\nvoid main() {\n#pragma mapbox: initialize lowp float base\n#pragma mapbox: initialize lowp float height\n#pragma mapbox: initialize mediump vec4 pattern_from\n#pragma mapbox: initialize mediump vec4 pattern_to\n#pragma mapbox: initialize lowp float pixel_ratio_from\n#pragma mapbox: initialize lowp float pixel_ratio_to\nvec2 pattern_tl_a=pattern_from.xy;vec2 pattern_br_a=pattern_from.zw;vec2 pattern_tl_b=pattern_to.xy;vec2 pattern_br_b=pattern_to.zw;vec2 imagecoord=mod(v_pos_a,1.0);vec2 pos=mix(pattern_tl_a/u_texsize,pattern_br_a/u_texsize,imagecoord);vec4 color1=texture2D(u_image,pos);vec2 imagecoord_b=mod(v_pos_b,1.0);vec2 pos2=mix(pattern_tl_b/u_texsize,pattern_br_b/u_texsize,imagecoord_b);vec4 color2=texture2D(u_image,pos2);vec4 mixedColor=mix(color1,color2,u_fade);gl_FragColor=mixedColor*v_lighting;\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","uniform mat4 u_matrix;uniform vec2 u_pixel_coord_upper;uniform vec2 u_pixel_coord_lower;uniform float u_height_factor;uniform vec3 u_scale;uniform float u_vertical_gradient;uniform lowp float u_opacity;uniform vec3 u_lightcolor;uniform lowp vec3 u_lightpos;uniform lowp float u_lightintensity;attribute vec2 a_pos;attribute vec4 a_normal_ed;varying vec2 v_pos_a;varying vec2 v_pos_b;varying vec4 v_lighting;\n#pragma mapbox: define lowp float base\n#pragma mapbox: define lowp float height\n#pragma mapbox: define lowp vec4 pattern_from\n#pragma mapbox: define lowp vec4 pattern_to\n#pragma mapbox: define lowp float pixel_ratio_from\n#pragma mapbox: define lowp float pixel_ratio_to\nvoid main() {\n#pragma mapbox: initialize lowp float base\n#pragma mapbox: initialize lowp float height\n#pragma mapbox: initialize mediump vec4 pattern_from\n#pragma mapbox: initialize mediump vec4 pattern_to\n#pragma mapbox: initialize lowp float pixel_ratio_from\n#pragma mapbox: initialize lowp float pixel_ratio_to\nvec2 pattern_tl_a=pattern_from.xy;vec2 pattern_br_a=pattern_from.zw;vec2 pattern_tl_b=pattern_to.xy;vec2 pattern_br_b=pattern_to.zw;float tileRatio=u_scale.x;float fromScale=u_scale.y;float toScale=u_scale.z;vec3 normal=a_normal_ed.xyz;float edgedistance=a_normal_ed.w;vec2 display_size_a=(pattern_br_a-pattern_tl_a)/pixel_ratio_from;vec2 display_size_b=(pattern_br_b-pattern_tl_b)/pixel_ratio_to;base=max(0.0,base);height=max(0.0,height);float t=mod(normal.x,2.0);float z=t > 0.0 ? height : base;gl_Position=u_matrix*vec4(a_pos,z,1);vec2 pos=normal.x==1.0 && normal.y==0.0 && normal.z==16384.0\n? a_pos\n: vec2(edgedistance,z*u_height_factor);v_pos_a=get_pattern_pos(u_pixel_coord_upper,u_pixel_coord_lower,fromScale*display_size_a,tileRatio,pos);v_pos_b=get_pattern_pos(u_pixel_coord_upper,u_pixel_coord_lower,toScale*display_size_b,tileRatio,pos);v_lighting=vec4(0.0,0.0,0.0,1.0);float directional=clamp(dot(normal/16383.0,u_lightpos),0.0,1.0);directional=mix((1.0-u_lightintensity),max((0.5+u_lightintensity),1.0),directional);if (normal.y !=0.0) {directional*=((1.0-u_vertical_gradient)+(u_vertical_gradient*clamp((t+base)*pow(height/150.0,0.5),mix(0.7,0.98,1.0-u_lightintensity),1.0)));}v_lighting.rgb+=clamp(directional*u_lightcolor,mix(vec3(0.0),vec3(0.3),1.0-u_lightcolor),vec3(1.0));v_lighting*=u_opacity;}"),fr=_r("#ifdef GL_ES\nprecision highp float;\n#endif\nuniform sampler2D u_image;varying vec2 v_pos;uniform vec2 u_dimension;uniform float u_zoom;uniform float u_maxzoom;uniform vec4 u_unpack;float getElevation(vec2 coord,float bias) {vec4 data=texture2D(u_image,coord)*255.0;data.a=-1.0;return dot(data,u_unpack)/4.0;}void main() {vec2 epsilon=1.0/u_dimension;float a=getElevation(v_pos+vec2(-epsilon.x,-epsilon.y),0.0);float b=getElevation(v_pos+vec2(0,-epsilon.y),0.0);float c=getElevation(v_pos+vec2(epsilon.x,-epsilon.y),0.0);float d=getElevation(v_pos+vec2(-epsilon.x,0),0.0);float e=getElevation(v_pos,0.0);float f=getElevation(v_pos+vec2(epsilon.x,0),0.0);float g=getElevation(v_pos+vec2(-epsilon.x,epsilon.y),0.0);float h=getElevation(v_pos+vec2(0,epsilon.y),0.0);float i=getElevation(v_pos+vec2(epsilon.x,epsilon.y),0.0);float exaggeration=u_zoom < 2.0 ? 0.4 : u_zoom < 4.5 ? 0.35 : 0.3;vec2 deriv=vec2((c+f+f+i)-(a+d+d+g),(g+h+h+i)-(a+b+b+c))/ pow(2.0,(u_zoom-u_maxzoom)*exaggeration+19.2562-u_zoom);gl_FragColor=clamp(vec4(deriv.x/2.0+0.5,deriv.y/2.0+0.5,1.0,1.0),0.0,1.0);\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","uniform mat4 u_matrix;uniform vec2 u_dimension;attribute vec2 a_pos;attribute vec2 a_texture_pos;varying vec2 v_pos;void main() {gl_Position=u_matrix*vec4(a_pos,0,1);highp vec2 epsilon=1.0/u_dimension;float scale=(u_dimension.x-2.0)/u_dimension.x;v_pos=(a_texture_pos/8192.0)*scale+epsilon;}"),hr=_r("uniform sampler2D u_image;varying vec2 v_pos;uniform vec2 u_latrange;uniform vec2 u_light;uniform vec4 u_shadow;uniform vec4 u_highlight;uniform vec4 u_accent;\n#define PI 3.141592653589793\nvoid main() {vec4 pixel=texture2D(u_image,v_pos);vec2 deriv=((pixel.rg*2.0)-1.0);float scaleFactor=cos(radians((u_latrange[0]-u_latrange[1])*(1.0-v_pos.y)+u_latrange[1]));float slope=atan(1.25*length(deriv)/scaleFactor);float aspect=deriv.x !=0.0 ? atan(deriv.y,-deriv.x) : PI/2.0*(deriv.y > 0.0 ? 1.0 :-1.0);float intensity=u_light.x;float azimuth=u_light.y+PI;float base=1.875-intensity*1.75;float maxValue=0.5*PI;float scaledSlope=intensity !=0.5 ? ((pow(base,slope)-1.0)/(pow(base,maxValue)-1.0))*maxValue : slope;float accent=cos(scaledSlope);vec4 accent_color=(1.0-accent)*u_accent*clamp(intensity*2.0,0.0,1.0);float shade=abs(mod((aspect+azimuth)/PI+0.5,2.0)-1.0);vec4 shade_color=mix(u_shadow,u_highlight,shade)*sin(scaledSlope)*clamp(intensity*2.0,0.0,1.0);gl_FragColor=accent_color*(1.0-shade_color.a)+shade_color;\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","uniform mat4 u_matrix;attribute vec2 a_pos;attribute vec2 a_texture_pos;varying vec2 v_pos;void main() {gl_Position=u_matrix*vec4(a_pos,0,1);v_pos=a_texture_pos/8192.0;}"),pr=_r("uniform lowp float u_device_pixel_ratio;varying vec2 v_width2;varying vec2 v_normal;varying float v_gamma_scale;\n#pragma mapbox: define highp vec4 color\n#pragma mapbox: define lowp float blur\n#pragma mapbox: define lowp float opacity\nvoid main() {\n#pragma mapbox: initialize highp vec4 color\n#pragma mapbox: initialize lowp float blur\n#pragma mapbox: initialize lowp float opacity\nfloat dist=length(v_normal)*v_width2.s;float blur2=(blur+1.0/u_device_pixel_ratio)*v_gamma_scale;float alpha=clamp(min(dist-(v_width2.t-blur2),v_width2.s-dist)/blur2,0.0,1.0);gl_FragColor=color*(alpha*opacity);\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","\n#define scale 0.015873016\nattribute vec2 a_pos_normal;attribute vec4 a_data;uniform mat4 u_matrix;uniform mediump float u_ratio;uniform vec2 u_units_to_pixels;uniform lowp float u_device_pixel_ratio;varying vec2 v_normal;varying vec2 v_width2;varying float v_gamma_scale;varying highp float v_linesofar;\n#pragma mapbox: define highp vec4 color\n#pragma mapbox: define lowp float blur\n#pragma mapbox: define lowp float opacity\n#pragma mapbox: define mediump float gapwidth\n#pragma mapbox: define lowp float offset\n#pragma mapbox: define mediump float width\nvoid main() {\n#pragma mapbox: initialize highp vec4 color\n#pragma mapbox: initialize lowp float blur\n#pragma mapbox: initialize lowp float opacity\n#pragma mapbox: initialize mediump float gapwidth\n#pragma mapbox: initialize lowp float offset\n#pragma mapbox: initialize mediump float width\nfloat ANTIALIASING=1.0/u_device_pixel_ratio/2.0;vec2 a_extrude=a_data.xy-128.0;float a_direction=mod(a_data.z,4.0)-1.0;v_linesofar=(floor(a_data.z/4.0)+a_data.w*64.0)*2.0;vec2 pos=floor(a_pos_normal*0.5);mediump vec2 normal=a_pos_normal-2.0*pos;normal.y=normal.y*2.0-1.0;v_normal=normal;gapwidth=gapwidth/2.0;float halfwidth=width/2.0;offset=-1.0*offset;float inset=gapwidth+(gapwidth > 0.0 ? ANTIALIASING : 0.0);float outset=gapwidth+halfwidth*(gapwidth > 0.0 ? 2.0 : 1.0)+(halfwidth==0.0 ? 0.0 : ANTIALIASING);mediump vec2 dist=outset*a_extrude*scale;mediump float u=0.5*a_direction;mediump float t=1.0-abs(u);mediump vec2 offset2=offset*a_extrude*scale*normal.y*mat2(t,-u,u,t);vec4 projected_extrude=u_matrix*vec4(dist/u_ratio,0.0,0.0);gl_Position=u_matrix*vec4(pos+offset2/u_ratio,0.0,1.0)+projected_extrude;float extrude_length_without_perspective=length(dist);float extrude_length_with_perspective=length(projected_extrude.xy/gl_Position.w*u_units_to_pixels);v_gamma_scale=extrude_length_without_perspective/extrude_length_with_perspective;v_width2=vec2(outset,inset);}"),dr=_r("uniform lowp float u_device_pixel_ratio;uniform sampler2D u_image;varying vec2 v_width2;varying vec2 v_normal;varying float v_gamma_scale;varying highp float v_lineprogress;\n#pragma mapbox: define lowp float blur\n#pragma mapbox: define lowp float opacity\nvoid main() {\n#pragma mapbox: initialize lowp float blur\n#pragma mapbox: initialize lowp float opacity\nfloat dist=length(v_normal)*v_width2.s;float blur2=(blur+1.0/u_device_pixel_ratio)*v_gamma_scale;float alpha=clamp(min(dist-(v_width2.t-blur2),v_width2.s-dist)/blur2,0.0,1.0);vec4 color=texture2D(u_image,vec2(v_lineprogress,0.5));gl_FragColor=color*(alpha*opacity);\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","\n#define MAX_LINE_DISTANCE 32767.0\n#define scale 0.015873016\nattribute vec2 a_pos_normal;attribute vec4 a_data;uniform mat4 u_matrix;uniform mediump float u_ratio;uniform lowp float u_device_pixel_ratio;uniform vec2 u_units_to_pixels;varying vec2 v_normal;varying vec2 v_width2;varying float v_gamma_scale;varying highp float v_lineprogress;\n#pragma mapbox: define lowp float blur\n#pragma mapbox: define lowp float opacity\n#pragma mapbox: define mediump float gapwidth\n#pragma mapbox: define lowp float offset\n#pragma mapbox: define mediump float width\nvoid main() {\n#pragma mapbox: initialize lowp float blur\n#pragma mapbox: initialize lowp float opacity\n#pragma mapbox: initialize mediump float gapwidth\n#pragma mapbox: initialize lowp float offset\n#pragma mapbox: initialize mediump float width\nfloat ANTIALIASING=1.0/u_device_pixel_ratio/2.0;vec2 a_extrude=a_data.xy-128.0;float a_direction=mod(a_data.z,4.0)-1.0;v_lineprogress=(floor(a_data.z/4.0)+a_data.w*64.0)*2.0/MAX_LINE_DISTANCE;vec2 pos=floor(a_pos_normal*0.5);mediump vec2 normal=a_pos_normal-2.0*pos;normal.y=normal.y*2.0-1.0;v_normal=normal;gapwidth=gapwidth/2.0;float halfwidth=width/2.0;offset=-1.0*offset;float inset=gapwidth+(gapwidth > 0.0 ? ANTIALIASING : 0.0);float outset=gapwidth+halfwidth*(gapwidth > 0.0 ? 2.0 : 1.0)+(halfwidth==0.0 ? 0.0 : ANTIALIASING);mediump vec2 dist=outset*a_extrude*scale;mediump float u=0.5*a_direction;mediump float t=1.0-abs(u);mediump vec2 offset2=offset*a_extrude*scale*normal.y*mat2(t,-u,u,t);vec4 projected_extrude=u_matrix*vec4(dist/u_ratio,0.0,0.0);gl_Position=u_matrix*vec4(pos+offset2/u_ratio,0.0,1.0)+projected_extrude;float extrude_length_without_perspective=length(dist);float extrude_length_with_perspective=length(projected_extrude.xy/gl_Position.w*u_units_to_pixels);v_gamma_scale=extrude_length_without_perspective/extrude_length_with_perspective;v_width2=vec2(outset,inset);}"),vr=_r("uniform lowp float u_device_pixel_ratio;uniform vec2 u_texsize;uniform float u_fade;uniform mediump vec3 u_scale;uniform sampler2D u_image;varying vec2 v_normal;varying vec2 v_width2;varying float v_linesofar;varying float v_gamma_scale;varying float v_width;\n#pragma mapbox: define lowp vec4 pattern_from\n#pragma mapbox: define lowp vec4 pattern_to\n#pragma mapbox: define lowp float pixel_ratio_from\n#pragma mapbox: define lowp float pixel_ratio_to\n#pragma mapbox: define lowp float blur\n#pragma mapbox: define lowp float opacity\nvoid main() {\n#pragma mapbox: initialize mediump vec4 pattern_from\n#pragma mapbox: initialize mediump vec4 pattern_to\n#pragma mapbox: initialize lowp float pixel_ratio_from\n#pragma mapbox: initialize lowp float pixel_ratio_to\n#pragma mapbox: initialize lowp float blur\n#pragma mapbox: initialize lowp float opacity\nvec2 pattern_tl_a=pattern_from.xy;vec2 pattern_br_a=pattern_from.zw;vec2 pattern_tl_b=pattern_to.xy;vec2 pattern_br_b=pattern_to.zw;float tileZoomRatio=u_scale.x;float fromScale=u_scale.y;float toScale=u_scale.z;vec2 display_size_a=(pattern_br_a-pattern_tl_a)/pixel_ratio_from;vec2 display_size_b=(pattern_br_b-pattern_tl_b)/pixel_ratio_to;vec2 pattern_size_a=vec2(display_size_a.x*fromScale/tileZoomRatio,display_size_a.y);vec2 pattern_size_b=vec2(display_size_b.x*toScale/tileZoomRatio,display_size_b.y);float aspect_a=display_size_a.y/v_width;float aspect_b=display_size_b.y/v_width;float dist=length(v_normal)*v_width2.s;float blur2=(blur+1.0/u_device_pixel_ratio)*v_gamma_scale;float alpha=clamp(min(dist-(v_width2.t-blur2),v_width2.s-dist)/blur2,0.0,1.0);float x_a=mod(v_linesofar/pattern_size_a.x*aspect_a,1.0);float x_b=mod(v_linesofar/pattern_size_b.x*aspect_b,1.0);float y=0.5*v_normal.y+0.5;vec2 texel_size=1.0/u_texsize;vec2 pos_a=mix(pattern_tl_a*texel_size-texel_size,pattern_br_a*texel_size+texel_size,vec2(x_a,y));vec2 pos_b=mix(pattern_tl_b*texel_size-texel_size,pattern_br_b*texel_size+texel_size,vec2(x_b,y));vec4 color=mix(texture2D(u_image,pos_a),texture2D(u_image,pos_b),u_fade);gl_FragColor=color*alpha*opacity;\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","\n#define scale 0.015873016\n#define LINE_DISTANCE_SCALE 2.0\nattribute vec2 a_pos_normal;attribute vec4 a_data;uniform mat4 u_matrix;uniform vec2 u_units_to_pixels;uniform mediump float u_ratio;uniform lowp float u_device_pixel_ratio;varying vec2 v_normal;varying vec2 v_width2;varying float v_linesofar;varying float v_gamma_scale;varying float v_width;\n#pragma mapbox: define lowp float blur\n#pragma mapbox: define lowp float opacity\n#pragma mapbox: define lowp float offset\n#pragma mapbox: define mediump float gapwidth\n#pragma mapbox: define mediump float width\n#pragma mapbox: define lowp float floorwidth\n#pragma mapbox: define lowp vec4 pattern_from\n#pragma mapbox: define lowp vec4 pattern_to\n#pragma mapbox: define lowp float pixel_ratio_from\n#pragma mapbox: define lowp float pixel_ratio_to\nvoid main() {\n#pragma mapbox: initialize lowp float blur\n#pragma mapbox: initialize lowp float opacity\n#pragma mapbox: initialize lowp float offset\n#pragma mapbox: initialize mediump float gapwidth\n#pragma mapbox: initialize mediump float width\n#pragma mapbox: initialize lowp float floorwidth\n#pragma mapbox: initialize mediump vec4 pattern_from\n#pragma mapbox: initialize mediump vec4 pattern_to\n#pragma mapbox: initialize lowp float pixel_ratio_from\n#pragma mapbox: initialize lowp float pixel_ratio_to\nfloat ANTIALIASING=1.0/u_device_pixel_ratio/2.0;vec2 a_extrude=a_data.xy-128.0;float a_direction=mod(a_data.z,4.0)-1.0;float a_linesofar=(floor(a_data.z/4.0)+a_data.w*64.0)*LINE_DISTANCE_SCALE;vec2 pos=floor(a_pos_normal*0.5);mediump vec2 normal=a_pos_normal-2.0*pos;normal.y=normal.y*2.0-1.0;v_normal=normal;gapwidth=gapwidth/2.0;float halfwidth=width/2.0;offset=-1.0*offset;float inset=gapwidth+(gapwidth > 0.0 ? ANTIALIASING : 0.0);float outset=gapwidth+halfwidth*(gapwidth > 0.0 ? 2.0 : 1.0)+(halfwidth==0.0 ? 0.0 : ANTIALIASING);mediump vec2 dist=outset*a_extrude*scale;mediump float u=0.5*a_direction;mediump float t=1.0-abs(u);mediump vec2 offset2=offset*a_extrude*scale*normal.y*mat2(t,-u,u,t);vec4 projected_extrude=u_matrix*vec4(dist/u_ratio,0.0,0.0);gl_Position=u_matrix*vec4(pos+offset2/u_ratio,0.0,1.0)+projected_extrude;float extrude_length_without_perspective=length(dist);float extrude_length_with_perspective=length(projected_extrude.xy/gl_Position.w*u_units_to_pixels);v_gamma_scale=extrude_length_without_perspective/extrude_length_with_perspective;v_linesofar=a_linesofar;v_width2=vec2(outset,inset);v_width=floorwidth;}"),gr=_r("uniform lowp float u_device_pixel_ratio;uniform sampler2D u_image;uniform float u_sdfgamma;uniform float u_mix;varying vec2 v_normal;varying vec2 v_width2;varying vec2 v_tex_a;varying vec2 v_tex_b;varying float v_gamma_scale;\n#pragma mapbox: define highp vec4 color\n#pragma mapbox: define lowp float blur\n#pragma mapbox: define lowp float opacity\n#pragma mapbox: define mediump float width\n#pragma mapbox: define lowp float floorwidth\nvoid main() {\n#pragma mapbox: initialize highp vec4 color\n#pragma mapbox: initialize lowp float blur\n#pragma mapbox: initialize lowp float opacity\n#pragma mapbox: initialize mediump float width\n#pragma mapbox: initialize lowp float floorwidth\nfloat dist=length(v_normal)*v_width2.s;float blur2=(blur+1.0/u_device_pixel_ratio)*v_gamma_scale;float alpha=clamp(min(dist-(v_width2.t-blur2),v_width2.s-dist)/blur2,0.0,1.0);float sdfdist_a=texture2D(u_image,v_tex_a).a;float sdfdist_b=texture2D(u_image,v_tex_b).a;float sdfdist=mix(sdfdist_a,sdfdist_b,u_mix);alpha*=smoothstep(0.5-u_sdfgamma/floorwidth,0.5+u_sdfgamma/floorwidth,sdfdist);gl_FragColor=color*(alpha*opacity);\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","\n#define scale 0.015873016\n#define LINE_DISTANCE_SCALE 2.0\nattribute vec2 a_pos_normal;attribute vec4 a_data;uniform mat4 u_matrix;uniform mediump float u_ratio;uniform lowp float u_device_pixel_ratio;uniform vec2 u_patternscale_a;uniform float u_tex_y_a;uniform vec2 u_patternscale_b;uniform float u_tex_y_b;uniform vec2 u_units_to_pixels;varying vec2 v_normal;varying vec2 v_width2;varying vec2 v_tex_a;varying vec2 v_tex_b;varying float v_gamma_scale;\n#pragma mapbox: define highp vec4 color\n#pragma mapbox: define lowp float blur\n#pragma mapbox: define lowp float opacity\n#pragma mapbox: define mediump float gapwidth\n#pragma mapbox: define lowp float offset\n#pragma mapbox: define mediump float width\n#pragma mapbox: define lowp float floorwidth\nvoid main() {\n#pragma mapbox: initialize highp vec4 color\n#pragma mapbox: initialize lowp float blur\n#pragma mapbox: initialize lowp float opacity\n#pragma mapbox: initialize mediump float gapwidth\n#pragma mapbox: initialize lowp float offset\n#pragma mapbox: initialize mediump float width\n#pragma mapbox: initialize lowp float floorwidth\nfloat ANTIALIASING=1.0/u_device_pixel_ratio/2.0;vec2 a_extrude=a_data.xy-128.0;float a_direction=mod(a_data.z,4.0)-1.0;float a_linesofar=(floor(a_data.z/4.0)+a_data.w*64.0)*LINE_DISTANCE_SCALE;vec2 pos=floor(a_pos_normal*0.5);mediump vec2 normal=a_pos_normal-2.0*pos;normal.y=normal.y*2.0-1.0;v_normal=normal;gapwidth=gapwidth/2.0;float halfwidth=width/2.0;offset=-1.0*offset;float inset=gapwidth+(gapwidth > 0.0 ? ANTIALIASING : 0.0);float outset=gapwidth+halfwidth*(gapwidth > 0.0 ? 2.0 : 1.0)+(halfwidth==0.0 ? 0.0 : ANTIALIASING);mediump vec2 dist=outset*a_extrude*scale;mediump float u=0.5*a_direction;mediump float t=1.0-abs(u);mediump vec2 offset2=offset*a_extrude*scale*normal.y*mat2(t,-u,u,t);vec4 projected_extrude=u_matrix*vec4(dist/u_ratio,0.0,0.0);gl_Position=u_matrix*vec4(pos+offset2/u_ratio,0.0,1.0)+projected_extrude;float extrude_length_without_perspective=length(dist);float extrude_length_with_perspective=length(projected_extrude.xy/gl_Position.w*u_units_to_pixels);v_gamma_scale=extrude_length_without_perspective/extrude_length_with_perspective;v_tex_a=vec2(a_linesofar*u_patternscale_a.x/floorwidth,normal.y*u_patternscale_a.y+u_tex_y_a);v_tex_b=vec2(a_linesofar*u_patternscale_b.x/floorwidth,normal.y*u_patternscale_b.y+u_tex_y_b);v_width2=vec2(outset,inset);}"),yr=_r("uniform float u_fade_t;uniform float u_opacity;uniform sampler2D u_image0;uniform sampler2D u_image1;varying vec2 v_pos0;varying vec2 v_pos1;uniform float u_brightness_low;uniform float u_brightness_high;uniform float u_saturation_factor;uniform float u_contrast_factor;uniform vec3 u_spin_weights;void main() {vec4 color0=texture2D(u_image0,v_pos0);vec4 color1=texture2D(u_image1,v_pos1);if (color0.a > 0.0) {color0.rgb=color0.rgb/color0.a;}if (color1.a > 0.0) {color1.rgb=color1.rgb/color1.a;}vec4 color=mix(color0,color1,u_fade_t);color.a*=u_opacity;vec3 rgb=color.rgb;rgb=vec3(dot(rgb,u_spin_weights.xyz),dot(rgb,u_spin_weights.zxy),dot(rgb,u_spin_weights.yzx));float average=(color.r+color.g+color.b)/3.0;rgb+=(average-rgb)*u_saturation_factor;rgb=(rgb-0.5)*u_contrast_factor+0.5;vec3 u_high_vec=vec3(u_brightness_low,u_brightness_low,u_brightness_low);vec3 u_low_vec=vec3(u_brightness_high,u_brightness_high,u_brightness_high);gl_FragColor=vec4(mix(u_high_vec,u_low_vec,rgb)*color.a,color.a);\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","uniform mat4 u_matrix;uniform vec2 u_tl_parent;uniform float u_scale_parent;uniform float u_buffer_scale;attribute vec2 a_pos;attribute vec2 a_texture_pos;varying vec2 v_pos0;varying vec2 v_pos1;void main() {gl_Position=u_matrix*vec4(a_pos,0,1);v_pos0=(((a_texture_pos/8192.0)-0.5)/u_buffer_scale )+0.5;v_pos1=(v_pos0*u_scale_parent)+u_tl_parent;}"),mr=_r("uniform sampler2D u_texture;varying vec2 v_tex;varying float v_fade_opacity;\n#pragma mapbox: define lowp float opacity\nvoid main() {\n#pragma mapbox: initialize lowp float opacity\nlowp float alpha=opacity*v_fade_opacity;gl_FragColor=texture2D(u_texture,v_tex)*alpha;\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","const float PI=3.141592653589793;attribute vec4 a_pos_offset;attribute vec4 a_data;attribute vec4 a_pixeloffset;attribute vec3 a_projected_pos;attribute float a_fade_opacity;uniform bool u_is_size_zoom_constant;uniform bool u_is_size_feature_constant;uniform highp float u_size_t;uniform highp float u_size;uniform highp float u_camera_to_center_distance;uniform highp float u_pitch;uniform bool u_rotate_symbol;uniform highp float u_aspect_ratio;uniform float u_fade_change;uniform mat4 u_matrix;uniform mat4 u_label_plane_matrix;uniform mat4 u_coord_matrix;uniform bool u_is_text;uniform bool u_pitch_with_map;uniform vec2 u_texsize;varying vec2 v_tex;varying float v_fade_opacity;\n#pragma mapbox: define lowp float opacity\nvoid main() {\n#pragma mapbox: initialize lowp float opacity\nvec2 a_pos=a_pos_offset.xy;vec2 a_offset=a_pos_offset.zw;vec2 a_tex=a_data.xy;vec2 a_size=a_data.zw;float a_size_min=floor(a_size[0]*0.5);vec2 a_pxoffset=a_pixeloffset.xy;vec2 a_minFontScale=a_pixeloffset.zw/256.0;highp float segment_angle=-a_projected_pos[2];float size;if (!u_is_size_zoom_constant && !u_is_size_feature_constant) {size=mix(a_size_min,a_size[1],u_size_t)/128.0;} else if (u_is_size_zoom_constant && !u_is_size_feature_constant) {size=a_size_min/128.0;} else {size=u_size;}vec4 projectedPoint=u_matrix*vec4(a_pos,0,1);highp float camera_to_anchor_distance=projectedPoint.w;highp float distance_ratio=u_pitch_with_map ?\ncamera_to_anchor_distance/u_camera_to_center_distance :\nu_camera_to_center_distance/camera_to_anchor_distance;highp float perspective_ratio=clamp(0.5+0.5*distance_ratio,0.0,4.0);size*=perspective_ratio;float fontScale=u_is_text ? size/24.0 : size;highp float symbol_rotation=0.0;if (u_rotate_symbol) {vec4 offsetProjectedPoint=u_matrix*vec4(a_pos+vec2(1,0),0,1);vec2 a=projectedPoint.xy/projectedPoint.w;vec2 b=offsetProjectedPoint.xy/offsetProjectedPoint.w;symbol_rotation=atan((b.y-a.y)/u_aspect_ratio,b.x-a.x);}highp float angle_sin=sin(segment_angle+symbol_rotation);highp float angle_cos=cos(segment_angle+symbol_rotation);mat2 rotation_matrix=mat2(angle_cos,-1.0*angle_sin,angle_sin,angle_cos);vec4 projected_pos=u_label_plane_matrix*vec4(a_projected_pos.xy,0.0,1.0);gl_Position=u_coord_matrix*vec4(projected_pos.xy/projected_pos.w+rotation_matrix*(a_offset/32.0*max(a_minFontScale,fontScale)+a_pxoffset/16.0),0.0,1.0);v_tex=a_tex/u_texsize;vec2 fade_opacity=unpack_opacity(a_fade_opacity);float fade_change=fade_opacity[1] > 0.5 ? u_fade_change :-u_fade_change;v_fade_opacity=max(0.0,min(1.0,fade_opacity[0]+fade_change));}"),xr=_r("#define SDF_PX 8.0\nuniform bool u_is_halo;uniform sampler2D u_texture;uniform highp float u_gamma_scale;uniform lowp float u_device_pixel_ratio;uniform bool u_is_text;varying vec2 v_data0;varying vec3 v_data1;\n#pragma mapbox: define highp vec4 fill_color\n#pragma mapbox: define highp vec4 halo_color\n#pragma mapbox: define lowp float opacity\n#pragma mapbox: define lowp float halo_width\n#pragma mapbox: define lowp float halo_blur\nvoid main() {\n#pragma mapbox: initialize highp vec4 fill_color\n#pragma mapbox: initialize highp vec4 halo_color\n#pragma mapbox: initialize lowp float opacity\n#pragma mapbox: initialize lowp float halo_width\n#pragma mapbox: initialize lowp float halo_blur\nfloat EDGE_GAMMA=0.105/u_device_pixel_ratio;vec2 tex=v_data0.xy;float gamma_scale=v_data1.x;float size=v_data1.y;float fade_opacity=v_data1[2];float fontScale=u_is_text ? size/24.0 : size;lowp vec4 color=fill_color;highp float gamma=EDGE_GAMMA/(fontScale*u_gamma_scale);lowp float buff=(256.0-64.0)/256.0;if (u_is_halo) {color=halo_color;gamma=(halo_blur*1.19/SDF_PX+EDGE_GAMMA)/(fontScale*u_gamma_scale);buff=(6.0-halo_width/fontScale)/SDF_PX;}lowp float dist=texture2D(u_texture,tex).a;highp float gamma_scaled=gamma*gamma_scale;highp float alpha=smoothstep(buff-gamma_scaled,buff+gamma_scaled,dist);gl_FragColor=color*(alpha*opacity*fade_opacity);\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","const float PI=3.141592653589793;attribute vec4 a_pos_offset;attribute vec4 a_data;attribute vec4 a_pixeloffset;attribute vec3 a_projected_pos;attribute float a_fade_opacity;uniform bool u_is_size_zoom_constant;uniform bool u_is_size_feature_constant;uniform highp float u_size_t;uniform highp float u_size;uniform mat4 u_matrix;uniform mat4 u_label_plane_matrix;uniform mat4 u_coord_matrix;uniform bool u_is_text;uniform bool u_pitch_with_map;uniform highp float u_pitch;uniform bool u_rotate_symbol;uniform highp float u_aspect_ratio;uniform highp float u_camera_to_center_distance;uniform float u_fade_change;uniform vec2 u_texsize;varying vec2 v_data0;varying vec3 v_data1;\n#pragma mapbox: define highp vec4 fill_color\n#pragma mapbox: define highp vec4 halo_color\n#pragma mapbox: define lowp float opacity\n#pragma mapbox: define lowp float halo_width\n#pragma mapbox: define lowp float halo_blur\nvoid main() {\n#pragma mapbox: initialize highp vec4 fill_color\n#pragma mapbox: initialize highp vec4 halo_color\n#pragma mapbox: initialize lowp float opacity\n#pragma mapbox: initialize lowp float halo_width\n#pragma mapbox: initialize lowp float halo_blur\nvec2 a_pos=a_pos_offset.xy;vec2 a_offset=a_pos_offset.zw;vec2 a_tex=a_data.xy;vec2 a_size=a_data.zw;float a_size_min=floor(a_size[0]*0.5);vec2 a_pxoffset=a_pixeloffset.xy;highp float segment_angle=-a_projected_pos[2];float size;if (!u_is_size_zoom_constant && !u_is_size_feature_constant) {size=mix(a_size_min,a_size[1],u_size_t)/128.0;} else if (u_is_size_zoom_constant && !u_is_size_feature_constant) {size=a_size_min/128.0;} else {size=u_size;}vec4 projectedPoint=u_matrix*vec4(a_pos,0,1);highp float camera_to_anchor_distance=projectedPoint.w;highp float distance_ratio=u_pitch_with_map ?\ncamera_to_anchor_distance/u_camera_to_center_distance :\nu_camera_to_center_distance/camera_to_anchor_distance;highp float perspective_ratio=clamp(0.5+0.5*distance_ratio,0.0,4.0);size*=perspective_ratio;float fontScale=u_is_text ? size/24.0 : size;highp float symbol_rotation=0.0;if (u_rotate_symbol) {vec4 offsetProjectedPoint=u_matrix*vec4(a_pos+vec2(1,0),0,1);vec2 a=projectedPoint.xy/projectedPoint.w;vec2 b=offsetProjectedPoint.xy/offsetProjectedPoint.w;symbol_rotation=atan((b.y-a.y)/u_aspect_ratio,b.x-a.x);}highp float angle_sin=sin(segment_angle+symbol_rotation);highp float angle_cos=cos(segment_angle+symbol_rotation);mat2 rotation_matrix=mat2(angle_cos,-1.0*angle_sin,angle_sin,angle_cos);vec4 projected_pos=u_label_plane_matrix*vec4(a_projected_pos.xy,0.0,1.0);gl_Position=u_coord_matrix*vec4(projected_pos.xy/projected_pos.w+rotation_matrix*(a_offset/32.0*fontScale+a_pxoffset),0.0,1.0);float gamma_scale=gl_Position.w;vec2 fade_opacity=unpack_opacity(a_fade_opacity);float fade_change=fade_opacity[1] > 0.5 ? u_fade_change :-u_fade_change;float interpolated_fade_opacity=max(0.0,min(1.0,fade_opacity[0]+fade_change));v_data0=a_tex/u_texsize;v_data1=vec3(gamma_scale,size,interpolated_fade_opacity);}"),br=_r("#define SDF_PX 8.0\n#define SDF 1.0\n#define ICON 0.0\nuniform bool u_is_halo;uniform sampler2D u_texture;uniform sampler2D u_texture_icon;uniform highp float u_gamma_scale;uniform lowp float u_device_pixel_ratio;varying vec4 v_data0;varying vec4 v_data1;\n#pragma mapbox: define highp vec4 fill_color\n#pragma mapbox: define highp vec4 halo_color\n#pragma mapbox: define lowp float opacity\n#pragma mapbox: define lowp float halo_width\n#pragma mapbox: define lowp float halo_blur\nvoid main() {\n#pragma mapbox: initialize highp vec4 fill_color\n#pragma mapbox: initialize highp vec4 halo_color\n#pragma mapbox: initialize lowp float opacity\n#pragma mapbox: initialize lowp float halo_width\n#pragma mapbox: initialize lowp float halo_blur\nfloat fade_opacity=v_data1[2];if (v_data1.w==ICON) {vec2 tex_icon=v_data0.zw;lowp float alpha=opacity*fade_opacity;gl_FragColor=texture2D(u_texture_icon,tex_icon)*alpha;\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\nreturn;}vec2 tex=v_data0.xy;float EDGE_GAMMA=0.105/u_device_pixel_ratio;float gamma_scale=v_data1.x;float size=v_data1.y;float fontScale=size/24.0;lowp vec4 color=fill_color;highp float gamma=EDGE_GAMMA/(fontScale*u_gamma_scale);lowp float buff=(256.0-64.0)/256.0;if (u_is_halo) {color=halo_color;gamma=(halo_blur*1.19/SDF_PX+EDGE_GAMMA)/(fontScale*u_gamma_scale);buff=(6.0-halo_width/fontScale)/SDF_PX;}lowp float dist=texture2D(u_texture,tex).a;highp float gamma_scaled=gamma*gamma_scale;highp float alpha=smoothstep(buff-gamma_scaled,buff+gamma_scaled,dist);gl_FragColor=color*(alpha*opacity*fade_opacity);\n#ifdef OVERDRAW_INSPECTOR\ngl_FragColor=vec4(1.0);\n#endif\n}","const float PI=3.141592653589793;attribute vec4 a_pos_offset;attribute vec4 a_data;attribute vec3 a_projected_pos;attribute float a_fade_opacity;uniform bool u_is_size_zoom_constant;uniform bool u_is_size_feature_constant;uniform highp float u_size_t;uniform highp float u_size;uniform mat4 u_matrix;uniform mat4 u_label_plane_matrix;uniform mat4 u_coord_matrix;uniform bool u_is_text;uniform bool u_pitch_with_map;uniform highp float u_pitch;uniform bool u_rotate_symbol;uniform highp float u_aspect_ratio;uniform highp float u_camera_to_center_distance;uniform float u_fade_change;uniform vec2 u_texsize;uniform vec2 u_texsize_icon;varying vec4 v_data0;varying vec4 v_data1;\n#pragma mapbox: define highp vec4 fill_color\n#pragma mapbox: define highp vec4 halo_color\n#pragma mapbox: define lowp float opacity\n#pragma mapbox: define lowp float halo_width\n#pragma mapbox: define lowp float halo_blur\nvoid main() {\n#pragma mapbox: initialize highp vec4 fill_color\n#pragma mapbox: initialize highp vec4 halo_color\n#pragma mapbox: initialize lowp float opacity\n#pragma mapbox: initialize lowp float halo_width\n#pragma mapbox: initialize lowp float halo_blur\nvec2 a_pos=a_pos_offset.xy;vec2 a_offset=a_pos_offset.zw;vec2 a_tex=a_data.xy;vec2 a_size=a_data.zw;float a_size_min=floor(a_size[0]*0.5);float is_sdf=a_size[0]-2.0*a_size_min;highp float segment_angle=-a_projected_pos[2];float size;if (!u_is_size_zoom_constant && !u_is_size_feature_constant) {size=mix(a_size_min,a_size[1],u_size_t)/128.0;} else if (u_is_size_zoom_constant && !u_is_size_feature_constant) {size=a_size_min/128.0;} else {size=u_size;}vec4 projectedPoint=u_matrix*vec4(a_pos,0,1);highp float camera_to_anchor_distance=projectedPoint.w;highp float distance_ratio=u_pitch_with_map ?\ncamera_to_anchor_distance/u_camera_to_center_distance :\nu_camera_to_center_distance/camera_to_anchor_distance;highp float perspective_ratio=clamp(0.5+0.5*distance_ratio,0.0,4.0);size*=perspective_ratio;float fontScale=size/24.0;highp float symbol_rotation=0.0;if (u_rotate_symbol) {vec4 offsetProjectedPoint=u_matrix*vec4(a_pos+vec2(1,0),0,1);vec2 a=projectedPoint.xy/projectedPoint.w;vec2 b=offsetProjectedPoint.xy/offsetProjectedPoint.w;symbol_rotation=atan((b.y-a.y)/u_aspect_ratio,b.x-a.x);}highp float angle_sin=sin(segment_angle+symbol_rotation);highp float angle_cos=cos(segment_angle+symbol_rotation);mat2 rotation_matrix=mat2(angle_cos,-1.0*angle_sin,angle_sin,angle_cos);vec4 projected_pos=u_label_plane_matrix*vec4(a_projected_pos.xy,0.0,1.0);gl_Position=u_coord_matrix*vec4(projected_pos.xy/projected_pos.w+rotation_matrix*(a_offset/32.0*fontScale),0.0,1.0);float gamma_scale=gl_Position.w;vec2 fade_opacity=unpack_opacity(a_fade_opacity);float fade_change=fade_opacity[1] > 0.5 ? u_fade_change :-u_fade_change;float interpolated_fade_opacity=max(0.0,min(1.0,fade_opacity[0]+fade_change));v_data0.xy=a_tex/u_texsize;v_data0.zw=a_tex/u_texsize_icon;v_data1=vec4(gamma_scale,size,interpolated_fade_opacity,is_sdf);}");function _r(t,e){var r=/#pragma mapbox: ([\w]+) ([\w]+) ([\w]+) ([\w]+)/g,n={};return{fragmentSource:t=t.replace(r,(function(t,e,r,i,a){return n[a]=!0,"define"===e?"\n#ifndef HAS_UNIFORM_u_"+a+"\nvarying "+r+" "+i+" "+a+";\n#else\nuniform "+r+" "+i+" u_"+a+";\n#endif\n":"\n#ifdef HAS_UNIFORM_u_"+a+"\n "+r+" "+i+" "+a+" = u_"+a+";\n#endif\n"})),vertexSource:e=e.replace(r,(function(t,e,r,i,a){var o="float"===i?"vec2":"vec4",s=a.match(/color/)?"color":o;return n[a]?"define"===e?"\n#ifndef HAS_UNIFORM_u_"+a+"\nuniform lowp float u_"+a+"_t;\nattribute "+r+" "+o+" a_"+a+";\nvarying "+r+" "+i+" "+a+";\n#else\nuniform "+r+" "+i+" u_"+a+";\n#endif\n":"vec4"===s?"\n#ifndef HAS_UNIFORM_u_"+a+"\n "+a+" = a_"+a+";\n#else\n "+r+" "+i+" "+a+" = u_"+a+";\n#endif\n":"\n#ifndef HAS_UNIFORM_u_"+a+"\n "+a+" = unpack_mix_"+s+"(a_"+a+", u_"+a+"_t);\n#else\n "+r+" "+i+" "+a+" = u_"+a+";\n#endif\n":"define"===e?"\n#ifndef HAS_UNIFORM_u_"+a+"\nuniform lowp float u_"+a+"_t;\nattribute "+r+" "+o+" a_"+a+";\n#else\nuniform "+r+" "+i+" u_"+a+";\n#endif\n":"vec4"===s?"\n#ifndef HAS_UNIFORM_u_"+a+"\n "+r+" "+i+" "+a+" = a_"+a+";\n#else\n "+r+" "+i+" "+a+" = u_"+a+";\n#endif\n":"\n#ifndef HAS_UNIFORM_u_"+a+"\n "+r+" "+i+" "+a+" = unpack_mix_"+s+"(a_"+a+", u_"+a+"_t);\n#else\n "+r+" "+i+" "+a+" = u_"+a+";\n#endif\n"}))}}var wr=Object.freeze({__proto__:null,prelude:Xe,background:Je,backgroundPattern:Ke,circle:$e,clippingMask:Qe,heatmap:tr,heatmapTexture:er,collisionBox:rr,collisionCircle:nr,debug:ir,fill:ar,fillOutline:or,fillOutlinePattern:sr,fillPattern:lr,fillExtrusion:ur,fillExtrusionPattern:cr,hillshadePrepare:fr,hillshade:hr,line:pr,lineGradient:dr,linePattern:vr,lineSDF:gr,raster:yr,symbolIcon:mr,symbolSDF:xr,symbolTextAndIcon:br}),Tr=function(){this.boundProgram=null,this.boundLayoutVertexBuffer=null,this.boundPaintVertexBuffers=[],this.boundIndexBuffer=null,this.boundVertexOffset=null,this.boundDynamicVertexBuffer=null,this.vao=null};Tr.prototype.bind=function(t,e,r,n,i,a,o,s){this.context=t;for(var l=this.boundPaintVertexBuffers.length!==n.length,u=0;!l&&u>16,s>>16],u_pixel_coord_lower:[65535&o,65535&s]}}kr.prototype.draw=function(t,e,r,n,i,a,o,s,l,u,c,f,h,p,d,v){var g,y=t.gl;if(!this.failedToCreate){for(var m in t.program.set(this.program),t.setDepthMode(r),t.setStencilMode(n),t.setColorMode(i),t.setCullFace(a),this.fixedUniforms)this.fixedUniforms[m].set(o[m]);p&&p.setUniforms(t,this.binderUniforms,f,{zoom:h});for(var x=(g={},g[y.LINES]=2,g[y.TRIANGLES]=3,g[y.LINE_STRIP]=1,g)[e],b=0,_=c.get();b<_.length;b+=1){var w=_[b],T=w.vaos||(w.vaos={});(T[s]||(T[s]=new Tr)).bind(t,this,l,p?p.getPaintVertexBuffers():[],u,w.vertexOffset,d,v),y.drawElements(e,w.primitiveLength*x,y.UNSIGNED_SHORT,w.primitiveOffset*x*2)}}};var Mr=function(e,r,n,i){var a=r.style.light,o=a.properties.get("position"),s=[o.x,o.y,o.z],l=t.create$1();"viewport"===a.properties.get("anchor")&&t.fromRotation(l,-r.transform.angle),t.transformMat3(s,s,l);var u=a.properties.get("color");return{u_matrix:e,u_lightpos:s,u_lightintensity:a.properties.get("intensity"),u_lightcolor:[u.r,u.g,u.b],u_vertical_gradient:+n,u_opacity:i}},Sr=function(e,r,n,i,a,o,s){return t.extend(Mr(e,r,n,i),Ar(o,r,s),{u_height_factor:-Math.pow(2,a.overscaledZ)/s.tileSize/8})},Er=function(t){return{u_matrix:t}},Lr=function(e,r,n,i){return t.extend(Er(e),Ar(n,r,i))},Cr=function(t,e){return{u_matrix:t,u_world:e}},Pr=function(e,r,n,i,a){return t.extend(Lr(e,r,n,i),{u_world:a})},Or=function(e,r,n,i){var a,o,s=e.transform;if("map"===i.paint.get("circle-pitch-alignment")){var l=ge(n,1,s.zoom);a=!0,o=[l,l]}else a=!1,o=s.pixelsToGLUnits;return{u_camera_to_center_distance:s.cameraToCenterDistance,u_scale_with_map:+("map"===i.paint.get("circle-pitch-scale")),u_matrix:e.translatePosMatrix(r.posMatrix,n,i.paint.get("circle-translate"),i.paint.get("circle-translate-anchor")),u_pitch_with_map:+a,u_device_pixel_ratio:t.browser.devicePixelRatio,u_extrude_scale:o}},Ir=function(t,e,r){var n=ge(r,1,e.zoom),i=Math.pow(2,e.zoom-r.tileID.overscaledZ),a=r.tileID.overscaleFactor();return{u_matrix:t,u_camera_to_center_distance:e.cameraToCenterDistance,u_pixels_to_tile_units:n,u_extrude_scale:[e.pixelsToGLUnits[0]/(n*i),e.pixelsToGLUnits[1]/(n*i)],u_overscale_factor:a}},Dr=function(t,e,r){return{u_matrix:t,u_inv_matrix:e,u_camera_to_center_distance:r.cameraToCenterDistance,u_viewport_size:[r.width,r.height]}},zr=function(t,e,r){return void 0===r&&(r=1),{u_matrix:t,u_color:e,u_overlay:0,u_overlay_scale:r}},Rr=function(t){return{u_matrix:t}},Fr=function(t,e,r,n){return{u_matrix:t,u_extrude_scale:ge(e,1,r),u_intensity:n}};var Br=function(e,r,n){var i=e.transform;return{u_matrix:Hr(e,r,n),u_ratio:1/ge(r,1,i.zoom),u_device_pixel_ratio:t.browser.devicePixelRatio,u_units_to_pixels:[1/i.pixelsToGLUnits[0],1/i.pixelsToGLUnits[1]]}},Nr=function(e,r,n){return t.extend(Br(e,r,n),{u_image:0})},jr=function(e,r,n,i){var a=e.transform,o=Vr(r,a);return{u_matrix:Hr(e,r,n),u_texsize:r.imageAtlasTexture.size,u_ratio:1/ge(r,1,a.zoom),u_device_pixel_ratio:t.browser.devicePixelRatio,u_image:0,u_scale:[o,i.fromScale,i.toScale],u_fade:i.t,u_units_to_pixels:[1/a.pixelsToGLUnits[0],1/a.pixelsToGLUnits[1]]}},Ur=function(e,r,n,i,a){var o=e.transform,s=e.lineAtlas,l=Vr(r,o),u="round"===n.layout.get("line-cap"),c=s.getDash(i.from,u),f=s.getDash(i.to,u),h=c.width*a.fromScale,p=f.width*a.toScale;return t.extend(Br(e,r,n),{u_patternscale_a:[l/h,-c.height/2],u_patternscale_b:[l/p,-f.height/2],u_sdfgamma:s.width/(256*Math.min(h,p)*t.browser.devicePixelRatio)/2,u_image:0,u_tex_y_a:c.y,u_tex_y_b:f.y,u_mix:a.t})};function Vr(t,e){return 1/ge(t,1,e.tileZoom)}function Hr(t,e,r){return t.translatePosMatrix(e.tileID.posMatrix,e,r.paint.get("line-translate"),r.paint.get("line-translate-anchor"))}var qr=function(t,e,r,n,i){return{u_matrix:t,u_tl_parent:e,u_scale_parent:r,u_buffer_scale:1,u_fade_t:n.mix,u_opacity:n.opacity*i.paint.get("raster-opacity"),u_image0:0,u_image1:1,u_brightness_low:i.paint.get("raster-brightness-min"),u_brightness_high:i.paint.get("raster-brightness-max"),u_saturation_factor:(o=i.paint.get("raster-saturation"),o>0?1-1/(1.001-o):-o),u_contrast_factor:(a=i.paint.get("raster-contrast"),a>0?1/(1-a):1+a),u_spin_weights:Gr(i.paint.get("raster-hue-rotate"))};var a,o};function Gr(t){t*=Math.PI/180;var e=Math.sin(t),r=Math.cos(t);return[(2*r+1)/3,(-Math.sqrt(3)*e-r+1)/3,(Math.sqrt(3)*e-r+1)/3]}var Zr,Yr=function(t,e,r,n,i,a,o,s,l,u){var c=i.transform;return{u_is_size_zoom_constant:+("constant"===t||"source"===t),u_is_size_feature_constant:+("constant"===t||"camera"===t),u_size_t:e?e.uSizeT:0,u_size:e?e.uSize:0,u_camera_to_center_distance:c.cameraToCenterDistance,u_pitch:c.pitch/360*2*Math.PI,u_rotate_symbol:+r,u_aspect_ratio:c.width/c.height,u_fade_change:i.options.fadeDuration?i.symbolFadeChange:1,u_matrix:a,u_label_plane_matrix:o,u_coord_matrix:s,u_is_text:+l,u_pitch_with_map:+n,u_texsize:u,u_texture:0}},Wr=function(e,r,n,i,a,o,s,l,u,c,f){var h=a.transform;return t.extend(Yr(e,r,n,i,a,o,s,l,u,c),{u_gamma_scale:i?Math.cos(h._pitch)*h.cameraToCenterDistance:1,u_device_pixel_ratio:t.browser.devicePixelRatio,u_is_halo:+f})},Xr=function(e,r,n,i,a,o,s,l,u,c){return t.extend(Wr(e,r,n,i,a,o,s,l,!0,u,!0),{u_texsize_icon:c,u_texture_icon:1})},Jr=function(t,e,r){return{u_matrix:t,u_opacity:e,u_color:r}},Kr=function(e,r,n,i,a,o){return t.extend(function(t,e,r,n){var i=r.imageManager.getPattern(t.from.toString()),a=r.imageManager.getPattern(t.to.toString()),o=r.imageManager.getPixelSize(),s=o.width,l=o.height,u=Math.pow(2,n.tileID.overscaledZ),c=n.tileSize*Math.pow(2,r.transform.tileZoom)/u,f=c*(n.tileID.canonical.x+n.tileID.wrap*u),h=c*n.tileID.canonical.y;return{u_image:0,u_pattern_tl_a:i.tl,u_pattern_br_a:i.br,u_pattern_tl_b:a.tl,u_pattern_br_b:a.br,u_texsize:[s,l],u_mix:e.t,u_pattern_size_a:i.displaySize,u_pattern_size_b:a.displaySize,u_scale_a:e.fromScale,u_scale_b:e.toScale,u_tile_units_to_pixels:1/ge(n,1,r.transform.tileZoom),u_pixel_coord_upper:[f>>16,h>>16],u_pixel_coord_lower:[65535&f,65535&h]}}(i,o,n,a),{u_matrix:e,u_opacity:r})},$r={fillExtrusion:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_lightpos:new t.Uniform3f(e,r.u_lightpos),u_lightintensity:new t.Uniform1f(e,r.u_lightintensity),u_lightcolor:new t.Uniform3f(e,r.u_lightcolor),u_vertical_gradient:new t.Uniform1f(e,r.u_vertical_gradient),u_opacity:new t.Uniform1f(e,r.u_opacity)}},fillExtrusionPattern:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_lightpos:new t.Uniform3f(e,r.u_lightpos),u_lightintensity:new t.Uniform1f(e,r.u_lightintensity),u_lightcolor:new t.Uniform3f(e,r.u_lightcolor),u_vertical_gradient:new t.Uniform1f(e,r.u_vertical_gradient),u_height_factor:new t.Uniform1f(e,r.u_height_factor),u_image:new t.Uniform1i(e,r.u_image),u_texsize:new t.Uniform2f(e,r.u_texsize),u_pixel_coord_upper:new t.Uniform2f(e,r.u_pixel_coord_upper),u_pixel_coord_lower:new t.Uniform2f(e,r.u_pixel_coord_lower),u_scale:new t.Uniform3f(e,r.u_scale),u_fade:new t.Uniform1f(e,r.u_fade),u_opacity:new t.Uniform1f(e,r.u_opacity)}},fill:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix)}},fillPattern:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_image:new t.Uniform1i(e,r.u_image),u_texsize:new t.Uniform2f(e,r.u_texsize),u_pixel_coord_upper:new t.Uniform2f(e,r.u_pixel_coord_upper),u_pixel_coord_lower:new t.Uniform2f(e,r.u_pixel_coord_lower),u_scale:new t.Uniform3f(e,r.u_scale),u_fade:new t.Uniform1f(e,r.u_fade)}},fillOutline:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_world:new t.Uniform2f(e,r.u_world)}},fillOutlinePattern:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_world:new t.Uniform2f(e,r.u_world),u_image:new t.Uniform1i(e,r.u_image),u_texsize:new t.Uniform2f(e,r.u_texsize),u_pixel_coord_upper:new t.Uniform2f(e,r.u_pixel_coord_upper),u_pixel_coord_lower:new t.Uniform2f(e,r.u_pixel_coord_lower),u_scale:new t.Uniform3f(e,r.u_scale),u_fade:new t.Uniform1f(e,r.u_fade)}},circle:function(e,r){return{u_camera_to_center_distance:new t.Uniform1f(e,r.u_camera_to_center_distance),u_scale_with_map:new t.Uniform1i(e,r.u_scale_with_map),u_pitch_with_map:new t.Uniform1i(e,r.u_pitch_with_map),u_extrude_scale:new t.Uniform2f(e,r.u_extrude_scale),u_device_pixel_ratio:new t.Uniform1f(e,r.u_device_pixel_ratio),u_matrix:new t.UniformMatrix4f(e,r.u_matrix)}},collisionBox:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_camera_to_center_distance:new t.Uniform1f(e,r.u_camera_to_center_distance),u_pixels_to_tile_units:new t.Uniform1f(e,r.u_pixels_to_tile_units),u_extrude_scale:new t.Uniform2f(e,r.u_extrude_scale),u_overscale_factor:new t.Uniform1f(e,r.u_overscale_factor)}},collisionCircle:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_inv_matrix:new t.UniformMatrix4f(e,r.u_inv_matrix),u_camera_to_center_distance:new t.Uniform1f(e,r.u_camera_to_center_distance),u_viewport_size:new t.Uniform2f(e,r.u_viewport_size)}},debug:function(e,r){return{u_color:new t.UniformColor(e,r.u_color),u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_overlay:new t.Uniform1i(e,r.u_overlay),u_overlay_scale:new t.Uniform1f(e,r.u_overlay_scale)}},clippingMask:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix)}},heatmap:function(e,r){return{u_extrude_scale:new t.Uniform1f(e,r.u_extrude_scale),u_intensity:new t.Uniform1f(e,r.u_intensity),u_matrix:new t.UniformMatrix4f(e,r.u_matrix)}},heatmapTexture:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_world:new t.Uniform2f(e,r.u_world),u_image:new t.Uniform1i(e,r.u_image),u_color_ramp:new t.Uniform1i(e,r.u_color_ramp),u_opacity:new t.Uniform1f(e,r.u_opacity)}},hillshade:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_image:new t.Uniform1i(e,r.u_image),u_latrange:new t.Uniform2f(e,r.u_latrange),u_light:new t.Uniform2f(e,r.u_light),u_shadow:new t.UniformColor(e,r.u_shadow),u_highlight:new t.UniformColor(e,r.u_highlight),u_accent:new t.UniformColor(e,r.u_accent)}},hillshadePrepare:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_image:new t.Uniform1i(e,r.u_image),u_dimension:new t.Uniform2f(e,r.u_dimension),u_zoom:new t.Uniform1f(e,r.u_zoom),u_maxzoom:new t.Uniform1f(e,r.u_maxzoom),u_unpack:new t.Uniform4f(e,r.u_unpack)}},line:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_ratio:new t.Uniform1f(e,r.u_ratio),u_device_pixel_ratio:new t.Uniform1f(e,r.u_device_pixel_ratio),u_units_to_pixels:new t.Uniform2f(e,r.u_units_to_pixels)}},lineGradient:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_ratio:new t.Uniform1f(e,r.u_ratio),u_device_pixel_ratio:new t.Uniform1f(e,r.u_device_pixel_ratio),u_units_to_pixels:new t.Uniform2f(e,r.u_units_to_pixels),u_image:new t.Uniform1i(e,r.u_image)}},linePattern:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_texsize:new t.Uniform2f(e,r.u_texsize),u_ratio:new t.Uniform1f(e,r.u_ratio),u_device_pixel_ratio:new t.Uniform1f(e,r.u_device_pixel_ratio),u_image:new t.Uniform1i(e,r.u_image),u_units_to_pixels:new t.Uniform2f(e,r.u_units_to_pixels),u_scale:new t.Uniform3f(e,r.u_scale),u_fade:new t.Uniform1f(e,r.u_fade)}},lineSDF:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_ratio:new t.Uniform1f(e,r.u_ratio),u_device_pixel_ratio:new t.Uniform1f(e,r.u_device_pixel_ratio),u_units_to_pixels:new t.Uniform2f(e,r.u_units_to_pixels),u_patternscale_a:new t.Uniform2f(e,r.u_patternscale_a),u_patternscale_b:new t.Uniform2f(e,r.u_patternscale_b),u_sdfgamma:new t.Uniform1f(e,r.u_sdfgamma),u_image:new t.Uniform1i(e,r.u_image),u_tex_y_a:new t.Uniform1f(e,r.u_tex_y_a),u_tex_y_b:new t.Uniform1f(e,r.u_tex_y_b),u_mix:new t.Uniform1f(e,r.u_mix)}},raster:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_tl_parent:new t.Uniform2f(e,r.u_tl_parent),u_scale_parent:new t.Uniform1f(e,r.u_scale_parent),u_buffer_scale:new t.Uniform1f(e,r.u_buffer_scale),u_fade_t:new t.Uniform1f(e,r.u_fade_t),u_opacity:new t.Uniform1f(e,r.u_opacity),u_image0:new t.Uniform1i(e,r.u_image0),u_image1:new t.Uniform1i(e,r.u_image1),u_brightness_low:new t.Uniform1f(e,r.u_brightness_low),u_brightness_high:new t.Uniform1f(e,r.u_brightness_high),u_saturation_factor:new t.Uniform1f(e,r.u_saturation_factor),u_contrast_factor:new t.Uniform1f(e,r.u_contrast_factor),u_spin_weights:new t.Uniform3f(e,r.u_spin_weights)}},symbolIcon:function(e,r){return{u_is_size_zoom_constant:new t.Uniform1i(e,r.u_is_size_zoom_constant),u_is_size_feature_constant:new t.Uniform1i(e,r.u_is_size_feature_constant),u_size_t:new t.Uniform1f(e,r.u_size_t),u_size:new t.Uniform1f(e,r.u_size),u_camera_to_center_distance:new t.Uniform1f(e,r.u_camera_to_center_distance),u_pitch:new t.Uniform1f(e,r.u_pitch),u_rotate_symbol:new t.Uniform1i(e,r.u_rotate_symbol),u_aspect_ratio:new t.Uniform1f(e,r.u_aspect_ratio),u_fade_change:new t.Uniform1f(e,r.u_fade_change),u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_label_plane_matrix:new t.UniformMatrix4f(e,r.u_label_plane_matrix),u_coord_matrix:new t.UniformMatrix4f(e,r.u_coord_matrix),u_is_text:new t.Uniform1i(e,r.u_is_text),u_pitch_with_map:new t.Uniform1i(e,r.u_pitch_with_map),u_texsize:new t.Uniform2f(e,r.u_texsize),u_texture:new t.Uniform1i(e,r.u_texture)}},symbolSDF:function(e,r){return{u_is_size_zoom_constant:new t.Uniform1i(e,r.u_is_size_zoom_constant),u_is_size_feature_constant:new t.Uniform1i(e,r.u_is_size_feature_constant),u_size_t:new t.Uniform1f(e,r.u_size_t),u_size:new t.Uniform1f(e,r.u_size),u_camera_to_center_distance:new t.Uniform1f(e,r.u_camera_to_center_distance),u_pitch:new t.Uniform1f(e,r.u_pitch),u_rotate_symbol:new t.Uniform1i(e,r.u_rotate_symbol),u_aspect_ratio:new t.Uniform1f(e,r.u_aspect_ratio),u_fade_change:new t.Uniform1f(e,r.u_fade_change),u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_label_plane_matrix:new t.UniformMatrix4f(e,r.u_label_plane_matrix),u_coord_matrix:new t.UniformMatrix4f(e,r.u_coord_matrix),u_is_text:new t.Uniform1i(e,r.u_is_text),u_pitch_with_map:new t.Uniform1i(e,r.u_pitch_with_map),u_texsize:new t.Uniform2f(e,r.u_texsize),u_texture:new t.Uniform1i(e,r.u_texture),u_gamma_scale:new t.Uniform1f(e,r.u_gamma_scale),u_device_pixel_ratio:new t.Uniform1f(e,r.u_device_pixel_ratio),u_is_halo:new t.Uniform1i(e,r.u_is_halo)}},symbolTextAndIcon:function(e,r){return{u_is_size_zoom_constant:new t.Uniform1i(e,r.u_is_size_zoom_constant),u_is_size_feature_constant:new t.Uniform1i(e,r.u_is_size_feature_constant),u_size_t:new t.Uniform1f(e,r.u_size_t),u_size:new t.Uniform1f(e,r.u_size),u_camera_to_center_distance:new t.Uniform1f(e,r.u_camera_to_center_distance),u_pitch:new t.Uniform1f(e,r.u_pitch),u_rotate_symbol:new t.Uniform1i(e,r.u_rotate_symbol),u_aspect_ratio:new t.Uniform1f(e,r.u_aspect_ratio),u_fade_change:new t.Uniform1f(e,r.u_fade_change),u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_label_plane_matrix:new t.UniformMatrix4f(e,r.u_label_plane_matrix),u_coord_matrix:new t.UniformMatrix4f(e,r.u_coord_matrix),u_is_text:new t.Uniform1i(e,r.u_is_text),u_pitch_with_map:new t.Uniform1i(e,r.u_pitch_with_map),u_texsize:new t.Uniform2f(e,r.u_texsize),u_texsize_icon:new t.Uniform2f(e,r.u_texsize_icon),u_texture:new t.Uniform1i(e,r.u_texture),u_texture_icon:new t.Uniform1i(e,r.u_texture_icon),u_gamma_scale:new t.Uniform1f(e,r.u_gamma_scale),u_device_pixel_ratio:new t.Uniform1f(e,r.u_device_pixel_ratio),u_is_halo:new t.Uniform1i(e,r.u_is_halo)}},background:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_opacity:new t.Uniform1f(e,r.u_opacity),u_color:new t.UniformColor(e,r.u_color)}},backgroundPattern:function(e,r){return{u_matrix:new t.UniformMatrix4f(e,r.u_matrix),u_opacity:new t.Uniform1f(e,r.u_opacity),u_image:new t.Uniform1i(e,r.u_image),u_pattern_tl_a:new t.Uniform2f(e,r.u_pattern_tl_a),u_pattern_br_a:new t.Uniform2f(e,r.u_pattern_br_a),u_pattern_tl_b:new t.Uniform2f(e,r.u_pattern_tl_b),u_pattern_br_b:new t.Uniform2f(e,r.u_pattern_br_b),u_texsize:new t.Uniform2f(e,r.u_texsize),u_mix:new t.Uniform1f(e,r.u_mix),u_pattern_size_a:new t.Uniform2f(e,r.u_pattern_size_a),u_pattern_size_b:new t.Uniform2f(e,r.u_pattern_size_b),u_scale_a:new t.Uniform1f(e,r.u_scale_a),u_scale_b:new t.Uniform1f(e,r.u_scale_b),u_pixel_coord_upper:new t.Uniform2f(e,r.u_pixel_coord_upper),u_pixel_coord_lower:new t.Uniform2f(e,r.u_pixel_coord_lower),u_tile_units_to_pixels:new t.Uniform1f(e,r.u_tile_units_to_pixels)}}};function Qr(e,r,n,i,a,o,s){for(var l=e.context,u=l.gl,c=e.useProgram("collisionBox"),f=[],h=0,p=0,d=0;d0){var _=t.create(),w=m;t.mul(_,y.placementInvProjMatrix,e.transform.glCoordMatrix),t.mul(_,_,y.placementViewportMatrix),f.push({circleArray:b,circleOffset:p,transform:w,invTransform:_}),p=h+=b.length/4}x&&c.draw(l,u.LINES,Mt.disabled,Et.disabled,e.colorModeForRenderPass(),Ct.disabled,Ir(m,e.transform,g),n.id,x.layoutVertexBuffer,x.indexBuffer,x.segments,null,e.transform.zoom,null,null,x.collisionVertexBuffer)}}if(s&&f.length){var T=e.useProgram("collisionCircle"),k=new t.StructArrayLayout2f1f2i16;k.resize(4*h),k._trim();for(var A=0,M=0,S=f;M=0&&(v[y.associatedIconIndex]={shiftedAnchor:S,angle:E})}else he(y.numGlyphs,p)}if(f){d.clear();for(var C=e.icon.placedSymbolArray,P=0;P0){var s=t.browser.now(),l=(s-e.timeAdded)/o,u=r?(s-r.timeAdded)/o:-1,c=n.getSource(),f=a.coveringZoomLevel({tileSize:c.tileSize,roundZoom:c.roundZoom}),h=!r||Math.abs(r.tileID.overscaledZ-f)>Math.abs(e.tileID.overscaledZ-f),p=h&&e.refreshedUponExpiration?1:t.clamp(h?l:1-u,0,1);return e.refreshedUponExpiration&&l>=1&&(e.refreshedUponExpiration=!1),r?{opacity:1,mix:1-p}:{opacity:p,mix:0}}return{opacity:1,mix:0}}var hn=new t.Color(1,0,0,1),pn=new t.Color(0,1,0,1),dn=new t.Color(0,0,1,1),vn=new t.Color(1,0,1,1),gn=new t.Color(0,1,1,1);function yn(t){var e=t.transform.padding;mn(t,t.transform.height-(e.top||0),3,hn),mn(t,e.bottom||0,3,pn),xn(t,e.left||0,3,dn),xn(t,t.transform.width-(e.right||0),3,vn);var r=t.transform.centerPoint;!function(t,e,r,n){var i=20,a=2;bn(t,e-a/2,r-i/2,a,i,n),bn(t,e-i/2,r-a/2,i,a,n)}(t,r.x,t.transform.height-r.y,gn)}function mn(t,e,r,n){bn(t,0,e+r/2,t.transform.width,r,n)}function xn(t,e,r,n){bn(t,e-r/2,0,r,t.transform.height,n)}function bn(e,r,n,i,a,o){var s=e.context,l=s.gl;l.enable(l.SCISSOR_TEST),l.scissor(r*t.browser.devicePixelRatio,n*t.browser.devicePixelRatio,i*t.browser.devicePixelRatio,a*t.browser.devicePixelRatio),s.clear({color:o}),l.disable(l.SCISSOR_TEST)}function _n(e,r,n){var i=e.context,a=i.gl,o=n.posMatrix,s=e.useProgram("debug"),l=Mt.disabled,u=Et.disabled,c=e.colorModeForRenderPass(),f="$debug";i.activeTexture.set(a.TEXTURE0),e.emptyTexture.bind(a.LINEAR,a.CLAMP_TO_EDGE),s.draw(i,a.LINE_STRIP,l,u,c,Ct.disabled,zr(o,t.Color.red),f,e.debugBuffer,e.tileBorderIndexBuffer,e.debugSegments);var h=r.getTileByID(n.key).latestRawTileData,p=h&&h.byteLength||0,d=Math.floor(p/1024),v=r.getTile(n).tileSize,g=512/Math.min(v,512)*(n.overscaledZ/e.transform.zoom)*.5,y=n.canonical.toString();n.overscaledZ!==n.canonical.z&&(y+=" => "+n.overscaledZ),function(t,e){t.initDebugOverlayCanvas();var r=t.debugOverlayCanvas,n=t.context.gl,i=t.debugOverlayCanvas.getContext("2d");i.clearRect(0,0,r.width,r.height),i.shadowColor="white",i.shadowBlur=2,i.lineWidth=1.5,i.strokeStyle="white",i.textBaseline="top",i.font="bold 36px Open Sans, sans-serif",i.fillText(e,5,5),i.strokeText(e,5,5),t.debugOverlayTexture.update(r),t.debugOverlayTexture.bind(n.LINEAR,n.CLAMP_TO_EDGE)}(e,y+" "+d+"kb"),s.draw(i,a.TRIANGLES,l,u,Lt.alphaBlended,Ct.disabled,zr(o,t.Color.transparent,g),f,e.debugBuffer,e.quadTriangleIndexBuffer,e.debugSegments)}var wn={symbol:function(e,r,n,i,a){if("translucent"===e.renderPass){var o=Et.disabled,s=e.colorModeForRenderPass();n.layout.get("text-variable-anchor")&&function(e,r,n,i,a,o,s){for(var l=r.transform,u="map"===a,c="map"===o,f=0,h=e;f256&&this.clearStencil(),r.setColorMode(Lt.disabled),r.setDepthMode(Mt.disabled);var i=this.useProgram("clippingMask");this._tileClippingMaskIDs={};for(var a=0,o=e;a256&&this.clearStencil();var t=this.nextStencilID++,e=this.context.gl;return new Et({func:e.NOTEQUAL,mask:255},t,255,e.KEEP,e.KEEP,e.REPLACE)},Tn.prototype.stencilModeForClipping=function(t){var e=this.context.gl;return new Et({func:e.EQUAL,mask:255},this._tileClippingMaskIDs[t.key],0,e.KEEP,e.KEEP,e.REPLACE)},Tn.prototype.stencilConfigForOverlap=function(t){var e,r=this.context.gl,n=t.sort((function(t,e){return e.overscaledZ-t.overscaledZ})),i=n[n.length-1].overscaledZ,a=n[0].overscaledZ-i+1;if(a>1){this.currentStencilSource=void 0,this.nextStencilID+a>256&&this.clearStencil();for(var o={},s=0;s=0;this.currentLayer--){var w=this.style._layers[i[this.currentLayer]],T=a[w.source],k=c[w.source];this._renderTileClippingMasks(w,k),this.renderLayer(this,T,w,k)}for(this.renderPass="translucent",this.currentLayer=0;this.currentLayer0?e.pop():null},Tn.prototype.isPatternMissing=function(t){if(!t)return!1;if(!t.from||!t.to)return!0;var e=this.imageManager.getPattern(t.from.toString()),r=this.imageManager.getPattern(t.to.toString());return!e||!r},Tn.prototype.useProgram=function(t,e){this.cache=this.cache||{};var r=""+t+(e?e.cacheKey:"")+(this._showOverdrawInspector?"/overdraw":"");return this.cache[r]||(this.cache[r]=new kr(this.context,wr[t],e,$r[t],this._showOverdrawInspector)),this.cache[r]},Tn.prototype.setCustomLayerDefaults=function(){this.context.unbindVAO(),this.context.cullFace.setDefault(),this.context.activeTexture.setDefault(),this.context.pixelStoreUnpack.setDefault(),this.context.pixelStoreUnpackPremultiplyAlpha.setDefault(),this.context.pixelStoreUnpackFlipY.setDefault()},Tn.prototype.setBaseState=function(){var t=this.context.gl;this.context.cullFace.set(!1),this.context.viewport.set([0,0,this.width,this.height]),this.context.blendEquation.set(t.FUNC_ADD)},Tn.prototype.initDebugOverlayCanvas=function(){if(null==this.debugOverlayCanvas){this.debugOverlayCanvas=t.window.document.createElement("canvas"),this.debugOverlayCanvas.width=512,this.debugOverlayCanvas.height=512;var e=this.context.gl;this.debugOverlayTexture=new t.Texture(this.context,this.debugOverlayCanvas,e.RGBA)}},Tn.prototype.destroy=function(){this.emptyTexture.destroy(),this.debugOverlayTexture&&this.debugOverlayTexture.destroy()};var kn=function(t,e){this.points=t,this.planes=e};kn.fromInvProjectionMatrix=function(e,r,n){var i=Math.pow(2,n),a=[[-1,1,-1,1],[1,1,-1,1],[1,-1,-1,1],[-1,-1,-1,1],[-1,1,1,1],[1,1,1,1],[1,-1,1,1],[-1,-1,1,1]].map((function(r){return t.transformMat4([],r,e)})).map((function(e){return t.scale$1([],e,1/e[3]/r*i)})),o=[[0,1,2],[6,5,4],[0,3,7],[2,1,5],[3,2,6],[0,4,5]].map((function(e){var r=t.sub([],a[e[0]],a[e[1]]),n=t.sub([],a[e[2]],a[e[1]]),i=t.normalize([],t.cross([],r,n)),o=-t.dot(i,a[e[1]]);return i.concat(o)}));return new kn(a,o)};var An=function(e,r){this.min=e,this.max=r,this.center=t.scale$2([],t.add([],this.min,this.max),.5)};An.prototype.quadrant=function(e){for(var r=[e%2==0,e<2],n=t.clone$2(this.min),i=t.clone$2(this.max),a=0;a=0;if(0===o)return 0;o!==r.length&&(n=!1)}if(n)return 2;for(var l=0;l<3;l++){for(var u=Number.MAX_VALUE,c=-Number.MAX_VALUE,f=0;fthis.max[l]-this.min[l])return 0}return 1};var Mn=function(t,e,r,n){if(void 0===t&&(t=0),void 0===e&&(e=0),void 0===r&&(r=0),void 0===n&&(n=0),isNaN(t)||t<0||isNaN(e)||e<0||isNaN(r)||r<0||isNaN(n)||n<0)throw new Error("Invalid value for edge-insets, top, bottom, left and right must all be numbers");this.top=t,this.bottom=e,this.left=r,this.right=n};Mn.prototype.interpolate=function(e,r,n){return null!=r.top&&null!=e.top&&(this.top=t.number(e.top,r.top,n)),null!=r.bottom&&null!=e.bottom&&(this.bottom=t.number(e.bottom,r.bottom,n)),null!=r.left&&null!=e.left&&(this.left=t.number(e.left,r.left,n)),null!=r.right&&null!=e.right&&(this.right=t.number(e.right,r.right,n)),this},Mn.prototype.getCenter=function(e,r){var n=t.clamp((this.left+e-this.right)/2,0,e),i=t.clamp((this.top+r-this.bottom)/2,0,r);return new t.Point(n,i)},Mn.prototype.equals=function(t){return this.top===t.top&&this.bottom===t.bottom&&this.left===t.left&&this.right===t.right},Mn.prototype.clone=function(){return new Mn(this.top,this.bottom,this.left,this.right)},Mn.prototype.toJSON=function(){return{top:this.top,bottom:this.bottom,left:this.left,right:this.right}};var Sn=function(e,r,n,i,a){this.tileSize=512,this.maxValidLatitude=85.051129,this._renderWorldCopies=void 0===a||a,this._minZoom=e||0,this._maxZoom=r||22,this._minPitch=null==n?0:n,this._maxPitch=null==i?60:i,this.setMaxBounds(),this.width=0,this.height=0,this._center=new t.LngLat(0,0),this.zoom=0,this.angle=0,this._fov=.6435011087932844,this._pitch=0,this._unmodified=!0,this._edgeInsets=new Mn,this._posMatrixCache={},this._alignedPosMatrixCache={}},En={minZoom:{configurable:!0},maxZoom:{configurable:!0},minPitch:{configurable:!0},maxPitch:{configurable:!0},renderWorldCopies:{configurable:!0},worldSize:{configurable:!0},centerOffset:{configurable:!0},size:{configurable:!0},bearing:{configurable:!0},pitch:{configurable:!0},fov:{configurable:!0},zoom:{configurable:!0},center:{configurable:!0},padding:{configurable:!0},centerPoint:{configurable:!0},unmodified:{configurable:!0},point:{configurable:!0}};Sn.prototype.clone=function(){var t=new Sn(this._minZoom,this._maxZoom,this._minPitch,this.maxPitch,this._renderWorldCopies);return t.tileSize=this.tileSize,t.latRange=this.latRange,t.width=this.width,t.height=this.height,t._center=this._center,t.zoom=this.zoom,t.angle=this.angle,t._fov=this._fov,t._pitch=this._pitch,t._unmodified=this._unmodified,t._edgeInsets=this._edgeInsets.clone(),t._calcMatrices(),t},En.minZoom.get=function(){return this._minZoom},En.minZoom.set=function(t){this._minZoom!==t&&(this._minZoom=t,this.zoom=Math.max(this.zoom,t))},En.maxZoom.get=function(){return this._maxZoom},En.maxZoom.set=function(t){this._maxZoom!==t&&(this._maxZoom=t,this.zoom=Math.min(this.zoom,t))},En.minPitch.get=function(){return this._minPitch},En.minPitch.set=function(t){this._minPitch!==t&&(this._minPitch=t,this.pitch=Math.max(this.pitch,t))},En.maxPitch.get=function(){return this._maxPitch},En.maxPitch.set=function(t){this._maxPitch!==t&&(this._maxPitch=t,this.pitch=Math.min(this.pitch,t))},En.renderWorldCopies.get=function(){return this._renderWorldCopies},En.renderWorldCopies.set=function(t){void 0===t?t=!0:null===t&&(t=!1),this._renderWorldCopies=t},En.worldSize.get=function(){return this.tileSize*this.scale},En.centerOffset.get=function(){return this.centerPoint._sub(this.size._div(2))},En.size.get=function(){return new t.Point(this.width,this.height)},En.bearing.get=function(){return-this.angle/Math.PI*180},En.bearing.set=function(e){var r=-t.wrap(e,-180,180)*Math.PI/180;this.angle!==r&&(this._unmodified=!1,this.angle=r,this._calcMatrices(),this.rotationMatrix=t.create$2(),t.rotate(this.rotationMatrix,this.rotationMatrix,this.angle))},En.pitch.get=function(){return this._pitch/Math.PI*180},En.pitch.set=function(e){var r=t.clamp(e,this.minPitch,this.maxPitch)/180*Math.PI;this._pitch!==r&&(this._unmodified=!1,this._pitch=r,this._calcMatrices())},En.fov.get=function(){return this._fov/Math.PI*180},En.fov.set=function(t){t=Math.max(.01,Math.min(60,t)),this._fov!==t&&(this._unmodified=!1,this._fov=t/180*Math.PI,this._calcMatrices())},En.zoom.get=function(){return this._zoom},En.zoom.set=function(t){var e=Math.min(Math.max(t,this.minZoom),this.maxZoom);this._zoom!==e&&(this._unmodified=!1,this._zoom=e,this.scale=this.zoomScale(e),this.tileZoom=Math.floor(e),this.zoomFraction=e-this.tileZoom,this._constrain(),this._calcMatrices())},En.center.get=function(){return this._center},En.center.set=function(t){t.lat===this._center.lat&&t.lng===this._center.lng||(this._unmodified=!1,this._center=t,this._constrain(),this._calcMatrices())},En.padding.get=function(){return this._edgeInsets.toJSON()},En.padding.set=function(t){this._edgeInsets.equals(t)||(this._unmodified=!1,this._edgeInsets.interpolate(this._edgeInsets,t,1),this._calcMatrices())},En.centerPoint.get=function(){return this._edgeInsets.getCenter(this.width,this.height)},Sn.prototype.isPaddingEqual=function(t){return this._edgeInsets.equals(t)},Sn.prototype.interpolatePadding=function(t,e,r){this._unmodified=!1,this._edgeInsets.interpolate(t,e,r),this._constrain(),this._calcMatrices()},Sn.prototype.coveringZoomLevel=function(t){var e=(t.roundZoom?Math.round:Math.floor)(this.zoom+this.scaleZoom(this.tileSize/t.tileSize));return Math.max(0,e)},Sn.prototype.getVisibleUnwrappedCoordinates=function(e){var r=[new t.UnwrappedTileID(0,e)];if(this._renderWorldCopies)for(var n=this.pointCoordinate(new t.Point(0,0)),i=this.pointCoordinate(new t.Point(this.width,0)),a=this.pointCoordinate(new t.Point(this.width,this.height)),o=this.pointCoordinate(new t.Point(0,this.height)),s=Math.floor(Math.min(n.x,i.x,a.x,o.x)),l=Math.floor(Math.max(n.x,i.x,a.x,o.x)),u=s-1;u<=l+1;u++)0!==u&&r.push(new t.UnwrappedTileID(u,e));return r},Sn.prototype.coveringTiles=function(e){var r=this.coveringZoomLevel(e),n=r;if(void 0!==e.minzoom&&re.maxzoom&&(r=e.maxzoom);var i=t.MercatorCoordinate.fromLngLat(this.center),a=Math.pow(2,r),o=[a*i.x,a*i.y,0],s=kn.fromInvProjectionMatrix(this.invProjMatrix,this.worldSize,r),l=e.minzoom||0;this.pitch<=60&&this._edgeInsets.top<.1&&(l=r);var u=function(t){return{aabb:new An([t*a,0,0],[(t+1)*a,a,0]),zoom:0,x:0,y:0,wrap:t,fullyVisible:!1}},c=[],f=[],h=r,p=e.reparseOverscaled?n:r;if(this._renderWorldCopies)for(var d=1;d<=3;d++)c.push(u(-d)),c.push(u(d));for(c.push(u(0));c.length>0;){var v=c.pop(),g=v.x,y=v.y,m=v.fullyVisible;if(!m){var x=v.aabb.intersects(s);if(0===x)continue;m=2===x}var b=v.aabb.distanceX(o),_=v.aabb.distanceY(o),w=Math.max(Math.abs(b),Math.abs(_)),T=3+(1<T&&v.zoom>=l)f.push({tileID:new t.OverscaledTileID(v.zoom===h?p:v.zoom,v.wrap,v.zoom,g,y),distanceSq:t.sqrLen([o[0]-.5-g,o[1]-.5-y])});else for(var k=0;k<4;k++){var A=(g<<1)+k%2,M=(y<<1)+(k>>1);c.push({aabb:v.aabb.quadrant(k),zoom:v.zoom+1,x:A,y:M,wrap:v.wrap,fullyVisible:m})}}return f.sort((function(t,e){return t.distanceSq-e.distanceSq})).map((function(t){return t.tileID}))},Sn.prototype.resize=function(t,e){this.width=t,this.height=e,this.pixelsToGLUnits=[2/t,-2/e],this._constrain(),this._calcMatrices()},En.unmodified.get=function(){return this._unmodified},Sn.prototype.zoomScale=function(t){return Math.pow(2,t)},Sn.prototype.scaleZoom=function(t){return Math.log(t)/Math.LN2},Sn.prototype.project=function(e){var r=t.clamp(e.lat,-this.maxValidLatitude,this.maxValidLatitude);return new t.Point(t.mercatorXfromLng(e.lng)*this.worldSize,t.mercatorYfromLat(r)*this.worldSize)},Sn.prototype.unproject=function(e){return new t.MercatorCoordinate(e.x/this.worldSize,e.y/this.worldSize).toLngLat()},En.point.get=function(){return this.project(this.center)},Sn.prototype.setLocationAtPoint=function(e,r){var n=this.pointCoordinate(r),i=this.pointCoordinate(this.centerPoint),a=this.locationCoordinate(e),o=new t.MercatorCoordinate(a.x-(n.x-i.x),a.y-(n.y-i.y));this.center=this.coordinateLocation(o),this._renderWorldCopies&&(this.center=this.center.wrap())},Sn.prototype.locationPoint=function(t){return this.coordinatePoint(this.locationCoordinate(t))},Sn.prototype.pointLocation=function(t){return this.coordinateLocation(this.pointCoordinate(t))},Sn.prototype.locationCoordinate=function(e){return t.MercatorCoordinate.fromLngLat(e)},Sn.prototype.coordinateLocation=function(t){return t.toLngLat()},Sn.prototype.pointCoordinate=function(e){var r=[e.x,e.y,0,1],n=[e.x,e.y,1,1];t.transformMat4(r,r,this.pixelMatrixInverse),t.transformMat4(n,n,this.pixelMatrixInverse);var i=r[3],a=n[3],o=r[0]/i,s=n[0]/a,l=r[1]/i,u=n[1]/a,c=r[2]/i,f=n[2]/a,h=c===f?0:(0-c)/(f-c);return new t.MercatorCoordinate(t.number(o,s,h)/this.worldSize,t.number(l,u,h)/this.worldSize)},Sn.prototype.coordinatePoint=function(e){var r=[e.x*this.worldSize,e.y*this.worldSize,0,1];return t.transformMat4(r,r,this.pixelMatrix),new t.Point(r[0]/r[3],r[1]/r[3])},Sn.prototype.getBounds=function(){return(new t.LngLatBounds).extend(this.pointLocation(new t.Point(0,0))).extend(this.pointLocation(new t.Point(this.width,0))).extend(this.pointLocation(new t.Point(this.width,this.height))).extend(this.pointLocation(new t.Point(0,this.height)))},Sn.prototype.getMaxBounds=function(){return this.latRange&&2===this.latRange.length&&this.lngRange&&2===this.lngRange.length?new t.LngLatBounds([this.lngRange[0],this.latRange[0]],[this.lngRange[1],this.latRange[1]]):null},Sn.prototype.setMaxBounds=function(t){t?(this.lngRange=[t.getWest(),t.getEast()],this.latRange=[t.getSouth(),t.getNorth()],this._constrain()):(this.lngRange=null,this.latRange=[-this.maxValidLatitude,this.maxValidLatitude])},Sn.prototype.calculatePosMatrix=function(e,r){void 0===r&&(r=!1);var n=e.key,i=r?this._alignedPosMatrixCache:this._posMatrixCache;if(i[n])return i[n];var a=e.canonical,o=this.worldSize/this.zoomScale(a.z),s=a.x+Math.pow(2,a.z)*e.wrap,l=t.identity(new Float64Array(16));return t.translate(l,l,[s*o,a.y*o,0]),t.scale(l,l,[o/t.EXTENT,o/t.EXTENT,1]),t.multiply(l,r?this.alignedProjMatrix:this.projMatrix,l),i[n]=new Float32Array(l),i[n]},Sn.prototype.customLayerMatrix=function(){return this.mercatorMatrix.slice()},Sn.prototype._constrain=function(){if(this.center&&this.width&&this.height&&!this._constraining){this._constraining=!0;var e,r,n,i,a=-90,o=90,s=-180,l=180,u=this.size,c=this._unmodified;if(this.latRange){var f=this.latRange;a=t.mercatorYfromLat(f[1])*this.worldSize,e=(o=t.mercatorYfromLat(f[0])*this.worldSize)-ao&&(i=o-g)}if(this.lngRange){var y=p.x,m=u.x/2;y-ml&&(n=l-m)}void 0===n&&void 0===i||(this.center=this.unproject(new t.Point(void 0!==n?n:p.x,void 0!==i?i:p.y))),this._unmodified=c,this._constraining=!1}},Sn.prototype._calcMatrices=function(){if(this.height){var e=this._fov/2,r=this.centerOffset;this.cameraToCenterDistance=.5/Math.tan(e)*this.height;var n=Math.PI/2+this._pitch,i=this._fov*(.5+r.y/this.height),a=Math.sin(i)*this.cameraToCenterDistance/Math.sin(t.clamp(Math.PI-n-i,.01,Math.PI-.01)),o=this.point,s=o.x,l=o.y,u=1.01*(Math.cos(Math.PI/2-this._pitch)*a+this.cameraToCenterDistance),c=this.height/50,f=new Float64Array(16);t.perspective(f,this._fov,this.width/this.height,c,u),f[8]=2*-r.x/this.width,f[9]=2*r.y/this.height,t.scale(f,f,[1,-1,1]),t.translate(f,f,[0,0,-this.cameraToCenterDistance]),t.rotateX(f,f,this._pitch),t.rotateZ(f,f,this.angle),t.translate(f,f,[-s,-l,0]),this.mercatorMatrix=t.scale([],f,[this.worldSize,this.worldSize,this.worldSize]),t.scale(f,f,[1,1,t.mercatorZfromAltitude(1,this.center.lat)*this.worldSize,1]),this.projMatrix=f,this.invProjMatrix=t.invert([],this.projMatrix);var h=this.width%2/2,p=this.height%2/2,d=Math.cos(this.angle),v=Math.sin(this.angle),g=s-Math.round(s)+d*h+v*p,y=l-Math.round(l)+d*p+v*h,m=new Float64Array(f);if(t.translate(m,m,[g>.5?g-1:g,y>.5?y-1:y,0]),this.alignedProjMatrix=m,f=t.create(),t.scale(f,f,[this.width/2,-this.height/2,1]),t.translate(f,f,[1,-1,0]),this.labelPlaneMatrix=f,f=t.create(),t.scale(f,f,[1,-1,1]),t.translate(f,f,[-1,-1,0]),t.scale(f,f,[2/this.width,2/this.height,1]),this.glCoordMatrix=f,this.pixelMatrix=t.multiply(new Float64Array(16),this.labelPlaneMatrix,this.projMatrix),!(f=t.invert(new Float64Array(16),this.pixelMatrix)))throw new Error("failed to invert matrix");this.pixelMatrixInverse=f,this._posMatrixCache={},this._alignedPosMatrixCache={}}},Sn.prototype.maxPitchScaleFactor=function(){if(!this.pixelMatrixInverse)return 1;var e=this.pointCoordinate(new t.Point(0,0)),r=[e.x*this.worldSize,e.y*this.worldSize,0,1];return t.transformMat4(r,r,this.pixelMatrix)[3]/this.cameraToCenterDistance},Sn.prototype.getCameraPoint=function(){var e=this._pitch,r=Math.tan(e)*(this.cameraToCenterDistance||1);return this.centerPoint.add(new t.Point(0,r))},Sn.prototype.getCameraQueryGeometry=function(e){var r=this.getCameraPoint();if(1===e.length)return[e[0],r];for(var n=r.x,i=r.y,a=r.x,o=r.y,s=0,l=e;s=3&&!t.some((function(t){return isNaN(t)}))){var e=this._map.dragRotate.isEnabled()&&this._map.touchZoomRotate.isEnabled()?+(t[3]||0):this._map.getBearing();return this._map.jumpTo({center:[+t[2],+t[1]],zoom:+t[0],bearing:e,pitch:+(t[4]||0)}),!0}return!1},Ln.prototype._updateHashUnthrottled=function(){var e=this.getHashString();try{t.window.history.replaceState(t.window.history.state,"",e)}catch(t){}};var Cn={linearity:.3,easing:t.bezier(0,0,.3,1)},Pn=t.extend({deceleration:2500,maxSpeed:1400},Cn),On=t.extend({deceleration:20,maxSpeed:1400},Cn),In=t.extend({deceleration:1e3,maxSpeed:360},Cn),Dn=t.extend({deceleration:1e3,maxSpeed:90},Cn),zn=function(t){this._map=t,this.clear()};function Rn(t,e){(!t.duration||t.duration0&&r-e[0].time>160;)e.shift()},zn.prototype._onMoveEnd=function(e){if(this._drainInertiaBuffer(),!(this._inertiaBuffer.length<2)){for(var r={zoom:0,bearing:0,pitch:0,pan:new t.Point(0,0),pinchAround:void 0,around:void 0},n=0,i=this._inertiaBuffer;n=this._clickTolerance||this._map.fire(new Bn(t.type,this._map,t))},Un.prototype.dblclick=function(t){return this._firePreventable(new Bn(t.type,this._map,t))},Un.prototype.mouseover=function(t){this._map.fire(new Bn(t.type,this._map,t))},Un.prototype.mouseout=function(t){this._map.fire(new Bn(t.type,this._map,t))},Un.prototype.touchstart=function(t){return this._firePreventable(new Nn(t.type,this._map,t))},Un.prototype.touchmove=function(t){this._map.fire(new Nn(t.type,this._map,t))},Un.prototype.touchend=function(t){this._map.fire(new Nn(t.type,this._map,t))},Un.prototype.touchcancel=function(t){this._map.fire(new Nn(t.type,this._map,t))},Un.prototype._firePreventable=function(t){if(this._map.fire(t),t.defaultPrevented)return{}},Un.prototype.isEnabled=function(){return!0},Un.prototype.isActive=function(){return!1},Un.prototype.enable=function(){},Un.prototype.disable=function(){};var Vn=function(t){this._map=t};Vn.prototype.reset=function(){this._delayContextMenu=!1,delete this._contextMenuEvent},Vn.prototype.mousemove=function(t){this._map.fire(new Bn(t.type,this._map,t))},Vn.prototype.mousedown=function(){this._delayContextMenu=!0},Vn.prototype.mouseup=function(){this._delayContextMenu=!1,this._contextMenuEvent&&(this._map.fire(new Bn("contextmenu",this._map,this._contextMenuEvent)),delete this._contextMenuEvent)},Vn.prototype.contextmenu=function(t){this._delayContextMenu?this._contextMenuEvent=t:this._map.fire(new Bn(t.type,this._map,t)),this._map.listens("contextmenu")&&t.preventDefault()},Vn.prototype.isEnabled=function(){return!0},Vn.prototype.isActive=function(){return!1},Vn.prototype.enable=function(){},Vn.prototype.disable=function(){};var Hn=function(t,e){this._map=t,this._el=t.getCanvasContainer(),this._container=t.getContainer(),this._clickTolerance=e.clickTolerance||1};function qn(t,e){for(var r={},n=0;nthis.numTouches)&&(this.aborted=!0),this.aborted||(void 0===this.startTime&&(this.startTime=e.timeStamp),n.length===this.numTouches&&(this.centroid=function(e){for(var r=new t.Point(0,0),n=0,i=e;n30)&&(this.aborted=!0)}}},Gn.prototype.touchend=function(t,e,r){if((!this.centroid||t.timeStamp-this.startTime>500)&&(this.aborted=!0),0===r.length){var n=!this.aborted&&this.centroid;if(this.reset(),n)return n}};var Zn=function(t){this.singleTap=new Gn(t),this.numTaps=t.numTaps,this.reset()};Zn.prototype.reset=function(){this.lastTime=1/0,delete this.lastTap,this.count=0,this.singleTap.reset()},Zn.prototype.touchstart=function(t,e,r){this.singleTap.touchstart(t,e,r)},Zn.prototype.touchmove=function(t,e,r){this.singleTap.touchmove(t,e,r)},Zn.prototype.touchend=function(t,e,r){var n=this.singleTap.touchend(t,e,r);if(n){var i=t.timeStamp-this.lastTime<500,a=!this.lastTap||this.lastTap.dist(n)<30;if(i&&a||this.reset(),this.count++,this.lastTime=t.timeStamp,this.lastTap=n,this.count===this.numTaps)return this.reset(),n}};var Yn=function(){this._zoomIn=new Zn({numTouches:1,numTaps:2}),this._zoomOut=new Zn({numTouches:2,numTaps:1}),this.reset()};Yn.prototype.reset=function(){this._active=!1,this._zoomIn.reset(),this._zoomOut.reset()},Yn.prototype.touchstart=function(t,e,r){this._zoomIn.touchstart(t,e,r),this._zoomOut.touchstart(t,e,r)},Yn.prototype.touchmove=function(t,e,r){this._zoomIn.touchmove(t,e,r),this._zoomOut.touchmove(t,e,r)},Yn.prototype.touchend=function(t,e,r){var n=this,i=this._zoomIn.touchend(t,e,r),a=this._zoomOut.touchend(t,e,r);return i?(this._active=!0,t.preventDefault(),setTimeout((function(){return n.reset()}),0),{cameraAnimation:function(e){return e.easeTo({duration:300,zoom:e.getZoom()+1,around:e.unproject(i)},{originalEvent:t})}}):a?(this._active=!0,t.preventDefault(),setTimeout((function(){return n.reset()}),0),{cameraAnimation:function(e){return e.easeTo({duration:300,zoom:e.getZoom()-1,around:e.unproject(a)},{originalEvent:t})}}):void 0},Yn.prototype.touchcancel=function(){this.reset()},Yn.prototype.enable=function(){this._enabled=!0},Yn.prototype.disable=function(){this._enabled=!1,this.reset()},Yn.prototype.isEnabled=function(){return this._enabled},Yn.prototype.isActive=function(){return this._active};var Wn=function(t){this.reset(),this._clickTolerance=t.clickTolerance||1};Wn.prototype.reset=function(){this._active=!1,this._moved=!1,delete this._lastPoint,delete this._eventButton},Wn.prototype._correctButton=function(t,e){return!1},Wn.prototype._move=function(t,e){return{}},Wn.prototype.mousedown=function(t,e){if(!this._lastPoint){var n=r.mouseButton(t);this._correctButton(t,n)&&(this._lastPoint=e,this._eventButton=n)}},Wn.prototype.mousemoveWindow=function(t,e){var r=this._lastPoint;if(r&&(t.preventDefault(),this._moved||!(e.dist(r)0&&(this._active=!0);var i=qn(n,r),a=new t.Point(0,0),o=new t.Point(0,0),s=0;for(var l in i){var u=i[l],c=this._touches[l];c&&(a._add(u),o._add(u.sub(c)),s++,i[l]=u)}if(this._touches=i,!(sMath.abs(t.x)}var oi=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e.prototype.reset=function(){t.prototype.reset.call(this),this._valid=void 0,delete this._firstMove,delete this._lastPoints},e.prototype._start=function(t){this._lastPoints=t,ai(t[0].sub(t[1]))&&(this._valid=!1)},e.prototype._move=function(t,e,r){var n=t[0].sub(this._lastPoints[0]),i=t[1].sub(this._lastPoints[1]);if(this._valid=this.gestureBeginsVertically(n,i,r.timeStamp),this._valid)return this._lastPoints=t,this._active=!0,{pitchDelta:(n.y+i.y)/2*-.5}},e.prototype.gestureBeginsVertically=function(t,e,r){if(void 0!==this._valid)return this._valid;var n=t.mag()>=2,i=e.mag()>=2;if(n||i){if(!n||!i)return void 0===this._firstMove&&(this._firstMove=r),r-this._firstMove<100&&void 0;var a=t.y>0==e.y>0;return ai(t)&&ai(e)&&a}},e}(Qn),si={panStep:100,bearingStep:15,pitchStep:10},li=function(){var t=si;this._panStep=t.panStep,this._bearingStep=t.bearingStep,this._pitchStep=t.pitchStep};function ui(t){return t*(2-t)}li.prototype.reset=function(){this._active=!1},li.prototype.keydown=function(t){var e=this;if(!(t.altKey||t.ctrlKey||t.metaKey)){var r=0,n=0,i=0,a=0,o=0;switch(t.keyCode){case 61:case 107:case 171:case 187:r=1;break;case 189:case 109:case 173:r=-1;break;case 37:t.shiftKey?n=-1:(t.preventDefault(),a=-1);break;case 39:t.shiftKey?n=1:(t.preventDefault(),a=1);break;case 38:t.shiftKey?i=1:(t.preventDefault(),o=-1);break;case 40:t.shiftKey?i=-1:(t.preventDefault(),o=1);break;default:return}return{cameraAnimation:function(s){var l=s.getZoom();s.easeTo({duration:300,easeId:"keyboardHandler",easing:ui,zoom:r?Math.round(l)+r*(t.shiftKey?2:1):l,bearing:s.getBearing()+n*e._bearingStep,pitch:s.getPitch()+i*e._pitchStep,offset:[-a*e._panStep,-o*e._panStep],center:s.getCenter()},{originalEvent:t})}}}},li.prototype.enable=function(){this._enabled=!0},li.prototype.disable=function(){this._enabled=!1,this.reset()},li.prototype.isEnabled=function(){return this._enabled},li.prototype.isActive=function(){return this._active};var ci=4.000244140625,fi=function(e,r){this._map=e,this._el=e.getCanvasContainer(),this._handler=r,this._delta=0,this._defaultZoomRate=.01,this._wheelZoomRate=.0022222222222222222,t.bindAll(["_onWheel","_onTimeout","_onScrollFrame","_onScrollFinished"],this)};fi.prototype.setZoomRate=function(t){this._defaultZoomRate=t},fi.prototype.setWheelZoomRate=function(t){this._wheelZoomRate=t},fi.prototype.isEnabled=function(){return!!this._enabled},fi.prototype.isActive=function(){return!!this._active||void 0!==this._finishTimeout},fi.prototype.isZooming=function(){return!!this._zooming},fi.prototype.enable=function(t){this.isEnabled()||(this._enabled=!0,this._aroundCenter=t&&"center"===t.around)},fi.prototype.disable=function(){this.isEnabled()&&(this._enabled=!1)},fi.prototype.wheel=function(e){if(this.isEnabled()){var r=e.deltaMode===t.window.WheelEvent.DOM_DELTA_LINE?40*e.deltaY:e.deltaY,n=t.browser.now(),i=n-(this._lastWheelEventTime||0);this._lastWheelEventTime=n,0!==r&&r%ci==0?this._type="wheel":0!==r&&Math.abs(r)<4?this._type="trackpad":i>400?(this._type=null,this._lastValue=r,this._timeout=setTimeout(this._onTimeout,40,e)):this._type||(this._type=Math.abs(i*r)<200?"trackpad":"wheel",this._timeout&&(clearTimeout(this._timeout),this._timeout=null,r+=this._lastValue)),e.shiftKey&&r&&(r/=4),this._type&&(this._lastWheelEvent=e,this._delta-=r,this._active||this._start(e)),e.preventDefault()}},fi.prototype._onTimeout=function(t){this._type="wheel",this._delta-=this._lastValue,this._active||this._start(t)},fi.prototype._start=function(e){if(this._delta){this._frameId&&(this._frameId=null),this._active=!0,this.isZooming()||(this._zooming=!0),this._finishTimeout&&(clearTimeout(this._finishTimeout),delete this._finishTimeout);var n=r.mousePos(this._el,e);this._around=t.LngLat.convert(this._aroundCenter?this._map.getCenter():this._map.unproject(n)),this._aroundPoint=this._map.transform.locationPoint(this._around),this._frameId||(this._frameId=!0,this._handler._triggerRenderFrame())}},fi.prototype.renderFrame=function(){return this._onScrollFrame()},fi.prototype._onScrollFrame=function(){var e=this;if(this._frameId&&(this._frameId=null,this.isActive())){var r=this._map.transform;if(0!==this._delta){var n="wheel"===this._type&&Math.abs(this._delta)>ci?this._wheelZoomRate:this._defaultZoomRate,i=2/(1+Math.exp(-Math.abs(this._delta*n)));this._delta<0&&0!==i&&(i=1/i);var a="number"==typeof this._targetZoom?r.zoomScale(this._targetZoom):r.scale;this._targetZoom=Math.min(r.maxZoom,Math.max(r.minZoom,r.scaleZoom(a*i))),"wheel"===this._type&&(this._startZoom=r.zoom,this._easing=this._smoothOutEasing(200)),this._delta=0}var o,s="number"==typeof this._targetZoom?this._targetZoom:r.zoom,l=this._startZoom,u=this._easing,c=!1;if("wheel"===this._type&&l&&u){var f=Math.min((t.browser.now()-this._lastWheelEventTime)/200,1),h=u(f);o=t.number(l,s,h),f<1?this._frameId||(this._frameId=!0):c=!0}else o=s,c=!0;return this._active=!0,c&&(this._active=!1,this._finishTimeout=setTimeout((function(){e._zooming=!1,e._handler._triggerRenderFrame(),delete e._targetZoom,delete e._finishTimeout}),200)),{noInertia:!0,needsRenderFrame:!c,zoomDelta:o-r.zoom,around:this._aroundPoint,originalEvent:this._lastWheelEvent}}},fi.prototype._smoothOutEasing=function(e){var r=t.ease;if(this._prevEase){var n=this._prevEase,i=(t.browser.now()-n.start)/n.duration,a=n.easing(i+.01)-n.easing(i),o=.27/Math.sqrt(a*a+1e-4)*.01,s=Math.sqrt(.0729-o*o);r=t.bezier(o,s,.25,1)}return this._prevEase={start:t.browser.now(),duration:e,easing:r},r},fi.prototype.reset=function(){this._active=!1};var hi=function(t,e){this._clickZoom=t,this._tapZoom=e};hi.prototype.enable=function(){this._clickZoom.enable(),this._tapZoom.enable()},hi.prototype.disable=function(){this._clickZoom.disable(),this._tapZoom.disable()},hi.prototype.isEnabled=function(){return this._clickZoom.isEnabled()&&this._tapZoom.isEnabled()},hi.prototype.isActive=function(){return this._clickZoom.isActive()||this._tapZoom.isActive()};var pi=function(){this.reset()};pi.prototype.reset=function(){this._active=!1},pi.prototype.dblclick=function(t,e){return t.preventDefault(),{cameraAnimation:function(r){r.easeTo({duration:300,zoom:r.getZoom()+(t.shiftKey?-1:1),around:r.unproject(e)},{originalEvent:t})}}},pi.prototype.enable=function(){this._enabled=!0},pi.prototype.disable=function(){this._enabled=!1,this.reset()},pi.prototype.isEnabled=function(){return this._enabled},pi.prototype.isActive=function(){return this._active};var di=function(){this._tap=new Zn({numTouches:1,numTaps:1}),this.reset()};di.prototype.reset=function(){this._active=!1,delete this._swipePoint,delete this._swipeTouch,delete this._tapTime,this._tap.reset()},di.prototype.touchstart=function(t,e,r){this._swipePoint||(this._tapTime&&t.timeStamp-this._tapTime>500&&this.reset(),this._tapTime?r.length>0&&(this._swipePoint=e[0],this._swipeTouch=r[0].identifier):this._tap.touchstart(t,e,r))},di.prototype.touchmove=function(t,e,r){if(this._tapTime){if(this._swipePoint){if(r[0].identifier!==this._swipeTouch)return;var n=e[0],i=n.y-this._swipePoint.y;return this._swipePoint=n,t.preventDefault(),this._active=!0,{zoomDelta:i/128}}}else this._tap.touchmove(t,e,r)},di.prototype.touchend=function(t,e,r){this._tapTime?this._swipePoint&&0===r.length&&this.reset():this._tap.touchend(t,e,r)&&(this._tapTime=t.timeStamp)},di.prototype.touchcancel=function(){this.reset()},di.prototype.enable=function(){this._enabled=!0},di.prototype.disable=function(){this._enabled=!1,this.reset()},di.prototype.isEnabled=function(){return this._enabled},di.prototype.isActive=function(){return this._active};var vi=function(t,e,r){this._el=t,this._mousePan=e,this._touchPan=r};vi.prototype.enable=function(t){this._inertiaOptions=t||{},this._mousePan.enable(),this._touchPan.enable(),this._el.classList.add("mapboxgl-touch-drag-pan")},vi.prototype.disable=function(){this._mousePan.disable(),this._touchPan.disable(),this._el.classList.remove("mapboxgl-touch-drag-pan")},vi.prototype.isEnabled=function(){return this._mousePan.isEnabled()&&this._touchPan.isEnabled()},vi.prototype.isActive=function(){return this._mousePan.isActive()||this._touchPan.isActive()};var gi=function(t,e,r){this._pitchWithRotate=t.pitchWithRotate,this._mouseRotate=e,this._mousePitch=r};gi.prototype.enable=function(){this._mouseRotate.enable(),this._pitchWithRotate&&this._mousePitch.enable()},gi.prototype.disable=function(){this._mouseRotate.disable(),this._mousePitch.disable()},gi.prototype.isEnabled=function(){return this._mouseRotate.isEnabled()&&(!this._pitchWithRotate||this._mousePitch.isEnabled())},gi.prototype.isActive=function(){return this._mouseRotate.isActive()||this._mousePitch.isActive()};var yi=function(t,e,r,n){this._el=t,this._touchZoom=e,this._touchRotate=r,this._tapDragZoom=n,this._rotationDisabled=!1,this._enabled=!0};yi.prototype.enable=function(t){this._touchZoom.enable(t),this._rotationDisabled||this._touchRotate.enable(t),this._tapDragZoom.enable(),this._el.classList.add("mapboxgl-touch-zoom-rotate")},yi.prototype.disable=function(){this._touchZoom.disable(),this._touchRotate.disable(),this._tapDragZoom.disable(),this._el.classList.remove("mapboxgl-touch-zoom-rotate")},yi.prototype.isEnabled=function(){return this._touchZoom.isEnabled()&&(this._rotationDisabled||this._touchRotate.isEnabled())&&this._tapDragZoom.isEnabled()},yi.prototype.isActive=function(){return this._touchZoom.isActive()||this._touchRotate.isActive()||this._tapDragZoom.isActive()},yi.prototype.disableRotation=function(){this._rotationDisabled=!0,this._touchRotate.disable()},yi.prototype.enableRotation=function(){this._rotationDisabled=!1,this._touchZoom.isEnabled()&&this._touchRotate.enable()};var mi=function(t){return t.zoom||t.drag||t.pitch||t.rotate},xi=function(t){function e(){t.apply(this,arguments)}return t&&(e.__proto__=t),e.prototype=Object.create(t&&t.prototype),e.prototype.constructor=e,e}(t.Event);function bi(t){return t.panDelta&&t.panDelta.mag()||t.zoomDelta||t.bearingDelta||t.pitchDelta}var _i=function(e,n){this._map=e,this._el=this._map.getCanvasContainer(),this._handlers=[],this._handlersById={},this._changes=[],this._inertia=new zn(e),this._bearingSnap=n.bearingSnap,this._previousActiveHandlers={},this._eventsInProgress={},this._addDefaultHandlers(n),t.bindAll(["handleEvent","handleWindowEvent"],this);var i=this._el;this._listeners=[[i,"touchstart",{passive:!1}],[i,"touchmove",{passive:!1}],[i,"touchend",void 0],[i,"touchcancel",void 0],[i,"mousedown",void 0],[i,"mousemove",void 0],[i,"mouseup",void 0],[t.window.document,"mousemove",{capture:!0}],[t.window.document,"mouseup",void 0],[i,"mouseover",void 0],[i,"mouseout",void 0],[i,"dblclick",void 0],[i,"click",void 0],[i,"keydown",{capture:!1}],[i,"keyup",void 0],[i,"wheel",{passive:!1}],[i,"contextmenu",void 0],[t.window,"blur",void 0]];for(var a=0,o=this._listeners;aa?Math.min(2,_):Math.max(.5,_),w=Math.pow(g,1-e),T=i.unproject(x.add(b.mult(e*w)).mult(v));i.setLocationAtPoint(i.renderWorldCopies?T.wrap():T,d)}n._fireMoveEvents(r)}),(function(t){n._afterEase(r,t)}),e),this},r.prototype._prepareEase=function(e,r,n){void 0===n&&(n={}),this._moving=!0,r||n.moving||this.fire(new t.Event("movestart",e)),this._zooming&&!n.zooming&&this.fire(new t.Event("zoomstart",e)),this._rotating&&!n.rotating&&this.fire(new t.Event("rotatestart",e)),this._pitching&&!n.pitching&&this.fire(new t.Event("pitchstart",e))},r.prototype._fireMoveEvents=function(e){this.fire(new t.Event("move",e)),this._zooming&&this.fire(new t.Event("zoom",e)),this._rotating&&this.fire(new t.Event("rotate",e)),this._pitching&&this.fire(new t.Event("pitch",e))},r.prototype._afterEase=function(e,r){if(!this._easeId||!r||this._easeId!==r){delete this._easeId;var n=this._zooming,i=this._rotating,a=this._pitching;this._moving=!1,this._zooming=!1,this._rotating=!1,this._pitching=!1,this._padding=!1,n&&this.fire(new t.Event("zoomend",e)),i&&this.fire(new t.Event("rotateend",e)),a&&this.fire(new t.Event("pitchend",e)),this.fire(new t.Event("moveend",e))}},r.prototype.flyTo=function(e,r){var n=this;if(!e.essential&&t.browser.prefersReducedMotion){var i=t.pick(e,["center","zoom","bearing","pitch","around"]);return this.jumpTo(i,r)}this.stop(),e=t.extend({offset:[0,0],speed:1.2,curve:1.42,easing:t.ease},e);var a=this.transform,o=this.getZoom(),s=this.getBearing(),l=this.getPitch(),u=this.getPadding(),c="zoom"in e?t.clamp(+e.zoom,a.minZoom,a.maxZoom):o,f="bearing"in e?this._normalizeBearing(e.bearing,s):s,h="pitch"in e?+e.pitch:l,p="padding"in e?e.padding:a.padding,d=a.zoomScale(c-o),v=t.Point.convert(e.offset),g=a.centerPoint.add(v),y=a.pointLocation(g),m=t.LngLat.convert(e.center||y);this._normalizeCenter(m);var x=a.project(y),b=a.project(m).sub(x),_=e.curve,w=Math.max(a.width,a.height),T=w/d,k=b.mag();if("minZoom"in e){var A=t.clamp(Math.min(e.minZoom,o,c),a.minZoom,a.maxZoom),M=w/a.zoomScale(A-o);_=Math.sqrt(M/k*2)}var S=_*_;function E(t){var e=(T*T-w*w+(t?-1:1)*S*S*k*k)/(2*(t?T:w)*S*k);return Math.log(Math.sqrt(e*e+1)-e)}function L(t){return(Math.exp(t)-Math.exp(-t))/2}function C(t){return(Math.exp(t)+Math.exp(-t))/2}var P=E(0),O=function(t){return C(P)/C(P+_*t)},I=function(t){return w*((C(P)*(L(e=P+_*t)/C(e))-L(P))/S)/k;var e},D=(E(1)-P)/_;if(Math.abs(k)<1e-6||!isFinite(D)){if(Math.abs(w-T)<1e-6)return this.easeTo(e,r);var z=Te.maxDuration&&(e.duration=0),this._zooming=!0,this._rotating=s!==f,this._pitching=h!==l,this._padding=!a.isPaddingEqual(p),this._prepareEase(r,!1),this._ease((function(e){var i=e*D,d=1/O(i);a.zoom=1===e?c:o+a.scaleZoom(d),n._rotating&&(a.bearing=t.number(s,f,e)),n._pitching&&(a.pitch=t.number(l,h,e)),n._padding&&(a.interpolatePadding(u,p,e),g=a.centerPoint.add(v));var y=1===e?m:a.unproject(x.add(b.mult(I(i))).mult(d));a.setLocationAtPoint(a.renderWorldCopies?y.wrap():y,g),n._fireMoveEvents(r)}),(function(){return n._afterEase(r)}),e),this},r.prototype.isEasing=function(){return!!this._easeFrameId},r.prototype.stop=function(){return this._stop()},r.prototype._stop=function(t,e){if(this._easeFrameId&&(this._cancelRenderFrame(this._easeFrameId),delete this._easeFrameId,delete this._onEaseFrame),this._onEaseEnd){var r=this._onEaseEnd;delete this._onEaseEnd,r.call(this,e)}if(!t){var n=this.handlers;n&&n.stop()}return this},r.prototype._ease=function(e,r,n){!1===n.animate||0===n.duration?(e(1),r()):(this._easeStart=t.browser.now(),this._easeOptions=n,this._onEaseFrame=e,this._onEaseEnd=r,this._easeFrameId=this._requestRenderFrame(this._renderFrameCallback))},r.prototype._renderFrameCallback=function(){var e=Math.min((t.browser.now()-this._easeStart)/this._easeOptions.duration,1);this._onEaseFrame(this._easeOptions.easing(e)),e<1?this._easeFrameId=this._requestRenderFrame(this._renderFrameCallback):this.stop()},r.prototype._normalizeBearing=function(e,r){e=t.wrap(e,-180,180);var n=Math.abs(e-r);return Math.abs(e-360-r)180?-360:r<-180?360:0}},r}(t.Evented),Ti=function(e){void 0===e&&(e={}),this.options=e,t.bindAll(["_updateEditLink","_updateData","_updateCompact"],this)};Ti.prototype.getDefaultPosition=function(){return"bottom-right"},Ti.prototype.onAdd=function(t){var e=this.options&&this.options.compact;return this._map=t,this._container=r.create("div","mapboxgl-ctrl mapboxgl-ctrl-attrib"),this._innerContainer=r.create("div","mapboxgl-ctrl-attrib-inner",this._container),e&&this._container.classList.add("mapboxgl-compact"),this._updateAttributions(),this._updateEditLink(),this._map.on("styledata",this._updateData),this._map.on("sourcedata",this._updateData),this._map.on("moveend",this._updateEditLink),void 0===e&&(this._map.on("resize",this._updateCompact),this._updateCompact()),this._container},Ti.prototype.onRemove=function(){r.remove(this._container),this._map.off("styledata",this._updateData),this._map.off("sourcedata",this._updateData),this._map.off("moveend",this._updateEditLink),this._map.off("resize",this._updateCompact),this._map=void 0,this._attribHTML=void 0},Ti.prototype._updateEditLink=function(){var e=this._editLink;e||(e=this._editLink=this._container.querySelector(".mapbox-improve-map"));var r=[{key:"owner",value:this.styleOwner},{key:"id",value:this.styleId},{key:"access_token",value:this._map._requestManager._customAccessToken||t.config.ACCESS_TOKEN}];if(e){var n=r.reduce((function(t,e,n){return e.value&&(t+=e.key+"="+e.value+(n=0)return!1;return!0}))).join(" | ");o!==this._attribHTML&&(this._attribHTML=o,t.length?(this._innerContainer.innerHTML=o,this._container.classList.remove("mapboxgl-attrib-empty")):this._container.classList.add("mapboxgl-attrib-empty"),this._editLink=null)}},Ti.prototype._updateCompact=function(){this._map.getCanvasContainer().offsetWidth<=640?this._container.classList.add("mapboxgl-compact"):this._container.classList.remove("mapboxgl-compact")};var ki=function(){t.bindAll(["_updateLogo"],this),t.bindAll(["_updateCompact"],this)};ki.prototype.onAdd=function(t){this._map=t,this._container=r.create("div","mapboxgl-ctrl");var e=r.create("a","mapboxgl-ctrl-logo");return e.target="_blank",e.rel="noopener nofollow",e.href="https://www.mapbox.com/",e.setAttribute("aria-label",this._map._getUIString("LogoControl.Title")),e.setAttribute("rel","noopener nofollow"),this._container.appendChild(e),this._container.style.display="none",this._map.on("sourcedata",this._updateLogo),this._updateLogo(),this._map.on("resize",this._updateCompact),this._updateCompact(),this._container},ki.prototype.onRemove=function(){r.remove(this._container),this._map.off("sourcedata",this._updateLogo),this._map.off("resize",this._updateCompact)},ki.prototype.getDefaultPosition=function(){return"bottom-left"},ki.prototype._updateLogo=function(t){t&&"metadata"!==t.sourceDataType||(this._container.style.display=this._logoRequired()?"block":"none")},ki.prototype._logoRequired=function(){if(this._map.style){var t=this._map.style.sourceCaches;for(var e in t)if(t[e].getSource().mapbox_logo)return!0;return!1}},ki.prototype._updateCompact=function(){var t=this._container.children;if(t.length){var e=t[0];this._map.getCanvasContainer().offsetWidth<250?e.classList.add("mapboxgl-compact"):e.classList.remove("mapboxgl-compact")}};var Ai=function(){this._queue=[],this._id=0,this._cleared=!1,this._currentlyRunning=!1};Ai.prototype.add=function(t){var e=++this._id;return this._queue.push({callback:t,id:e,cancelled:!1}),e},Ai.prototype.remove=function(t){for(var e=this._currentlyRunning,r=0,n=e?this._queue.concat(e):this._queue;re.maxZoom)throw new Error("maxZoom must be greater than or equal to minZoom");if(null!=e.minPitch&&null!=e.maxPitch&&e.minPitch>e.maxPitch)throw new Error("maxPitch must be greater than or equal to minPitch");if(null!=e.minPitch&&e.minPitch<0)throw new Error("minPitch must be greater than or equal to 0");if(null!=e.maxPitch&&e.maxPitch>Ci)throw new Error("maxPitch must be less than or equal to 60");var i=new Sn(e.minZoom,e.maxZoom,e.minPitch,e.maxPitch,e.renderWorldCopies);if(n.call(this,i,e),this._interactive=e.interactive,this._maxTileCacheSize=e.maxTileCacheSize,this._failIfMajorPerformanceCaveat=e.failIfMajorPerformanceCaveat,this._preserveDrawingBuffer=e.preserveDrawingBuffer,this._antialias=e.antialias,this._trackResize=e.trackResize,this._bearingSnap=e.bearingSnap,this._refreshExpiredTiles=e.refreshExpiredTiles,this._fadeDuration=e.fadeDuration,this._crossSourceCollisions=e.crossSourceCollisions,this._crossFadingFactor=1,this._collectResourceTiming=e.collectResourceTiming,this._renderTaskQueue=new Ai,this._controls=[],this._mapId=t.uniqueId(),this._locale=t.extend({},Mi,e.locale),this._requestManager=new t.RequestManager(e.transformRequest,e.accessToken),"string"==typeof e.container){if(this._container=t.window.document.getElementById(e.container),!this._container)throw new Error("Container '"+e.container+"' not found.")}else{if(!(e.container instanceof Ei))throw new Error("Invalid type: 'container' must be a String or HTMLElement.");this._container=e.container}if(e.maxBounds&&this.setMaxBounds(e.maxBounds),t.bindAll(["_onWindowOnline","_onWindowResize","_contextLost","_contextRestored"],this),this._setupContainer(),this._setupPainter(),void 0===this.painter)throw new Error("Failed to initialize WebGL.");this.on("move",(function(){return r._update(!1)})),this.on("moveend",(function(){return r._update(!1)})),this.on("zoom",(function(){return r._update(!0)})),void 0!==t.window&&(t.window.addEventListener("online",this._onWindowOnline,!1),t.window.addEventListener("resize",this._onWindowResize,!1)),this.handlers=new _i(this,e);var a="string"==typeof e.hash&&e.hash||void 0;this._hash=e.hash&&new Ln(a).addTo(this),this._hash&&this._hash._onHashChange()||(this.jumpTo({center:e.center,zoom:e.zoom,bearing:e.bearing,pitch:e.pitch}),e.bounds&&(this.resize(),this.fitBounds(e.bounds,t.extend({},e.fitBoundsOptions,{duration:0})))),this.resize(),this._localIdeographFontFamily=e.localIdeographFontFamily,e.style&&this.setStyle(e.style,{localIdeographFontFamily:e.localIdeographFontFamily}),e.attributionControl&&this.addControl(new Ti({customAttribution:e.customAttribution})),this.addControl(new ki,e.logoPosition),this.on("style.load",(function(){r.transform.unmodified&&r.jumpTo(r.style.stylesheet)})),this.on("data",(function(e){r._update("style"===e.dataType),r.fire(new t.Event(e.dataType+"data",e))})),this.on("dataloading",(function(e){r.fire(new t.Event(e.dataType+"dataloading",e))}))}n&&(i.__proto__=n),i.prototype=Object.create(n&&n.prototype),i.prototype.constructor=i;var a={showTileBoundaries:{configurable:!0},showPadding:{configurable:!0},showCollisionBoxes:{configurable:!0},showOverdrawInspector:{configurable:!0},repaint:{configurable:!0},vertices:{configurable:!0},version:{configurable:!0}};return i.prototype._getMapId=function(){return this._mapId},i.prototype.addControl=function(e,r){if(void 0===r&&e.getDefaultPosition&&(r=e.getDefaultPosition()),void 0===r&&(r="top-right"),!e||!e.onAdd)return this.fire(new t.ErrorEvent(new Error("Invalid argument to map.addControl(). Argument must be a control with onAdd and onRemove methods.")));var n=e.onAdd(this);this._controls.push(e);var i=this._controlPositions[r];return-1!==r.indexOf("bottom")?i.insertBefore(n,i.firstChild):i.appendChild(n),this},i.prototype.removeControl=function(e){if(!e||!e.onRemove)return this.fire(new t.ErrorEvent(new Error("Invalid argument to map.removeControl(). Argument must be a control with onAdd and onRemove methods.")));var r=this._controls.indexOf(e);return r>-1&&this._controls.splice(r,1),e.onRemove(this),this},i.prototype.resize=function(e){var r=this._containerDimensions(),n=r[0],i=r[1];this._resizeCanvas(n,i),this.transform.resize(n,i),this.painter.resize(n,i);var a=!this._moving;return a&&(this.stop(),this.fire(new t.Event("movestart",e)).fire(new t.Event("move",e))),this.fire(new t.Event("resize",e)),a&&this.fire(new t.Event("moveend",e)),this},i.prototype.getBounds=function(){return this.transform.getBounds()},i.prototype.getMaxBounds=function(){return this.transform.getMaxBounds()},i.prototype.setMaxBounds=function(e){return this.transform.setMaxBounds(t.LngLatBounds.convert(e)),this._update()},i.prototype.setMinZoom=function(t){if((t=null==t?-2:t)>=-2&&t<=this.transform.maxZoom)return this.transform.minZoom=t,this._update(),this.getZoom()=this.transform.minZoom)return this.transform.maxZoom=t,this._update(),this.getZoom()>t&&this.setZoom(t),this;throw new Error("maxZoom must be greater than the current minZoom")},i.prototype.getMaxZoom=function(){return this.transform.maxZoom},i.prototype.setMinPitch=function(t){if((t=null==t?0:t)<0)throw new Error("minPitch must be greater than or equal to 0");if(t>=0&&t<=this.transform.maxPitch)return this.transform.minPitch=t,this._update(),this.getPitch()Ci)throw new Error("maxPitch must be less than or equal to 60");if(t>=this.transform.minPitch)return this.transform.maxPitch=t,this._update(),this.getPitch()>t&&this.setPitch(t),this;throw new Error("maxPitch must be greater than the current minPitch")},i.prototype.getMaxPitch=function(){return this.transform.maxPitch},i.prototype.getRenderWorldCopies=function(){return this.transform.renderWorldCopies},i.prototype.setRenderWorldCopies=function(t){return this.transform.renderWorldCopies=t,this._update()},i.prototype.project=function(e){return this.transform.locationPoint(t.LngLat.convert(e))},i.prototype.unproject=function(e){return this.transform.pointLocation(t.Point.convert(e))},i.prototype.isMoving=function(){return this._moving||this.handlers.isMoving()},i.prototype.isZooming=function(){return this._zooming||this.handlers.isZooming()},i.prototype.isRotating=function(){return this._rotating||this.handlers.isRotating()},i.prototype._createDelegatedListener=function(t,e,r){var n,i=this;if("mouseenter"===t||"mouseover"===t){var a=!1;return{layer:e,listener:r,delegates:{mousemove:function(n){var o=i.getLayer(e)?i.queryRenderedFeatures(n.point,{layers:[e]}):[];o.length?a||(a=!0,r.call(i,new Bn(t,i,n.originalEvent,{features:o}))):a=!1},mouseout:function(){a=!1}}}}if("mouseleave"===t||"mouseout"===t){var o=!1;return{layer:e,listener:r,delegates:{mousemove:function(n){(i.getLayer(e)?i.queryRenderedFeatures(n.point,{layers:[e]}):[]).length?o=!0:o&&(o=!1,r.call(i,new Bn(t,i,n.originalEvent)))},mouseout:function(e){o&&(o=!1,r.call(i,new Bn(t,i,e.originalEvent)))}}}}return{layer:e,listener:r,delegates:(n={},n[t]=function(t){var n=i.getLayer(e)?i.queryRenderedFeatures(t.point,{layers:[e]}):[];n.length&&(t.features=n,r.call(i,t),delete t.features)},n)}},i.prototype.on=function(t,e,r){if(void 0===r)return n.prototype.on.call(this,t,e);var i=this._createDelegatedListener(t,e,r);for(var a in this._delegatedListeners=this._delegatedListeners||{},this._delegatedListeners[t]=this._delegatedListeners[t]||[],this._delegatedListeners[t].push(i),i.delegates)this.on(a,i.delegates[a]);return this},i.prototype.once=function(t,e,r){if(void 0===r)return n.prototype.once.call(this,t,e);var i=this._createDelegatedListener(t,e,r);for(var a in i.delegates)this.once(a,i.delegates[a]);return this},i.prototype.off=function(t,e,r){var i=this;if(void 0===r)return n.prototype.off.call(this,t,e);return this._delegatedListeners&&this._delegatedListeners[t]&&function(n){for(var a=n[t],o=0;o180;){var s=n.locationPoint(e);if(s.x>=0&&s.y>=0&&s.x<=n.width&&s.y<=n.height)break;e.lng>n.center.lng?e.lng-=360:e.lng+=360}return e}Ri.prototype.down=function(t,e){this.mouseRotate.mousedown(t,e),this.mousePitch&&this.mousePitch.mousedown(t,e),r.disableDrag()},Ri.prototype.move=function(t,e){var r=this.map,n=this.mouseRotate.mousemoveWindow(t,e);if(n&&n.bearingDelta&&r.setBearing(r.getBearing()+n.bearingDelta),this.mousePitch){var i=this.mousePitch.mousemoveWindow(t,e);i&&i.pitchDelta&&r.setPitch(r.getPitch()+i.pitchDelta)}},Ri.prototype.off=function(){var t=this.element;r.removeEventListener(t,"mousedown",this.mousedown),r.removeEventListener(t,"touchstart",this.touchstart,{passive:!1}),r.removeEventListener(t,"touchmove",this.touchmove),r.removeEventListener(t,"touchend",this.touchend),r.removeEventListener(t,"touchcancel",this.reset),this.offTemp()},Ri.prototype.offTemp=function(){r.enableDrag(),r.removeEventListener(t.window,"mousemove",this.mousemove),r.removeEventListener(t.window,"mouseup",this.mouseup)},Ri.prototype.mousedown=function(e){this.down(t.extend({},e,{ctrlKey:!0,preventDefault:function(){return e.preventDefault()}}),r.mousePos(this.element,e)),r.addEventListener(t.window,"mousemove",this.mousemove),r.addEventListener(t.window,"mouseup",this.mouseup)},Ri.prototype.mousemove=function(t){this.move(t,r.mousePos(this.element,t))},Ri.prototype.mouseup=function(t){this.mouseRotate.mouseupWindow(t),this.mousePitch&&this.mousePitch.mouseupWindow(t),this.offTemp()},Ri.prototype.touchstart=function(t){1!==t.targetTouches.length?this.reset():(this._startPos=this._lastPos=r.touchPos(this.element,t.targetTouches)[0],this.down({type:"mousedown",button:0,ctrlKey:!0,preventDefault:function(){return t.preventDefault()}},this._startPos))},Ri.prototype.touchmove=function(t){1!==t.targetTouches.length?this.reset():(this._lastPos=r.touchPos(this.element,t.targetTouches)[0],this.move({preventDefault:function(){return t.preventDefault()}},this._lastPos))},Ri.prototype.touchend=function(t){0===t.targetTouches.length&&this._startPos&&this._lastPos&&this._startPos.dist(this._lastPos)e.getEast()||r.latitudee.getNorth())},n.prototype._setErrorState=function(){switch(this._watchState){case"WAITING_ACTIVE":this._watchState="ACTIVE_ERROR",this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-active"),this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-active-error");break;case"ACTIVE_LOCK":this._watchState="ACTIVE_ERROR",this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-active"),this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-active-error"),this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-waiting");break;case"BACKGROUND":this._watchState="BACKGROUND_ERROR",this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-background"),this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-background-error"),this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-waiting")}},n.prototype._onSuccess=function(e){if(this._map){if(this._isOutOfMapMaxBounds(e))return this._setErrorState(),this.fire(new t.Event("outofmaxbounds",e)),this._updateMarker(),void this._finish();if(this.options.trackUserLocation)switch(this._lastKnownPosition=e,this._watchState){case"WAITING_ACTIVE":case"ACTIVE_LOCK":case"ACTIVE_ERROR":this._watchState="ACTIVE_LOCK",this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-waiting"),this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-active-error"),this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-active");break;case"BACKGROUND":case"BACKGROUND_ERROR":this._watchState="BACKGROUND",this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-waiting"),this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-background-error"),this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-background")}this.options.showUserLocation&&"OFF"!==this._watchState&&this._updateMarker(e),this.options.trackUserLocation&&"ACTIVE_LOCK"!==this._watchState||this._updateCamera(e),this.options.showUserLocation&&this._dotElement.classList.remove("mapboxgl-user-location-dot-stale"),this.fire(new t.Event("geolocate",e)),this._finish()}},n.prototype._updateCamera=function(e){var r=new t.LngLat(e.coords.longitude,e.coords.latitude),n=e.coords.accuracy,i=this._map.getBearing(),a=t.extend({bearing:i},this.options.fitBoundsOptions);this._map.fitBounds(r.toBounds(n),a,{geolocateSource:!0})},n.prototype._updateMarker=function(e){if(e){var r=new t.LngLat(e.coords.longitude,e.coords.latitude);this._accuracyCircleMarker.setLngLat(r).addTo(this._map),this._userLocationDotMarker.setLngLat(r).addTo(this._map),this._accuracy=e.coords.accuracy,this.options.showUserLocation&&this.options.showAccuracyCircle&&this._updateCircleRadius()}else this._userLocationDotMarker.remove(),this._accuracyCircleMarker.remove()},n.prototype._updateCircleRadius=function(){var t=this._map._container.clientHeight/2,e=this._map.unproject([0,t]),r=this._map.unproject([1,t]),n=e.distanceTo(r),i=Math.ceil(2*this._accuracy/n);this._circleElement.style.width=i+"px",this._circleElement.style.height=i+"px"},n.prototype._onZoom=function(){this.options.showUserLocation&&this.options.showAccuracyCircle&&this._updateCircleRadius()},n.prototype._onError=function(e){if(this._map){if(this.options.trackUserLocation)if(1===e.code){this._watchState="OFF",this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-waiting"),this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-active"),this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-active-error"),this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-background"),this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-background-error"),this._geolocateButton.disabled=!0;var r=this._map._getUIString("GeolocateControl.LocationNotAvailable");this._geolocateButton.title=r,this._geolocateButton.setAttribute("aria-label",r),void 0!==this._geolocationWatchID&&this._clearWatch()}else{if(3===e.code&&qi)return;this._setErrorState()}"OFF"!==this._watchState&&this.options.showUserLocation&&this._dotElement.classList.add("mapboxgl-user-location-dot-stale"),this.fire(new t.Event("error",e)),this._finish()}},n.prototype._finish=function(){this._timeoutId&&clearTimeout(this._timeoutId),this._timeoutId=void 0},n.prototype._setupUI=function(e){var n=this;if(this._container.addEventListener("contextmenu",(function(t){return t.preventDefault()})),this._geolocateButton=r.create("button","mapboxgl-ctrl-geolocate",this._container),r.create("span","mapboxgl-ctrl-icon",this._geolocateButton).setAttribute("aria-hidden",!0),this._geolocateButton.type="button",!1===e){t.warnOnce("Geolocation support is not available so the GeolocateControl will be disabled.");var i=this._map._getUIString("GeolocateControl.LocationNotAvailable");this._geolocateButton.disabled=!0,this._geolocateButton.title=i,this._geolocateButton.setAttribute("aria-label",i)}else{var a=this._map._getUIString("GeolocateControl.FindMyLocation");this._geolocateButton.title=a,this._geolocateButton.setAttribute("aria-label",a)}this.options.trackUserLocation&&(this._geolocateButton.setAttribute("aria-pressed","false"),this._watchState="OFF"),this.options.showUserLocation&&(this._dotElement=r.create("div","mapboxgl-user-location-dot"),this._userLocationDotMarker=new Ui(this._dotElement),this._circleElement=r.create("div","mapboxgl-user-location-accuracy-circle"),this._accuracyCircleMarker=new Ui({element:this._circleElement,pitchAlignment:"map"}),this.options.trackUserLocation&&(this._watchState="OFF"),this._map.on("zoom",this._onZoom)),this._geolocateButton.addEventListener("click",this.trigger.bind(this)),this._setup=!0,this.options.trackUserLocation&&this._map.on("movestart",(function(e){var r=e.originalEvent&&"resize"===e.originalEvent.type;e.geolocateSource||"ACTIVE_LOCK"!==n._watchState||r||(n._watchState="BACKGROUND",n._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-background"),n._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-active"),n.fire(new t.Event("trackuserlocationend")))}))},n.prototype.trigger=function(){if(!this._setup)return t.warnOnce("Geolocate control triggered before added to a map"),!1;if(this.options.trackUserLocation){switch(this._watchState){case"OFF":this._watchState="WAITING_ACTIVE",this.fire(new t.Event("trackuserlocationstart"));break;case"WAITING_ACTIVE":case"ACTIVE_LOCK":case"ACTIVE_ERROR":case"BACKGROUND_ERROR":Hi--,qi=!1,this._watchState="OFF",this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-waiting"),this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-active"),this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-active-error"),this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-background"),this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-background-error"),this.fire(new t.Event("trackuserlocationend"));break;case"BACKGROUND":this._watchState="ACTIVE_LOCK",this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-background"),this._lastKnownPosition&&this._updateCamera(this._lastKnownPosition),this.fire(new t.Event("trackuserlocationstart"))}switch(this._watchState){case"WAITING_ACTIVE":this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-waiting"),this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-active");break;case"ACTIVE_LOCK":this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-active");break;case"ACTIVE_ERROR":this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-waiting"),this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-active-error");break;case"BACKGROUND":this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-background");break;case"BACKGROUND_ERROR":this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-waiting"),this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-background-error")}if("OFF"===this._watchState&&void 0!==this._geolocationWatchID)this._clearWatch();else if(void 0===this._geolocationWatchID){var e;this._geolocateButton.classList.add("mapboxgl-ctrl-geolocate-waiting"),this._geolocateButton.setAttribute("aria-pressed","true"),++Hi>1?(e={maximumAge:6e5,timeout:0},qi=!0):(e=this.options.positionOptions,qi=!1),this._geolocationWatchID=t.window.navigator.geolocation.watchPosition(this._onSuccess,this._onError,e)}}else t.window.navigator.geolocation.getCurrentPosition(this._onSuccess,this._onError,this.options.positionOptions),this._timeoutId=setTimeout(this._finish,1e4);return!0},n.prototype._clearWatch=function(){t.window.navigator.geolocation.clearWatch(this._geolocationWatchID),this._geolocationWatchID=void 0,this._geolocateButton.classList.remove("mapboxgl-ctrl-geolocate-waiting"),this._geolocateButton.setAttribute("aria-pressed","false"),this.options.showUserLocation&&this._updateMarker(null)},n}(t.Evented),Zi={maxWidth:100,unit:"metric"},Yi=function(e){this.options=t.extend({},Zi,e),t.bindAll(["_onMove","setUnit"],this)};function Wi(t,e,r){var n=r&&r.maxWidth||100,i=t._container.clientHeight/2,a=t.unproject([0,i]),o=t.unproject([n,i]),s=a.distanceTo(o);if(r&&"imperial"===r.unit){var l=3.2808*s;l>5280?Xi(e,n,l/5280,t._getUIString("ScaleControl.Miles")):Xi(e,n,l,t._getUIString("ScaleControl.Feet"))}else r&&"nautical"===r.unit?Xi(e,n,s/1852,t._getUIString("ScaleControl.NauticalMiles")):s>=1e3?Xi(e,n,s/1e3,t._getUIString("ScaleControl.Kilometers")):Xi(e,n,s,t._getUIString("ScaleControl.Meters"))}function Xi(t,e,r,n){var i,a,o,s=(i=r,(a=Math.pow(10,(""+Math.floor(i)).length-1))*((o=i/a)>=10?10:o>=5?5:o>=3?3:o>=2?2:o>=1?1:function(t){var e=Math.pow(10,Math.ceil(-Math.log(t)/Math.LN10));return Math.round(t*e)/e}(o))),l=s/r;t.style.width=e*l+"px",t.innerHTML=s+" "+n}Yi.prototype.getDefaultPosition=function(){return"bottom-left"},Yi.prototype._onMove=function(){Wi(this._map,this._container,this.options)},Yi.prototype.onAdd=function(t){return this._map=t,this._container=r.create("div","mapboxgl-ctrl mapboxgl-ctrl-scale",t.getContainer()),this._map.on("move",this._onMove),this._onMove(),this._container},Yi.prototype.onRemove=function(){r.remove(this._container),this._map.off("move",this._onMove),this._map=void 0},Yi.prototype.setUnit=function(t){this.options.unit=t,Wi(this._map,this._container,this.options)};var Ji=function(e){this._fullscreen=!1,e&&e.container&&(e.container instanceof t.window.HTMLElement?this._container=e.container:t.warnOnce("Full screen control 'container' must be a DOM element.")),t.bindAll(["_onClickFullscreen","_changeIcon"],this),"onfullscreenchange"in t.window.document?this._fullscreenchange="fullscreenchange":"onmozfullscreenchange"in t.window.document?this._fullscreenchange="mozfullscreenchange":"onwebkitfullscreenchange"in t.window.document?this._fullscreenchange="webkitfullscreenchange":"onmsfullscreenchange"in t.window.document&&(this._fullscreenchange="MSFullscreenChange")};Ji.prototype.onAdd=function(e){return this._map=e,this._container||(this._container=this._map.getContainer()),this._controlContainer=r.create("div","mapboxgl-ctrl mapboxgl-ctrl-group"),this._checkFullscreenSupport()?this._setupUI():(this._controlContainer.style.display="none",t.warnOnce("This device does not support fullscreen mode.")),this._controlContainer},Ji.prototype.onRemove=function(){r.remove(this._controlContainer),this._map=null,t.window.document.removeEventListener(this._fullscreenchange,this._changeIcon)},Ji.prototype._checkFullscreenSupport=function(){return!!(t.window.document.fullscreenEnabled||t.window.document.mozFullScreenEnabled||t.window.document.msFullscreenEnabled||t.window.document.webkitFullscreenEnabled)},Ji.prototype._setupUI=function(){var e=this._fullscreenButton=r.create("button","mapboxgl-ctrl-fullscreen",this._controlContainer);r.create("span","mapboxgl-ctrl-icon",e).setAttribute("aria-hidden",!0),e.type="button",this._updateTitle(),this._fullscreenButton.addEventListener("click",this._onClickFullscreen),t.window.document.addEventListener(this._fullscreenchange,this._changeIcon)},Ji.prototype._updateTitle=function(){var t=this._getTitle();this._fullscreenButton.setAttribute("aria-label",t),this._fullscreenButton.title=t},Ji.prototype._getTitle=function(){return this._map._getUIString(this._isFullscreen()?"FullscreenControl.Exit":"FullscreenControl.Enter")},Ji.prototype._isFullscreen=function(){return this._fullscreen},Ji.prototype._changeIcon=function(){(t.window.document.fullscreenElement||t.window.document.mozFullScreenElement||t.window.document.webkitFullscreenElement||t.window.document.msFullscreenElement)===this._container!==this._fullscreen&&(this._fullscreen=!this._fullscreen,this._fullscreenButton.classList.toggle("mapboxgl-ctrl-shrink"),this._fullscreenButton.classList.toggle("mapboxgl-ctrl-fullscreen"),this._updateTitle())},Ji.prototype._onClickFullscreen=function(){this._isFullscreen()?t.window.document.exitFullscreen?t.window.document.exitFullscreen():t.window.document.mozCancelFullScreen?t.window.document.mozCancelFullScreen():t.window.document.msExitFullscreen?t.window.document.msExitFullscreen():t.window.document.webkitCancelFullScreen&&t.window.document.webkitCancelFullScreen():this._container.requestFullscreen?this._container.requestFullscreen():this._container.mozRequestFullScreen?this._container.mozRequestFullScreen():this._container.msRequestFullscreen?this._container.msRequestFullscreen():this._container.webkitRequestFullscreen&&this._container.webkitRequestFullscreen()};var Ki={closeButton:!0,closeOnClick:!0,className:"",maxWidth:"240px"},$i=function(e){function n(r){e.call(this),this.options=t.extend(Object.create(Ki),r),t.bindAll(["_update","_onClose","remove","_onMouseMove","_onMouseUp","_onDrag"],this)}return e&&(n.__proto__=e),n.prototype=Object.create(e&&e.prototype),n.prototype.constructor=n,n.prototype.addTo=function(e){return this._map&&this.remove(),this._map=e,this.options.closeOnClick&&this._map.on("click",this._onClose),this.options.closeOnMove&&this._map.on("move",this._onClose),this._map.on("remove",this.remove),this._update(),this._trackPointer?(this._map.on("mousemove",this._onMouseMove),this._map.on("mouseup",this._onMouseUp),this._container&&this._container.classList.add("mapboxgl-popup-track-pointer"),this._map._canvasContainer.classList.add("mapboxgl-track-pointer")):this._map.on("move",this._update),this.fire(new t.Event("open")),this},n.prototype.isOpen=function(){return!!this._map},n.prototype.remove=function(){return this._content&&r.remove(this._content),this._container&&(r.remove(this._container),delete this._container),this._map&&(this._map.off("move",this._update),this._map.off("move",this._onClose),this._map.off("click",this._onClose),this._map.off("remove",this.remove),this._map.off("mousemove",this._onMouseMove),this._map.off("mouseup",this._onMouseUp),this._map.off("drag",this._onDrag),delete this._map),this.fire(new t.Event("close")),this},n.prototype.getLngLat=function(){return this._lngLat},n.prototype.setLngLat=function(e){return this._lngLat=t.LngLat.convert(e),this._pos=null,this._trackPointer=!1,this._update(),this._map&&(this._map.on("move",this._update),this._map.off("mousemove",this._onMouseMove),this._container&&this._container.classList.remove("mapboxgl-popup-track-pointer"),this._map._canvasContainer.classList.remove("mapboxgl-track-pointer")),this},n.prototype.trackPointer=function(){return this._trackPointer=!0,this._pos=null,this._update(),this._map&&(this._map.off("move",this._update),this._map.on("mousemove",this._onMouseMove),this._map.on("drag",this._onDrag),this._container&&this._container.classList.add("mapboxgl-popup-track-pointer"),this._map._canvasContainer.classList.add("mapboxgl-track-pointer")),this},n.prototype.getElement=function(){return this._container},n.prototype.setText=function(e){return this.setDOMContent(t.window.document.createTextNode(e))},n.prototype.setHTML=function(e){var r,n=t.window.document.createDocumentFragment(),i=t.window.document.createElement("body");for(i.innerHTML=e;r=i.firstChild;)n.appendChild(r);return this.setDOMContent(n)},n.prototype.getMaxWidth=function(){return this._container&&this._container.style.maxWidth},n.prototype.setMaxWidth=function(t){return this.options.maxWidth=t,this._update(),this},n.prototype.setDOMContent=function(t){return this._createContent(),this._content.appendChild(t),this._update(),this},n.prototype.addClassName=function(t){this._container&&this._container.classList.add(t)},n.prototype.removeClassName=function(t){this._container&&this._container.classList.remove(t)},n.prototype.toggleClassName=function(t){if(this._container)return this._container.classList.toggle(t)},n.prototype._createContent=function(){this._content&&r.remove(this._content),this._content=r.create("div","mapboxgl-popup-content",this._container),this.options.closeButton&&(this._closeButton=r.create("button","mapboxgl-popup-close-button",this._content),this._closeButton.type="button",this._closeButton.setAttribute("aria-label","Close popup"),this._closeButton.innerHTML="×",this._closeButton.addEventListener("click",this._onClose))},n.prototype._onMouseUp=function(t){this._update(t.point)},n.prototype._onMouseMove=function(t){this._update(t.point)},n.prototype._onDrag=function(t){this._update(t.point)},n.prototype._update=function(t){var e=this,n=this._lngLat||this._trackPointer;if(this._map&&n&&this._content&&(this._container||(this._container=r.create("div","mapboxgl-popup",this._map.getContainer()),this._tip=r.create("div","mapboxgl-popup-tip",this._container),this._container.appendChild(this._content),this.options.className&&this.options.className.split(" ").forEach((function(t){return e._container.classList.add(t)})),this._trackPointer&&this._container.classList.add("mapboxgl-popup-track-pointer")),this.options.maxWidth&&this._container.style.maxWidth!==this.options.maxWidth&&(this._container.style.maxWidth=this.options.maxWidth),this._map.transform.renderWorldCopies&&!this._trackPointer&&(this._lngLat=Fi(this._lngLat,this._pos,this._map.transform)),!this._trackPointer||t)){var i=this._pos=this._trackPointer&&t?t:this._map.project(this._lngLat),a=this.options.anchor,o=Qi(this.options.offset);if(!a){var s,l=this._container.offsetWidth,u=this._container.offsetHeight;s=i.y+o.bottom.ythis._map.transform.height-u?["bottom"]:[],i.xthis._map.transform.width-l/2&&s.push("right"),a=0===s.length?"bottom":s.join("-")}var c=i.add(o[a]).round();r.setTransform(this._container,Bi[a]+" translate("+c.x+"px,"+c.y+"px)"),Ni(this._container,a,"popup")}},n.prototype._onClose=function(){this.remove()},n}(t.Evented);function Qi(e){if(e){if("number"==typeof e){var r=Math.round(Math.sqrt(.5*Math.pow(e,2)));return{center:new t.Point(0,0),top:new t.Point(0,e),"top-left":new t.Point(r,r),"top-right":new t.Point(-r,r),bottom:new t.Point(0,-e),"bottom-left":new t.Point(r,-r),"bottom-right":new t.Point(-r,-r),left:new t.Point(e,0),right:new t.Point(-e,0)}}if(e instanceof t.Point||Array.isArray(e)){var n=t.Point.convert(e);return{center:n,top:n,"top-left":n,"top-right":n,bottom:n,"bottom-left":n,"bottom-right":n,left:n,right:n}}return{center:t.Point.convert(e.center||[0,0]),top:t.Point.convert(e.top||[0,0]),"top-left":t.Point.convert(e["top-left"]||[0,0]),"top-right":t.Point.convert(e["top-right"]||[0,0]),bottom:t.Point.convert(e.bottom||[0,0]),"bottom-left":t.Point.convert(e["bottom-left"]||[0,0]),"bottom-right":t.Point.convert(e["bottom-right"]||[0,0]),left:t.Point.convert(e.left||[0,0]),right:t.Point.convert(e.right||[0,0])}}return Qi(new t.Point(0,0))}var ta={version:t.version,supported:e,setRTLTextPlugin:t.setRTLTextPlugin,getRTLTextPluginStatus:t.getRTLTextPluginStatus,Map:Oi,NavigationControl:zi,GeolocateControl:Gi,AttributionControl:Ti,ScaleControl:Yi,FullscreenControl:Ji,Popup:$i,Marker:Ui,Style:Ye,LngLat:t.LngLat,LngLatBounds:t.LngLatBounds,Point:t.Point,MercatorCoordinate:t.MercatorCoordinate,Evented:t.Evented,config:t.config,prewarm:function(){jt().acquire(Rt)},clearPrewarmedResources:function(){var t=Bt;t&&(t.isPreloaded()&&1===t.numActive()?(t.release(Rt),Bt=null):console.warn("Could not clear WebWorkers since there are active Map instances that still reference it. 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n=r(56131);function i(){this.regionalOptions=[],this.regionalOptions[""]={invalidCalendar:"Calendar {0} not found",invalidDate:"Invalid {0} date",invalidMonth:"Invalid {0} month",invalidYear:"Invalid {0} year",differentCalendars:"Cannot mix {0} and {1} dates"},this.local=this.regionalOptions[""],this.calendars={},this._localCals={}}function a(t,e,r,n){if(this._calendar=t,this._year=e,this._month=r,this._day=n,0===this._calendar._validateLevel&&!this._calendar.isValid(this._year,this._month,this._day))throw(u.local.invalidDate||u.regionalOptions[""].invalidDate).replace(/\{0\}/,this._calendar.local.name)}function o(t,e){return"000000".substring(0,e-(t=""+t).length)+t}function s(){this.shortYearCutoff="+10"}function l(t){this.local=this.regionalOptions[t]||this.regionalOptions[""]}n(i.prototype,{instance:function(t,e){t=(t||"gregorian").toLowerCase(),e=e||"";var r=this._localCals[t+"-"+e];if(!r&&this.calendars[t]&&(r=new 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0===arguments.length?this._day:this.set(t,"d")},date:function(t,e,r){if(!this._calendar.isValid(t,e,r))throw(u.local.invalidDate||u.regionalOptions[""].invalidDate).replace(/\{0\}/,this._calendar.local.name);return this._year=t,this._month=e,this._day=r,this},leapYear:function(){return this._calendar.leapYear(this)},epoch:function(){return this._calendar.epoch(this)},formatYear:function(){return this._calendar.formatYear(this)},monthOfYear:function(){return this._calendar.monthOfYear(this)},weekOfYear:function(){return this._calendar.weekOfYear(this)},daysInYear:function(){return this._calendar.daysInYear(this)},dayOfYear:function(){return this._calendar.dayOfYear(this)},daysInMonth:function(){return this._calendar.daysInMonth(this)},dayOfWeek:function(){return this._calendar.dayOfWeek(this)},weekDay:function(){return this._calendar.weekDay(this)},extraInfo:function(){return this._calendar.extraInfo(this)},add:function(t,e){return this._calendar.add(this,t,e)},set:function(t,e){return this._calendar.set(this,t,e)},compareTo:function(t){if(this._calendar.name!==t._calendar.name)throw(u.local.differentCalendars||u.regionalOptions[""].differentCalendars).replace(/\{0\}/,this._calendar.local.name).replace(/\{1\}/,t._calendar.local.name);var e=this._year!==t._year?this._year-t._year:this._month!==t._month?this.monthOfYear()-t.monthOfYear():this._day-t._day;return 0===e?0:e<0?-1:1},calendar:function(){return this._calendar},toJD:function(){return this._calendar.toJD(this)},fromJD:function(t){return this._calendar.fromJD(t)},toJSDate:function(){return this._calendar.toJSDate(this)},fromJSDate:function(t){return this._calendar.fromJSDate(t)},toString:function(){return(this.year()<0?"-":"")+o(Math.abs(this.year()),4)+"-"+o(this.month(),2)+"-"+o(this.day(),2)}}),n(s.prototype,{_validateLevel:0,newDate:function(t,e,r){return null==t?this.today():(t.year&&(this._validate(t,e,r,u.local.invalidDate||u.regionalOptions[""].invalidDate),r=t.day(),e=t.month(),t=t.year()),new a(this,t,e,r))},today:function(){return this.fromJSDate(new Date)},epoch:function(t){return this._validate(t,this.minMonth,this.minDay,u.local.invalidYear||u.regionalOptions[""].invalidYear).year()<0?this.local.epochs[0]:this.local.epochs[1]},formatYear:function(t){var e=this._validate(t,this.minMonth,this.minDay,u.local.invalidYear||u.regionalOptions[""].invalidYear);return(e.year()<0?"-":"")+o(Math.abs(e.year()),4)},monthsInYear:function(t){return this._validate(t,this.minMonth,this.minDay,u.local.invalidYear||u.regionalOptions[""].invalidYear),12},monthOfYear:function(t,e){var r=this._validate(t,e,this.minDay,u.local.invalidMonth||u.regionalOptions[""].invalidMonth);return(r.month()+this.monthsInYear(r)-this.firstMonth)%this.monthsInYear(r)+this.minMonth},fromMonthOfYear:function(t,e){var r=(e+this.firstMonth-2*this.minMonth)%this.monthsInYear(t)+this.minMonth;return this._validate(t,r,this.minDay,u.local.invalidMonth||u.regionalOptions[""].invalidMonth),r},daysInYear:function(t){var e=this._validate(t,this.minMonth,this.minDay,u.local.invalidYear||u.regionalOptions[""].invalidYear);return this.leapYear(e)?366:365},dayOfYear:function(t,e,r){var n=this._validate(t,e,r,u.local.invalidDate||u.regionalOptions[""].invalidDate);return n.toJD()-this.newDate(n.year(),this.fromMonthOfYear(n.year(),this.minMonth),this.minDay).toJD()+1},daysInWeek:function(){return 7},dayOfWeek:function(t,e,r){var n=this._validate(t,e,r,u.local.invalidDate||u.regionalOptions[""].invalidDate);return(Math.floor(this.toJD(n))+2)%this.daysInWeek()},extraInfo:function(t,e,r){return this._validate(t,e,r,u.local.invalidDate||u.regionalOptions[""].invalidDate),{}},add:function(t,e,r){return this._validate(t,this.minMonth,this.minDay,u.local.invalidDate||u.regionalOptions[""].invalidDate),this._correctAdd(t,this._add(t,e,r),e,r)},_add:function(t,e,r){if(this._validateLevel++,"d"===r||"w"===r){var n=t.toJD()+e*("w"===r?this.daysInWeek():1),i=t.calendar().fromJD(n);return this._validateLevel--,[i.year(),i.month(),i.day()]}try{var a=t.year()+("y"===r?e:0),o=t.monthOfYear()+("m"===r?e:0);i=t.day(),"y"===r?(t.month()!==this.fromMonthOfYear(a,o)&&(o=this.newDate(a,t.month(),this.minDay).monthOfYear()),o=Math.min(o,this.monthsInYear(a)),i=Math.min(i,this.daysInMonth(a,this.fromMonthOfYear(a,o)))):"m"===r&&(function(t){for(;oe-1+t.minMonth;)a++,o-=e,e=t.monthsInYear(a)}(this),i=Math.min(i,this.daysInMonth(a,this.fromMonthOfYear(a,o))));var s=[a,this.fromMonthOfYear(a,o),i];return this._validateLevel--,s}catch(t){throw this._validateLevel--,t}},_correctAdd:function(t,e,r,n){if(!(this.hasYearZero||"y"!==n&&"m"!==n||0!==e[0]&&t.year()>0==e[0]>0)){var 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Array(i),o=new Array(i),s=new Array(i);for(r=0;r=1?(r=1,e-1):Math.floor(r*e),i=t[n],a=t[n+1],o=n>0?t[n-1]:2*i-a,s=na&&(i=e.slice(a,i),s[o]?s[o]+=i:s[++o]=i),(r=r[0])===(n=n[0])?s[o]?s[o]+=n:s[++o]=n:(s[++o]=null,l.push({i:o,x:G(r,n)})),a=X.lastIndex;return a=`\n", + " - 12 Sonderzeichen ``` #$%&'\\^_|~`@ ``` \n", + "\n", + "- ASCII ist heute noch der \"kleinste gemeinsame Nenner\" im Codierungs-Chaos.\n", + "- Die ersten 128 Unicode-Zeichen sind identisch mit ASCII.\n", + "\n", + "### ISO 8859-Zeichensätze\n", + "\n", + "- ASCII nutzt nur 7 Bits. \n", + "- In einem Byte kann man durch Setzen des 8. Bits weitere 128 Zeichen unterbringen. \n", + "- 1987/88 wurden im ISO 8859-Standard verschiedene 1-Byte-Codierungen festgelegt, die alle ASCII-kompatibel sind, darunter:\n", + "\n", + ":::{.narrow}\n", + " |Codierung | Region | Sprachen|\n", + " |:-----------|:----------|:-------|\n", + " |ISO 8859-1 (Latin-1) | Westeuropa | Deutsch, Französisch,...,Isländisch\n", + " |ISO 8859-2 (Latin-2) | Osteuropa | slawische Sprachen mit lateinischer Schrift\n", + " |ISO 8859-3 (Latin-3) | Südeuropa | Türkisch, Maltesisch,...\n", + " |ISO 8859-4 (Latin-4) | Nordeuropa | Estnisch, Lettisch, Litauisch, Grönländisch, Sami\n", + " |ISO 8859-5 (Latin/Cyrillic) | Osteuropa | slawische Sprachen mit kyrillischer Schrift\n", + " |ISO 8859-6 (Latin/Arabic) | |\n", + " |ISO 8859-7 (Latin/Greek) | |\n", + " |...| | \n", + " |ISO 8859-15 (Latin-9)| | 1999: Revision von Latin-1: jetzt mit Euro-Zeichen! \n", + " \n", + ":::\n", + " \n", + "## Unicode \n", + "\n", + "Das Ziel des Unicode-Consortiums ist eine einheitliche Codierung für alle Schriften der Welt.\n", + "\n", + "- Unicode Version 1 erschien 1991\n", + "- Unicode Version 15 erschien 2021 mit 149 186 Zeichen (das sind 4489 mehr als Unicode 14), darunter: \n", + " - 161 Schriften \n", + " - mathematische und technische Symbole\n", + " - Emojis und andere Symbole, Steuer- und Formatierungszeichen\n", + "- davon entfallen über 90 000 Zeichen auf die CJK-Schriften (Chinesisch/Japanisch/Koreanisch) \n", + " \n", + " \n", + "### technische Details\n", + "\n", + "- Jedem Zeichen wird ein `codepoint` zugeordnet. Das ist einfach eine fortlaufende Nummer.\n", + "- Diese Nummer wird hexadezimal notiert\n", + " - entweder 4-stellig als `U+XXXX` (0-te Ebene) \n", + " - oder 5...6-stellig als `U+XXXXXX` (weitere Ebenen)\n", + "- Jede Ebene geht von `U+XY0000` bis `U+XYFFFF`, kann also $2^{16}=65\\;534$ Zeichen enthalten. \n", + "- Vorgesehen sind bisher 17 Ebenen `XY=00` bis `XY=10`, also der Wertebereich von `U+0000` bis `U+10FFFF`.\n", + "- Damit sind maximal 21 Bits pro Zeichen nötig.\n", + "- Die Gesamtzahl der damit möglichen Codepoints ist etwas kleiner als 0x10FFFF, da aus technischen Gründen gewisse Bereiche nicht verwendet werden. Sie beträgt etwa 1.1 Millionen, es ist also noch viel Platz. \n", + "- Bisher wurden nur Codepoints aus den Ebenen \n", + " - Ebene 0 = BMP _Basic Multilingual Plane_ `U+0000 - U+FFFF`,\n", + " - Ebene 1 = SMP _Supplementary Multilingual Plane_ `U+010000 - U+01FFFF`,\n", + " - Ebene 2 = SIP _Supplementary Ideographic Plane_ `U+020000 - U+02FFFF`, \n", + " - Ebene 3 = TIP _Tertiary Ideographic Plane_ `U+030000 - U+03FFFF` und\n", + " - Ebene 14 = SSP _Supplementary Special-purpose Plane_ `U+0E0000 - U+0EFFFF` vergeben.\n", + "- `U+0000` bis `U+007F` ist identisch mit ASCII\n", + "- `U+0000` bis `U+00FF` ist identisch mit ISO 8859-1 (Latin-1)\n", + "\n", + "### Eigenschaften von Unicode-Zeichen\n", + "\n", + "Im Standard wird jedes Zeichen beschrieben duch\n", + "\n", + " - seinen Codepoint (Nummer) \n", + " - einen Namen (welcher nur aus ASCII-Großbuchstaben, Ziffern und Minuszeichen besteht) und \n", + " - verschiedene Attributen wie\n", + " - Laufrichtung der Schrift \n", + " - Kategorie: Großbuchstabe, Kleinbuchstabe, modifizierender Buchstabe, Ziffer, Satzzeichen, Symbol, Seperator,....\n", + "\n", + "Im Unicode-Standard sieht das dann so aus: (zur Vereinfachung nur Codepoint und Name)\n", + "```\n", + "...\n", + "U+0041 LATIN CAPITAL LETTER A\n", + "U+0042 LATIN CAPITAL LETTER B\n", + "U+0043 LATIN CAPITAL LETTER C\n", + "U+0044 LATIN CAPITAL LETTER D\n", + "...\n", + "U+00E9 LATIN SMALL LETTER E WITH ACUTE\n", + "U+00EA LATIN SMALL LETTER E WITH CIRCUMFLEX\n", + "...\n", + "U+0641 ARABIC LETTER FEH\n", + "U+0642 ARABIC LETTER QAF\n", + "...\n", + "U+21B4 RIGHTWARDS ARROW WITH CORNER DOWNWARDS\n", + "...\n", + "```\n", + "\n", + "Wie sieht 'RIGHTWARDS ARROW WITH CORNER DOWNWARDS' aus?\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8eaf4a41", + "metadata": {}, + "outputs": [], + "source": [ + "'\\U21b4'" + ] + }, + { + "cell_type": "markdown", + "id": "1c1f742a", + "metadata": {}, + "source": [ + "### Eine Auswahl an Schriften \n", + "\n", + "::: {.content-visible when-format=\"html\"}\n", + "\n", + ":::{.callout-note}\n", + "Falls im Folgenden einzelne Zeichen oder Schriften in Ihrem Browser nicht darstellbar sind, müssen Sie geeignete \n", + "Fonts auf Ihrem Rechner installieren. \n", + "\n", + "Alternativ können Sie die PDF-Version dieser Seite verwenden. Dort sind alle Fonts eingebunden.\n", + ":::\n", + "\n", + ":::\n", + "\n", + "Eine kleine Hilfsfunktion:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "823bfab7", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "printuc(c, n):\n", + "print n characters from unicode table, starting with character c \n", + "\"\"\"\n", + "function printuc(c, n)\n", + " for i in 0:n-1\n", + " print(c + i)\n", + " end\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "50893728", + "metadata": {}, + "source": [ + "__Kyrillisch__\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8caca4e0", + "metadata": {}, + "outputs": [], + "source": [ + "printuc('\\U0400', 100)" + ] + }, + { + "cell_type": "markdown", + "id": "4400710f", + "metadata": {}, + "source": [ + "__Tamilisch__\n", + "\n", + ":::{.cellmerge}\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "85bb89e4", + "metadata": {}, + "outputs": [], + "source": [ + "#| echo: true\n", + "#| output: false\n", + "printuc('\\U0be7',20)" + ] + }, + { + "cell_type": "markdown", + "id": "3904378b", + "metadata": {}, + "source": [ + "\\begingroup\\setmonofont{Noto Sans Tamil}\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "13461be4", + "metadata": {}, + "outputs": [], + "source": [ + "#| echo: false\n", + "#| output: true\n", + "printuc('\\U0be7',20)" + ] + }, + { + "cell_type": "markdown", + "id": "e8ed18a7", + "metadata": {}, + "source": [ + "\\endgroup\n", + "\n", + ":::\n", + "\n", + "__Schach__\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8f6b4cee", + "metadata": {}, + "outputs": [], + "source": [ + "printuc('\\U2654', 12)" + ] + }, + { + "cell_type": "markdown", + "id": "f9ca81ef", + "metadata": {}, + "source": [ + "__Mathematische Operatoren__\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "60c00c29", + "metadata": {}, + "outputs": [], + "source": [ + "printuc('\\U2200', 255)" + ] + }, + { + "cell_type": "markdown", + "id": "1e023c33", + "metadata": {}, + "source": [ + "__Runen__\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "361517d3", + "metadata": {}, + "outputs": [], + "source": [ + "printuc('\\U16a0', 40)" + ] + }, + { + "cell_type": "markdown", + "id": "067f18ed", + "metadata": {}, + "source": [ + ":::{.cellmerge}\n", + "\n", + "__Scheibe (Diskus) von Phaistos__\n", + "\n", + "- Diese Schrift ist nicht entziffert. \n", + "- Es ist unklar, welche Sprache dargestellt wird.\n", + "- Es gibt nur ein einziges Dokument in dieser Schrift: die Tonscheibe von Phaistos aus der Bronzezeit \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9ac8d6c5", + "metadata": {}, + "outputs": [], + "source": [ + "#| echo: true\n", + "#| output: false\n", + "printuc('\\U101D0', 46 )" + ] + }, + { + "cell_type": "markdown", + "id": "ab85dc8a", + "metadata": {}, + "source": [ + "\\begingroup\\setmonofont{Phaistos.otf}\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "599a342d", + "metadata": {}, + "outputs": [], + "source": [ + "#| echo: false\n", + "#| output: true\n", + "printuc('\\U101D0', 46 )" + ] + }, + { + "cell_type": "markdown", + "id": "c5ccd262", + "metadata": {}, + "source": [ + "\\endgroup\n", + "\n", + ":::\n", + "\n", + "### Unicode transformation formats: UTF-8, UTF-16, UTF-32\n", + "\n", + "_Unicode transformation formats_ legen fest, wie eine Folge von Codepoints als eine Folge von Bytes dargestellt wird. \n", + "\n", + "Da die Codepoints unterschiedlich lang sind, kann man sie nicht einfach hintereinander schreiben. Wo hört einer auf und fängt der nächste an? \n", + "\n", + "- __UTF-32__: Das einfachste, aber auch speicheraufwändigste, ist, sie alle auf gleiche Länge zu bringen. Jeder Codepoint wird in 4 Bytes = 32 Bit kodiert. \n", + "- Bei __UTF-16__ wird ein Codepoint entweder mit 2 Bytes oder mit 4 Bytes dargestellt. \n", + "- Bei __UTF-8__ wird ein Codepoint mit 1,2,3 oder 4 Bytes dargestellt. \n", + "- __UTF-8__ ist das Format mit der höchsten Verbreitung. Es wird auch von Julia verwendet. \n", + "\n", + "\n", + "### UTF-8\n", + "\n", + "- Für jeden Codepoint werden 1, 2, 3 oder 4 volle Bytes verwendet. \n", + "\n", + "- Bei einer Codierung mit variabler Länge muss man erkennen können, welche Bytefolgen zusammengehören:\n", + " - Ein Byte der Form 0xxxxxxx steht für einen ASCII-Codepoint der Länge 1.\n", + " - Ein Byte der Form 110xxxxx startet einen 2-Byte-Code.\n", + " - Ein Byte der Form 1110xxxx startet einen 3-Byte-Code.\n", + " - Ein Byte der Form 11110xxx startet einen 4-Byte-Code.\n", + " - Alle weiteren Bytes eines 2-,3- oder 4-Byte-Codes haben die Form 10xxxxxx. \n", + "\n", + "- Damit ist der Platz, der für den Codepoint zur Verfügung steht (Anzahl der x):\n", + " - Ein-Byte-Code: 7 Bits\n", + " - Zwei-Byte-Code: 5 + 6 = 11 Bits\n", + " - Drei-Byte-Code: 4 + 6 + 6 = 16 Bits\n", + " - Vier-Byte-Code: 3 + 6 + 6 + 6 = 21 Bits\n", + "\n", + "- Damit ist jeder ASCII-Text automatisch auch ein korrekt codierter UTF-8-Text.\n", + "\n", + "- Sollten die bisher für Unicode festgelegten 17 Ebenen = 21 Bit = 1.1 Mill. mögliche Zeichen mal erweitert werden, dann wird UTF-8 auf 5- und 6-Byte-Codes erweitert. \n", + " \n", + "\n", + "## Zeichen und Zeichenketten in Julia\n", + "\n", + "### Zeichen: `Char` \n", + "\n", + "Der Datentyp `Char` kodiert ein einzelnes Unicode-Zeichen. \n", + "\n", + "- Julia verwendet dafür einfachen Anführungszeichen: `'a'`. \n", + "- Ein `Char` belegt 4 Bytes Speicher und \n", + "- repräsentiert einen Unicode-Codepoint.\n", + "- `Char`s können von/zu `UInt`s umgewandelt werden und \n", + "- der Integer-Wert ist gleich dem Unicode-codepoint.\n", + "\n", + "\n", + "### Zeichenketten: `String`\n", + "\n", + "- Für Strings verwendet Julia doppelte Anführungszeichen: `\"a\"`.\n", + "- Sie sind UTF-8-codiert, d.h., ein Zeichen kann zwischen 1 und 4 Bytes lang sein.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a8ea6e75", + "metadata": {}, + "outputs": [], + "source": [ + "@show typeof('a') sizeof('a') typeof(\"a\") sizeof(\"a\");" + ] + }, + { + "cell_type": "markdown", + "id": "ab924ce4", + "metadata": {}, + "source": [ + "- `Char`s können von/zu `UInt`s umgewandelt werden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dac49645", + "metadata": {}, + "outputs": [], + "source": [ + "UInt('a')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "98bd57af", + "metadata": {}, + "outputs": [], + "source": [ + "b = Char(0x2656)" + ] + }, + { + "cell_type": "markdown", + "id": "74470851", + "metadata": {}, + "source": [ + "__Bei einem Nicht-ASCII-String unterscheiden sich Anzahl der Bytes und Anzahl der Zeichen:__\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0edfc402", + "metadata": {}, + "outputs": [], + "source": [ + "asciistr = \"Hello World!\"\n", + "@show length(asciistr) ncodeunits(asciistr);" + ] + }, + { + "cell_type": "markdown", + "id": "2c2ce448", + "metadata": {}, + "source": [ + "(Das Leerzeichen zählt natürlich auch.)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c171aa8d", + "metadata": {}, + "outputs": [], + "source": [ + "str = \"😄 Hellö 🎶\"\n", + "@show length(str) ncodeunits(str);" + ] + }, + { + "cell_type": "markdown", + "id": "e0467145", + "metadata": {}, + "source": [ + "__Iteration über einen String iteriert über die Zeichen:__\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "802e421f", + "metadata": {}, + "outputs": [], + "source": [ + "for i in str\n", + " println(i, \" \", typeof(i))\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "b434c61b", + "metadata": {}, + "source": [ + "### Verkettung von Strings\n", + "\n", + "\"Strings mit Verkettung bilden ein nichtkommutatives Monoid.\"\n", + "\n", + "Deshalb wird in Julia die Verkettung multiplikativ geschrieben.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dba97090", + "metadata": {}, + "outputs": [], + "source": [ + " str * asciistr * str" + ] + }, + { + "cell_type": "markdown", + "id": "c2f3a520", + "metadata": {}, + "source": [ + "Damit sind auch Potenzen mit natürlichem Exponenten definiert.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e8804720", + "metadata": {}, + "outputs": [], + "source": [ + "str^3, str^0" + ] + }, + { + "cell_type": "markdown", + "id": "ffd0fd4c", + "metadata": {}, + "source": [ + "### Stringinterpolation\n", + "\n", + "Das Dollarzeichen hat in Strings eine Sonderfunktion, die wir schon oft in \n", + "`print()`-Anweisungen genutzt haben. MAn kann damit eine Variable oder einen Ausdruck interpolieren:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b8248a55", + "metadata": {}, + "outputs": [], + "source": [ + "a = 33.4\n", + "b = \"x\"\n", + "\n", + "s = \"Das Ergebnis für $b ist gleich $a und die verdoppelte Wurzel daraus ist $(2sqrt(a))\\n\"" + ] + }, + { + "cell_type": "markdown", + "id": "b2039521", + "metadata": {}, + "source": [ + "### Backslash escape sequences \n", + "\n", + "Der _backslash_ `\\` hat in Stringkonstanten ebenfalls eine Sonderfunktion. \n", + "Julia benutzt die von C und anderen Sprachen bekannten _backslash_-Codierungen für Sonderzeichen und für Dollarzeichen und Backslash selbst:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f896516b", + "metadata": {}, + "outputs": [], + "source": [ + "s = \"So bekommt man \\'Anführungszeichen\\\" und ein \\$-Zeichen und einen\\nZeilenumbruch und ein \\\\ usw... \"\n", + "print(s)" + ] + }, + { + "cell_type": "markdown", + "id": "6258cdb2", + "metadata": {}, + "source": [ + "### Triple-Quotes\n", + "\n", + "Man kann Strings auch mit Triple-Quotes begrenzen. \n", + "In dieser Form bleiben Zeilenumbrüche und Anführungszeichen erhalten:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e7913161", + "metadata": {}, + "outputs": [], + "source": [ + "s = \"\"\"\n", + " Das soll\n", + "ein \"längerer\" \n", + " 'Text' sein.\n", + "\"\"\"\n", + "\n", + "print(s)" + ] + }, + { + "cell_type": "markdown", + "id": "15de1886", + "metadata": {}, + "source": [ + "### Raw strings\n", + "\n", + "In einem `raw string` sind alle backslash-Codierungen außer `\\\"` abgeschaltet:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a040859a", + "metadata": {}, + "outputs": [], + "source": [ + "s = raw\"Ein $ und ein \\ und zwei \\\\ und ein 'bla'...\"\n", + "print(s)" + ] + }, + { + "cell_type": "markdown", + "id": "6e24746e", + "metadata": {}, + "source": [ + "## Weitere Funktionen für Zeichen und Strings (Auswahl)\n", + "\n", + "### Tests für Zeichen\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f79e914f", + "metadata": {}, + "outputs": [], + "source": [ + "@show isdigit('0') isletter('Ψ') isascii('\\U2655') islowercase('α') \n", + "@show isnumeric('½') iscntrl('\\n') ispunct(';');" + ] + }, + { + "cell_type": "markdown", + "id": "d39076f7", + "metadata": {}, + "source": [ + "### Anwendung auf Strings\n", + "\n", + "Diese Tests lassen sich z.B. mit `all()`, `any()` oder `count()` auf Strings anwenden:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b6055040", + "metadata": {}, + "outputs": [], + "source": [ + "all(ispunct, \";.:\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "29fd91ef", + "metadata": {}, + "outputs": [], + "source": [ + "any(isdigit, \"Es ist 3 Uhr! 🕒\" )" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "73a589b9", + "metadata": {}, + "outputs": [], + "source": [ + "count(islowercase, \"Hello, du!!\")" + ] + }, + { + "cell_type": "markdown", + "id": "5bdff431", + "metadata": {}, + "source": [ + "### Weitere String-Funktionen\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a24b1569", + "metadata": {}, + "outputs": [], + "source": [ + "@show startswith(\"Lampenschirm\", \"Lamp\") occursin(\"pensch\", \"Lampenschirm\") \n", + "@show endswith(\"Lampenschirm\", \"irm\"); " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "89003024", + "metadata": {}, + "outputs": [], + "source": [ + "@show uppercase(\"Eis\") lowercase(\"Eis\") titlecase(\"eiSen\");" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "01910748", + "metadata": {}, + "outputs": [], + "source": [ + "# remove newline from end of string\n", + "\n", + "@show chomp(\"Eis\\n\") chomp(\"Eis\");" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d618c466", + "metadata": {}, + "outputs": [], + "source": [ + "split(\"π ist irrational.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "da05d6b9", + "metadata": {}, + "outputs": [], + "source": [ + "replace(\"π ist irrational.\", \"ist\" => \"ist angeblich\")" + ] + }, + { + "cell_type": "markdown", + "id": "4e198e74", + "metadata": {}, + "source": [ + "## Indizierung von Strings\n", + "\n", + "Strings sind nicht mutierbar aber indizierbar. Dabei gibt es ein paar Besonderheiten.\n", + "\n", + "- Der Index nummeriert die Bytes des Strings. \n", + "- Bei einem nicht-ASCII-String sind nicht alle Indizes gültig, denn\n", + "- ein gültiger Index adressiert immer ein Unicode-Zeichen.\n", + "\n", + "Unser Beispielstring:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4686b303", + "metadata": {}, + "outputs": [], + "source": [ + "str" + ] + }, + { + "cell_type": "markdown", + "id": "6c1a2fe1", + "metadata": {}, + "source": [ + "Das erste Zeichen\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "eb0e9898", + "metadata": {}, + "outputs": [], + "source": [ + "str[1]" + ] + }, + { + "cell_type": "markdown", + "id": "50049fee", + "metadata": {}, + "source": [ + "Dieses Zeichen ist in UTF8-Kodierung 4 Bytes lang. Damit sind 2,3 und 4 ungültige Indizes. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a6a3005a", + "metadata": {}, + "outputs": [], + "source": [ + "str[2]" + ] + }, + { + "cell_type": "markdown", + "id": "5c428767", + "metadata": {}, + "source": [ + "Erst das 5. Byte ist ein neues Zeichen:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "29febb49", + "metadata": {}, + "outputs": [], + "source": [ + "str[5]" + ] + }, + { + "cell_type": "markdown", + "id": "0daa1973", + "metadata": {}, + "source": [ + "Auch bei der Adressierung von Substrings müssen Anfang und Ende jeweils gültige Indizes sein, d.h., der Endindex muss ebenfalls das erste Byte eines Zeichens indizieren und dieses Zeichen ist das letzte des Teilstrings. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dbbc0c47", + "metadata": {}, + "outputs": [], + "source": [ + "str[1:7]" + ] + }, + { + "cell_type": "markdown", + "id": "b7fd7042", + "metadata": {}, + "source": [ + "Die Funktion `eachindex()` liefert einen Iterator über die gültigen Indizes:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6e2b8427", + "metadata": {}, + "outputs": [], + "source": [ + "for i in eachindex(str)\n", + " c = str[i]\n", + " println(\"$i: $c\")\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "f651e9bf", + "metadata": {}, + "source": [ + "Wie üblich macht collect() aus einem Iterator einen Vektor.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a591c148", + "metadata": {}, + "outputs": [], + "source": [ + "collect(eachindex(str))" + ] + }, + { + "cell_type": "markdown", + "id": "a7f9cb60", + "metadata": {}, + "source": [ + "Die Funktion `nextind()` liefert den nächsten gültigen Index.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d568dd47", + "metadata": {}, + "outputs": [], + "source": [ + "@show nextind(str, 1) nextind(str, 2); " + ] + }, + { + "cell_type": "markdown", + "id": "91af5e34", + "metadata": {}, + "source": [ + "Warum verwendet Julia einen Byte-Index und keinen Zeichenindex? Der Hauptgrund dürfte die Effizienz der Indizierung sein.\n", + "\n", + "- In einem langen String, z.B. einem Buchtext, ist die Stelle `s[123455]` mit einem Byte-Index schnell zu finden. \n", + "- Ein Zeichen-Index müsste in der UTF-8-Codierung den ganzen String durchlaufen, um das n-te Zeichen zu finden, da die Zeichen 1,2,3 oder 4 Bytes lang sein können.\n", + "\n", + "\n", + "Einige Funktionen liefern Indizes oder Ranges als Resultat. Sie liefern immer gültige Indizes:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b62bbd82", + "metadata": {}, + "outputs": [], + "source": [ + "findfirst('l', str)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "93def2b5", + "metadata": {}, + "outputs": [], + "source": [ + "findfirst(\"Hel\", str)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e96565a7", + "metadata": {}, + "outputs": [], + "source": [ + "str2 = \"αβγδϵ\"^3" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e251544c", + "metadata": {}, + "outputs": [], + "source": [ + "n = findfirst('γ', str2)" + ] + }, + { + "cell_type": "markdown", + "id": "be81789e", + "metadata": {}, + "source": [ + "So kann man ab dem nächsten nach `n=5` gültigen Index weitersuchen:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ad89b2c9", + "metadata": {}, + "outputs": [], + "source": [ + "findnext('γ', str2, nextind(str2, n))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/5_TricksHelp.ipynb b/nb/5_TricksHelp.ipynb new file mode 100644 index 0000000..2a2e751 --- /dev/null +++ b/nb/5_TricksHelp.ipynb @@ -0,0 +1,562 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "2ffe347c", + "metadata": {}, + "source": [ + "# Julia Dokumentation\n", + "\n", + "[https://docs.julialang.org/](https://docs.julialang.org/) die offizielle Dokumentation\n", + "\n", + "Einige Seiten mit Übersichten:\n", + "\n", + " - [https://docs.julialang.org/en/v1/base/punctuation/](https://docs.julialang.org/en/v1/base/punctuation/) Verzeichnis der Symbole\n", + " - [https://docs.julialang.org/en/v1/manual/unicode-input/](https://docs.julialang.org/en/v1/manual/unicode-input/) Verzeichnis spezieller Unicode-Symbole und deren Eingabe in Julia via Tab-Vervollständigung\n", + " - [https://docs.julialang.org/en/v1/manual/mathematical-operations/#Rounding-functions](https://docs.julialang.org/en/v1/manual/mathematical-operations/#Rounding-functions) Liste mathematischer Funktionen \n", + "\n", + "---------\n", + "\n", + "\n", + "\n", + "# Hilfe und praktische Tipps\n", + "\n", + "----\n", + "\n", + "\n", + "## Julia REPL (Read - Eval - Print - Loop)\n", + "\n", + "Start von Julia in einem Terminal:\n", + "```\n", + "julia>\n", + "```\n", + "\n", + "| Kommando | Wirkung |\n", + "| :----------------------------| :------------------------ |\n", + "| `exit()` oder `Ctrl-d` | exit Julia |\n", + "| `Ctrl-c` | interrupt |\n", + "| `Ctrl-l` | clear screen |\n", + "| Kommando mit `;` beenden | Ausgabe unterdrückt |\n", + "| `include(\"filename.jl\")` | Datei mit Julia-Code einlesen und ausführen |\n", + "\n", + "\n", + "-----\n", + "\n", + "Der REPL hat verschiedene Modi: \n", + "\n", + "| Modus | Prompt | Modus starten | Modus verlassen |\n", + "| :- | :- | :- | :- |\n", + "|||||\n", + "| default| `julia>` | | |\n", + "|||||\n", + "| Package manager | `pkg>` | `]` | `backspace` |\n", + "|||||\n", + "| Help | `help?>` | `?`| `backspace `|\n", + "|||||\n", + "|Shell | `shell>` | `;` | `backspace`|\n", + "|||||\n", + "\n", + "--------\n", + "\n", + "\n", + "## Jupyter notebooks (IJulia)\n", + "\n", + "Die Modi sind als Einzeiler in einer eigenen Input-Zelle nutzbar: \n", + "\n", + "(i) ein Kommando des Paket-Managers:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d6c200e5", + "metadata": {}, + "outputs": [], + "source": [ + "] status " + ] + }, + { + "cell_type": "markdown", + "id": "9caf3630", + "metadata": {}, + "source": [ + "(ii) eine Help-Abfrage:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c923aa16", + "metadata": {}, + "outputs": [], + "source": [ + "?sin" + ] + }, + { + "cell_type": "markdown", + "id": "bfc75d15", + "metadata": {}, + "source": [ + "(iii) Ein Shell-Kommando:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3617aff8", + "metadata": {}, + "outputs": [], + "source": [ + ";ls .." + ] + }, + { + "cell_type": "markdown", + "id": "bdce3ab2", + "metadata": {}, + "source": [ + "## Der Paket-Manager\n", + "\n", + "- Über 7000 Pakete, siehe [https://julialang.org/packages/](https://julialang.org/packages/)\n", + "- Bevor sie mit `using Module` verwendet werden können, müssen sie heruntergeladen und installiert werden.\n", + "- Dazu dient der `package manager`\n", + "- 2 Betriebsarten: \n", + " - als normale Julia-Anweisungen, die auch in einer `.jl`-Programmdatei stehen können:\n", + " ```\n", + " using Pkg\n", + " Pkg.add(\"TollesPaket\")\n", + " ```\n", + " - im speziellen pkg-Modus des Julia-REPLs:\n", + " ```\n", + " ] add TollesPaket\n", + " ```\n", + "----- \n", + "\n", + "### Einige Funktionen\n", + "\n", + "| Funktion | `pkg` - Mode | Erklärung |\n", + "|:------------------------|:----------------------|:----------------------------------------------------------|\n", + "| `Pkg.add(\"MyPack\")` | `pkg> add MyPack` | add `MyPack.jl` to current environment |\n", + "| `Pkg.rm(\"MyPack\")` | `pkg> remove MyPack` | remove `MyPack.jl` from current environment |\n", + "| `Pkg.update()` | `pkg> update` | update packages in current environment |\n", + "| `Pkg.activate(\"mydir\")` | `pkg> activate mydir` | activate directory as current environment |\n", + "| `Pkg.status()` | `pkg> status` | list packages |\n", + "\n", + "\n", + "### Installierte Pakete und Environments \n", + "\n", + "- Julia und der Paketmanager verwalten \n", + " 1. eine Liste der mit dem Kommando `Pkg.add()` bzw. `]add` explizit installierten Pakete mit genauer Versionsbezeichnung in einer Datei `Project.toml` und \n", + " 2. eine Liste aller dabei auch als implizite Abhängigkeiten installierten Pakete in der Datei `Manifest.toml`. \n", + "- Das Verzeichnis, in dem diese Dateien stehen, ist das `environment` und wird mit `Pkg.status()` bzw. `]status` angezeigt. \n", + "- Im Normalfall sieht das so aus: \n", + "```\n", + "(@v1.7) pkg> status\n", + " Status `~/.julia/environments/v1.7/Project.toml`\n", + " [1dea7af3] OrdinaryDiffEq v6.7.1\n", + " [91a5bcdd] Plots v1.27.1\n", + " [438e738f] PyCall v1.93.1\n", + "```\n", + "- Man kann für verschiedene Projekte eigene `environments` benutzen. Dazu kann man entweder Julia mit \n", + "```\n", + "julia --project=path/to/myproject\n", + "```\n", + "starten oder in Julia das environment mit `Pkg.activate(\"path/to/myproject\")` aktivieren. Dann werden `Project.toml, Manifest.toml` dort angelegt und verwaltet. (Die Installation der Paketdateien erfolgt weiterhin irgendwo unter `$HOME/.julia`) \n", + "\n", + "\n", + "### Zum Installieren von Paketen auf unserem Jupyter-Server `misun103`:\n", + "- Es gibt ein zentrales Repository, in dem alle von mir erwähnten Pakete bereits installiert sind. \n", + "- Dort haben Sie keine Schreibrechte.\n", + "- Sie können aber zusätzliche Pakete in Ihrem `Home` installieren. Dazu ist als erster Befehl nötig, das aktuelle Verzeichnis zu aktivieren: \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "103bd8a1", + "metadata": {}, + "outputs": [], + "source": [ + "] activate ." + ] + }, + { + "cell_type": "markdown", + "id": "077e93f2", + "metadata": {}, + "source": [ + "(Man beachte den Punkt!)\n", + "\n", + "----\n", + "\n", + "Danach können Sie mit `add` im Pkg-Modus auch Pakete installieren:\n", + "\n", + "```\n", + "] add TollesPaket\n", + "```\n", + "\n", + "\n", + "Achtung! Das kann dauern! Viele Pakete haben komplexe Abhängigkeiten und lösen die Installation von weiteren Paketen aus. Viele Pakete werden beim Installieren vorkompiliert. Im REPL sieht man den Installationsfortschritt, im Jupyter-Notebook nicht.\n", + "\n", + "\n", + "## Eingebaute Hilfe und Informationen\n", + "Mit `?` und der `Tab`-Taste kommt man oft weiter. \n", + "\n", + "\n", + "\n", + "### weitere Hilfe: `@which`, `fieldnames()`, `methods()`, `names()`, `pwd()`\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4f099673", + "metadata": {}, + "outputs": [], + "source": [ + "# Die Zuordnung zu einem Modul zeigt @which an:\n", + "\n", + "@which(sqrt)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "44276c0d", + "metadata": {}, + "outputs": [], + "source": [ + "# Die Komponenten einer struct oder eines anderen zusammengesetzten Typs:\n", + "\n", + "fieldnames(Rational)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a200a34f", + "metadata": {}, + "outputs": [], + "source": [ + "fieldnames(Complex)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d99bfda9", + "metadata": {}, + "outputs": [], + "source": [ + "# alle Methoden einer Funktion\n", + "\n", + "methods(sqrt)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b3e6f127", + "metadata": {}, + "outputs": [], + "source": [ + "# alle Methoden einer Funktion bei bestimmten Argumenttypen. Die Argumenttypen müssen als Tupel angegeben werden\n", + "\n", + "methods(sqrt, (Number,)) # Komma nötig für 1-elementiges Tupel " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e74572ad", + "metadata": {}, + "outputs": [], + "source": [ + "# für einen Typ gibt methods() alle Konstruktoren aus\n", + "\n", + "methods(Int64)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e4de6078", + "metadata": {}, + "outputs": [], + "source": [ + "# names(Module) gibt alle von einem Modul exportierte Namen aus. \n", + "# genau wie auch\n", + "#\n", + "# ?Module \n", + "#\n", + "# funktioniert es erst, wenn das Modul mit 'using Module' geladen ist.\n", + "# Oft ist es besser, wenn die using-Anweisung in einer eigenen Zelle steht.\n", + "\n", + "using Plots" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f1df8377", + "metadata": {}, + "outputs": [], + "source": [ + "names(Plots)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3654fab2", + "metadata": {}, + "outputs": [], + "source": [ + "# Julia kürzt den interaktiven Output. \n", + "# ein explizites print() zeigt alles:\n", + "\n", + "print(names(Plots))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dc9ca3b6", + "metadata": {}, + "outputs": [], + "source": [ + "# eine andere Möglichkeit der Ausgabe mit Überlänge in Jupyter\n", + "\n", + "show(stdout, MIME(\"text/plain\"), names(Plots))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9fa0f216", + "metadata": {}, + "outputs": [], + "source": [ + "# pwd() \"print working directory\" zeigt, in welchem Verzeichnis Julia gerade operiert. \n", + "#\n", + "# Wichtig für die Ein/Ausgabe mit Dateien, z.B. include()\n", + "\n", + "pwd()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "99c19918", + "metadata": {}, + "outputs": [], + "source": [ + "include(\"Jupyter.jl\") # Datei mit Julia-Code einlesen und abarbeiten" + ] + }, + { + "cell_type": "markdown", + "id": "1464d951", + "metadata": {}, + "source": [ + "## Informationen zu Typen\n", + "\n", + "### `subtypes()`, `supertypes()`, `typemax()`, `typemin()`, `fieldnames()`, `Base.return_types()`, `dump()`\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1358c363", + "metadata": {}, + "outputs": [], + "source": [ + "subtypes(Real) # die letzten zwei sind durch das 'using Plots' dazugekommen" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e35fb7da", + "metadata": {}, + "outputs": [], + "source": [ + "supertypes(Real)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "53be4687", + "metadata": {}, + "outputs": [], + "source": [ + "typemax(Int64), typemin(Int64), fieldnames(Complex)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3a9ed940", + "metadata": {}, + "outputs": [], + "source": [ + "Base.return_types(sqrt, (Float64,))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "207af4bd", + "metadata": {}, + "outputs": [], + "source": [ + "Base.return_types(sqrt, (Complex{Int64},))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "66b42304", + "metadata": {}, + "outputs": [], + "source": [ + "# dump() zeigt alle Teile eines zusammengesetzten Objekts\n", + "\n", + "x = 3//4 + 75im\n", + "dump(x)" + ] + }, + { + "cell_type": "markdown", + "id": "9c6edfea", + "metadata": {}, + "source": [ + "## Der Julia JIT _(just in time)_ Compiler\n", + "\n", + "Julia baut auf die Werkzeuge des _LLVM Compiler Infrastructure Projects_ auf.\n", + "\n", + "\n", + "Stages of Compilation \n", + "\n", + "| stage & result | introspection command |\n", + "| :--- | :--- |\n", + "|Parse ==> Abstract Syntax Tree (AST) | `Meta.parse()` |\n", + "| Lowering: transform AST ==> Static Single Assignment (SSA) form | `@code_lowered`|\n", + "| Type Inference | `@code_warntype`, `@code_typed` |\n", + "| Generate LLVM intermediate representation | `@code_llvm`|\n", + "| Generate native machine code | `@code_native` |\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4d433ab8", + "metadata": {}, + "outputs": [], + "source": [ + "function f(x,y)\n", + " z = x^2 + log(y)\n", + " return 2z\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "de444d8a", + "metadata": {}, + "outputs": [], + "source": [ + "p = Meta.parse( \"function f(x,y); z=x^2+log(y); return 2x; end \")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1ddf17aa", + "metadata": {}, + "outputs": [], + "source": [ + "using TreeView" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "70d267d7", + "metadata": {}, + "outputs": [], + "source": [ + "walk_tree(p)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b19b64ec", + "metadata": {}, + "outputs": [], + "source": [ + "@code_lowered f(2,4)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "57eb03f9", + "metadata": {}, + "outputs": [], + "source": [ + "@code_warntype f(2,4)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cf273a25", + "metadata": {}, + "outputs": [], + "source": [ + "@code_typed f(2,4)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "28779f6b", + "metadata": {}, + "outputs": [], + "source": [ + "@code_llvm f(2,4)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "02711d1f", + "metadata": {}, + "outputs": [], + "source": [ + "@code_native f(2,4)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/6_ArraysEtcP1.ipynb b/nb/6_ArraysEtcP1.ipynb new file mode 100644 index 0000000..408b0c7 --- /dev/null +++ b/nb/6_ArraysEtcP1.ipynb @@ -0,0 +1,303 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "fcc03529", + "metadata": {}, + "source": [ + "# Container\n", + "\n", + "\n", + "Julia bietet eine große Auswahl von Containertypen mit weitgehend ähnlichem Interface an. \n", + "Wir stellen hier `Tuple`, `Range`, `Array`, `Vector` und `Matrix` vor. \n", + "\n", + "Diese Container sind: \n", + "\n", + "- **iterierbar:** Man kann über die Elemente des Containers iterieren: \n", + "```julia \n", + "for x ∈ container ... end\n", + "```\n", + "- **indizierbar:** Man kann auf Elemente über ihren Index zugreifen: \n", + "```julia\n", + "x = container[i]\n", + "``` \n", + "und einige sind \n", + "\n", + "- **mutierbar** (nur `Array`, `Vector` und `Matrix`): Man kann Elemente hinzufügen, entfernen und ändern.\n", + "\n", + "Weiterhin gibt es eine Reihe gemeinsamer Funktionen, z.B.\n", + "\n", + "- `length(container)` --- Anzahl der Elemente\n", + "- `eltype(container)` --- Typ der Elemente\n", + "- `isempty(container)` --- Test, ob Container leer ist\n", + "- `empty!(container)` --- leert Container (nur wenn mutierbar)\n", + "\n", + "\n", + "## Tupeln\n", + "\n", + "Ein Tupel ist ein nicht mutierbarer Container von Elementen. Es ist also nicht möglich, neue Elemente dazuzufügen oder den Wert eines Elements zu ändern. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3b33212e", + "metadata": {}, + "outputs": [], + "source": [ + "t = (33, 4.5, \"Hello\")\n", + "\n", + "@show t[2] # indizierbar\n", + "\n", + "for i ∈ t println(i) end # iterierbar" + ] + }, + { + "cell_type": "markdown", + "id": "e65e4da8", + "metadata": {}, + "source": [ + "Ein Tupel ist ein **inhomogener** Typ. Jedes Element hat seinen eigenen Typ und das zeigt sich auch im Typ des Tupels:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3d21cc5b", + "metadata": {}, + "outputs": [], + "source": [ + "typeof(t)" + ] + }, + { + "cell_type": "markdown", + "id": "74fcc47e", + "metadata": {}, + "source": [ + "Man verwendet Tupel gerne als Rückgabewerte von Funktionen, um mehr als ein Objekt zurückzulieferen.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6ffc0cdc", + "metadata": {}, + "outputs": [], + "source": [ + "# Ganzzahldivision und Rest: \n", + "# Quotient und Rest werden den Variablen q und r zugewiesen\n", + "\n", + "q, r = divrem(71, 6)\n", + "@show q r;" + ] + }, + { + "cell_type": "markdown", + "id": "e7a04cdd", + "metadata": {}, + "source": [ + "Wie man hier sieht, kann man in bestimmten Konstrukten die Klammern auch weglassen.\n", + "Dieses *implict tuple packing/unpacking* verwendet man auch gerne in Mehrfachzuweisungen:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2a260b6e", + "metadata": {}, + "outputs": [], + "source": [ + "x, y, z = 12, 17, 203" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3447dffb", + "metadata": {}, + "outputs": [], + "source": [ + "y" + ] + }, + { + "cell_type": "markdown", + "id": "8694ec4a", + "metadata": {}, + "source": [ + "Manche Funktionen bestehen auf Tupeln als Argument oder geben immer Tupeln zurück. Dann braucht man manchmal ein Tupel aus einem Element. \n", + "\n", + "Das notiert man so:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "24856f9b", + "metadata": {}, + "outputs": [], + "source": [ + "x = (13,) # ein 1-Element-Tupel" + ] + }, + { + "cell_type": "markdown", + "id": "11ac465d", + "metadata": {}, + "source": [ + "Das Komma - und nicht die Klammern -- macht das Tupel. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "87474e9d", + "metadata": {}, + "outputs": [], + "source": [ + "x= (13) # kein Tupel" + ] + }, + { + "cell_type": "markdown", + "id": "da35087d", + "metadata": {}, + "source": [ + "## Ranges\n", + "\n", + "Wir haben *range*-Objekte schon in numerischen `for`-Schleifen verwendet.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3bfc9415", + "metadata": {}, + "outputs": [], + "source": [ + "r = 1:1000\n", + "typeof(r)" + ] + }, + { + "cell_type": "markdown", + "id": "7d2c6838", + "metadata": {}, + "source": [ + "Es gibt verschiedene *range*-Typen. Wie man sieht, sind es über den Zahlentyp parametrisierte Typen und `UnitRange` ist z.B. ein *range* mit der Schrittweite 1. Ihre Konstruktoren heißen in der Regel `range()`. \n", + "\n", + "Der Doppelpunkt ist eine spezielle Syntax. \n", + "\n", + "- `a:b` wird vom Parser umgesetzt zu `range(a, b)` \n", + "- `a:b:c` wird umgesetzt zu `range(a, c, step=b)`\n", + "\n", + "\n", + "*Ranges* sind offensichtlich iterierbar, nicht mutierbar aber indizierbar.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "28aecb9e", + "metadata": {}, + "outputs": [], + "source": [ + "(3:100)[20] # das zwanzigste Element" + ] + }, + { + "cell_type": "markdown", + "id": "350affb7", + "metadata": {}, + "source": [ + "Wir erinnern an die Semantik der `for`-Schleife: `for i in 1:1000` heißt **nicht**:\n", + "\n", + "- 'Die Schleifenvariable `i` wird bei jedem Durchlauf um eins erhöht' **sondern** \n", + "- 'Der Schleifenvariable werden nacheinander die Werte 1,2,3,...,1000 aus dem Container zugewiesen'. \n", + "\n", + "Allerdings wäre es sehr ineffektiv, diesen Container tatsächlich explizit anzulegen. \n", + "\n", + "- _Ranges_ sind \"lazy\" Vektoren, die nie wirklich irgendwo als konkrete Liste abgespeichert werden. Das macht sie als Iteratoren in `for`-Schleifen so nützlich: speichersparend und schnell.\n", + "- Sie sind 'Rezepte' oder Generatoren, die auf die Abfrage 'Gib mir dein nächstes Element!' antworten.\n", + "- Tatsächlich ist der Muttertyp `AbstractRange` ein Subtyp von `AbstractVector`.\n", + "\n", + "Das Macro `@allocated` gibt aus, wieviel Bytes an Speicher bei der Auswertung eines Ausdrucks alloziert wurden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "14ea84bd", + "metadata": {}, + "outputs": [], + "source": [ + "@allocated [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c900fd32", + "metadata": {}, + "outputs": [], + "source": [ + "@allocated 1:20" + ] + }, + { + "cell_type": "markdown", + "id": "0a763f8b", + "metadata": {}, + "source": [ + "Zum Umwandeln in einen 'richtigen' Vektor dient die Funktion `collect()`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0e0be9dd", + "metadata": {}, + "outputs": [], + "source": [ + "collect(20:-3:1)" + ] + }, + { + "cell_type": "markdown", + "id": "568f2f9f", + "metadata": {}, + "source": [ + "Recht nützlich, z.B. beim Vorbereiten von Daten zum Plotten, ist der *range*-Typ `LinRange`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8596862b", + "metadata": {}, + "outputs": [], + "source": [ + "LinRange(2, 50, 300)" + ] + }, + { + "cell_type": "markdown", + "id": "f148954b", + "metadata": {}, + "source": [ + "`LinRange(start, stop, n)` erzeugt eine äquidistante Liste von `n` Werten von denen der erste und der letzte die vorgegebenen Grenzen sind. \n", + "Mit `collect()` kann man bei Bedarf auch daraus den entsprechenden Vektor gewinnen.\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/7_ArraysP2.ipynb b/nb/7_ArraysP2.ipynb new file mode 100644 index 0000000..02bab53 --- /dev/null +++ b/nb/7_ArraysP2.ipynb @@ -0,0 +1,2054 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "5c227958", + "metadata": {}, + "source": [ + "# Vektoren, Matrizen, Arrays\n", + "\n", + "## Allgemeines \n", + "\n", + "Kommen wir nun zu den wohl wichtigsten Containern für numerische Mathematik: \n", + "\n", + "- Vektoren `Vector{T}` \n", + "- Matrizen `Matrix{T}` mit zwei Indizes \n", + "- N-dimensionale Arrays mit N Indizes `Array{T,N}`\n", + "\n", + "Tatsächlich ist `Vector{T}` ein Alias für `Array{T,1}` und `Matrix{T}` ein Alias für `Array{T,2}`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ee55f3c2", + "metadata": {}, + "outputs": [], + "source": [ + "Vector{Float64} === Array{Float64,1} && Matrix{Float64} === Array{Float64,2}" + ] + }, + { + "cell_type": "markdown", + "id": "bc271209", + "metadata": {}, + "source": [ + "Beim Anlegen durch eine explizite Elementliste wird der 'kleinste gemeinsame Typ' für den Typparameter `T` ermittelt.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "93a9f521", + "metadata": {}, + "outputs": [], + "source": [ + "v = [33, \"33\", 1.2]" + ] + }, + { + "cell_type": "markdown", + "id": "3d2a9699", + "metadata": {}, + "source": [ + "Falls `T` ein numerischer Typ ist, werden die Elemente in diesen Typ umgewandelt.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6810b420", + "metadata": {}, + "outputs": [], + "source": [ + "v = [3//7, 4, 2im]" + ] + }, + { + "cell_type": "markdown", + "id": "cff4245f", + "metadata": {}, + "source": [ + "Informationen über einen Array liefern die Funktionen:\n", + "\n", + "- `length(A)` --- Anzahl der Elemente\n", + "- `eltype(A)` --- Typ der Elemente\n", + "- `ndims(A)` --- Anzahl der Dimensionen (Indizes)\n", + "- `size(A)` --- Tupel mit den Dimensionen des Arrays \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "79c5010b", + "metadata": {}, + "outputs": [], + "source": [ + "v1 = [12, 13, 15]\n", + "\n", + "m1 = [ 1 2.5\n", + " 6 -3 ]\n", + "\n", + "for f ∈ (length, eltype, ndims, size)\n", + " println(\"$(f)(v) = $(f(v)), $(f)(m1) = $(f(m1))\")\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "dd306f62", + "metadata": {}, + "source": [ + "- Die Stärke des 'klassischen' Arrays für das wissenschaftliche Rechnen besteht darin, dass es einfach nur ein zusammenhängendes Speichersegment ist, in dem die Komponenten gleicher Länge (z.B. 64 Bit) geordnet hintereinander abgespeichert sind. Damit ist der Speicherbedarf minimal und die Zugriffsgeschwindigkeit auf eine Komponente, sowohl beim Lesen als auch beim Modifizieren, maximal. Der Platz der Komponente `v[i]` ist sofort aus `i` berechenbar. \n", + "- Julias `Array{T,N}` (und damit Vektoren und Matrizen) ist für die üblichen numerischen Typen `T` in dieser Weise implementiert. Die Elemente werden *unboxed* gespeichert. Im Gegensatz dazu ist z.B. ein `Vector{Any}` implementiert als Liste von Adressen von Objekten *(boxed)* und nicht als Liste der Objekte selbst. \n", + "- Julias `Array{T,N}` speichert seine Elemente direkt *(unboxed)*, wenn `isbitstype(T) == true`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3227cda0", + "metadata": {}, + "outputs": [], + "source": [ + "isbitstype(Float64), \n", + "isbitstype(Complex{Rational{Int64}}), \n", + "isbitstype(String)" + ] + }, + { + "cell_type": "markdown", + "id": "dd9c87cf", + "metadata": {}, + "source": [ + "## Vektoren\n", + "\n", + "### Listen-artige Funktionen \n", + "\n", + "- `push!(vector, items...)` --- fügt Elemente am Ende des Vektors an\n", + "- `pushfirst!(vector, items...)` --- fügt Elemente am Anfang des Vektors an\n", + "- `pop!(vector)` --- entfernt letztes Element und liefert es als Ergebnis zurück,\n", + "- `popfirst!(vector)` --- entfernt erstes Element und liefert es zurück \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f49c51ee", + "metadata": {}, + "outputs": [], + "source": [ + "v = Float64[] # leerer Vector{Float64}\n", + "\n", + "push!(v, 3, 7)\n", + "pushfirst!(v, 1)\n", + "\n", + "a = pop!(v)\n", + "println(\"a= $a\")\n", + "\n", + "push!(v, 17)" + ] + }, + { + "cell_type": "markdown", + "id": "d0bae695", + "metadata": {}, + "source": [ + "Ein `push!()` kann sehr aufwändig sein, da eventuell neuer Speicher alloziert und dann der ganze bestehende Vektor umkopiert werden muss. Julia optimiert das Speichermanagement. Es wird in einem solchen Fall Speicher auf Vorrat alloziert, so dass weitere `push!`s sehr schnell sind und man 'fast O(1)-Geschwindigkeit' erreicht. \n", + "\n", + "Trotzdem sollte man bei zeitkritischem Code und sehr großen Feldern Operationen wie `push!()` oder `resize()` vermeiden.\n", + "\n", + "### Weitere Konstruktoren\n", + "\n", + "Man kann Vektoren mit vorgegebener Länge und Typ uninitialisiert anlegen. Das geht am Schnellsten, die Elemente sind zufállige Bitmuster.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5dd7319a", + "metadata": {}, + "outputs": [], + "source": [ + "# fixe Länge 1000, uninitialisiert\n", + "\n", + "v = Vector{Float64}(undef, 1000)\n", + "v[345]" + ] + }, + { + "cell_type": "markdown", + "id": "d154d1d5", + "metadata": {}, + "source": [ + "- `zeros(n)` legt einen `Vector{Float64}` der Länge `n` an und initialisiert mit Null. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a4a098b6", + "metadata": {}, + "outputs": [], + "source": [ + "v = zeros(7) " + ] + }, + { + "cell_type": "markdown", + "id": "20e95a21", + "metadata": {}, + "source": [ + "- `zeros(T,n)` legt einen Nullvektor vom Typ `T` an.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3914deb9", + "metadata": {}, + "outputs": [], + "source": [ + "v=zeros(Int, 4)" + ] + }, + { + "cell_type": "markdown", + "id": "6ea61c0a", + "metadata": {}, + "source": [ + "- `fill(x, n)` legt `Vector{typeof(x)}` der Länfe `n` an und füllt mit `x`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "92180908", + "metadata": {}, + "outputs": [], + "source": [ + "v = fill(sqrt(2), 5)" + ] + }, + { + "cell_type": "markdown", + "id": "177266ed", + "metadata": {}, + "source": [ + "- `similar(v)` legt einen uninitialisierten Vektor von gleichem Typ und Größe wie `v` an.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b5479424", + "metadata": {}, + "outputs": [], + "source": [ + "w = similar(v)" + ] + }, + { + "cell_type": "markdown", + "id": "4ad4add1", + "metadata": {}, + "source": [ + "### Konstruktion durch implizite Schleife _(list comprehension)_\n", + "\n", + "Implizite `for`-Schleifen sind eine weitere Methode, Vektoren zu erzeugen.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2a281cdf", + "metadata": {}, + "outputs": [], + "source": [ + "v4 = [i for i in 1.0:8]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "afb33a9c", + "metadata": {}, + "outputs": [], + "source": [ + "v5 = [log(i^2) for i in 1:4 ]" + ] + }, + { + "cell_type": "markdown", + "id": "cde23de5", + "metadata": {}, + "source": [ + "Man kann sogar noch ein `if` unterbringen.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "88638841", + "metadata": {}, + "outputs": [], + "source": [ + "v6 = [i^2 for i in 1:8 if i%3 != 2]" + ] + }, + { + "cell_type": "markdown", + "id": "1ee31e25", + "metadata": {}, + "source": [ + "### Bitvektoren {#sec-bitvec}\n", + "\n", + "Neben `Vector{Bool}` gibt es noch den speziellen Datentyp `BitVector` (und allgemeiner auch `BitArray`) zur Speicherung von Feldern mit Wahrheitswerten. \n", + "\n", + "Während für die Speicherung eines `Bool`s ein Byte verwendet wird, erfolgt die Speicherung in einem BitVector bitweise. \n", + "\n", + "Der Konstruktor wandelt einen \n", + "`Vector{Bool}` in einen `BitVector` um.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "115aa38e", + "metadata": {}, + "outputs": [], + "source": [ + "vb = BitVector([true, false, true, true])" + ] + }, + { + "cell_type": "markdown", + "id": "dd064777", + "metadata": {}, + "source": [ + "Für die Gegenrichtung gibt es `collect()`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "035f3ce7", + "metadata": {}, + "outputs": [], + "source": [ + "collect(vb)" + ] + }, + { + "cell_type": "markdown", + "id": "b40e16c8", + "metadata": {}, + "source": [ + "BitVectoren entstehen z.B. als Ergebnis von elementweisen Vergleichen (s. @sec-broadcast).\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6b67988d", + "metadata": {}, + "outputs": [], + "source": [ + "v4 .> 3.5" + ] + }, + { + "cell_type": "markdown", + "id": "6095e15c", + "metadata": {}, + "source": [ + "### Indizierung\n", + "\n", + "Für den Mathematiker sind Indizes Ordinalzahlen. Also __startet die Indexzählung mit 1.__\n", + "\n", + "Als Index kann man verwenden:\n", + "\n", + " - Integer\n", + " - Integer-wertigen Range (gleiche Länge oder kürzer)\n", + " - Integer-Vektor (gleiche Länge oder kürzer)\n", + " - Bool-Vektor oder BitVector (gleiche Länge)\n", + " \n", + " \n", + "Mit Indizes kann man Arrayelemente/teile lesen und schreiben.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1e8f2011", + "metadata": {}, + "outputs": [], + "source": [ + "v = [ 3i + 5.2 for i in 1:8]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "61efc9b0", + "metadata": {}, + "outputs": [], + "source": [ + "v[5]" + ] + }, + { + "cell_type": "markdown", + "id": "005efaab", + "metadata": {}, + "source": [ + "Bei Zuweisungen wird die rechte Seite wenn nötig mit `convert(T,x)` in den Vektorelementetyp umgewandelt.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d29b8ddb", + "metadata": {}, + "outputs": [], + "source": [ + "v[6] = 9999\n", + "v" + ] + }, + { + "cell_type": "markdown", + "id": "4c1b08f5", + "metadata": {}, + "source": [ + "Überschreiten der Indexgrenzen führt zu einem `BoundsError`. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d8e26873", + "metadata": {}, + "outputs": [], + "source": [ + "v[77]" + ] + }, + { + "cell_type": "markdown", + "id": "43567db7", + "metadata": {}, + "source": [ + "Mit einem `range`-Objekt kann man einen Teilvektor adressieren.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "15f45e9d", + "metadata": {}, + "outputs": [], + "source": [ + "vp = v[3:5]\n", + "vp" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c52da06e", + "metadata": {}, + "outputs": [], + "source": [ + "vp = v[1:2:7] # range mit Schrittweite\n", + "vp" + ] + }, + { + "cell_type": "markdown", + "id": "d6e45504", + "metadata": {}, + "source": [ + "- Bei der Verwendung als Index kann in einem Range der Spezialwert `end` verwendet werden.\n", + "- Bei der Verwendung als Index kann der \"leere\" Range `:` als Abkürzung von `1:end` verwendet werden. Das ist nützlich bei Matrizen: `A[:, 3]` addresiert die gesamte 3. Spalte von `A`. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6f73e624", + "metadata": {}, + "outputs": [], + "source": [ + "v[6:end] = [7, 7, 7]\n", + "v" + ] + }, + { + "cell_type": "markdown", + "id": "ff325674", + "metadata": {}, + "source": [ + "#### Indirekte Indizierung\n", + "\n", + "Die indirekte Indizierung mit einem *Vector of Integers/Indices* erfolgt nach der Formel \n", + "\n", + "\n", + "$v[ [i_1,\\ i_2,\\ i_3,...]] = [\\ v[i_1],\\ v[i_2],\\ v[i_3],...]$\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bf53ca2b", + "metadata": {}, + "outputs": [], + "source": [ + "v[ [1, 3, 4] ]" + ] + }, + { + "cell_type": "markdown", + "id": "7b2f2bc8", + "metadata": {}, + "source": [ + "ist also gleich\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4f5fec9d", + "metadata": {}, + "outputs": [], + "source": [ + "[ v[1], v[3], v[4] ]" + ] + }, + { + "cell_type": "markdown", + "id": "d24e3956", + "metadata": {}, + "source": [ + "#### Indizierung mit einem Vektor von Wahrheitswerten\n", + "\n", + "Als Index kann man auch einen `Vector{Bool}` oder `BitVector` (s. @sec-bitvec) **derselben Länge** verwenden. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9af04e7e", + "metadata": {}, + "outputs": [], + "source": [ + "v[ [true, true, false, false, true, false, true, true] ]" + ] + }, + { + "cell_type": "markdown", + "id": "7d64ac85", + "metadata": {}, + "source": [ + "Das ist nützlich, da man z.B.\n", + "\n", + " - Tests broadcasten kann (s. @sec-broadcast),\n", + " - diese Tests dann einen BitVector liefern und\n", + " - bei Bedarf solche Bitvektoren durch die Bit-weisen Operatoren `&` und `|` verknüpft werden können. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "670b80ea", + "metadata": {}, + "outputs": [], + "source": [ + "v[ (v .> 13) .& (v.<20) ]" + ] + }, + { + "cell_type": "markdown", + "id": "7bc7e5fb", + "metadata": {}, + "source": [ + "## Matrizen und Arrays\n", + "\n", + "Die bisher vorgestellten Methoden für Vektoren übertragen sich auch auf höherdimensionale Arrays.\n", + "\n", + "Man kann sie uninitialisiert anlegen:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f4c8b14c", + "metadata": {}, + "outputs": [], + "source": [ + "A = Array{Float64,3}(undef, 6,9,3)" + ] + }, + { + "cell_type": "markdown", + "id": "b692ddb4", + "metadata": {}, + "source": [ + "In den meisten Funktionen kann man die Dimensionen auch als Tupel übergeben. Die obige Anweisung lässt sich auch so schreiben:\n", + "\n", + "```julia\n", + "A = Array{Float64, 3}(undef, (6,9,3)) \n", + "```\n", + "\n", + "Funktionen wie `zeros()` usw. funktionieren natürlich auch.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c7b17431", + "metadata": {}, + "outputs": [], + "source": [ + "m2 = zeros(3, 4, 2) # oder zeros((3,4,2)) " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f361ecf8", + "metadata": {}, + "outputs": [], + "source": [ + "M = fill(5 , (3, 3)) # oder fill(5, 3, 3)" + ] + }, + { + "cell_type": "markdown", + "id": "68ac511a", + "metadata": {}, + "source": [ + "Die Funktion `similar()`, die einen Array gleicher Größe uninitialisiert erzeugt, kann auch einen Typ als weiteres Argument bekommen.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3a0958e2", + "metadata": {}, + "outputs": [], + "source": [ + "M2 = similar(M, Float64)" + ] + }, + { + "cell_type": "markdown", + "id": "027fb6d6", + "metadata": {}, + "source": [ + "### Konstruktion durch explizite Elementliste\n", + "\n", + "Während man Vektoren kommagetrennt in eckigen Klammern notiert, ist die Notation für höherdimensionale Objekte etwas anders. \n", + "\n", + "- Eine Matrix:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ba838fe7", + "metadata": {}, + "outputs": [], + "source": [ + "M2 = [2 3 -1\n", + " 4 5 -2]" + ] + }, + { + "cell_type": "markdown", + "id": "5254a785", + "metadata": {}, + "source": [ + "- dieselbe Matrix:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4878b4e0", + "metadata": {}, + "outputs": [], + "source": [ + "M2 = [2 3 -1; 4 5 -2]" + ] + }, + { + "cell_type": "markdown", + "id": "48b415e9", + "metadata": {}, + "source": [ + "- Ein Array mit 3 Indizes:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c0e45334", + "metadata": {}, + "outputs": [], + "source": [ + "M3 = [2 3 -1 \n", + " 4 5 6 ;;;\n", + " 7 8 9\n", + " 11 12 13]" + ] + }, + { + "cell_type": "markdown", + "id": "aedabca8", + "metadata": {}, + "source": [ + "- und nochmal die Matrix `M2`:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3537604f", + "metadata": {}, + "outputs": [], + "source": [ + "M2 = [2;4;; 3;5;; -1;-2]" + ] + }, + { + "cell_type": "markdown", + "id": "8b21f42d", + "metadata": {}, + "source": [ + "Im letzten Beispiel kommen diese Regeln zur Anwendung:\n", + "\n", + "- Trenner ist das Semikolon.\n", + "- Ein Semikolon `;` erhöht den 1. Index.\n", + "- Zwei Semikolons `;;` erhöhen den 2. Index.\n", + "- Drei Semikolons `;;;` erhöhen den 3. Index usw. \n", + "\n", + "In den Beispielen davor wurde folgende Syntaktische Verschönerung (_syntactic sugar_) angewendet:\n", + "\n", + "- Leerzeichen trennen wie 2 Semikolons -- erhöht also den 2. Index: $\\quad a_{12}\\quad a_{13}\\quad a_{14}\\ ...$\n", + "- Zeilenumbruch trennt wie ein Semikolon -- erhöht also den 1. Index.\n", + "\n", + "\n", + ":::{.callout-important}\n", + "\n", + "- Vektorschreibweise mit Komma als Trenner geht nur bei Vektoren, nicht mit \"Semikolon, Leerzeichen, Newline' mischen! \n", + "- Vektoren mit einem Index; $1\\!\\times\\!n$-Matrizen und $n\\!\\times\\!1$-Matrizen sind drei verschiedene Dinge!\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5068d43b", + "metadata": {}, + "outputs": [], + "source": [ + "v1 = [2,3,4]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "251a03fc", + "metadata": {}, + "outputs": [], + "source": [ + "v2 = [2;3;4]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "12be7f1d", + "metadata": {}, + "outputs": [], + "source": [ + "v3 = [2 3 4]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "41a648f3", + "metadata": {}, + "outputs": [], + "source": [ + "v3 = [2;3;4;;]" + ] + }, + { + "cell_type": "markdown", + "id": "e16508b2", + "metadata": {}, + "source": [ + ":::\n", + "\n", + "\n", + "Einen \"vector of vectors\" a la C/C++ kann man natürlich auch konstruieren. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8d20c99f", + "metadata": {}, + "outputs": [], + "source": [ + "v = [[2,3,4], [5,6,7,8]]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7acc9cd7", + "metadata": {}, + "outputs": [], + "source": [ + "v[2][3]" + ] + }, + { + "cell_type": "markdown", + "id": "36081804", + "metadata": {}, + "source": [ + "Das sollte man nur in Spezialfällen tun. Die Array-Sprache von Julia ist in der Regel bequemer und schneller.\n", + "\n", + "### Indizes, Teilfelder, Slices\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8dbddd28", + "metadata": {}, + "outputs": [], + "source": [ + "# 6x6 Matrix mit Zufallszahlen gleichverteilt aus [0,1) ∈ Float64\n", + "A = rand(6,6)" + ] + }, + { + "cell_type": "markdown", + "id": "86dcdd80", + "metadata": {}, + "source": [ + "Die übliche Indexnotation:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6457e824", + "metadata": {}, + "outputs": [], + "source": [ + "A[2, 3] = 77.77777\n", + "A" + ] + }, + { + "cell_type": "markdown", + "id": "ed38064b", + "metadata": {}, + "source": [ + "Man kann mit Ranges Teilfelder adressieren:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "865b7b29", + "metadata": {}, + "outputs": [], + "source": [ + "B = A[1:2, 1:3]" + ] + }, + { + "cell_type": "markdown", + "id": "eafd8cc8", + "metadata": {}, + "source": [ + "Das Adressieren von Teilen mit geringerer Dimension wird auch *slicing* genannt.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "aba3e4ef", + "metadata": {}, + "outputs": [], + "source": [ + "# die 3. Spalte als Vektor (slicing)\n", + "\n", + "C = A[:, 3]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "14259946", + "metadata": {}, + "outputs": [], + "source": [ + "# die 3. Zeile als Vektor (slicing)\n", + "\n", + "E = A[3, :]" + ] + }, + { + "cell_type": "markdown", + "id": "bec96c71", + "metadata": {}, + "source": [ + "Natürlich sind damit auch Zuweisungen möglich:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "82f68a6e", + "metadata": {}, + "outputs": [], + "source": [ + "# Man kann slices und Teilfeldern auch etwas zuweisen \n", + "\n", + "A[2, :] = [1,2,3,4,5,6]\n", + "A" + ] + }, + { + "cell_type": "markdown", + "id": "23dd1440", + "metadata": {}, + "source": [ + "## Verhalten bei Zuweisungen, `copy()` und `deepcopy()`, Views\n", + "\n", + "### Zuweisungen und Kopien\n", + "\n", + "- Variablen sind Referenzen auf Objekte. \n", + "- _Eine Zuweisung zu einer Variablen erzeugt kein neues Objekt._\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2499e260", + "metadata": {}, + "outputs": [], + "source": [ + "A = [1, 2, 3]\n", + "B = A" + ] + }, + { + "cell_type": "markdown", + "id": "4c9e3a04", + "metadata": {}, + "source": [ + "`A` und `B` sind jetzt Namen desselben Objekts.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9fdad306", + "metadata": {}, + "outputs": [], + "source": [ + "A[1] = 77\n", + "@show B;" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c51812e7", + "metadata": {}, + "outputs": [], + "source": [ + "B[3] = 300\n", + "@show A;" + ] + }, + { + "cell_type": "markdown", + "id": "00fe556c", + "metadata": {}, + "source": [ + "Dieses Verhalten spart viel Zeit und Speicher, ist aber nicht immer gewünscht. \n", + "Die Funktion `copy()` erzeugt eine 'echte' Kopie des Objekts.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b71aff22", + "metadata": {}, + "outputs": [], + "source": [ + "A = [1, 2, 3]\n", + "B = copy(A)\n", + "A[1] = 100\n", + "@show A B;" + ] + }, + { + "cell_type": "markdown", + "id": "03f55f43", + "metadata": {}, + "source": [ + "Die Funktion \n", + "`deepcopy(A)` kopiert rekursiv. Auch von den Elementen, aus denen `A` besteht, werden (wieder rekursive) Kopien erstellt. \n", + "\n", + "Solange ein Array nur primitive Objekte (Zahlen) enthält, sind `copy()` und `deepcopy()` äquivalent. \n", + "\n", + "Das folgende Beispiel zeigt den Unterschied zwischen `copy()` und `deepcopy()`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "75c537cc", + "metadata": {}, + "outputs": [], + "source": [ + "mutable struct Person\n", + " name :: String\n", + " age :: Int\n", + "end\n", + "\n", + "A = [Person(\"Meier\", 20), Person(\"Müller\", 21), Person(\"Schmidt\", 23)]\n", + "B = A\n", + "C = copy(A)\n", + "D = deepcopy(A)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5721ca90", + "metadata": {}, + "outputs": [], + "source": [ + "A[1] = Person(\"Mustermann\", 83)\n", + "A[3].age = 199 \n", + "\n", + "@show B C D;" + ] + }, + { + "cell_type": "markdown", + "id": "f9ebeba5", + "metadata": {}, + "source": [ + "### Views\n", + "\n", + "Wenn man mittels *indices/ranges/slices* einer Variablen ein Teilstück eines Arrays zuweist, \n", + "wird von Julia grundsätzlich **ein neues Objekt** konstruiert.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d17cb1dd", + "metadata": {}, + "outputs": [], + "source": [ + "A = [1 2 3\n", + " 3 4 5]\n", + "\n", + "v = A[:, 2]\n", + "@show v\n", + "\n", + "A[1, 2] = 77\n", + "@show A v;" + ] + }, + { + "cell_type": "markdown", + "id": "3b5120b7", + "metadata": {}, + "source": [ + "Manchmal möchte man aber gerade hier eine Referenz-Semantik haben im Sinne von: \"Vektor `v` soll der 2. Spaltenvektor von `A` sein und auch bleiben (d.h., sich mitändern, wenn sich `A` ändert).\"\n", + "\n", + "Dies bezeichnet man in Julia als *views*: Wir wollen, dass die Variable `v` nur einen 'alternativen Blick' auf die Matrix `A` darstellt.\n", + "\n", + "Das kann man erreichen durch das `@view`-Macro: \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c86c7a1f", + "metadata": {}, + "outputs": [], + "source": [ + "A = [1 2 3\n", + " 3 4 5]\n", + "\n", + "v = @view A[:,2]\n", + "@show v\n", + "\n", + "A[1, 2] = 77\n", + "@show v;" + ] + }, + { + "cell_type": "markdown", + "id": "d076c1a5", + "metadata": {}, + "source": [ + "Diese Technik wird von Julia aus Effizienzgründen auch bei einigen Funktionen der linearen Algebra verwendet. \n", + "Ein Beispiel ist der Operator `'`, der zu einer Matrix `A` die adjungierte Matrix `A'` liefert.\n", + "\n", + "- Die adjungierte _(adjoint)_ Matrix `A'` ist die transponierte und elementweise komplex-konjugierte Matrix zu `A`. \n", + "- Der Parser macht daraus den Funktionsaufruf `adjoint(A)`. \n", + "- Für reelle Matrizen ist die Adjungierte gleich der transponierten Matrix.\n", + "- Julia implementiert `adjoint()` als _lazy function_, d.h., \n", + "- es wird aus Effizienzgründen kein neues Objekt konstruiert, sondern nur ein alternativer 'View' auf die Matrix (\"mit vertauschten Indizes\") und ein alternativer 'View' auf die Einträge (mit Vorzeichenwechsel im Imaginärteil).\n", + "- Aus Vektoren macht `adjoint()` eine $1\\!\\times\\!n$-Matrix (einen Zeilenvektor).\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f3bae50e", + "metadata": {}, + "outputs": [], + "source": [ + "A = [ 1. 2.\n", + " 3. 4.]\n", + "B = A'" + ] + }, + { + "cell_type": "markdown", + "id": "67138cff", + "metadata": {}, + "source": [ + "Die Matrix `B` ist nur ein modifizierter 'View' auf `A`:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "829acf4c", + "metadata": {}, + "outputs": [], + "source": [ + "A[1, 2] =10\n", + "B" + ] + }, + { + "cell_type": "markdown", + "id": "e3c2a66c", + "metadata": {}, + "source": [ + "Aus Vektoren macht `adjoint()` eine $1\\!\\times\\!n$-Matrix (einen Zeilenvektor).\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "78065100", + "metadata": {}, + "outputs": [], + "source": [ + "v = [1, 2, 3]\n", + "v'" + ] + }, + { + "cell_type": "markdown", + "id": "a5d85afa", + "metadata": {}, + "source": [ + "Eine weitere solche Funktion, die einen alternativen 'View', eine andere Indizierung, derselben Daten \n", + "liefert, ist `reshape()`. \n", + "\n", + "Hier wird ein Vektor mit 12 Einträgen in eine 3x4-Matrix verwandelt.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7c31328d", + "metadata": {}, + "outputs": [], + "source": [ + "A = [1,2,3,4,5,6,7,8,9,10,11,12]\n", + "\n", + "B = reshape(A, 3, 4) " + ] + }, + { + "cell_type": "markdown", + "id": "ab0bb6f9", + "metadata": {}, + "source": [ + "## Speicherung eines Arrays\n", + "\n", + "- Speicher wird linear adressiert. Eine Matrix kann zeilenweise _(row major)_ oder spaltenweise _(column major)_ im Speicher angeordnet sein. \n", + "- C/C++/Python(NumPy) verwenden eine zeilenweise Speicherung: Die 4 Elemente einer 2x2-Matrix sind abgespeichert in der Reihenfolge $a_{11},a_{12},a_{21},a_{22}$. \n", + "- Julia, Fortran, Matlab speichern spaltenweise: $a_{11},a_{21},a_{12},a_{22}$. \n", + "\n", + "Diese Information ist wichtig, um effizient über Matrizen zu iterieren:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e6b341f8", + "metadata": {}, + "outputs": [], + "source": [ + "function column_major_add(A, B)\n", + " (n,m) = size(A)\n", + " for j = 1:m\n", + " for i = 1:n # innere Schleife durchläuft eine Spalte\n", + " A[i,j] += B[i,j]\n", + " end\n", + " end\n", + "end\n", + "\n", + "function row_major_add(A, B)\n", + " (n,m) = size(A)\n", + " for i = 1:n\n", + " for j = 1:m # inere Schleife durchläuft eine Zeile\n", + " A[i,j] += B[i,j]\n", + " end\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "02e841a6", + "metadata": {}, + "outputs": [], + "source": [ + "A = rand(10000, 10000);\n", + "B = rand(10000, 10000);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "977e691b", + "metadata": {}, + "outputs": [], + "source": [ + "using BenchmarkTools\n", + "\n", + "@benchmark row_major_add($A, $B) " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1e5df44b", + "metadata": {}, + "outputs": [], + "source": [ + "@benchmark column_major_add($A, $B)" + ] + }, + { + "cell_type": "markdown", + "id": "c75b3f1d", + "metadata": {}, + "source": [ + "### Lokalität von Speicherzugriffen und _Caching_\n", + "\n", + "Wir haben gesehen, dass die Reihenfolge von innerem und äußerem Loop einen erheblichen Geschwindigkeitsunterschied macht:\n", + "\n", + "__Es ist effizienter, wenn die innerste Schleife über den linken Index läuft__, also eine Spalte und nicht eine Zeile durchläuft. Die Ursache dafür liegt in der Architektur moderner Prozessoren.\n", + "\n", + "- Speicherzugriffe erfolgt über mehrere Cache-Ebenen. \n", + "- Ein _cache miss_, der ein Nachladen aus langsameren Caches auslöst, bremst aus.\n", + "- Es werden immer gleich größere Speicherblöcke nachgeladen, um die Häufigkeit von _cache misses_ zu minimieren.\n", + "- Daher ist es wichtig, Speicherzugriffe möglichst lokal zu organisieren.\n", + "\n", + "::: {.content-visible when-format=\"html\"}\n", + "![Speicherhierarchie von Intel-Prozessoren, aus: Victor Eijkhout,_Introduction to High-Performance Scientific Computing_, [https://theartofhpc.com/](https://theartofhpc.com/)](../images/cache.png){width=\"75%\"}\n", + "\n", + ":::\n", + "\n", + "::: {.content-visible when-format=\"pdf\"}\n", + "![Speicherhierarchie von Intel-Prozessoren, aus: Victor Eijkhout,_Introduction to High-Performance Scientific Computing_, [https://theartofhpc.com/](https://theartofhpc.com/)](../images/cache.png){width=\"70%\"}\n", + ":::\n", + "\n", + "\n", + "## Mathematische Operationen mit Arrays\n", + "\n", + "Arrays der gleichen Dimension (z.B. alle $7\\!\\times\\!3$-Matrizen) bilden einen linearen Raum. \n", + "\n", + " - Sie können mit Skalaren multipliziert werden und\n", + " - sie können addiert und subtrahiert werden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "af7e8988", + "metadata": {}, + "outputs": [], + "source": [ + "0.5 * [2, 3, 4, 5]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b37890ac", + "metadata": {}, + "outputs": [], + "source": [ + "0.5 * [ 1 3\n", + " 2 7] - [ 2 3; 1 2]" + ] + }, + { + "cell_type": "markdown", + "id": "62d17bc4", + "metadata": {}, + "source": [ + "### Matrixprodukt\n", + "\n", + "Das Matrixprodukt ist definiert für \n", + "\n", + ":::{.narrow}\n", + "\n", + "| 1. Faktor | 2. Faktor | Produkt |\n", + "| :-: | :-: | :-: |\n", + "| $(n\\!\\times\\!m)$-Matrix | $(m\\!\\times\\!k)$-Matrix | $(n\\times k)$-Matrix|\n", + "| $(n\\!\\times\\!m)$-Matrix | $m$-Vektor | $n$-Vektor |\n", + "| $(1\\!\\times\\!m)$-Zeilenvektor | $(m\\!\\times\\!n)$-Matrix | $n$-Vektor |\n", + "| $(1\\!\\times\\!m)$-Zeilenvektor | $m$-Vektor | Skalarprodukt |\n", + "| $m$-Vektor | $(1\\times n)$-Zeilenvektor | $(m\\!\\times\\!n)$-Matrix |\n", + "\n", + ":::\n", + "\n", + "Beispiele:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bfd0201f", + "metadata": {}, + "outputs": [], + "source": [ + "A = [1 2 3\n", + " 4 5 6]\n", + "v = [2, 3]\n", + "w = [1, 3, 4];" + ] + }, + { + "cell_type": "markdown", + "id": "78eb3a67", + "metadata": {}, + "source": [ + "- (2,3)-Matrix `*` (3,2)-Matrix\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5012734f", + "metadata": {}, + "outputs": [], + "source": [ + "A * A'" + ] + }, + { + "cell_type": "markdown", + "id": "6853f87e", + "metadata": {}, + "source": [ + "- (3,2)-Matrix `*` (2,3)-Matrix\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0043d2e3", + "metadata": {}, + "outputs": [], + "source": [ + "A' * A" + ] + }, + { + "cell_type": "markdown", + "id": "2f8fef4c", + "metadata": {}, + "source": [ + "- (2,3)-Matrix `*` 3-Vektor\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b12cbb35", + "metadata": {}, + "outputs": [], + "source": [ + "A * w" + ] + }, + { + "cell_type": "markdown", + "id": "80ba832f", + "metadata": {}, + "source": [ + "- (1,2)-Vektore `*` (2,3)-Matrix\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f832930e", + "metadata": {}, + "outputs": [], + "source": [ + "v' * A" + ] + }, + { + "cell_type": "markdown", + "id": "30ccb92a", + "metadata": {}, + "source": [ + "- (3,2)-Matrix `*` 2-Vektor\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "20668407", + "metadata": {}, + "outputs": [], + "source": [ + "A' * v" + ] + }, + { + "cell_type": "markdown", + "id": "11148039", + "metadata": {}, + "source": [ + "- (1,2)-Vektor `*` 2-Vektor (Skalarprodukt)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b7f89eac", + "metadata": {}, + "outputs": [], + "source": [ + "v' * v" + ] + }, + { + "cell_type": "markdown", + "id": "a6c08a07", + "metadata": {}, + "source": [ + "2-Vektor `*` (1,3)-Vektor (äußeres Produkt) \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "71f47541", + "metadata": {}, + "outputs": [], + "source": [ + "v * w'" + ] + }, + { + "cell_type": "markdown", + "id": "7d1fe459", + "metadata": {}, + "source": [ + "## Broadcasting {#sec-broadcast}\n", + "\n", + "- Beim _broadcasting_ werden Operationen oder Funktionen __elementweise__ auf Arrays angewendet.\n", + "- Die Syntax dafür ist ein Punkt _vor_ einem Operationszeichen oder _nach_ einem Funktionsnamen. \n", + "- Der Parser setzt `f.(x,y)` um zu `broadcast(f, x, y)` und analog für Operatoren `x .⊙ y` zu `broadcast(⊙, z, y)`. \n", + "- Dabei werden Operanden, denen eine oder mehrere Dimensionen fehlen, in diesen Dimensionen (virtuell) vervielfältigt. \n", + "- Das *broadcasting* von Zuweisungen `.=`, `.+=`,... verändert die Semantik. Es wird kein neues Objekt erzeugt, sondern die Werte werden in das links stehende Objekt (welches die richtige Dimension haben muss) eingetragen.\n", + "\n", + "\n", + "Einige Beispiele:\n", + "\n", + "- Elementweise Anwendung einer Funktion\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3b2f54bd", + "metadata": {}, + "outputs": [], + "source": [ + "sin.([1, 2, 3])" + ] + }, + { + "cell_type": "markdown", + "id": "9e2b6b10", + "metadata": {}, + "source": [ + "- Das Folgende liefert nicht die algebraische [Wurzel aus einer Matrix](https://de.wikipedia.org/wiki/Quadratwurzel_einer_Matrix), sondern die elementweise Wurzel aus jedem Eintrag. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "eed676ee", + "metadata": {}, + "outputs": [], + "source": [ + "A = [8 2\n", + " 3 4]\n", + "\n", + "sqrt.(A)" + ] + }, + { + "cell_type": "markdown", + "id": "ae8a2b5e", + "metadata": {}, + "source": [ + "- Das Folgende liefert nicht $A^2$, sondern die Einträge werden quadriert.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0cc93370", + "metadata": {}, + "outputs": [], + "source": [ + "A.^2 " + ] + }, + { + "cell_type": "markdown", + "id": "3f8e55c6", + "metadata": {}, + "source": [ + "- Zum Vergleich das Ergenmis der algebraischen Operationen:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f1b97fa1", + "metadata": {}, + "outputs": [], + "source": [ + "@show A^2 A^(1/2);" + ] + }, + { + "cell_type": "markdown", + "id": "6e3c2f80", + "metadata": {}, + "source": [ + "- Broadcasting geht auch mit Funktionen mehrerer Variablen.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "14763047", + "metadata": {}, + "outputs": [], + "source": [ + "hyp(a,b) = sqrt(a^2+b^2)\n", + "\n", + "B = [3 4\n", + " 5 7]\n", + "\n", + "hyp.(A, B) " + ] + }, + { + "cell_type": "markdown", + "id": "7c23f048", + "metadata": {}, + "source": [ + "Bei Operanden verschiedener Dimension wird der Operand mit fehlenden Dimensionen in diesen durch Vervielfältigung virtuell \n", + "'aufgeblasen'.\n", + "\n", + "Wir addieren einen Skalar zu einer Matrix:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d1186a3d", + "metadata": {}, + "outputs": [], + "source": [ + "A = [ 1 2 3\n", + " 4 5 6]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ca261d61", + "metadata": {}, + "outputs": [], + "source": [ + "A .+ 300" + ] + }, + { + "cell_type": "markdown", + "id": "88d70780", + "metadata": {}, + "source": [ + "Der Skalar wurde durch Replikation auf dieselbe Dimension wie die Matrix gebracht. Wir lassen uns von `broadcast()` die Form des 2. Operanden nach dem *broadcasting* anzeigen: \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c48e84e2", + "metadata": {}, + "outputs": [], + "source": [ + "broadcast( (x,y) -> y, A, 300)" + ] + }, + { + "cell_type": "markdown", + "id": "021a47a6", + "metadata": {}, + "source": [ + "(Natürlich findet diese Replikation nur virtuell statt. Dieses Objekt wird bei anderen Operationen nicht wirklich erzeugt.)\n", + "\n", + "Als weiteres Beispiel: Matrix und (Spalten-)Vektor\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "769ea0eb", + "metadata": {}, + "outputs": [], + "source": [ + "A .+ [10, 20]" + ] + }, + { + "cell_type": "markdown", + "id": "458cdda2", + "metadata": {}, + "source": [ + "Der Vektor wird durch Wiederholung der Spalten aufgeblasen:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fa093187", + "metadata": {}, + "outputs": [], + "source": [ + "broadcast((x,y)->y, A, [10,20])" + ] + }, + { + "cell_type": "markdown", + "id": "a5fa929f", + "metadata": {}, + "source": [ + "Matrix und Zeilenvektor: Der Zeilenvektor wird zeilenweise vervielfältigt:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c3d35884", + "metadata": {}, + "outputs": [], + "source": [ + "A .* [1,2,3]' # Adjungierter Vektor" + ] + }, + { + "cell_type": "markdown", + "id": "01cd8879", + "metadata": {}, + "source": [ + "Der 2. Operand wird von `broadcast()` durch Vervielfältigung der Zeilen 'aufgeblasen'.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2e90d0b0", + "metadata": {}, + "outputs": [], + "source": [ + "broadcast((x,y)->y, A, [1,2,3]')" + ] + }, + { + "cell_type": "markdown", + "id": "6d5febb2", + "metadata": {}, + "source": [ + "#### _Broadcasting_ bei Zuweisungen\n", + "\n", + "Zuweisungen `=`, `+=`, `/=`,..., bei denen links ein Name steht, laufen in Julia so ab, dass aus der rechten Seite ein Objekt konstruiert und diesem Objekt der neue Name zugewiesen wird. \n", + "\n", + "Beim Arbeiten mit Arrays will man allerdings sehr oft aus Effizienzgründen einen bestehenden Array weiterverwenden. Die rechts berechneten Einträge sollen in das bereits existierende Objekt auf der linken Seite eingetragen werden. \n", + "\n", + "Das erreicht man mit den Broadcast-Varianten `.=`, `.+=`,... der Zuweisungsoperatoren.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "14dece22", + "metadata": {}, + "outputs": [], + "source": [ + "A .= 3" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3b73a744", + "metadata": {}, + "outputs": [], + "source": [ + "A .+= [1, 4]" + ] + }, + { + "cell_type": "markdown", + "id": "33ad4d5e", + "metadata": {}, + "source": [ + "## Weitere Array-Funktionen - eine Auswahl\n", + "\n", + "Julia stellt eine große Anzahl von Funktionen bereit, die mit Arrays arbeiten.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "04f8dc09", + "metadata": {}, + "outputs": [], + "source": [ + "A = [22 -17 8 ; 4 6 9]" + ] + }, + { + "cell_type": "markdown", + "id": "58ce80a0", + "metadata": {}, + "source": [ + "- Finde das Maximum\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "34487039", + "metadata": {}, + "outputs": [], + "source": [ + "maximum(A)" + ] + }, + { + "cell_type": "markdown", + "id": "d17e1a0d", + "metadata": {}, + "source": [ + "- Finde das Maximum jeder Spalte\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "801f2031", + "metadata": {}, + "outputs": [], + "source": [ + "maximum(A, dims=1) " + ] + }, + { + "cell_type": "markdown", + "id": "2478bd06", + "metadata": {}, + "source": [ + "- Finde das Maximum jeder Zeile\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "85671a6a", + "metadata": {}, + "outputs": [], + "source": [ + "maximum(A, dims=2)" + ] + }, + { + "cell_type": "markdown", + "id": "acb7426d", + "metadata": {}, + "source": [ + "- Finde das Minimum und seine Position\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e6dd832a", + "metadata": {}, + "outputs": [], + "source": [ + "amin, i = findmin(A)" + ] + }, + { + "cell_type": "markdown", + "id": "42cca03b", + "metadata": {}, + "source": [ + "- Was ist ein `CatesianIndex`?\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f07d0f44", + "metadata": {}, + "outputs": [], + "source": [ + "dump(i)" + ] + }, + { + "cell_type": "markdown", + "id": "ad46031d", + "metadata": {}, + "source": [ + "- Extrahiere die Indizes des Minimum als Tupel\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "73fee196", + "metadata": {}, + "outputs": [], + "source": [ + "i.I" + ] + }, + { + "cell_type": "markdown", + "id": "eb657bc1", + "metadata": {}, + "source": [ + "- Summe und Produkt aller Einträge\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "56363941", + "metadata": {}, + "outputs": [], + "source": [ + "sum(A), prod(A)" + ] + }, + { + "cell_type": "markdown", + "id": "c7cf919e", + "metadata": {}, + "source": [ + "- Spaltensumme (1. Index wird reduziert)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c6fecc3b", + "metadata": {}, + "outputs": [], + "source": [ + "sum(A, dims=1) " + ] + }, + { + "cell_type": "markdown", + "id": "5081b4da", + "metadata": {}, + "source": [ + "- Zeilensummen (2. Index wird reduziert)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a1099f5a", + "metadata": {}, + "outputs": [], + "source": [ + "sum(A, dims=2) " + ] + }, + { + "cell_type": "markdown", + "id": "05404237", + "metadata": {}, + "source": [ + "- Summiere nach elementweiser Anwendung einer Funktion\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fcd3a0a8", + "metadata": {}, + "outputs": [], + "source": [ + "sum(x->sqrt(abs(x)), A) # sum_ij sqrt(|a_ij|)" + ] + }, + { + "cell_type": "markdown", + "id": "59f9b755", + "metadata": {}, + "source": [ + "- Reduziere (falte) den Array mit einer Funktion\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a7ecdced", + "metadata": {}, + "outputs": [], + "source": [ + "reduce(+, A) # equivalent to sum(A)" + ] + }, + { + "cell_type": "markdown", + "id": "c72dff31", + "metadata": {}, + "source": [ + "- `mapreduce(f, op, array)`: Wende `f` auf alle Einträge an, dann reduziere mit `op`\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "99dc2a14", + "metadata": {}, + "outputs": [], + "source": [ + "mapreduce(x -> x^2, +, A ) # Summe der Quadrate aller Einträge" + ] + }, + { + "cell_type": "markdown", + "id": "de530920", + "metadata": {}, + "source": [ + "- Gibt es Elemente in A, die > 5 sind? \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "53d33e6c", + "metadata": {}, + "outputs": [], + "source": [ + "any(x -> x>5, A) " + ] + }, + { + "cell_type": "markdown", + "id": "9dea54d7", + "metadata": {}, + "source": [ + "- Wieviele Elemente in A sind > 5?\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7dbdc21b", + "metadata": {}, + "outputs": [], + "source": [ + "count(x-> x>5, A) " + ] + }, + { + "cell_type": "markdown", + "id": "6c57c62e", + "metadata": {}, + "source": [ + "- sind alle Einträge positiv?\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "394308c2", + "metadata": {}, + "outputs": [], + "source": [ + "all(x-> x>0, A)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/9_functs.ipynb b/nb/9_functs.ipynb new file mode 100644 index 0000000..fada2fe --- /dev/null +++ b/nb/9_functs.ipynb @@ -0,0 +1,1142 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "87512b9c", + "metadata": {}, + "source": [ + "# Funktionen und Operatoren\n", + "\n", + "Funktionen verarbeiten ihre Argumente zu einem Ergebnis, das sie beim Aufruf zurückliefern.\n", + "\n", + "## Formen\n", + "\n", + "Funktionen können in verschiedenen Formen definiert werden:\n", + "\n", + "I. Als `function ... end`-Block\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2cdf33d6", + "metadata": {}, + "outputs": [], + "source": [ + "function hyp(x,y)\n", + " sqrt(x^2+y^2)\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "d22901e3", + "metadata": {}, + "source": [ + "II. Als \"Einzeiler\" \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "338f000a", + "metadata": {}, + "outputs": [], + "source": [ + "hyp(x, y) = sqrt(x^2 + y^2)" + ] + }, + { + "cell_type": "markdown", + "id": "f14a745f", + "metadata": {}, + "source": [ + "III. Als anonyme Funktionen\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "44319487", + "metadata": {}, + "outputs": [], + "source": [ + "(x, y) -> sqrt(x^2 + y^2)" + ] + }, + { + "cell_type": "markdown", + "id": "d8f8978c", + "metadata": {}, + "source": [ + "### Block-Form und `return`\n", + "\n", + "\n", + "- Mit `return` wird die Abarbeitung der Funktion beendet und zum aufrufenden Kontext zurückgekehrt.\n", + "- Ohne `return` wird der Wert des letzten Ausdrucks als Funktionswert zurückgegeben.\n", + "\n", + "Die beiden Definitionen\n", + "\n", + "```julia\n", + "function xsinrecipx(x)\n", + " if x == 0 \n", + " return 0.0\n", + " end \n", + " return x * sin(1/x)\n", + "end\n", + "```\n", + "und ohne das zweite explizite `return` in der letzten Zeile: \n", + "\n", + "```julia\n", + "function xsinrecipx(x)\n", + " if x == 0 \n", + " return 0.0\n", + " end \n", + " x * sin(1/x)\n", + "end\n", + "```\n", + "\n", + "sind also äquivalent.\n", + "\n", + "\n", + "- Eine Funktion, die \"nichts\" zurückgibt (_void functions_ in der C-Welt), gibt den Wert `nothing` vom Typ `Nothing` zurück. (So wie ein Objekt vom Typ `Bool` die beiden Werte `true` und `false` haben kann, so kann ein Objekt vom Typ `Nothing` nur einen einzigen Wert, eben `nothing`, annehmen.)\n", + "- Eine leere `return`-Anweisung ist äquivalent zu `return nothing`. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "721d72e8", + "metadata": {}, + "outputs": [], + "source": [ + "function fn(x)\n", + " println(x)\n", + " return \n", + "end\n", + "\n", + "a = fn(2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f6847d6a", + "metadata": {}, + "outputs": [], + "source": [ + "a" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "483d2b6b", + "metadata": {}, + "outputs": [], + "source": [ + "@show a typeof(a);" + ] + }, + { + "cell_type": "markdown", + "id": "66a0d115", + "metadata": {}, + "source": [ + "### Einzeiler-Form\n", + "\n", + "Die Einzeilerform ist eine ganz normale Zuweisung, bei der links eine Funktion steht.\n", + "\n", + "```julia\n", + "hyp(x, y) = sqrt(x^2 + y^2)\n", + "```\n", + "\n", + "Julia kennt zwei Möglichkeiten, mehrere Anweisungen zu einem Block zusammenzufassen, der an Stelle einer Einzelanweisung stehen kann: \n", + "\n", + "- `begin ... end`-Block\n", + "- Eingeklammerte durch Semikolon getrennte Anweisungen.\n", + "\n", + "In beiden Fällen ist der Wert des Blockes der Wert der letzten Anweisung.\n", + "\n", + "Damit funktioniert auch\n", + "```julia\n", + "hyp(x, y) = (z = x^2; z += y^2; sqrt(z))\n", + "```\n", + "\n", + "und\n", + "```julia\n", + "hyp(x, y) = begin \n", + " z = x^2\n", + " z += y^2 \n", + " sqrt(z) \n", + " end\n", + "```\n", + "\n", + "### Anonyme Funktionen\n", + "\n", + "Anonyme FUnktionen kann man der Anonymität entreisen, indem man ihnen einen Namen zuweist. \n", + "```julia\n", + "hyp = (x,y) -> sqrt(x^2 + y^2)\n", + "```\n", + "Ihre eigentliche Anwendung ist aber im Aufruf einer *(higher order)* Funktion, die eine Funktion als Argument erwartet. \n", + "\n", + "Typische Anwendungen sind `map(f, collection)`, welches eine Funktion auf alle Elemente einer Kollektion anwendet. In Julia funktioniert auch `map(f(x,y), collection1, collection2)`:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e07295eb", + "metadata": {}, + "outputs": [], + "source": [ + "map( (x,y) -> sqrt(x^2 + y^2), [3, 5, 8], [4, 12, 15])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b8ca9baf", + "metadata": {}, + "outputs": [], + "source": [ + "map( x->3x^3, 1:8 )" + ] + }, + { + "cell_type": "markdown", + "id": "9ba0e8db", + "metadata": {}, + "source": [ + "Ein weiteres Beispiel ist `filter(test, collection)`, wobei ein Test eine Funktion ist, die ein `Bool` zurückgibt.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "12731194", + "metadata": {}, + "outputs": [], + "source": [ + "filter(x -> ( x%3 == 0 && x%5 == 0), 1:100 )" + ] + }, + { + "cell_type": "markdown", + "id": "f4af9755", + "metadata": {}, + "source": [ + "## Argumentübergabe\n", + "\n", + "\n", + "- Beim Funktionsaufruf werden von den als Funktionsargumente zu übergebenden Objekten keine Kopien gemacht. Die Variablen in der Funktion verweisen auf die Originalobjekte. Julia nennt dieses Konzept _pass_by_sharing_. \n", + "- Funktionen können also ihre Argumente wirksam modifizieren, falls es sich um _mutable_ Objekte, wie z.B. `Vector`, `Array` handelt.\n", + "- Es ist eine Konvention in Julia, dass die Namen von solchen argumentmodifizierenden Funktionen mit einem Ausrufungszeichen enden. Weiterhin steht dann üblicherweise das Argument, das modifiziert wird, an erster Stelle und es ist auch der Rückgabewert der Funktion. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d34f0256", + "metadata": {}, + "outputs": [], + "source": [ + "V = [1, 2, 3]\n", + "\n", + "W = fill!(V, 17)\n", + " # '===' ist Test auf Identität\n", + "@show V W V===W; # V und W benennen dasselbe Objekt " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f83f5e37", + "metadata": {}, + "outputs": [], + "source": [ + "function fill_first!(V, x)\n", + " V[1] = x\n", + " return V \n", + "end \n", + "\n", + "U = fill_first!(V, 42)\n", + "\n", + "@show V U V===U;" + ] + }, + { + "cell_type": "markdown", + "id": "7476eab9", + "metadata": {}, + "source": [ + "## Varianten von Funktionsargumenten\n", + "\n", + "- Es gibt Positionsargumente (1. Argument, 2. Argument, ....) und _keyword_-Argumente, die beim Aufruf durch ihren Namen angesprochen werden müssen. \n", + "- Sowohl Positions- als auch _keyword_-Argumente können _default_-Werte haben. Beim Aufruf können diese Argumente weggelassen werden.\n", + "- Die Reihenfolge der Deklaration muss sein:\n", + " 1. Positionsargumente ohne Defaultwert, \n", + " 2. Positionsargumente mit Defaultwert,\n", + " 3. --- Semikolon ---,\n", + " 4. kommagetrennte Liste der Keywordargumente (mit oder ohne Defaultwert) \n", + "- Beim Aufruf können _keyword_-Argumente an beliebigen Stellen in beliebiger Reihenfolge stehen. Man kann sie wieder durch ein Semikolon von den Positionsargumenten abtrennen, muss aber nicht.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e67e1006", + "metadata": {}, + "outputs": [], + "source": [ + "fa(x, y=42; a) = println(\"x=$x, y=$y, a=$a\")\n", + "\n", + "fa(6, a=4, 7)\n", + "fa(6, 7; a=4)\n", + "fa(a=-2, 6)" + ] + }, + { + "cell_type": "markdown", + "id": "1d889283", + "metadata": {}, + "source": [ + "Eine Funktion nur mit _keyword_-Argumenten wird so deklariert:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e79269ee", + "metadata": {}, + "outputs": [], + "source": [ + "fkw(; x=10, y) = println(\"x=$x, y=$y\")\n", + "\n", + "fkw(y=2)" + ] + }, + { + "cell_type": "markdown", + "id": "14d197af", + "metadata": {}, + "source": [ + "## Funktionen sind ganz normale Objekte\n", + "\n", + " - Sie können zugewiesen werden\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2e0a4b89", + "metadata": {}, + "outputs": [], + "source": [ + "f2 = sqrt\n", + "f2(2)" + ] + }, + { + "cell_type": "markdown", + "id": "6f0fef37", + "metadata": {}, + "source": [ + "- Sie können als Argumente an Funktionen übergeben werden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c6db6121", + "metadata": {}, + "outputs": [], + "source": [ + "# sehr naive numerische Integration\n", + "\n", + "function Riemann_integrate(f, a, b; NInter=1000)\n", + " delta = (b-a)/NInter\n", + " s = 0\n", + " for i in 0:NInter-1\n", + " s += delta * f(a + delta/2 + i * delta)\n", + " end\n", + " return s\n", + "end\n", + "\n", + "\n", + "Riemann_integrate(sin, 0, π)" + ] + }, + { + "cell_type": "markdown", + "id": "b8eb1978", + "metadata": {}, + "source": [ + "- Sie können von Funktionen erzeugt und als Ergebnis `return`t werden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "67e640ce", + "metadata": {}, + "outputs": [], + "source": [ + "function generate_add_func(x)\n", + " function addx(y)\n", + " return x+y\n", + " end\n", + " return addx\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a78dd669", + "metadata": {}, + "outputs": [], + "source": [ + "h = generate_add_func(4)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "23b557af", + "metadata": {}, + "outputs": [], + "source": [ + "h(1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "440b7568", + "metadata": {}, + "outputs": [], + "source": [ + "h(2), h(10)" + ] + }, + { + "cell_type": "markdown", + "id": "ab655f0f", + "metadata": {}, + "source": [ + "Die obige Funktion `generate_add_func()` lässt sich auch kürzer definieren. Der innere Funktionsname `addx()` ist sowieso lokal und außerhalb nicht verfügbar. Also kann man eine anonyme Funktion verwenden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d0b76e9c", + "metadata": {}, + "outputs": [], + "source": [ + "generate_add_func(x) = y -> x + y" + ] + }, + { + "cell_type": "markdown", + "id": "9dcb1129", + "metadata": {}, + "source": [ + "## Zusammensetzung von Funktionen: die Operatoren $\\circ$ und `|>`\n", + "\n", + "- Die Zusammensetzung _(composition)_ von Funktionen kann auch mit dem Operator $\\circ$ (`\\circ + Tab`) geschrieben werden \n", + "\n", + "$$(f\\circ g)(x) = f(g(x))$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fcaf335f", + "metadata": {}, + "outputs": [], + "source": [ + "(sqrt ∘ + )(9, 16)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "48dd034e", + "metadata": {}, + "outputs": [], + "source": [ + "f = cos ∘ sin ∘ (x->2x)\n", + "f(.2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2ecd0bb3", + "metadata": {}, + "outputs": [], + "source": [ + "@show map(uppercase ∘ first, [\"ein\", \"paar\", \"grüne\", \"Blätter\"]);" + ] + }, + { + "cell_type": "markdown", + "id": "64c2f8ca", + "metadata": {}, + "source": [ + "- Es gibt auch einen Operator, mit dem Funktionen \"von rechts\" wirken und zusammengesetzt werden können _(piping)_\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8cdef694", + "metadata": {}, + "outputs": [], + "source": [ + "25 |> sqrt" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4fd01026", + "metadata": {}, + "outputs": [], + "source": [ + "1:10 |> sum |> sqrt" + ] + }, + { + "cell_type": "markdown", + "id": "d8c6e6f3", + "metadata": {}, + "source": [ + "- Natürlich kann man auch diese Operatoren 'broadcasten' (s. @sec-broadcast). Hier wirkt ein Vektor von Funktionen elementweise auf einen Vektor von Argumenten:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "94691aad", + "metadata": {}, + "outputs": [], + "source": [ + "[\"a\", \"list\", \"of\", \"strings\"] .|> [length, uppercase, reverse, titlecase]" + ] + }, + { + "cell_type": "markdown", + "id": "f4b75c54", + "metadata": {}, + "source": [ + "## Die `do`-Notation\n", + "\n", + "Eine syntaktische Besonderheit zur Definition anonymer Funktionen als Argumente anderer Funktionen ist die `do`-Notation.\n", + "\n", + "Sei `higherfunc(f,a,...)` eine Funktion, deren 1. Argument eine Funktion ist. \n", + "\n", + "Dann kann man `higherfunc()` auch ohne erstes Argument aufrufen und statt dessen die Funktion in einem unmittelbar folgenden `do`-Block definieren:\n", + "\n", + "```julia\n", + "higherfunc(a, b) do x, y\n", + " Körper von f(x,y)\n", + "end\n", + "```\n", + "\n", + "Am Beispiel von `Riemann_integrate()` sieht das so aus:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "76c02df9", + "metadata": {}, + "outputs": [], + "source": [ + "# das ist dasselbe wie Riemann_integrate(x->x^2, 0, 2)\n", + "\n", + "Riemann_integrate(0, 2) do x x^2 end" + ] + }, + { + "cell_type": "markdown", + "id": "a708ad3e", + "metadata": {}, + "source": [ + "Der Sinn besteht natürlich in der Anwendung mit komplexeren Funktionen, wie diesem aus zwei Teilstücken zusammengesetzten Integranden:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e3012c9b", + "metadata": {}, + "outputs": [], + "source": [ + "r = Riemann_integrate(0, π) do x\n", + " z1 = sin(x)\n", + " z2 = log(1+x)\n", + " if x > 1 \n", + " return z1^2\n", + " else\n", + " return 1/z2^2\n", + " end\n", + " end" + ] + }, + { + "cell_type": "markdown", + "id": "c38a800c", + "metadata": {}, + "source": [ + "## Funktionsartige Objekte\n", + "\n", + "Durch Definition einer geeigneten Methode für einen Typ kann man beliebige Objekte *callable* machen, d.h., sie anschließend wie Funktionen aufrufen.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5de4f59a", + "metadata": {}, + "outputs": [], + "source": [ + "# struct speichert die Koeffiziente eines Polynoms 2. Grades\n", + "struct Poly2Grad \n", + " a0::Float64\n", + " a1::Float64\n", + " a2::Float64\n", + "end\n", + "\n", + "p1 = Poly2Grad(2,5,1)\n", + "p2 = Poly2Grad(3,1,-0.4)" + ] + }, + { + "cell_type": "markdown", + "id": "8b0b62a3", + "metadata": {}, + "source": [ + "Die folgende Methode macht diese Struktur `callable`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0a5cb287", + "metadata": {}, + "outputs": [], + "source": [ + "function (p::Poly2Grad)(x)\n", + " p.a2 * x^2 + p.a1 * x + p.a0\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "a5149012", + "metadata": {}, + "source": [ + "Jetzt kann man die Objekte, wenn gewünscht, auch wie Funktionen verwenden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b271dbf1", + "metadata": {}, + "outputs": [], + "source": [ + "@show p2(5) p1(-0.7) p1;" + ] + }, + { + "cell_type": "markdown", + "id": "b355c1b0", + "metadata": {}, + "source": [ + "## Operatoren und spezielle Formen\n", + "\n", + "- Infix-Operatoren wie `+,*,>,∈,...` sind Funktionen.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4f71f917", + "metadata": {}, + "outputs": [], + "source": [ + "+(3, 7)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b19e79cf", + "metadata": {}, + "outputs": [], + "source": [ + "f = +" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "869917d4", + "metadata": {}, + "outputs": [], + "source": [ + "f(3, 7)" + ] + }, + { + "cell_type": "markdown", + "id": "490bceac", + "metadata": {}, + "source": [ + "- Auch Konstruktionen wie `x[i]`, `a.x`, `[x; y]` werden vom Parser zu Funktionsaufrufen umgewandelt.\n", + "\n", + ":::{.narrow}\n", + "\n", + "| | |\n", + "| :-: | :------------ |\n", + "| x[i] | getindex(x, i) |\n", + "| x[i] = z | setindex!(x, z, i) |\n", + "| a.x | getproperty(a, :x) | \n", + "| a.x = z | setproperty!(a, :x, z) |\n", + "| [x; y;...] | vcat(x, y, ...) |\n", + " :Spezielle Formen [(Auswahl)](https://docs.julialang.org/en/v1/manual/functions/#Operators-With-Special-Names)\n", + "\n", + ":::\n", + "\n", + "(Der Doppelpunkt vor einer Variablen macht diese zu einem Symbol.)\n", + "\n", + ":::{.callout-note}\n", + "Für diese Funktionen kann man eigene Methoden implementieren. Zum Beispiel könnten bei einem eigenen Typ das Setzen eines Feldes (`setproperty!()`) die Gültigkeit des Wertes prüfen oder weitere Aktionen veranlassen. \n", + "\n", + "Prinzipiell können `get/setproperty` auch Dinge tun, die gar nichts mit einem tatsächlich vorhandenen Feld der Struktur zu tun haben. \n", + ":::\n", + "\n", + "## Update-Form\n", + "\n", + "Alle arithmetischen Infix-Operatoren haben eine update-Form: Der Ausdruck\n", + "```julia\n", + "x = x ⊙ y\n", + "```\n", + "kann auch geschrieben werden als\n", + "```julia\n", + "x ⊙= y\n", + "```\n", + "\n", + "Beide Formen sind semantisch äquivalent. Insbesondere wird in beiden Formen der Variablen `x` ein auf der rechten Seite geschaffenes neues Objekt zugewiesen. \n", + "\n", + "Ein Speicherplatz- und Zeit-sparendes __in-place-update__ eines Arrays/Vektors/Matrix ist möglich entweder durch explizite Indizierung\n", + "```julia\n", + "for i in eachindex(x)\n", + " x[i] += y[i]\n", + "end\n", + "```\n", + "oder durch die dazu semantisch äquivalente _broadcast_-Form (s. @sec-broadcast):\n", + "```julia\n", + "x .= x .+ y\n", + "```\n", + "\n", + "\n", + "\n", + "## Vorrang und Assoziativität von Operatoren {#sec-vorrang}\n", + "\n", + "Zu berechnende Ausdrücke \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4d92cc97", + "metadata": {}, + "outputs": [], + "source": [ + " -2^3+500/2/10==8 && 13 > 7 + 1 || 9 < 2" + ] + }, + { + "cell_type": "markdown", + "id": "ec6b89f6", + "metadata": {}, + "source": [ + "werden vom Parser in eine Baumstruktur überführt.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9f607850", + "metadata": {}, + "outputs": [], + "source": [ + "using TreeView\n", + "\n", + "walk_tree(Meta.parse(\"-2^3+500/2/10==8 && 13 > 7 + 1 || 9 < 2\"))" + ] + }, + { + "cell_type": "markdown", + "id": "68328dda", + "metadata": {}, + "source": [ + "- Die Auswertung solcher Ausdrücke wird durch \n", + " - Vorrang _(precedence)_ und \n", + " - Assoziativität geregelt.\n", + "- 'Vorrang' definiert, welche Operatoren stärker binden im Sinne von \"Punktrechnung geht vor Strichrechnung\".\n", + "- 'Assoziativität' bestimmt die Auswertungsreihenfolge bei gleichen oder gleichrangigen Operatoren.\n", + "- [Vollständige Dokumentation](https://docs.julialang.org/en/v1/manual/mathematical-operations/#Operator-Precedence-and-Associativity)\n", + "\n", + "### Assoziativität\n", + "\n", + "Sowohl Addition und Subtraktion als auch Multiplikation und Divison sind jeweils gleichrangig und linksassoziativ, d.h. es wird von links ausgewertet.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "71fdbe34", + "metadata": {}, + "outputs": [], + "source": [ + "200/5/2 # wird von links ausgewertet als (200/5)/2 " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fc26727a", + "metadata": {}, + "outputs": [], + "source": [ + "200/2*5 # wird von links ausgewertet als (200/2)*5" + ] + }, + { + "cell_type": "markdown", + "id": "0253c57a", + "metadata": {}, + "source": [ + "Zuweisungen wie `=`, `+=`, `*=`,... sind gleichrangig und rechtsassoziativ.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7f9891ea", + "metadata": {}, + "outputs": [], + "source": [ + "x = 1\n", + "y = 10\n", + "\n", + "# wird von rechts ausgewertet: x += (y += (z = (a = 20)))\n", + "\n", + "x += y += z = a = 20 \n", + "\n", + "@show x y z a;" + ] + }, + { + "cell_type": "markdown", + "id": "9eeccc4c", + "metadata": {}, + "source": [ + "Natürlich kann man die Assoziativität in Julia auch abfragen. Die entsprechenden Funktionen werden nicht expizit aus dem `Base`-Modul exportiert, deshalb muss man den Modulnamen beim Aufruf angeben. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "23fe3c28", + "metadata": {}, + "outputs": [], + "source": [ + "for i in (:/, :+=, :(=), :^)\n", + " a = Base.operator_associativity(i)\n", + " println(\"Operation $i is $(a)-assoziative\")\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "148b459a", + "metadata": {}, + "source": [ + "Also ist der Potenzoperator rechtsassoziativ.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d1ad2685", + "metadata": {}, + "outputs": [], + "source": [ + "2^3^2 # rechtsassoziativ, = 2^(3^2) " + ] + }, + { + "cell_type": "markdown", + "id": "86c59c17", + "metadata": {}, + "source": [ + "### Vorrang\n", + "\n", + "- Julia ordnet den Operatoren Vorrangstufen von 1 bis 17 zu: \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9c97eee7", + "metadata": {}, + "outputs": [], + "source": [ + "for i in (:+, :-, :*, :/, :^, :(=))\n", + " p = Base.operator_precedence(i)\n", + " println(\"Vorrang von $i = $p\") \n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "177ecf6d", + "metadata": {}, + "source": [ + "- 11 ist kleiner als 12, also geht 'Punktrechnung vor Strichrechnung'\n", + "- Der Potenz-Operator `^` hat eine höhere _precedence_.\n", + "- Zuweisungen haben die kleinste _precedence_\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "30c88bf2", + "metadata": {}, + "outputs": [], + "source": [ + "# Zuweisung hat kleinsten Vorrang, daher Auswertung als x = (3 < 4)\n", + "\n", + "x = 3 < 4 \n", + "x" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b4a0a3ee", + "metadata": {}, + "outputs": [], + "source": [ + "(y = 3) < 4 # Klammern schlagen natürlich jeden Vorrang\n", + "y" + ] + }, + { + "cell_type": "markdown", + "id": "0384575c", + "metadata": {}, + "source": [ + "Nochmal zum Beispiel vom Anfang von @sec-vorrang:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "56488075", + "metadata": {}, + "outputs": [], + "source": [ + "-2^3+500/2/10==8 && 13 > 7 + 1 || 9 < 2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "543e7874", + "metadata": {}, + "outputs": [], + "source": [ + "for i ∈ (:^, :+, :/, :(==), :&&, :>, :|| )\n", + " print(i, \" \")\n", + " println(Base.operator_precedence(i))\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "bcb7fc77", + "metadata": {}, + "source": [ + "Nach diesen Vorrangregeln wird der Beispielausdruck also wie folgt ausgewertet:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "89af1388", + "metadata": {}, + "outputs": [], + "source": [ + "((-(2^3)+((500/2)/10)==8) && (13 > (7 + 1))) || (9 < 2)" + ] + }, + { + "cell_type": "markdown", + "id": "509a3955", + "metadata": {}, + "source": [ + "(Das entspricht natürlich dem oben gezeigten *parse-tree*)\n", + "\n", + "Es gilt also für den Vorrang:\n", + "\n", + "> Potenz > Multiplikation/Division > Addition/Subtraktion > Vergleiche > logisches && > logisches || > Zuweisung\n", + "\n", + "Damit wird ein Ausdruck wie \n", + "```julia\n", + " a = x <= y + z && x > z/2 \n", + "``` \n", + "sinnvoll ausgewertet als `a = ((x <= (y+z)) && (x < (z/2)))`\n", + "\n", + "\n", + "- Eine Besonderheit sind noch\n", + " \n", + " - unäre Operatoren, also insbesondere `+` und `-` als Vorzeichen \n", + " - _juxtaposition_, also Zahlen direkt vor Variablen oder Klammern ohne `*`-Symbol\n", + " \n", + " Beide haben Vorrang noch vor Multiplikation und Division. \n", + "\n", + ":::{.callout-important}\n", + "Damit ändert sich die Bedeutung von Ausdrücken, wenn man _juxtaposition_ anwendet:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c134b798", + "metadata": {}, + "outputs": [], + "source": [ + "1/2*π, 1/2π" + ] + }, + { + "cell_type": "markdown", + "id": "aafaa2d1", + "metadata": {}, + "source": [ + "::: \n", + " \n", + "- Im Vergleich zum Potenzoperator `^` gilt (s. [https://discourse.julialang.org/t/confused-about-operator-precedence-for-2-3x/8214/7](https://discourse.julialang.org/t/confused-about-operator-precedence-for-2-3x/8214/7) ):\n", + " \n", + " > Unary operators, including juxtaposition, bind tighter than ^ on the right but looser on the left.\n", + "\n", + "Beispiele:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "61fc5df5", + "metadata": {}, + "outputs": [], + "source": [ + "-2^2 # -(2^2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8c609c3b", + "metadata": {}, + "outputs": [], + "source": [ + "x = 5\n", + "2x^2 # 2(x^2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "44a6345d", + "metadata": {}, + "outputs": [], + "source": [ + "2^-2 # 2^(-2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "660dfb1f", + "metadata": {}, + "outputs": [], + "source": [ + "2^2x # 2^(2x)" + ] + }, + { + "cell_type": "markdown", + "id": "0fecdb42", + "metadata": {}, + "source": [ + "- Funktionsanwendung `f(...)` hat Vorrang vor allen Operatoren\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "198bb0f8", + "metadata": {}, + "outputs": [], + "source": [ + "sin(x)^2 === (sin(x))^2 # nicht sin(x^2)" + ] + }, + { + "cell_type": "markdown", + "id": "f153e028", + "metadata": {}, + "source": [ + "### Zusätzliche Operatoren\n", + "\n", + "Der [Julia-Parser](https://github.com/JuliaLang/julia/blob/master/src/julia-parser.scm#L13-L31) definiert für zahlreiche Unicode-Zeichen einen Vorrang auf Vorrat, so dass diese Zeichen von Paketen und selbstgeschriebenem Code als Operatoren benutzt werden können. \n", + "\n", + "So haben z.B.\n", + "```julia\n", + " ∧ ⊗ ⊘ ⊙ ⊚ ⊛ ⊠ ⊡ ⊓ ∗ ∙ ∤ ⅋ ≀ ⊼ ⋄ ⋆ ⋇ ⋉ ⋊ ⋋ ⋌ ⋏ ⋒ ⟑ ⦸ ⦼ ⦾ ⦿ ⧶ ⧷ ⨇ ⨰ ⨱ ⨲ ⨳ ⨴ ⨵ ⨶ ⨷ ⨸ ⨻ ⨼ ⨽ ⩀ ⩃ ⩄ ⩋ ⩍ ⩎ ⩑ ⩓ ⩕ ⩘ ⩚ ⩜ ⩞ ⩟ ⩠ ⫛\n", + "```\n", + "\n", + "den Vorrang 12 wie Multiplikation/Division (und sind wie diese linksassoziativ) \n", + "und z.B.\n", + "```julia\n", + " ⊕ ⊖ ⊞ ⊟ |++| ∪ ∨ ⊔ ± ∓ ∔ ∸ ≏ ⊎ ⊻ ⊽ ⋎ ⋓ ⧺ ⧻ ⨈ ⨢ ⨣ ⨤ ⨥ ⨦ ⨧ ⨨ ⨩ ⨪ ⨫ ⨬ ⨭ ⨮ ⨹ ⨺ ⩁ ⩂ ⩅ ⩊ ⩌ ⩏ ⩐ ⩒ ⩔ ⩖ ⩗ \n", + "```\n", + "haben den Vorrang 11 wie Addition/Subtraktion.\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/Erste_Bsp.ipynb b/nb/Erste_Bsp.ipynb new file mode 100644 index 0000000..44381b0 --- /dev/null +++ b/nb/Erste_Bsp.ipynb @@ -0,0 +1,341 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9bb241ad", + "metadata": {}, + "source": [ + "# Erste Miniprogramme\n", + "\n", + "\n", + "## Was sollte man zum Programmieren können?\n", + "\n", + "\n", + "- **Denken in Algorithmen:** \n", + " Welche Schritte sind zur Lösung des Problems nötig? Welche Daten müssen gespeichert, welche Datenstrukturen angelegt werden? Welche Fälle können auftreten und müssen erkannt und behandelt werden? \n", + "- **Umsetzung des Algorithmus in ein Programm:** \n", + " Welche Datenstrukturen, Konstrukte, Funktionen... stellt die Programmiersprache bereit? \n", + "- **Formale Syntax:** \n", + " Menschen verstehen 'broken English'; Computer verstehen kein 'broken C++' oder 'broken Julia'. Die Syntax muss beherrscht werden.\n", + "- **„Ökosystem“ der Sprache:** \n", + " Wie führe ich meinen Code aus? Wie funktionieren die Entwicklungsumgebungen? Welche Optionen versteht der Compiler? Wie installiere ich Zusatzbibliotheken? Wie lese ich Fehlermeldungen? Wo kann ich mich informieren? \n", + "- **die Kunst des Debugging:** \n", + " Programmieranfänger sind oft glücklich, wenn sie alle Syntaxfehler eliminiert haben und das Programm endlich 'durchläuft'. Bei komplexeren Programmen fängt die Arbeit jetzt erst an, denn nun muss getestet und die Fehler im Algorithmus gefunden und behoben werden. \n", + "- **Gefühl für die Effizienz und Komplexität von Algorithmen**\n", + "- **Besonderheiten der Computerarithmetik**, insbesondere der Gleitkommazahlen\n", + "\n", + "Das erschließt sich nicht alles auf einmal. Haben Sie Geduld mit sich und 'spielen' Sie mit der Sprache. \n", + "\n", + "Das Folgende soll eine kleine Anregung dazu sein.\n", + "\n", + "## Project Euler\n", + "\n", + "Eine hübsche Quelle für Programmieraufgaben mit mathematischem Charakter und sehr unterschiedlichen Schwierigkeitsgraden ist [Project Euler](https://projecteuler.net/). \n", + "Die Aufgaben sind so gestaltet, dass keinerlei Eingaben notwendig und das gesuchte Ergebnis eine einzige Zahl ist. So kann man sich voll auf das Programmieren des Algorithmus konzentrieren. \n", + "\n", + "---------\n", + "\n", + "### Beispiel 1\n", + "\n", + "::::::{.content-hidden unless-format=\"xxx\"}\n", + "\n", + "https://github.com/luckytoilet/projecteuler-solutions/blob/master/Solutions.md\n", + "https://math.stackexchange.com/questions/3370978/iterating-sum-of-squares-of-decimal-digits-of-an-integer-how-big-can-it-grow\n", + "aufg. 92\n", + "\n", + ":::\n", + "\n", + "::: {.callout-note icon=false .titlenormal}\n", + "## Project Euler Problem No 1\n", + "\n", + "If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.\n", + "\n", + "Find the sum of all the multiples of 3 or 5 below 1000.\n", + "\n", + ":::\n", + "\n", + "1. Algorithmus: \n", + " - Teste alle natürlichen Zahlen <1000 auf Teilbarkeit durch 3 oder durch 5 und\n", + " - summiere die teilbaren Zahlen auf.\n", + "\n", + "2. Umsetzung:\n", + "\n", + " Wie liefert Julia den Rest der Ganzzahldivision? Solche Funktionen heißen typischerweise `rem()` (für *remainder*) oder `mod()`. [Nachlesen in der Doku](https://docs.julialang.org/en/v1/base/math/#Base.rem) oder ausprobieren von `?rem` und `?mod` in der Julia-REPL zeigt, dass es beides gibt. Der Unterschied liegt in der Behandlung negativer ganzer Zahlen. Für natürliche Zahlen `n,m` liefern `mod(n,m)` und `rem(n,m)` dasselbe und letzteres hat auch noch die Infix-Form `n % m`. \n", + " \n", + " Wie testet man eine Reihe von Werten durch und summiert auf? Da gibt es ein Standardmuster: `for`-Schleife und Akkumulatorvariable: \n", + "\n", + ":::{.callout-caution icon=\"false\" collapse=\"true\" .titlenormal}\n", + "\n", + "## Eine Lösungsvariante:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b5ec6b90", + "metadata": {}, + "outputs": [], + "source": [ + "s = 0 # Akkumulatorvariable initialisieren\n", + "for i in 1:999 # Schleife \n", + " if i % 3 == 0 || i % 5 == 0 # Test\n", + " s += i # Zu Akkumulator addieren \n", + " end # Ende Test\n", + "end # Ende Schleife\n", + "println(\" Die Antwort ist: $s\") # Ausgabe des Ergebnisses " + ] + }, + { + "cell_type": "markdown", + "id": "e4de7d69", + "metadata": {}, + "source": [ + ":::\n", + "\n", + "Natürlich geht das auch etwas kürzer:\n", + "\n", + ":::{.callout-caution icon=\"false\" collapse=\"true\" .titlenormal}\n", + "\n", + "## Noch eine Lösungsvariante:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "772bbe68", + "metadata": {}, + "outputs": [], + "source": [ + "sum([i for i in 1:999 if i%3==0||i%5==0])" + ] + }, + { + "cell_type": "markdown", + "id": "b9b95d73", + "metadata": {}, + "source": [ + ":::\n", + "\n", + "\n", + "-----------\n", + "\n", + "### Beispiel 2\n", + "\n", + "\n", + "::: {.callout-note icon=false .titlenormal}\n", + "## Project Euler Problem No 92\n", + "A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before.\n", + "\n", + "For example,\n", + "\n", + "| 44 → 32 → 13 → 10 → **1** → **1**\n", + "| 85 → **89** → 145 → 42 → 20 → 4 → 16 → 37 → 58 → **89**\n", + "\n", + "Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most amazing is that EVERY starting number will eventually arrive at 1 or 89.\n", + "\n", + "How many starting numbers below ten million will arrive at 89?\n", + ":::\n", + "\n", + "Programme kann man [*top-down* und *bottom-up*](https://de.wikipedia.org/wiki/Top-Down-_und_Bottom-Up-Design) entwickeln.\n", + "*Top-down* würde hier wohl bedeuten: „Wir fangen mit einer Schleife `for i = 1:9999999` an.“ Der andere Weg führt über einzeln testbare Komponenten und ist oft zielführender. (Und ab einer gewissen Projektgröße nähert man sich sowieso von 'top' und 'bottom' gleichzeitig dem Ziel.)\n", + "\n", + "##### Funktion Nr. 1\n", + "Es soll untersucht werden, wie sich die Zahlen unter dem wiederholten Berechnen der 'Quadratquersumme' (Summe der Quadrate der Ziffern) verhalten. Also sollte man eine Funktion schreiben und testen, die diese 'Quadratquersumme' berechnet. \n", + "\n", + "\n", + ":::{.callout-caution icon=\"false\" collapse=\"true\" .titlenormal}\n", + "\n", + "## `q2sum(n)` berechnet die Summe der Quadrate der Ziffern von n im Dezimalsystem:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c0730a2a", + "metadata": {}, + "outputs": [], + "source": [ + "#| output: false\n", + "function q2sum(n)\n", + " s = 0 # Akkumulator für die Summe\n", + " while n > 9 # solange noch mehrstellig...\n", + " q, r = divrem(n, 10) # berechne Ganzzahlquotient und Rest bei Division durch 10\n", + " s += r^2 # addiere quadrierte Ziffer zum Akkumulator\n", + " n = q # mache weiter mit der durch 10 geteilten Zahl\n", + " end\n", + " s += n^2 # addiere das Quadrat der letzten Ziffer\n", + " return s\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "1caa208b", + "metadata": {}, + "source": [ + ":::\n", + "... und das testen wir jetzt natürlich:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "72341556", + "metadata": {}, + "outputs": [], + "source": [ + "for i in [1, 7, 33, 111, 321, 1000, 73201]\n", + " j = q2sum(i)\n", + " println(\"Quadratquersumme von $i = $j\")\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "5eeb2626", + "metadata": {}, + "source": [ + "Im Sinne der Aufgabe wenden wir die Funktion wiederholt an:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "da47c136", + "metadata": {}, + "outputs": [], + "source": [ + "n = 129956799\n", + "for i in 1:14\n", + " n = q2sum(n)\n", + " println(n)\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "e67b1670", + "metadata": {}, + "source": [ + "... und haben hier einen der '89er Zyklen' getroffen.\n", + "\n", + "\n", + "#### Funktion Nr. 2\n", + "\n", + "Wir müssen testen, ob die wiederholte Anwendung der Funktion `q2sum()` schließlich zu **1** führt oder in diesem **89er**-Zyklus endet.\n", + "\n", + ":::{.callout-caution icon=\"false\" collapse=\"true\" .titlenormal}\n", + "\n", + "## `q2test(n)` ermittelt, ob wiederholte Quadratquersummenbildung in den 89er-Zyklus führt:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3868d34e", + "metadata": {}, + "outputs": [], + "source": [ + "#| output: false\n", + "function q2test(n)\n", + " while n !=1 && n != 89 # solange wir nicht bei 1 oder 89 angekommen sind....\n", + " n = q2sum(n) # wiederholen \n", + " end\n", + " if n==1 return false end # keine 89er-Zahl\n", + " return true # 89er-Zahl gefunden\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "10ce44d1", + "metadata": {}, + "source": [ + ":::\n", + "\n", + "... und damit können wir die Aufgabe lösen:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "54521e6a", + "metadata": {}, + "outputs": [], + "source": [ + "c = 0 # mal wieder ein Akkumulator\n", + "for i = 1 : 10_000_000 - 1 # so kann man in Julia Tausenderblöcke zur besseren Lesbarkeit abtrennen\n", + " if q2test(i) # q2test() gibt einen Boolean zurück, kein weiterer Test nötig \n", + " c += 1 # 'if x == true' ist redundant, 'if x' reicht völlig \n", + " end \n", + "end\n", + "println(\"$c numbers below ten million arrive at 89.\")" + ] + }, + { + "cell_type": "markdown", + "id": "4a545b8c", + "metadata": {}, + "source": [ + "Zahlen, bei denen die iterierte Quadratquersummenbildung bei 1 endet, heißen übrigens [fröhliche Zahlen](https://de.wikipedia.org/wiki/Fr%C3%B6hliche_Zahl) und wir haben gerade die Anzahl der traurigen Zahlen kleiner als 10.000.000 berechnet.\n", + "\n", + "Hier nochmal das vollständige Programm:\n", + "\n", + ":::{.callout-caution icon=\"false\" collapse=\"true\" .titlenormal}\n", + "## unsere Lösung von Project Euler No 92:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a7253bc1", + "metadata": {}, + "outputs": [], + "source": [ + "function q2sum(n)\n", + " s = 0 \n", + " while n > 9 \n", + " q, r = divrem(n, 10)\n", + " s += r^2 \n", + " n = q \n", + " end\n", + " s += n^2 \n", + " return s\n", + "end\n", + "\n", + "function q2test(n)\n", + " while n !=1 && n != 89 \n", + " n = q2sum(n) \n", + " end\n", + " if n==1 return false end \n", + " return true \n", + "end\n", + "\n", + "c = 0\n", + "for i = 1 : 10_000_000 - 1 \n", + " if q2test(i)\n", + " c += 1\n", + " end \n", + "end\n", + "println(\"$c numbers below ten million arrive at 89.\")" + ] + }, + { + "cell_type": "markdown", + "id": "772bec11", + "metadata": {}, + "source": [ + ":::" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/Pi.ipynb b/nb/Pi.ipynb new file mode 100644 index 0000000..d81ece9 --- /dev/null +++ b/nb/Pi.ipynb @@ -0,0 +1,233 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "0b96655f", + "metadata": {}, + "source": [ + "# Ein Beispiel zur Stabilität von Gleitkommaarithmetik\n", + "\n", + "## Berechnung von $\\pi$ nach Archimedes\n", + "\n", + "\n", + "\n", + "Eine untere Schranke für $2\\pi$, den Umfang des Einheitskreises, erhält man durch die\n", + "Summe der Seitenlängen eines dem Einheitskreis eingeschriebenen regelmäßigen $n$-Ecks.\n", + " Die Abbildung links zeigt, wie man beginnend mit einem Viereck der Seitenlänge $s_4=\\sqrt{2}$ die Eckenzahl iterativ verdoppelt.\n", + "\n", + "| Abb. 1 | Abb.2 |\n", + "| :-: | :-: |\n", + "| ![](../images/pi1.png) | ![](../images/pi2.png) |\n", + "\n", + "Die zweite Abbildung zeigt die Geometrie der Eckenverdoppelung.\n", + "\n", + "Mit\n", + "$|\\overline{AC}|= s_{n},\\quad |\\overline{AB}|= |\\overline{BC}|= s_{2n},\\quad |\\overline{MN}| =a, \\quad |\\overline{NB}| =1-a,$ liefert Pythagoras für die Dreiecke $MNA$ und\n", + " $NBA$ jeweils\n", + "$$\n", + " a^2 + \\left(\\frac{s_{n}}{2}\\right)^2 = 1\\qquad\\text{bzw.} \\qquad\n", + " (1-a)^2 + \\left(\\frac{s_{n}}{2}\\right)^2 = s_{2n}^2\n", + "$$\n", + "Elimination von $a$ liefert die Rekursion\n", + "$$\n", + " s_{2n} = \\sqrt{2-\\sqrt{4-s_n^2}} \\qquad\\text{mit Startwert}\\qquad\n", + " s_4=\\sqrt{2}\n", + "$$\n", + "für die Länge $s_n$ **einer** Seite des eingeschriebenen regelmäßigen\n", + "$n$-Ecks.\n", + "\n", + "\n", + "Die Folge $(n\\cdot s_n)$\n", + "konvergiert monoton von unten gegen den\n", + "Grenzwert $2\\pi$:\n", + "$$\n", + " n\\, s_n \\rightarrow 2\\pi % \\qquad\\text{und} \\qquad {n c_n}\\downarrow 2\\pi\n", + "$$\n", + "Der relative Fehler der Approximation von 2π durch ein $n$-Eck ist:\n", + "$$\n", + " \\epsilon_n = \\left| \\frac{n\\, s_n-2 \\pi}{2\\pi} \\right|\n", + "$$\n", + "\n", + "\n", + "## Zwei Iterationsvorschriften^[nach: Christoph Überhuber, „Computer-Numerik“ Bd. 1, Springer 1995, Kap. 2.3]\n", + "Die Gleichung\n", + "$$\n", + " s_{2n} = \\sqrt{2-\\sqrt{4-s_n^2}}\\qquad \\qquad \\textrm{(Iteration A)}\n", + "$$\n", + "ist mathematisch äquivalent zu\n", + "$$\n", + " s_{2n} = \\frac{s_n}{\\sqrt{2+\\sqrt{4-s_n^2}}} \\qquad \\qquad \\textrm{(Iteration B)}\n", + "$$\n", + "\n", + "(Bitte nachrechnen!) \n", + "\n", + "\n", + "\n", + "Allerdings ist Iteration A schlecht konditioniert und numerisch instabil, wie der folgende Code zeigt. Ausgegeben wird die jeweils berechnete Näherung für π.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fa3be89a", + "metadata": {}, + "outputs": [], + "source": [ + "using Printf\n", + "\n", + "iterationA(s) = sqrt(2 - sqrt(4 - s^2))\n", + "iterationB(s) = s / sqrt(2 + sqrt(4 - s^2))\n", + "\n", + "s_B = s_A = sqrt(2) # Startwert \n", + "\n", + "ϵ(x) = abs(x - 2π)/2π # rel. Fehler \n", + "\n", + "ϵ_A = Float64[] # Vektoren für den Plot\n", + "ϵ_B = Float64[]\n", + "is = Float64[]\n", + "\n", + "@printf \"\"\" approx. Wert von π\n", + " n-Eck Iteration A Iteration B\n", + "\"\"\"\n", + "\n", + "for i in 3:35\n", + " push!(is, i)\n", + " s_A = iterationA(s_A) \n", + " s_B = iterationB(s_B) \n", + " doublePi_A = 2^i * s_A\n", + " doublePi_B = 2^i * s_B\n", + " push!(ϵ_A, ϵ(doublePi_A))\n", + " push!(ϵ_B, ϵ(doublePi_B))\n", + " @printf \"%14i %20.15f %20.15f\\n\" 2^i doublePi_A/2 doublePi_B/2 \n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "7ce50a85", + "metadata": {}, + "source": [ + "Während Iteration B sich stabilisiert bei einem innerhalb der Maschinengenauigkeit korrekten Wert für π, wird Iteration A schnell instabil. Ein Plot der relativen Fehler $\\epsilon_i$ bestätigt das:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5004b70e", + "metadata": {}, + "outputs": [], + "source": [ + "using CairoMakie\n", + "\n", + "F = Figure(resolution=(800,500))\n", + "ax = Axis(F[1, 1], xlabel = \"Iterationsschritte\", ylabel = \"rel. Fehler\",\n", + " yscale = log10, xticks=2:2:35, yticks=LogTicks(-20:0))\n", + "\n", + "scatterlines!(ax, is, ϵ_A, label = \"Iteration A\" )\n", + "scatterlines!(ax, is, ϵ_B, marker=:xcross, label = \"Iteration B\" )\n", + "\n", + "axislegend(position=:rc)\n", + "F" + ] + }, + { + "cell_type": "markdown", + "id": "7a93c5e3", + "metadata": {}, + "source": [ + "## Stabilität und Auslöschung\n", + "\n", + "Bei $i=26$ erreicht Iteration B einen relativen Fehler in der Größe des Maschinenepsilons:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "527eee0e", + "metadata": {}, + "outputs": [], + "source": [ + "ϵ_B[22:28]" + ] + }, + { + "cell_type": "markdown", + "id": "6f2f4475", + "metadata": {}, + "source": [ + "Weitere Iterationen verbessern das Ergebnis nicht mehr. Sie stabilisieren sich bei einem relativen Fehler von etwa 2.5 Maschinenepsilon:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3b2a8b77", + "metadata": {}, + "outputs": [], + "source": [ + "ϵ_B[end]/eps(Float64)" + ] + }, + { + "cell_type": "markdown", + "id": "6ff2d4b8", + "metadata": {}, + "source": [ + "Die Form Iteration A ist instabil. Bereits bei $i=16$ beginnt der relative Fehler wieder zu wachsen.\n", + "\n", + "Ursache ist eine typische Auslöschung. Die Seitenlängen $s_n$ werden sehr schnell klein. Damit ist\n", + "$a_n=\\sqrt{4-s_n^2}$ nur noch wenig kleiner als 2 und bei der Berechnung von $s_{2n}=\\sqrt{2-a_n}$ tritt ein typischer Auslöschungseffekt auf.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ca6c5ca2", + "metadata": {}, + "outputs": [], + "source": [ + "setprecision(80) # precision für BigFloat\n", + "\n", + "s = sqrt(BigFloat(2))\n", + "\n", + "@printf \" a = √(4-s^2) als BigFloat und als Float64\\n\\n\"\n", + "\n", + "for i = 3:44\n", + " s = iterationA(s)\n", + " x = sqrt(4-s^2)\n", + " if i > 20\n", + " @printf \"%i %30.26f %20.16f \\n\" i x Float64(x)\n", + " end \n", + "end\n" + ] + }, + { + "cell_type": "markdown", + "id": "5e4994b3", + "metadata": {}, + "source": [ + "Man sieht die Abnahme der Zahl der signifikanten Ziffern. Man sieht auch, dass eine Verwendung von `BigFloat` mit einer Mantissenlänge von hier 80 Bit das Einsetzen des Auslöschungseffekts nur etwas hinaussschieben kann. \n", + "\n", + "**Gegen instabile Algorithmen helfen in der Regel nur bessere, stabile Algorithmen und nicht genauere Maschinenzahlen!**\n", + "\n", + ":::{.content-hidden unless-format=\"xxx\"}\n", + "\n", + "Offensichtlich tritt bei der Berechnung von $2-a_n$ bereits relativ früh\n", + "eine Abnahme der Anzahl der signifikanten Ziffern (Auslöschung) auf, \n", + "bevor schließlich bei der Berechnung von $a_n=\\sqrt{4-s_n^2}$ \n", + "selbst schon Auslöschung zu einem unbrauchbaren Ergebnis führt.\n", + "\n", + ":::" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/Pi2.ipynb b/nb/Pi2.ipynb new file mode 100644 index 0000000..89f002c --- /dev/null +++ b/nb/Pi2.ipynb @@ -0,0 +1,313 @@ +{ + "cells": [ + { + "cell_type": "raw", + "id": "9d63401b", + "metadata": {}, + "source": [ + "---\n", + "format:\n", + " html:\n", + " include-in-header:\n", + " text: |\n", + " \n", + "---" + ] + }, + { + "cell_type": "markdown", + "id": "405d242e", + "metadata": {}, + "source": [ + "# Ein Beispiel zur Stabilität von Gleitkommaarithmetik\n", + "\n", + "## Berechnung von $\\pi$ nach Archimedes\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f17a5fcb", + "metadata": {}, + "outputs": [], + "source": [ + "#| error: false\n", + "#| echo: false\n", + "#| output: false\n", + "using PlotlyJS, Random\n", + "using HypertextLiteral\n", + "using JSON, UUIDs\n", + "using Base64\n", + "\n", + "\n", + "## see https://github.com/JuliaPlots/PlotlyJS.jl/blob/master/src/PlotlyJS.jl\n", + "## https://discourse.julialang.org/t/encode-a-plot-to-base64/27765/3\n", + "function IJulia.display_dict(p::PlotlyJS.SyncPlot)\n", + " Dict(\n", + " # \"application/vnd.plotly.v1+json\" => JSON.lower(p),\n", + " # \"text/plain\" => sprint(show, \"text/plain\", p),\n", + " \"text/html\" => let\n", + " buf = IOBuffer()\n", + " show(buf, MIME(\"text/html\"), p)\n", + " #close(buf)\n", + " #String(resize!(buf.data, buf.size))\n", + " String(take!(buf))\n", + " end,\n", + " \"image/png\" => let\n", + " buf = IOBuffer()\n", + " buf64 = Base64EncodePipe(buf)\n", + " show(buf64, MIME(\"image/png\"), p)\n", + " close(buf64)\n", + " #String(resize!(buf.data, buf.size))\n", + " String(take!(buf))\n", + " end,\n", + "\n", + " )\n", + " end\n", + "\n", + " function Base.show(io::IO, mimetype::MIME\"text/html\", p::PlotlyJS.SyncPlot)\n", + " uuid = string(UUIDs.uuid4())\n", + " show(io,mimetype,@htl(\"\"\"\n", + "

\n", + " \n", + "\"\"\"))\n", + "end " + ] + }, + { + "cell_type": "markdown", + "id": "7745166c", + "metadata": {}, + "source": [ + "Eine untere Schranke für $2\\pi$, den Umfang des Einheitskreises, erhält man durch die\n", + "Summe der Seitenlängen eines dem Einheitskreis eingeschriebenen regelmäßigen $n$-Ecks.\n", + " Die Abbildung links zeigt, wie man beginnend mit einem Viereck der Seitenlänge $s_4=\\sqrt{2}$ die Eckenzahl iterativ verdoppelt.\n", + "\n", + ":::{.narrow}\n", + "\n", + "| Abb. 1 | Abb.2 |\n", + "| :-: | :-: |\n", + "| ![](../images/pi1.png) | ![](../images/pi2.png) |\n", + ": {tbl-colwidths=\"[57,43]\"}\n", + "\n", + ":::\n", + "\n", + "\n", + "Die zweite Abbildung zeigt die Geometrie der Eckenverdoppelung.\n", + "\n", + "Mit\n", + "$|\\overline{AC}|= s_{n},\\quad |\\overline{AB}|= |\\overline{BC}|= s_{2n},\\quad |\\overline{MN}| =a, \\quad |\\overline{NB}| =1-a,$ liefert Pythagoras für die Dreiecke $MNA$ und\n", + " $NBA$ jeweils\n", + "$$\n", + " a^2 + \\left(\\frac{s_{n}}{2}\\right)^2 = 1\\qquad\\text{bzw.} \\qquad\n", + " (1-a)^2 + \\left(\\frac{s_{n}}{2}\\right)^2 = s_{2n}^2\n", + "$$\n", + "Elimination von $a$ liefert die Rekursion\n", + "$$\n", + " s_{2n} = \\sqrt{2-\\sqrt{4-s_n^2}} \\qquad\\text{mit Startwert}\\qquad\n", + " s_4=\\sqrt{2}\n", + "$$\n", + "für die Länge $s_n$ **einer** Seite des eingeschriebenen regelmäßigen\n", + "$n$-Ecks.\n", + "\n", + "\n", + "Die Folge $(n\\cdot s_n)$\n", + "konvergiert monoton von unten gegen den\n", + "Grenzwert $2\\pi$:\n", + "$$\n", + " n\\, s_n \\rightarrow 2\\pi % \\qquad\\text{und} \\qquad {n c_n}\\downarrow 2\\pi\n", + "$$\n", + "Der relative Fehler der Approximation von 2π durch ein $n$-Eck ist:\n", + "$$\n", + " \\epsilon_n = \\left| \\frac{n\\, s_n-2 \\pi}{2\\pi} \\right|\n", + "$$\n", + "\n", + "\n", + "## Zwei Iterationsvorschriften^[nach: Christoph Überhuber, „Computer-Numerik“ Bd. 1, Springer 1995, Kap. 2.3]\n", + "Die Gleichung\n", + "$$\n", + " s_{2n} = \\sqrt{2-\\sqrt{4-s_n^2}}\\qquad \\qquad \\textrm{(Iteration A)}\n", + "$$\n", + "ist mathematisch äquivalent zu\n", + "$$\n", + " s_{2n} = \\frac{s_n}{\\sqrt{2+\\sqrt{4-s_n^2}}} \\qquad \\qquad \\textrm{(Iteration B)}\n", + "$$\n", + "\n", + "(Bitte nachrechnen!) \n", + "\n", + "\n", + "\n", + "Allerdings ist Iteration A schlecht konditioniert und numerisch instabil, wie der folgende Code zeigt. Ausgegeben wird die jeweils berechnete Näherung für π.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d83237c5", + "metadata": {}, + "outputs": [], + "source": [ + "using Printf\n", + "\n", + "iterationA(s) = sqrt(2 - sqrt(4 - s^2))\n", + "iterationB(s) = s / sqrt(2 + sqrt(4 - s^2))\n", + "\n", + "s_B = s_A = sqrt(2) # Startwert \n", + "\n", + "ϵ(x) = abs(x - 2π)/2π # rel. Fehler \n", + "\n", + "ϵ_A = Float64[] # Vektoren für den Plot\n", + "ϵ_B = Float64[]\n", + "is = Float64[]\n", + "\n", + "@printf \"\"\" approx. Wert von π\n", + " n-Eck Iteration A Iteration B\n", + "\"\"\"\n", + "\n", + "for i in 3:35\n", + " push!(is, i)\n", + " s_A = iterationA(s_A) \n", + " s_B = iterationB(s_B) \n", + " doublePi_A = 2^i * s_A\n", + " doublePi_B = 2^i * s_B\n", + " push!(ϵ_A, ϵ(doublePi_A))\n", + " push!(ϵ_B, ϵ(doublePi_B))\n", + " @printf \"%14i %20.15f %20.15f\\n\" 2^i doublePi_A/2 doublePi_B/2 \n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "dcdecd41", + "metadata": {}, + "source": [ + "Während Iteration B sich stabilisiert bei einem innerhalb der Maschinengenauigkeit korrekten Wert für π, wird Iteration A schnell instabil. Ein Plot der relativen Fehler $\\epsilon_i$ bestätigt das:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4404adb1", + "metadata": {}, + "outputs": [], + "source": [ + "using PlotlyJS\n", + "\n", + "layout = Layout(xaxis_title=\"Iterationsschritte\", yaxis_title=\"rel. Fehler\",\n", + " yaxis_type=\"log\", yaxis_exponentformat=\"power\", \n", + " xaxis_tick0=2, xaxis_dtick=2)\n", + "\n", + "plot([scatter(x=is, y=ϵ_A, mode=\"markers+lines\", name=\"Iteration A\", yscale=:log10), \n", + " scatter(x=is, y=ϵ_B, mode=\"markers+lines\", name=\"Iteration B\", yscale=:log10)],\n", + " layout) \n" + ] + }, + { + "cell_type": "markdown", + "id": "ac5d56d5", + "metadata": {}, + "source": [ + "## Stabilität und Auslöschung\n", + "\n", + "Bei $i=26$ erreicht Iteration B einen relativen Fehler in der Größe des Maschinenepsilons:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e807fa2b", + "metadata": {}, + "outputs": [], + "source": [ + "ϵ_B[22:28]" + ] + }, + { + "cell_type": "markdown", + "id": "68979310", + "metadata": {}, + "source": [ + "Weitere Iterationen verbessern das Ergebnis nicht mehr. Sie stabilisieren sich bei einem relativen Fehler von etwa 2.5 Maschinenepsilon:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6a9f7b29", + "metadata": {}, + "outputs": [], + "source": [ + "ϵ_B[end]/eps(Float64)" + ] + }, + { + "cell_type": "markdown", + "id": "09be0e03", + "metadata": {}, + "source": [ + "Die Form Iteration A ist instabil. Bereits bei $i=16$ beginnt der relative Fehler wieder zu wachsen.\n", + "\n", + "Ursache ist eine typische Auslöschung. Die Seitenlängen $s_n$ werden sehr schnell klein. Damit ist\n", + "$a_n=\\sqrt{4-s_n^2}$ nur noch wenig kleiner als 2 und bei der Berechnung von $s_{2n}=\\sqrt{2-a_n}$ tritt ein typischer Auslöschungseffekt auf.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2ccb85ad", + "metadata": {}, + "outputs": [], + "source": [ + "setprecision(80) # precision für BigFloat\n", + "\n", + "s = sqrt(BigFloat(2))\n", + "\n", + "@printf \" a = √(4-s^2) als BigFloat und als Float64\\n\\n\"\n", + "\n", + "for i = 3:44\n", + " s = iterationA(s)\n", + " x = sqrt(4-s^2)\n", + " if i > 20\n", + " @printf \"%i %30.26f %20.16f \\n\" i x Float64(x)\n", + " end \n", + "end\n" + ] + }, + { + "cell_type": "markdown", + "id": "27616d4d", + "metadata": {}, + "source": [ + "Man sieht die Abnahme der Zahl der signifikanten Ziffern. Man sieht auch, dass eine Verwendung von `BigFloat` mit einer Mantissenlänge von hier 80 Bit das Einsetzen des Auslöschungseffekts nur etwas hinaussschieben kann. \n", + "\n", + "**Gegen instabile Algorithmen helfen in der Regel nur bessere, stabile Algorithmen und nicht genauere Maschinenzahlen!**\n", + "\n", + ":::{.content-hidden unless-format=\"xxx\"}\n", + "\n", + "Offensichtlich tritt bei der Berechnung von $2-a_n$ bereits relativ früh\n", + "eine Abnahme der Anzahl der signifikanten Ziffern (Auslöschung) auf, \n", + "bevor schließlich bei der Berechnung von $a_n=\\sqrt{4-s_n^2}$ \n", + "selbst schon Auslöschung zu einem unbrauchbaren Ergebnis führt.\n", + "\n", + ":::" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/ablaufsteuerung.ipynb b/nb/ablaufsteuerung.ipynb new file mode 100644 index 0000000..10687ed --- /dev/null +++ b/nb/ablaufsteuerung.ipynb @@ -0,0 +1,83 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "cdcef88f", + "metadata": {}, + "source": [ + "# Verzweigungen\n", + "\n", + "::: {.column-margin}\n", + ":::\n", + "\n", + "### If\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "13854f8c", + "metadata": {}, + "outputs": [], + "source": [ + "x = 3\n", + "y = 66\n", + "\n", + "if x\n", + "2. als Editor/IDE **Visual Studio Code** installieren: \n", + "3. im VS Code Editor die **Julia language extension** installieren: \n", + "\n", + "Einstieg:\n", + "\n", + "- In VS Code eine neue Datei mit der Endung `.jl` anlegen\n", + "- Julia-Code schreiben\n", + "- {{< kbd Shift-Enter >}} oder {{< kbd Ctrl-Enter >}} am Ende einer Anweisung oder eines Blocks startet ein Julia-REPL, Code wird ins REPL kopiert und ausgeführt \n", + "- [Tastenbelegungen für VS Code](https://code.visualstudio.com/docs/getstarted/keybindings#_keyboard-shortcuts-reference)\n", + "und [Julia in VS Code](https://www.julia-vscode.org/docs/stable/userguide/keybindings/)\n", + "\n", + "\n", + "\n", + "## Arbeiten auf dem [Jupyterhub-Webserver](https://misun103.mathematik.uni-leipzig.de/)\n", + "\n", + "### Jupyterhub & Jupyter\n", + "\n", + "- [Jupyterhub](https://de.wikipedia.org/wiki/Project_Jupyter) ist ein Multi-User-Server für Jupyter.\n", + "- Jupyter ist eine web-basierte interaktive Programmierumgebung, die\n", + "- ursprünglich in und für Python geschrieben, inzwischen eine\n", + " Vielzahl von Programmiersprachen nutzen kann.\n", + "- In Jupyter bearbeitet man sogenannte *notebooks*. Das sind strukturiere Textdateien (JSON), erkennbar an der Dateiendung \n", + " `*.ipynb`.\n", + "\n", + "Unser Jupyterhub-Server: \n", + "\n", + "Nach dem Einloggen in Jupyterhub erscheint ein Dateimanager:\n", + "\n", + "![Jupyterhub Dateimanager](../images/notebook001.png)\n", + "\n", + "Mit diesem kann man:\n", + "\n", + "- vorhandene *notebooks* öffnen,\n", + "- neue *notebooks* anlegen,\n", + "- Dateien, z.B. *notebooks*, vom lokalen Rechner hochladen,\n", + "- die Sitzung mit `Logout` beenden (bitte nicht vergessen!). \n", + "\n", + "### Jupyter notebooks\n", + "\n", + "![Jupyter Notebook](../images/notebook003.png)\n", + "\n", + "\n", + "*Notebooks* bestehen aus Zellen. Zellen können \n", + "\n", + "- Code oder \n", + "- Text/Dokumentation (Markdown) \n", + "\n", + "enthalten. In Textzellen können mit die Auszeichnungssprache [Markdown](https://de.wikipedia.org/wiki/Markdown) zur Formatierung und LaTeX für mathematische Gleichungen verwendet werden. \n", + "\n", + "Es sei empfohlen, die Punkte `User Interface Tour` und `Keyboard Shortcuts` im `Help`-Menü anzuschauen. Die Zelle, die man gerade bearbeitet, kann im `command mode` oder `edit mode` sein. \n", + "\n", + "\n", + "\n", + "```{html}\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
Einige Kommandos
command modeedit mode
Mode aktivierenESC
\n", + "```\n", + "\n", + "\n", + "\n", + "| | *command mode* | *edit mode* |\n", + "|:-------|:---------------:|:-----------:|\n", + "| Mode aktivieren | `ESC` | Doppelklick oder `Enter` in Zelle |\n", + "| neue Zelle | `b` | `Alt-Enter` |\n", + "| Zelle löschen | `dd` | |\n", + "| Notebook speichern | `s` | `Ctrl-s` |\n", + "\n", + "\n", + "\n", + "- Notebook speichern:\n", + "\n", + " - `Ctrl-s` in Edit Mode\n", + " - `s` in Command mode\n", + " - `Menu -> File -> Save & Checkpoint`\n", + " - `Menu -> File -> Rename`: Umbenennen (falls es noch\n", + " \\\"Untitled1\\\" heißt) `
`{=html}`
`{=html}\n", + "\n", + "- Notebook schließen:\n", + "\n", + " - `Menu -> File -> Close & Halt` `
`{=html}`
`{=html}\n", + "\n", + "- Ausführen von Julia:\n", + "\n", + " - `Ctrl-Enter`: Run cell\n", + " - `Shift-Enter`: Run cell, move to next cell\n", + " - `Alt-Enter`: run cell, insert new cell below\n", + "\n", + "\n", + "\n", + "bla backslash\n", + "\n", + "![](../images/notebook002.png)\n", + "\n", + "bla backslash\n", + "\n", + "\n", + "------------------------------------------------------------------------\n", + "\n", + "Wenn eine Zelle \\\"arbeitet\\\", wird ihre Zellen-Nummer zu einem `*` und\n", + "die `kernel busy`-Anzeige (Voller schwarzer Punkt oben rechts neben der\n", + "Julia-Version) erscheint. Falls das zu lange dauert (ein *infinite loop*\n", + "ist schnell programmiert), dann\n", + "\n", + "- `Menu -> Kernel -> Interrupt` anklicken; falls das wirkungslos ist,\n", + "- `Menu -> Kernel -> Restart` anklicken.\n", + "\n", + "Danach müssen alle Zellen, die weiterhin benötigte Definitionen,\n", + "`using`-Anweisungen etc enthalten, wieder ausgeführt werden!\n", + "\n", + "------------------------------------------------------------------------\n", + "\n", + "**Am Ende der Arbeit bitte immer:**\n", + "\n", + "- `Menu -> File -> Save & Checkpoint`\n", + "- `Menu -> File -> Close & Halt`\n", + "- `Logout`\n", + ":::\n", + "\n", + "::: {#73820119 .cell .markdown}\n", + "#### Markdown-Zellen\n", + "\n", + "neben den üblichen Markdown-Elementen können auch diese auch\n", + "`HTML`-Anweisungen und Mathematische Formeln in LaTeX-Form enthalten.\n", + "LaTeX-Formeln werden in `$...$` oder `$$...$$` (Display-Form)\n", + "eingeschlossen.\n", + ":::\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/example.ipynb b/nb/example.ipynb new file mode 100644 index 0000000..81caba6 --- /dev/null +++ b/nb/example.ipynb @@ -0,0 +1,146 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "1847e5bc", + "metadata": {}, + "source": [ + "# Some Julia Code\n", + "\n", + "\n", + "1. ?forvarianrte\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fd1a489b", + "metadata": {}, + "outputs": [], + "source": [ + "?for" + ] + }, + { + "cell_type": "markdown", + "id": "62aee612", + "metadata": {}, + "source": [ + "## Einfache rechnerei\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "23afd224", + "metadata": {}, + "outputs": [], + "source": [ + "2^33+33" + ] + }, + { + "cell_type": "markdown", + "id": "d1f050b2", + "metadata": {}, + "source": [ + "## colored console graphs produced by `Benchmarktools.jl`\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a9b6a7c8", + "metadata": {}, + "outputs": [], + "source": [ + "using BenchmarkTools\n", + "\n", + "@benchmark sum(rand(1000))" + ] + }, + { + "cell_type": "markdown", + "id": "948d948e", + "metadata": {}, + "source": [ + "## structure of floating point numbers\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fbe94ce0", + "metadata": {}, + "outputs": [], + "source": [ + "function printbitsf64(x::Float64)\n", + " s = bitstring(x)\n", + " printstyled(s[1], color = :blue, reverse=true)\n", + " printstyled(s[2:12], color = :green, reverse=true)\n", + " printstyled(s[13:end], color=:red, bold=true, reverse=true)\n", + " print(\"\\n\")\n", + "end\n", + "\n", + "printbitsf64(27.56640625)" + ] + }, + { + "cell_type": "markdown", + "id": "611f43fa", + "metadata": {}, + "source": [ + "### illustrate machine epsilon...\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "294f9e7e", + "metadata": {}, + "outputs": [], + "source": [ + "Eps=0.5\n", + "while 1 != 1 + Eps\n", + " Eps /= 2\n", + " printbitsf64(1+Eps)\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "34e578b1", + "metadata": {}, + "source": [ + "### ... some ugly colors\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9771dbc3", + "metadata": {}, + "outputs": [], + "source": [ + "function printbits2f64(x::Float64)\n", + " s = bitstring(x)\n", + " printstyled(s[1], color = 142, reverse=true)\n", + " printstyled(s[2:12], color = 190, reverse=false, underline=true)\n", + " printstyled(s[13:end], color= 27, bold=true, reverse=true)\n", + " print(\"\\n\")\n", + "end\n", + "\n", + "printbits2f64(27.56640625)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/first_contact.ipynb b/nb/first_contact.ipynb new file mode 100644 index 0000000..d59d129 --- /dev/null +++ b/nb/first_contact.ipynb @@ -0,0 +1,628 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "e009ef80", + "metadata": {}, + "source": [ + "# First Contact\n", + "\n", + "Dieses Kapitel soll beim 'Loslegen' helfen. Es läßt viele Details weg und die Codebeispiele sind oft eher suboptimal. \n", + "\n", + "\n", + "## Julia als Taschenrechner\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b488cb23", + "metadata": {}, + "outputs": [], + "source": [ + "#| eval: true\n", + "#| echo: false\n", + "#| output: false\n", + "\n", + "using REPL, Markdown\n", + "\n", + "function mhelp(s,n,m)\n", + " helptxt = Core.eval(Main, REPL.helpmode(s))\n", + " helpstr=Markdown.plaininline(helptxt)\n", + " print(\"...\\n\", join(split(helpstr,'\\n')[n:m],'\\n'), \"\\n...\")\n", + "end;\n", + "\n", + "function Tab(s)\n", + " l = filter(x->startswith(x,s), REPL.doc_completions(s))\n", + " println.(l[2:end])\n", + " return # return nothing, since broadcast println produces empty vector\n", + "end\n", + "\n", + "▷ = |>\n", + "\n", + "# IJulia.set_verbose(true)" + ] + }, + { + "cell_type": "markdown", + "id": "76000398", + "metadata": {}, + "source": [ + "Berechne $\\qquad 12^{1/3} + \\frac{3\\sqrt{2}}{\\sin(0.5)-\\cos(\\frac{\\pi}{4})\\log(3)}+ e^5$\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0f9feb86", + "metadata": {}, + "outputs": [], + "source": [ + "12^(1/3) + 3sqrt(2) / (sin(.5) - cos(pi/4)*log(3)) + exp(5)" + ] + }, + { + "cell_type": "markdown", + "id": "3e9fad84", + "metadata": {}, + "source": [ + "Man beachte:\n", + "\n", + "- Potenzen schreibt man `a^b`.\n", + "- Die Konstante `pi` ist vordefiniert.\n", + "- `log()` ist der natürliche Logarithmus.\n", + "- Das Multiplikationszeichen `a*b` kann nach einer Zahl weggelassen werden, wenn eine Variable, Funktion oder Klammer folgt.\n", + "\n", + "\n", + "## Die wichtigsten Tasten: `Tab` und `?`\n", + "\n", + "Man drücke beim Programmieren immer wieder die Tabulatortaste, sobald 2...3 Buchstaben eines Wortes getippt sind. Es werden dann mögliche Ergänzungen angezeigt bzw. ergänzt, wenn die Ergänzung eindeutig ist. Das spart Zeit und bildet ungemein:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "734300ba", + "metadata": {}, + "outputs": [], + "source": [ + "lo = \"lo\" #| hide_line\n", + "lo ▷ Tab" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "155bc575", + "metadata": {}, + "outputs": [], + "source": [ + "pri = \"pri\" #| hide_line\n", + "pri ▷ Tab" + ] + }, + { + "cell_type": "markdown", + "id": "ba74dc32", + "metadata": {}, + "source": [ + "Die eingebaute Julia-Hilfe `?name` zu allen Funktionen und Konstrukten ist sehr umfassend. Hier ein eher kurzes Beispiel: \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1b941a97", + "metadata": {}, + "outputs": [], + "source": [ + "?for" + ] + }, + { + "cell_type": "markdown", + "id": "c8f7da7b", + "metadata": {}, + "source": [ + ":::{.content-hidden unless-format=\"xxx\"}\n", + "\n", + "::: {.cell }\n", + "``` {.julia .cell-code}\n", + "?for\n", + "```\n", + "\n", + "::: {.cell-output .cell-output-stdout}\n", + "```\n", + "search: for foreach foldr floor mapfoldr factorial EOFError OverflowError\n", + "\n", + "for loops repeatedly evaluate a block of statements while iterating over a sequence of values.\n", + "\n", + "Examples\n", + "\n", + "julia> for i in [1, 4, 0]\n", + " println(i)\n", + " end\n", + "1\n", + "4\n", + "0\n", + "\n", + "```\n", + ":::\n", + ":::\n", + ":::\n", + "\n", + "\n", + "## Variablen und Zuweisungen\n", + "\n", + "Variablen entstehen durch Zuweisung *(assignment)* mit dem Zuweisungsoperator `=` . Danach können sie in weiteren Anweisungen verwendet werden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "da1dc7ec", + "metadata": {}, + "outputs": [], + "source": [ + "x = 1 + sqrt(5) \n", + "y = x / 2" + ] + }, + { + "cell_type": "markdown", + "id": "37b29541", + "metadata": {}, + "source": [ + "Im interaktiven Betrieb zeigt Julia das Ergebnis der letzten Operation an.\n", + "\n", + ":::{.callout-note .titlenormal}\n", + "Zuweisungen sind keine mathematischen Gleichungen. Die Semantik des Zuweisungsoperators (Gleichheitszeichens) ist: \n", + "\n", + "- berechne die rechte Seite und\n", + "- weise das Ergebnis der linken Seite zu.\n", + "\n", + "Ausdrücke wie `x + y = sin(2)` sind daher unzulässig. Links darf nur ein Variablenname stehen.\n", + ":::\n", + "\n", + "\n", + "## Datentypen\n", + "\n", + "Julia ist eine [stark typisierte](https://de.wikipedia.org/wiki/Starke_Typisierung) Sprache. Alle Objekte haben einen Typ. \n", + "So gibt es unter anderem die Basistypen \n", + "\n", + "- Ganze Zahlen *(integers)*,\n", + "- Gleitkommazahlen *(floating point numbers)*,\n", + "- Zeichenketten *(strings)* und \n", + "- Wahrheitswerte *(booleans)*.\n", + "\n", + "Den Typ einer Variablen kann man mit der Funktion `typeof()` ermitteln. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "173f7324", + "metadata": {}, + "outputs": [], + "source": [ + "#| warning: true\n", + "#| error: true\n", + "for x ∈ (42, 12.0, 3.3e4, \"Hallo!\", true)\n", + " println(\"x = \", x, \" ..... Typ: \", typeof(x))\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "13a8984f", + "metadata": {}, + "source": [ + "Die Standard-Gleitkommazahl hat eine Länge von 64 Bit, entspricht also einer `double` in C/C++/Java.\n", + "\n", + "Julia ist eine [dynamisch typisierte](https://de.wikipedia.org/wiki/Dynamische_Typisierung) Sprache. \n", + "Variablen haben keinen Typ. Sie sind typlose Referenzen (Zeiger) auf Objekte. \n", + "Wenn man vom „Typ einer Variablen“ spricht, meint man den Typ des Objektes, das der Variablen gerade zugewiesen ist. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cd3b3e96", + "metadata": {}, + "outputs": [], + "source": [ + "x = sqrt(2)\n", + "\n", + "println( typeof(x), \" - Wert von x = $x\" )\n", + "\n", + "x = \"Jetzt bin ich keine Gleitkommazahl mehr!\"\n", + "\n", + "println( typeof(x), \" - Wert von x = $x\" )" + ] + }, + { + "cell_type": "markdown", + "id": "eae463bf", + "metadata": {}, + "source": [ + "## Druckanweisungen\n", + "Die Funktion `println()` unterscheidet sich von `print()` dadurch, dass sie am Ende einen Zeilenvorschub ausgibt.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "df98312b", + "metadata": {}, + "outputs": [], + "source": [ + "print(y)\n", + "print(\"...die Zeile geht weiter...\")\n", + "print(\"immernoch...\")\n", + "println(y)\n", + "println(\"Neue Zeile\")\n", + "println(\"Neue Zeile\")" + ] + }, + { + "cell_type": "markdown", + "id": "b74dcb3f", + "metadata": {}, + "source": [ + "Beide Funkionen können als Argument eine Liste von *strings* und Variablen bekommen. Man kann Variablen auch in *strings* einbetten, indem man dem Variablennamen ein Dollarzeichen voranstellt *(string interpolation)*.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3b76d855", + "metadata": {}, + "outputs": [], + "source": [ + "x = 23\n", + "y = 3x + 5\n", + "zz = \"Fertig!\"\n", + "println(\"x= \", x, \" ...und y= \", y, \"...\", zz) # 1. Variante\n", + "println(\"x= $x ...und y= $y...$zz\") # Variante mit string interpolation" + ] + }, + { + "cell_type": "markdown", + "id": "c06fc5da", + "metadata": {}, + "source": [ + ":::{.callout-note .titlenormal collapse=true icon=false }\n", + "## Wenn man ein Dollarzeichen drucken will...\n", + "\n", + "muss man einen *backslash* voranstellen. Wenn man einen *backslash* drucken will, muss man ihn verdoppeln.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "00a46544", + "metadata": {}, + "outputs": [], + "source": [ + "println(\"Ein Dollar: 1\\$ und drei backslashs: \\\\\\\\\\\\ \")" + ] + }, + { + "cell_type": "markdown", + "id": "3ba46a2c", + "metadata": {}, + "source": [ + ":::\n", + "\n", + "## Funktionen\n", + "Funktionsdefinitionen beginnen mit dem Schlüsselwort `function` und enden mit dem Schlüsselwort `end`. In der Regel haben sie eine oder mehrere Argumente und geben beim Aufruf ein berechnetes Objekt mit der `return`-Anweisung zurück.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6e83b8e2", + "metadata": {}, + "outputs": [], + "source": [ + "function hypotenuse(a, b) # heute besonders umständlich\n", + " c2 = a^2 + b^2\n", + " c = sqrt(c2)\n", + " return c \n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "6ae72d3a", + "metadata": {}, + "source": [ + "Nach ihrer Definition kann die Funktion benutzt (aufgerufen) werden. Die in der Definition verwendeten Variablen `a,b,c,c2` sind lokale Variablen und stehen außerhalb der Funktionsdefinition nicht zur Verfügung. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2b68ec32", + "metadata": {}, + "outputs": [], + "source": [ + "#| error: true\n", + "x = 3\n", + "z = hypotenuse(x, 4)\n", + "println(\"z = $z\")\n", + "println(\"c = $c\")" + ] + }, + { + "cell_type": "markdown", + "id": "d62b25c3", + "metadata": {}, + "source": [ + "Sehr einfache Funktionen können auch als Einzeiler definiert werden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "436bf54a", + "metadata": {}, + "outputs": [], + "source": [ + "hypotenuse(a, b) = sqrt(a^2+b^2)" + ] + }, + { + "cell_type": "markdown", + "id": "13485711", + "metadata": {}, + "source": [ + "## Tests\n", + "Tests liefern einen Wahrheitswert zurück. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fbfc37d5", + "metadata": {}, + "outputs": [], + "source": [ + "x = 3^2\n", + "x < 2^3" + ] + }, + { + "cell_type": "markdown", + "id": "d43e3179", + "metadata": {}, + "source": [ + "Neben den üblichen arithmetischen Vergleichen `==, !=, <, <= ,> ,>=` \n", + "gibt es noch viele andere Tests. Natürlich kann man das Ergebnis eines Tests auch einer Variablen zuweisen, welche dann vom Typ `Bool` ist. Die logischen Operatoren `&&`, `||` und Negation `!` können in Tests verwendet werden. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7e289c8e", + "metadata": {}, + "outputs": [], + "source": [ + "test1 = \"Auto\" in [\"Fahrrad\", \"Auto\", \"Bahn\"]\n", + "test2 = x == 100 || !(x <= 30 && x > 8)\n", + "test3 = startswith(\"Lampenschirm\", \"Lamp\") \n", + "println(\"$test1 $test2 $test3\")" + ] + }, + { + "cell_type": "markdown", + "id": "0ca8fc84", + "metadata": {}, + "source": [ + "## Verzweigungen\n", + "Verzweigungen (bedingte Anweisungen) haben die Form \n", + "\n", + "```default\n", + "if \n", + " \n", + " \n", + " ...\n", + "end\n", + "``` \n", + "\n", + "\n", + "Ein `else`-Zweig und `elseif`-Zweige sind möglich.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6ab36f93", + "metadata": {}, + "outputs": [], + "source": [ + "x = sqrt(100)\n", + "\n", + "if x > 20\n", + " println(\"Seltsam!\")\n", + "else\n", + " println(\"OK\")\n", + " y = x + 3\n", + "end " + ] + }, + { + "cell_type": "markdown", + "id": "3247aa40", + "metadata": {}, + "source": [ + "Einrückungen verbessern die Lesbarkeit, sind aber fakultativ. Zeilenumbrüche trennen Anweisungen. Das ist auch durch Semikolon möglich. Obiger Codeblock ist für Julia identisch zu folgender Zeile:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6b6f3846", + "metadata": {}, + "outputs": [], + "source": [ + "# Bitte nicht so programmieren! Sie werden es bereuen!\n", + "x=sqrt(100); if x > 20 println(\"Seltsam!\") else println(\"OK\"); y = x + 3 end " + ] + }, + { + "cell_type": "markdown", + "id": "4f8718ea", + "metadata": {}, + "source": [ + "Es wird dringend empfohlen, von Anfang an den eigenen Code übersichtlich mit sauberen Einrückungen zu formatieren!\n", + "\n", + "\n", + "## Einfache `for`-Schleifen\n", + "\n", + "zum wiederholten Abarbeiten von Anweisungen haben die Form\n", + "```default\n", + "for = Start:Ende\n", + " \n", + " \n", + " ...\n", + "end\n", + "```\n", + "Beispiel:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e2518e65", + "metadata": {}, + "outputs": [], + "source": [ + "sum = 0\n", + "for i = 1:100\n", + " sum = sum + i\n", + "end \n", + "sum" + ] + }, + { + "cell_type": "markdown", + "id": "3fa36879", + "metadata": {}, + "source": [ + "## Arrays\n", + "1-dimensionale Arrays (Vektoren) sind eine einfache Form von Containern. Man kann sie mit echigen Klammern anlegen\n", + "und auf die Elemente per Index zugreifen. Die Indizierung beginnt mit 1. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cf56b9fc", + "metadata": {}, + "outputs": [], + "source": [ + "v = [12, 33.2, 17, 19, 22]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2e6ae1f4", + "metadata": {}, + "outputs": [], + "source": [ + "typeof(v)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "18a71a80", + "metadata": {}, + "outputs": [], + "source": [ + "v[1] = v[4] + 10\n", + "v" + ] + }, + { + "cell_type": "markdown", + "id": "6833c60b", + "metadata": {}, + "source": [ + "Man kann leere Vektoren anlegen und sie verlängern.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "49a0d406", + "metadata": {}, + "outputs": [], + "source": [ + "v = [] # leerer Vektor\n", + "push!(v, 42)\n", + "push!(v, 13)\n", + "v" + ] + }, + { + "cell_type": "markdown", + "id": "ca3e6d8e", + "metadata": {}, + "source": [ + ":::{.callout-note icon=\"false\" .titlenormal collapse=\"true\" font-variant-ligatures=\"no-contextual\" }\n", + "\n", + "## Nachtrag: wie die Wirkung der Tab-Taste auf dieser Seite simuliert wurde...\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "087b10f7", + "metadata": {}, + "outputs": [], + "source": [ + "using REPL\n", + "\n", + "function Tab(s)\n", + " l = filter(x->startswith(x,s), REPL.doc_completions(s))\n", + " println.(l[2:end])\n", + " return # return nothing, since broadcast println produces empty vector\n", + "end\n", + "\n", + "▷ = |> # https://docs.julialang.org/en/v1/manual/functions/#Function-composition-and-piping\n", + "\n", + "pri = \"pri\";" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0b8be63e", + "metadata": {}, + "outputs": [], + "source": [ + "pri ▷ Tab" + ] + }, + { + "cell_type": "markdown", + "id": "cd067cf0", + "metadata": {}, + "source": [ + ":::" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/first_contact.nbconvert.ipynb b/nb/first_contact.nbconvert.ipynb new file mode 100644 index 0000000..865f4a1 --- /dev/null +++ b/nb/first_contact.nbconvert.ipynb @@ -0,0 +1,493 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "cd3f6abe", + "metadata": {}, + "source": [ + "# First Contact\n", + "\n", + "Dieses Kapitel enthält einige \"pädagogische Halbwahrheiten\", d.h., es vereinfacht und lässt Details weg.\n", + "\n", + "## Julia als Taschenrechner\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0dbe789e", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:34.132000Z", + "iopub.status.busy": "2023-03-08T16:05:33.746000Z", + "iopub.status.idle": "2023-03-08T16:05:37.286000Z", + "shell.execute_reply": "2023-03-08T16:05:37.175000Z" + } + }, + "outputs": [], + "source": [ + "#| eval: true\n", + "#| echo: false\n", + "#| output: false\n", + "IJulia.set_verbose(true)" + ] + }, + { + "cell_type": "markdown", + "id": "a2b52996", + "metadata": {}, + "source": [ + "Berechne $\\qquad 12^{1/3} + \\frac{3\\sqrt{2}}{\\sin(0.5)-\\cos(\\frac{\\pi}{4})\\log(3)}+ e^5$\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c831420f", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:37.336000Z", + "iopub.status.busy": "2023-03-08T16:05:37.335000Z", + "iopub.status.idle": "2023-03-08T16:05:37.620000Z", + "shell.execute_reply": "2023-03-08T16:05:37.618000Z" + } + }, + "outputs": [], + "source": [ + "12^(1/3) + 3sqrt(2) / (sin(.5) - cos(pi/4)*log(3)) + exp(5)" + ] + }, + { + "cell_type": "markdown", + "id": "a9f3359b", + "metadata": {}, + "source": [ + "Man beachte:\n", + "\n", + "- Potenzen schreibt man `a^b`.\n", + "- Die Konstante `pi` ist vordefiniert.\n", + "- `log()` ist der natürliche Logarithmus.\n", + "- Das Multiplikationszeichen `a*b` kann nach einer Zahl weggelassen werden, wenn eine Variable, Funktion oder Klammer folgt.\n", + "\n", + "\n", + "## Variablen und Zuweisungen\n", + "\n", + "Variablen entstehen durch Zuweisung *(assignment)*. Durch Zuweisung definierte Variablen können danach in weiteren Anweisungen verwendet werden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5ff20c70", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:37.625000Z", + "iopub.status.busy": "2023-03-08T16:05:37.624000Z", + "iopub.status.idle": "2023-03-08T16:05:37.657000Z", + "shell.execute_reply": "2023-03-08T16:05:37.655000Z" + } + }, + "outputs": [], + "source": [ + "x = 1 + sqrt(5) \n", + "y = x / 2" + ] + }, + { + "cell_type": "markdown", + "id": "e7db7bb5", + "metadata": {}, + "source": [ + ":::{.indentb}\n", + "Zuweisungen sind keine mathematischen Gleichungen. Die Semantik des Zuweisungsoperators (d.h., des Gleichheitszeichens) ist: \n", + "\n", + "- berechne die rechte Seite und\n", + "- weise das Ergebnis der linken Seite zu.\n", + "\n", + "Ausdrücke wie `x + y = sin(2)` sind daher unzulässig, links darf nur ein Variablenname stehen.\n", + ":::\n", + "\n", + "\n", + "## Datentypen\n", + "\n", + "Julia ist eine [stark typisierte](https://de.wikipedia.org/wiki/Starke_Typisierung) Sprache. Alle Objekte haben einen Typ. \n", + "So gibt es unter anderem die Basistypen \n", + "\n", + "- Ganze Zahlen *(integers)*,\n", + "- Gleitkommazahlen *(floating point numbers)*,\n", + "- Zeichenketten *(strings)* und \n", + "- Wahrheitswerte *(booleans)*.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ae3af394", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:37.662000Z", + "iopub.status.busy": "2023-03-08T16:05:37.661000Z", + "iopub.status.idle": "2023-03-08T16:05:38.219000Z", + "shell.execute_reply": "2023-03-08T16:05:38.217000Z" + } + }, + "outputs": [], + "source": [ + "#| warning: true\n", + "#| error: true\n", + "for x ∈ (42, 12.0, 3.3e4, \"Hallo!\", true)\n", + " println(\"x = \", x, \" ..... Typ: \", typeof(x))\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "213bef1c", + "metadata": {}, + "source": [ + "Die Standard-Gleitkommazahl hat eine Länge von 64 Bit, entspricht also einer `double` in C/C++/Java.\n", + "\n", + "Julia ist eine [dynamisch typisierte](https://de.wikipedia.org/wiki/Dynamische_Typisierung) Sprache. \n", + "Variablen haben keinen Typ. Sie sind typlose Referenzen (Zeiger) auf Objekte. \n", + "Wenn man vom „Typ einer Variablen“ spricht, meint man den Typ des Objektes, das der Variablen gerade zugewiesen ist. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2d6c0d1b", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:38.225000Z", + "iopub.status.busy": "2023-03-08T16:05:38.223000Z", + "iopub.status.idle": "2023-03-08T16:05:38.316000Z", + "shell.execute_reply": "2023-03-08T16:05:38.315000Z" + } + }, + "outputs": [], + "source": [ + "x = sqrt(2)\n", + "println( typeof(x) )\n", + "x = \"Jetzt bin ich keine Gleitkommazahl mehr!\"\n", + "println( typeof(x) )" + ] + }, + { + "cell_type": "markdown", + "id": "f2329446", + "metadata": {}, + "source": [ + "## Druckanweisungen\n", + "Die Funktion `println()` unterscheidet sich von `print()` dadurch, dass sie am Ende einen Zeilenvorschub ausgibt.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d4a7260d", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:38.321000Z", + "iopub.status.busy": "2023-03-08T16:05:38.320000Z", + "iopub.status.idle": "2023-03-08T16:05:38.369000Z", + "shell.execute_reply": "2023-03-08T16:05:38.367000Z" + } + }, + "outputs": [], + "source": [ + "print(y)\n", + "print(\"...die Zeile geht weiter...\")\n", + "print(\"immernoch...\")\n", + "println(y)\n", + "println(\"Neue Zeile\")\n", + "println(\"Neue Zeile\")" + ] + }, + { + "cell_type": "markdown", + "id": "dccc9577", + "metadata": {}, + "source": [ + "Beide Funkionen können als Argument eine Liste von *strings* und Variablen bekommen. Man kann Variablen auch in *strings* einbetten, indem man dem Variablennamen ein Dollarzeichen voranstellt *(string interpolation)*.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7a2116bd", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:38.374000Z", + "iopub.status.busy": "2023-03-08T16:05:38.373000Z", + "iopub.status.idle": "2023-03-08T16:05:38.402000Z", + "shell.execute_reply": "2023-03-08T16:05:38.400000Z" + } + }, + "outputs": [], + "source": [ + "x = 23\n", + "y = 3x + 5\n", + "zz = \"Fertig!\"\n", + "println(\"x= \", x, \" ...und y= \", y, \"...\", zz) # 1. Variante\n", + "println(\"x= $x ...und y= $y...$zz\") # Variante mit string interpolation" + ] + }, + { + "cell_type": "markdown", + "id": "ae5eaf6f", + "metadata": {}, + "source": [ + ":::{.indentb}\n", + "Wenn man ein Dollarzeichen drucken will, muss man einen *backslash* voranstellen. Wenn man einen *backslash* drucken will, muss man ihn verdoppeln.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f7d26a60", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:38.407000Z", + "iopub.status.busy": "2023-03-08T16:05:38.406000Z", + "iopub.status.idle": "2023-03-08T16:05:38.434000Z", + "shell.execute_reply": "2023-03-08T16:05:38.432000Z" + } + }, + "outputs": [], + "source": [ + "println(\"Ein Dollar: 1\\$ und drei backslashs: \\\\\\\\\\\\ \")" + ] + }, + { + "cell_type": "markdown", + "id": "f40cee12", + "metadata": {}, + "source": [ + ":::\n", + "\n", + "## Funktionen\n", + "Funktionsdefinitionen beginnen mit dem Schlüsselwort `function` und enden mit dem Schlüsselwort `end`. In der Regel haben sie eine oder mehrere Argumente und geben beim Aufruf ein berechnetes Objekt mit der `return`-Anweisung zurück.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b6574086", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:38.439000Z", + "iopub.status.busy": "2023-03-08T16:05:38.438000Z", + "iopub.status.idle": "2023-03-08T16:05:38.633000Z", + "shell.execute_reply": "2023-03-08T16:05:38.631000Z" + } + }, + "outputs": [], + "source": [ + "function hypotenuse(a, b)\n", + " c2 = a^2 + b^2\n", + " c = sqrt(c2)\n", + " return c \n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "d70272a0", + "metadata": {}, + "source": [ + "Nach ihrer Definition kann die Funktion benutzt (aufgerufen) werden. Die in der Definition verwendeten Variablen `a,b,c,c2` sind lokale Variablen und stehen außerhalb der Funktionsdefinition nicht zur Verfügung. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5df842f6", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:38.638000Z", + "iopub.status.busy": "2023-03-08T16:05:38.636000Z", + "iopub.status.idle": "2023-03-08T16:05:39.346000Z", + "shell.execute_reply": "2023-03-08T16:05:39.344000Z" + } + }, + "outputs": [], + "source": [ + "#| error: true\n", + "x = 3\n", + "z = hypotenuse(x, 4)\n", + "println(z)\n", + "println(c)" + ] + }, + { + "cell_type": "markdown", + "id": "dc012140", + "metadata": {}, + "source": [ + "Sehr einfache Funktionen können auch kürzer als Einzeiler definiert werden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6aec78b0", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:39.351000Z", + "iopub.status.busy": "2023-03-08T16:05:39.350000Z", + "iopub.status.idle": "2023-03-08T16:05:39.381000Z", + "shell.execute_reply": "2023-03-08T16:05:39.379000Z" + } + }, + "outputs": [], + "source": [ + "hypotenuse(a, b) = sqrt(a^2+b^2)" + ] + }, + { + "cell_type": "markdown", + "id": "d57bc14f", + "metadata": {}, + "source": [ + "## Tests\n", + "Tests liefern einen Wahrheitswert zurück. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0e42d502", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:39.387000Z", + "iopub.status.busy": "2023-03-08T16:05:39.386000Z", + "iopub.status.idle": "2023-03-08T16:05:39.420000Z", + "shell.execute_reply": "2023-03-08T16:05:39.418000Z" + } + }, + "outputs": [], + "source": [ + "x = 2^8\n", + "x < 3" + ] + }, + { + "cell_type": "markdown", + "id": "814e4e5c", + "metadata": {}, + "source": [ + "Neben den üblichen arithmetischen Vergleichen `==, !=, <, <= ,> ,>=` \n", + "gibt es noch viele andere Tests. Natürlich kann man das Ergebnis eines Tests auch einer Variablen zuweisen, welche dann vom Typ `Bool` ist. Die logischen Operatoren `&&`, `||` und Negation `!` können in Tests verwendet werden. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3899c1c9", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:39.425000Z", + "iopub.status.busy": "2023-03-08T16:05:39.424000Z", + "iopub.status.idle": "2023-03-08T16:05:39.479000Z", + "shell.execute_reply": "2023-03-08T16:05:39.477000Z" + } + }, + "outputs": [], + "source": [ + "test1 = \"Auto\" in [\"Fahrrad\", \"Auto\", \"Bahn\"]\n", + "test2 = x == 100 || x in [1,2,4,7]\n", + "test3 = startswith(\"Lampenschirm\", \"Lamp\") \n", + "println(\"$test1 $test2 $test3\")" + ] + }, + { + "cell_type": "markdown", + "id": "067897ae", + "metadata": {}, + "source": [ + "## Verzweigungen\n", + "Verzweigungen (bedingte Anweisungen) haben die Form `if end`. Ein `else`-Zweig ist möglich.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "34db87a5", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:39.484000Z", + "iopub.status.busy": "2023-03-08T16:05:39.483000Z", + "iopub.status.idle": "2023-03-08T16:05:39.518000Z", + "shell.execute_reply": "2023-03-08T16:05:39.516000Z" + } + }, + "outputs": [], + "source": [ + "x = sqrt(100)\n", + "\n", + "if x > 20\n", + " println(\"Seltsam!\")\n", + "else\n", + " println(\"OK\")\n", + " y = x + 3\n", + "end " + ] + }, + { + "cell_type": "markdown", + "id": "2c0677f6", + "metadata": {}, + "source": [ + "Einrückungen und Zeilenumbrüche verbessern die Lesbarkeit, sind aber fakultativ. Anweisungen können auch durch Semikolon getrennt werden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3b169201", + "metadata": { + "execution": { + "iopub.execute_input": "2023-03-08T16:05:39.523000Z", + "iopub.status.busy": "2023-03-08T16:05:39.521000Z", + "iopub.status.idle": "2023-03-08T16:05:39.554000Z", + "shell.execute_reply": "2023-03-08T16:05:39.552000Z" + } + }, + "outputs": [], + "source": [ + "if x > 20 println(\"Seltsam!\") else println(\"OK\"); y = x + 3 end " + ] + }, + { + "cell_type": "markdown", + "id": "f225e8eb", + "metadata": {}, + "source": [ + "## Einfache Schleifen\n", + "\n", + "\n", + "\n", + "## Arrays\n", + "1-dimensionale Arrays (Vektoren) sind eine einfache Form von Containern. Man kann sie mit echigen Klammern anlegen\n", + "\n", + "\n", + "und auf die Elemente per Index zugreifen. Die Indizierung beginnt mit 1. \n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/intro.ipynb b/nb/intro.ipynb new file mode 100644 index 0000000..1da6084 --- /dev/null +++ b/nb/intro.ipynb @@ -0,0 +1,114 @@ +{ + "cells": [ + { + "cell_type": "raw", + "id": "10c7d783", + "metadata": {}, + "source": [ + "---\n", + "title: Introduction\n", + "---" + ] + }, + { + "cell_type": "markdown", + "id": "f2e8fc05", + "metadata": {}, + "source": [ + "## Noch eine Programmiersprache?\n", + "\n", + "Die Ziele der Schöpfer von Julia kann man in [Why we created Julia](https://julialang.org/blog/2012/02/why-we-created-julia/) nachlesen. Kurzfassung:\n", + "\n", + "“We want a language that is\n", + "\n", + "open source\n", + "with the speed of C\n", + "obvious, familiar mathematical notation like Matlab\n", + "as usable for general programming as Python\n", + "as easy for statistics as R\n", + "as natural for string processing as Perl\n", + "as powerful for linear algebra as Matlab\n", + "as good at gluing programs together as the shell\n", + "dirt simple to learn, yet keeps the most serious hackers happy”\n", + "\n", + "\n", + "\"Wir wollen eine Sprache, die\n", + "\n", + "- *open source* ist \n", + "- die Geschwindigkeit von C hat \n", + "- obvious, familiar mathematical notation like Matlab\n", + "- as usable for general programming as Python\n", + "- as easy for statistics as R\n", + "- as natural for string processing as Perl\n", + "- as powerful for linear algebra as Matlab\n", + "- as good at gluing programs together as the shell\n", + "- dirt simple to learn, yet keeps the most serious hackers happy\"\n", + "\n", + "vs code: erzeuge eine Datei mit der Endung `.jl`, starte ein REPL mit dem Kommando \n", + "Alt-Enter am Ende einer Zeile oder Anweisung f\"uhrt dazu, dass die Anweisung \n", + "is REPL kopiert und ausgefuehrt wird\n", + "\n", + "alt-enter execute in julia Repl\n", + "shift-enter: ex. and move to next line\n", + "\n", + "die Erstinstallation von Paketen kann sehr lange dauern. \n", + "\n", + "im Jupyterhub sind die im Kurs nenötigten Pakete vorinstalliert. \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## colored console graphs produced by `Benchmarktools.jl`\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "62fcada8", + "metadata": {}, + "outputs": [], + "source": [ + "using BenchmarkTools\n", + "\n", + "@benchmark sum(rand(1000))" + ] + }, + { + "cell_type": "markdown", + "id": "00dc9599", + "metadata": {}, + "source": [ + "## structure of floating point numbers\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ccc6afab", + "metadata": {}, + "outputs": [], + "source": [ + "function printbitsf64(x::Float64)\n", + " s = bitstring(x)\n", + " printstyled(s[1], color = :blue, reverse=true)\n", + " printstyled(s[2:12], color = :green, reverse=true)\n", + " printstyled(s[13:end], color=:red, bold=true, reverse=true)\n", + " print(\"\\n\")\n", + "end\n", + "\n", + "printbitsf64(27.56640625)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/makie.ipynb b/nb/makie.ipynb new file mode 100644 index 0000000..229ff81 --- /dev/null +++ b/nb/makie.ipynb @@ -0,0 +1,77 @@ +{ + "cells": [ + { + "cell_type": "raw", + "id": "7d6e8e63", + "metadata": {}, + "source": [ + "---\n", + "title: makie\n", + "---" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fff03da7", + "metadata": {}, + "outputs": [], + "source": [ + "using CairoMakie\n", + "\n", + "\n", + "f = Figure()\n", + "Axis(f[1, 1])\n", + "\n", + "xs = 1:0.2:10\n", + "ys_low = -0.2 .* sin.(xs) .- 0.25\n", + "ys_high = 0.2 .* sin.(xs) .+ 0.25\n", + "\n", + "band!(xs, ys_low, ys_high)\n", + "band!(xs, ys_low .- 1, ys_high .-1, color = :red)\n", + "\n", + "f" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "242380da", + "metadata": {}, + "outputs": [], + "source": [ + "f = Figure()\n", + "Axis(f[1, 1])\n", + "\n", + "xs = LinRange(0, 10, 100)\n", + "ys = LinRange(0, 15, 100)\n", + "zs = [cos(x) * sin(y) for x in xs, y in ys]\n", + "\n", + "contour!(zs,levels=-1:0.1:1)\n", + "\n", + "f" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ff5c9a2d", + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax, hm = heatmap(randn(20, 20))\n", + "Colorbar(fig[1, 2], hm)\n", + "fig" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/numerictypes.ipynb b/nb/numerictypes.ipynb new file mode 100644 index 0000000..d407b74 --- /dev/null +++ b/nb/numerictypes.ipynb @@ -0,0 +1,1407 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "3a993968", + "metadata": {}, + "source": [ + "# Maschinenzahlen\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4f4dbb6a", + "metadata": {}, + "outputs": [], + "source": [ + "for x ∈ ( 3, 3.3e4, Int16(20), Float32(3.3e4), UInt16(9) )\n", + " @show x sizeof(x) typeof(x)\n", + " println()\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "82bbdd01", + "metadata": {}, + "source": [ + "## Ganze Zahlen *(integers)*\n", + "\n", + "Ganze Zahlen werden grundsätzlich als Bitmuster fester Länge gespeichert. Damit ist der Wertebereich endlich. \n", + "**Innerhalb dieses Wertebereichs** sind Addition, Subtraktion, Multiplikation und die Ganzzahldivision mit Rest \n", + "exakte Operationen ohne Rundungsfehler. \n", + "\n", + "Ganze Zahlen gibt es in den zwei Sorten `Signed` (mit Vorzeichen) und `Unsigned`, die man als Maschinenmodelle für ℤ bzw. ℕ auffassen kann.\n", + "\n", + "\n", + "### *Unsigned integers*\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ab84c4da", + "metadata": {}, + "outputs": [], + "source": [ + "subtypes(Unsigned)" + ] + }, + { + "cell_type": "markdown", + "id": "7f458fcd", + "metadata": {}, + "source": [ + "UInts sind Binärzahlen mit n=8, 16, 32, 64 oder 128 Bits Länge und einem entsprechenden Wertebereich von\n", + "$$\n", + "0 \\le x < 2^n \n", + "$$\n", + "Sie werden im *scientific computing* eher selten verwendet. Bei hardwarenaher Programmierung dienen sie z.B. dem Umgang mit Binärdaten und Speicheradressen. Deshalb werden sie von Julia standardmäßig auch als Hexadezimalzahlen (mit Präfix `0x` und Ziffern `0-9a-f`) dargestellt.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3b6b30a0", + "metadata": {}, + "outputs": [], + "source": [ + "x = 0x0033efef\n", + "@show x typeof(x) Int(x)\n", + "\n", + "z = UInt(32)\n", + "@show z typeof(z);" + ] + }, + { + "cell_type": "markdown", + "id": "25774520", + "metadata": {}, + "source": [ + "### *Signed Integers* \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "341e9267", + "metadata": {}, + "outputs": [], + "source": [ + "subtypes(Signed)" + ] + }, + { + "cell_type": "markdown", + "id": "a8ea7009", + "metadata": {}, + "source": [ + "*Integers* haben den Wertebereich\n", + "$$\n", + "-2^{n-1} \\le x < 2^{n-1} \n", + "$$\n", + "\n", + "\n", + "In Julia sind ganze Zahlen standardmäßig 64 Bit groß:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "79490021", + "metadata": {}, + "outputs": [], + "source": [ + "x = 42\n", + "typeof(x)" + ] + }, + { + "cell_type": "markdown", + "id": "295048cd", + "metadata": {}, + "source": [ + "Sie haben daher den Wertebereich: \n", + "$$\n", + "-9.223.372.036.854.775.808 \\le x \\le 9.223.372.036.854.775.807\n", + "$$\n", + "\n", + "Negative Zahlen werden im Zweierkomplement dargestellt:\n", + "\n", + "$x \\Rightarrow -x$ entspricht: _flip all bits, then add 1_\n", + "\n", + "Das sieht so aus:\n", + "\n", + "::: {.content-visible when-format=\"html\"}\n", + "![Eine Darstellung des fiktiven Datentyps `Int4`](../images/Int4.png){width=50%}\n", + ":::\n", + "\n", + "::: {.content-visible when-format=\"pdf\"}\n", + "![Eine Darstellung des fiktiven Datentyps `Int4`](../images/Int4.png){width=50%}\n", + ":::\n", + "\n", + "Das höchstwertige Bit zeigt das Vorzeichen an. Sein „Umkippen“ entspricht allerdings nicht der Operation `x → -x`.\n", + "\n", + ":::{.callout-important}\n", + "Die gesamte Ganzzahlarithmetik ist eine __Arithmetik modulo $2^n$__\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "677353d7", + "metadata": {}, + "outputs": [], + "source": [ + "x = 2^62 - 10 + 2^62" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7da20d70", + "metadata": {}, + "outputs": [], + "source": [ + "x + 20" + ] + }, + { + "cell_type": "markdown", + "id": "2cdce6d7", + "metadata": {}, + "source": [ + "Keine Fehlermeldung, keine Warnung! Ganzzahlen fester Länge liegen nicht auf einer Geraden, sondern auf einem Kreis!\n", + "\n", + ":::\n", + "\n", + "Schauen wir uns ein paar *Integers* mal an:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "098d82f4", + "metadata": {}, + "outputs": [], + "source": [ + "using Printf\n", + "\n", + "for i in (1, 2, 7, -7, 2^50, -1, Int16(7), Int8(7))\n", + " s = bitstring(i)\n", + " t = typeof(i)\n", + " @printf \"%20i %-5s ⇒ %s\\n\" i t s \n", + "end " + ] + }, + { + "cell_type": "markdown", + "id": "388bed6e", + "metadata": {}, + "source": [ + "... und noch etwas mehr *introspection*:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e164bb25", + "metadata": {}, + "outputs": [], + "source": [ + "typemin(Int64), typemax(Int64)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2c94b3df", + "metadata": {}, + "outputs": [], + "source": [ + "typemin(UInt64), typemax(UInt64)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1d2f77c9", + "metadata": {}, + "outputs": [], + "source": [ + "typemin(Int8), typemax(Int8)" + ] + }, + { + "cell_type": "markdown", + "id": "74d88d56", + "metadata": {}, + "source": [ + "## Arithmetik ganzer Zahlen\n", + "\n", + "#### Addition, Multiplikation\n", + "Die Operationen `+`,`-`,`*` haben die übliche exakte Arithmetik **modulo $2^{64}$**.\n", + "\n", + "#### Potenzen `a^b`\n", + "\n", + "- Potenzen `a^n` werden für natürliche Exponenten `n` ebenfalls modulo $2^{64}$ exakt berechnet. \n", + "- Für negative Exponenten ist das Ergebnis eine Gleitkommazahl.\n", + "- `0^0` ist [selbstverständlich](https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero#cite_note-T4n3B-4) gleich 1.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "46b5e26a", + "metadata": {}, + "outputs": [], + "source": [ + "(-2)^63, 2^64, 3^(-3), 0^0 " + ] + }, + { + "cell_type": "markdown", + "id": "0187fb1e", + "metadata": {}, + "source": [ + "- Für natürliche Exponenten wird [*exponentiation by squaring*](https://de.wikipedia.org/wiki/Bin%C3%A4re_Exponentiation) verwendet, so dass z.B. `x^23` nur 7 Multiplikationen benötigt: \n", + "$$\n", + "x^{23} = \\left( \\left( (x^2)^2 \\cdot x \\right)^2 \\cdot x \\right)^2 \\cdot x \n", + "$$\n", + "\n", + "#### Division\n", + "\n", + "- Division `/` erzeugt eine Gleitkommazahl.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "67cb4661", + "metadata": {}, + "outputs": [], + "source": [ + "x = 40/5" + ] + }, + { + "cell_type": "markdown", + "id": "94408807", + "metadata": {}, + "source": [ + "#### Ganzzahldivision und Rest\n", + "\n", + "- Die Funktionen `div(a,b)`, `rem(a,b)` und `divrem(a,b)` berechnen den Quotient der Ganzzahldivision, den dazugehörigen Rest *(remainder)* bzw. beides als Tupel. \n", + "- Für `div(a,b)` gibt es die Operatorform `a ÷ b` (Eingabe: `\\div`) und für `rem(a,b)` die Operatorform `a % b`. \n", + "- Standardmäßig wird bei der Division „zur Null hin gerundet“, wodurch der dazugehörige Rest dasselbe Vorzeichen wie der Dividend `a` trägt: \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3ccdabcf", + "metadata": {}, + "outputs": [], + "source": [ + "@show divrem( 27, 4)\n", + "@show ( 27 ÷ 4, 27 % 4) \n", + "@show (-27 ÷ 4, -27 % 4 )\n", + "@show ( 27 ÷ -4, 27 % -4);" + ] + }, + { + "cell_type": "markdown", + "id": "5222cddb", + "metadata": {}, + "source": [ + "- Eine von `RoundToZero` abweichende Rundungsregel kann bei den Funktionen als optionales 3. Argument angegeben werden. \n", + "- `?RoundingMode` zeigt die möglichen Rundungsregeln an. \n", + "- Für die Rundungsregel `RoundDown` („in Richtung minus unendlich\"), wodurch der dazugehörige Rest dasselbe Vorzeichen wie der Divisor `b` bekommt, gibt es auch die Funktionen `fld(a,b)` *(floored division)* und `mod(a,b)`:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "be29f9d4", + "metadata": {}, + "outputs": [], + "source": [ + "@show divrem(-27, 4, RoundDown)\n", + "@show (fld(-27, 4), mod(-27, 4))\n", + "@show (fld( 27, -4), mod( 27, -4));" + ] + }, + { + "cell_type": "markdown", + "id": "84e604f7", + "metadata": {}, + "source": [ + "Für alle Rundungsregeln gilt:\n", + "```\n", + "div(a, b, RoundingMode) * b + rem(a, b, RoundingMode) = a\n", + "```\n", + "\n", + "#### Der Datentyp `BigInt`\n", + "\n", + "Der Datentyp `BigInt` ermöglicht Ganzzahlen beliebiger Länge. Der benötigte Speicher wird dynamisch allokiert.\n", + "\n", + "Numerische Konstanten haben automatisch einen ausreichend großen Typ:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ad97d8a3", + "metadata": {}, + "outputs": [], + "source": [ + "z = 10\n", + "@show typeof(z)\n", + "z = 10_000_000_000_000_000 # 10 Billiarden\n", + "@show typeof(z)\n", + "z = 10_000_000_000_000_000_000 # 10 Trillionen\n", + "@show typeof(z)\n", + "z = 10_000_000_000_000_000_000_000_000_000_000_000_000_000 # 10 Sextilliarden\n", + "@show typeof(z);" + ] + }, + { + "cell_type": "markdown", + "id": "b7da46f1", + "metadata": {}, + "source": [ + "Meist wird man allerdings den Datentyp `BigInt` explizit anfordern müssen, damit nicht modulo $2^{64}$ gerechnet wird:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "89d35c00", + "metadata": {}, + "outputs": [], + "source": [ + "@show 3^300 BigInt(3)^300;" + ] + }, + { + "cell_type": "markdown", + "id": "16d1d9cc", + "metadata": {}, + "source": [ + "*Arbitrary precision arithmetic* kostet einiges an Speicherplatz und Rechenzeit.\n", + "\n", + "Wir vergleichen den Zeit- und Speicherbedarf bei der Aufsummation von 10 Millionen Ganzzahlen als `Int64` und als `BigInt`. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d7e4a838", + "metadata": {}, + "outputs": [], + "source": [ + "# 10^7 Zufallszahlen, gleichverteilt zwischen -10^7 und 10^7 \n", + "vec_int = rand(-10^7:10^7, 10^7)\n", + "\n", + "# Dieselben Zahlen als BigInts\n", + "vec_bigint = BigInt.(vec_int)" + ] + }, + { + "cell_type": "markdown", + "id": "5df8fda6", + "metadata": {}, + "source": [ + "Einen ersten Eindruck vom Zeit- und Speicherbedarf gibt das `@time`-Macro:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e37fa19f", + "metadata": {}, + "outputs": [], + "source": [ + "@time x = sum(vec_int)\n", + "@show x typeof(x)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a58adeb1", + "metadata": {}, + "outputs": [], + "source": [ + "@time x = sum(vec_bigint)\n", + "@show x typeof(x);" + ] + }, + { + "cell_type": "markdown", + "id": "17081476", + "metadata": {}, + "source": [ + "Durch die Just-in-Time-Compilation von Julia ist die einmalige Ausführung einer Funktion wenig aussagekräftig. Das Paket `BenchmarkTools` stellt u.a. das Macro `@benchmark` bereit, das eine Funktion mehrfach aufruft und die Ausführungszeiten als Histogramm darstellt.\n", + "\n", + ":::{.ansitight}\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a5944727", + "metadata": {}, + "outputs": [], + "source": [ + "using BenchmarkTools\n", + "\n", + "@benchmark sum($vec_int)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "eb32dbfa", + "metadata": {}, + "outputs": [], + "source": [ + "@benchmark sum($vec_bigint)" + ] + }, + { + "cell_type": "markdown", + "id": "11e20069", + "metadata": {}, + "source": [ + ":::\n", + "Die `BigInt`-Addition ist mehr als 30 mal langsamer. \n", + "\n", + "\n", + "\n", + ":::{.content-hidden unless-format=\"xxx\"}\n", + "Die folgende Funktion soll die Summe aller Zahlen von 1 bis n mit der Arithmetik des Datentyps T berechnen.\n", + "Auf Grund der *type promotion rules* reicht es für `T ≥ Int64` dazu aus, die Akkumulatorvariable mit einer Zahl vom Typ T zu initialisieren. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ad42844a", + "metadata": {}, + "outputs": [], + "source": [ + "function mysum(n, T)\n", + " s = T(0)\n", + " for i = 1:n\n", + " s += i \n", + " end\n", + " return s\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "184457e8", + "metadata": {}, + "source": [ + "Einen ersten Eindruck vom Zeit- und Speicherbedarf gibt das `@time`-Macro:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c92af0db", + "metadata": {}, + "outputs": [], + "source": [ + "@time x = mysum(10_000_000, Int64)\n", + "@show x typeof(x);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e58be090", + "metadata": {}, + "outputs": [], + "source": [ + "@time x = mysum(10_000_000, BigInt)\n", + "@show x typeof(x);" + ] + }, + { + "cell_type": "markdown", + "id": "bfe545fd", + "metadata": {}, + "source": [ + "Durch die Just-in-Time-Compilation von Julia ist die einmalige Ausführung einer Funktion wenig aussagekräftig. Das Paket `BenchmarkTools` stellt u.a. das Macro `@benchmark` bereit, das eine Funktion mehrfach aufruft und die Ausführungszeiten als Histogramm darstellt.\n", + "\n", + ":::{.ansitight}\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3ae14185", + "metadata": {}, + "outputs": [], + "source": [ + "using BenchmarkTools\n", + "\n", + "@benchmark mysum(10_000_000, Int64)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d7513870", + "metadata": {}, + "outputs": [], + "source": [ + "@benchmark mysum(10_000_000, BigInt)" + ] + }, + { + "cell_type": "markdown", + "id": "4835712f", + "metadata": {}, + "source": [ + "Die Berechnung von $\\sum_{n=1}^{10000000} n$ dauert auf meinem PC mit den Standard-64bit-Integern im Schnitt 2 Nanosekunden, in *arbitrary precision arithmetic* über eine Sekunde, wobei auch noch fast 500MB Speicher allokiert werden. \n", + "\n", + ":::\n", + ":::\n", + "\n", + "\n", + "## Gleitkommazahlen\n", + "\n", + "Aus _floating point numbers_ kann man im Deutschen **[Gleit|Fließ]--[Komma|Punkt]--Zahlen** machen \n", + "und tatsächlich kommen alle 4 Varianten in der Literatur vor. \n", + "\n", + "In der Numerischen Mathematik spricht man auch gerne von **Maschinenzahlen**.\n", + "\n", + "\n", + "### Grundidee \n", + "\n", + "- Eine „feste Anzahl von Vor- und Nachkommastellen“ ist für viele Probleme ungeeignet.\n", + "- Eine Trennung zwischen „gültigen Ziffern“ und Größenordnung wie in der wissenschaftlichen Notation\n", + " $$ 345.2467 \\times 10^3\\qquad 34.52467\\times 10^4\\qquad \\underline{3.452467\\times 10^5}\\qquad 0.3452467\\times 10^6\\qquad 0.03452467\\times 10^7$$ \n", + " ist wesentlich flexibler. \n", + "- Zur Eindeutigkeit legt man fest: Die Darstellung mit genau einer Ziffer vor dem Komma ist die __Normalisierte Darstellung__.\n", + "- Bei Binärzahlen `1.01101`: ist diese Ziffer immer gleich Eins und man kann auf das Abspeichern dieser Ziffer verzichten.\n", + "\n", + "\n", + ":::{.callout-note }\n", + " \n", + "## Maschinenzahlen\n", + "\n", + "Die Menge der Maschinenzahlen $𝕄(b, m, e_{min}, e_{max})$ ist charakterisiert durch die verwendete Basis $b$, die Mantissenlänge $m$ und den Wertebereich des Exponenten $\\{e_{min}, ... ,e_{max}\\}$. \n", + "\n", + "In unserer Konvention hat die Mantisse einer normalisierten Maschinenzahl eine Ziffer (der Basis $b$) ungleich Null vor dem Komma und $m-1$ Nachkommastellen. \n", + "\n", + "Wenn $b=2$ ist, braucht man daher nur $m-1$ Bits zur Speicherung der Mantisse normalisierter Gleitkommazahlen. \n", + "\n", + "Der Standard IEEE 754, der von der Mahrzahl der modernen Prozessoren und Programmiersprachen implementiert wird, definiert \n", + "\n", + "- `Float32` als $𝕄(2, 24, -126, 127 )$ und \n", + "- `Float64` als $𝕄(2, 53, -1022, 1023 ).$\n", + "\n", + ":::\n", + "\n", + "### Aufbau von `Float64` nach [Standard IEEE 754](https://de.wikipedia.org/wiki/IEEE_754)\n", + "\n", + "\n", + "::: {.content-visible when-format=\"html\"}\n", + "![Aufbau einer `Float64` (Quelle:^[Quelle: Codekaizen, CC BY-SA 4.0, via Wikimedia Commons ])\n", + "](../images/1024px-IEEE_754_Double_Floating_Point_Format.png)\n", + ":::\n", + "\n", + "::: {.content-visible when-format=\"pdf\"}\n", + "![Aufbau einer `Float64` \\mysmall{(Quelle: \\href{https://commons.wikimedia.org/wiki/File:IEEE_754_Double_Floating_Point_Format.svg}{Codekaizen}, \\href{https://creativecommons.org/licenses/by-sa/4.0}{CC BY-SA 4.0}, via Wikimedia Commons)}\n", + "](../images/1024px-IEEE_754_Double_Floating_Point_Format.png){width=\"70%\"}\n", + ":::\n", + "\n", + "\n", + "- 1 Vorzeichenbit $S$\n", + "- 11 Bits für den Exponenten, also $0\\le E \\le 2047$\n", + "- die Werte $E=0$ und $E=(11111111111)_2=2047$ sind reserviert für die Codierung von Spezialwerten wie\n", + "$\\pm0, \\pm\\infty$, NaN _(Not a Number)_ und denormalisierte Zahlen.\n", + "- 52 Bits für die Mantisse $M,\\quad 0\\le M<1$, das entspricht etwa 16 Dezimalstellen\n", + "- Damit wird folgende Zahl dargestellt:\n", + "$$ x=(-1)^S \\cdot(1+M)\\cdot 2^{E-1023}$$\n", + "\n", + "Ein Beispiel:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8433da22", + "metadata": {}, + "outputs": [], + "source": [ + "x = 27.56640625\n", + "bitstring(x)" + ] + }, + { + "cell_type": "markdown", + "id": "7be4f1fc", + "metadata": {}, + "source": [ + "Das geht auch schöner:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "98311a9b", + "metadata": {}, + "outputs": [], + "source": [ + "function printbitsf64(x::Float64)\n", + " s = bitstring(x)\n", + " printstyled(s[1], color = :blue, reverse=true)\n", + " printstyled(s[2:12], color = :green, reverse=true)\n", + " printstyled(s[13:end], color=:red, bold=true, reverse=true)\n", + " print(\"\\n\")\n", + "end\n", + "\n", + "printbitsf64(x)" + ] + }, + { + "cell_type": "markdown", + "id": "728867d2", + "metadata": {}, + "source": [ + "und wir können S (in blau),E (grün) und M (rot) ablesen:\n", + "$$\n", + "\\begin{aligned}\n", + "S &= 0\\\\\n", + "E &= (10000000011)_2 = 2^{10} + 2^1 + 2^0 = 1027\\\\\n", + "M &= (.1011100100001)_2 = \\frac{1}{2} + \\frac{1}{2^3} + \\frac{1}{2^4} + \\frac{1}{2^5} + \\frac{1}{2^8} + \\frac{1}{2^{12}}\\\\\n", + "x &=(-1)^S \\cdot(1+M)\\cdot 2^{E-1023}\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "\n", + "... und damit die Zahl rekonstruieren:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f4403c1c", + "metadata": {}, + "outputs": [], + "source": [ + "x = (1 + 1/2 + 1/8 + 1/16 + 1/32 + 1/256 + 1/4096) * 2^4" + ] + }, + { + "cell_type": "markdown", + "id": "9346d953", + "metadata": {}, + "source": [ + "- Die Maschinenzahlen 𝕄 bilden eine endliche, diskrete Untermenge von ℝ. Es gibt eine kleinste und eine größte Maschinenzahl und abgesehen davon haben alle x∈𝕄 einen Vorgänger und Nachfolger in 𝕄.\n", + "- Was ist der Nachfolger von x in 𝕄? Dazu setzen wir das kleinste Mantissenbit von 0 auf 1. \n", + "- Die Umwandlung eines Strings aus Nullen und Einsen in die entsprechende Maschinenzahl ist z.B. so möglich:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "be8c52e0", + "metadata": {}, + "outputs": [], + "source": [ + "ux = parse(UInt64, \"0100000000111011100100010000000000000000000000000000000000000001\", base=2)\n", + "reinterpret(Float64, ux)" + ] + }, + { + "cell_type": "markdown", + "id": "165a8689", + "metadata": {}, + "source": [ + "Das kann man in Julia allerdings auch einfacher haben:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3901ed32", + "metadata": {}, + "outputs": [], + "source": [ + "y = nextfloat(x)" + ] + }, + { + "cell_type": "markdown", + "id": "d8b2e005", + "metadata": {}, + "source": [ + "Der Vorgänger von x ist:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ed502537", + "metadata": {}, + "outputs": [], + "source": [ + "z = prevfloat(x)\n", + "println(z)\n", + "printbitsf64(z)" + ] + }, + { + "cell_type": "markdown", + "id": "973c7660", + "metadata": {}, + "source": [ + "## Maschinenepsilon\n", + "\n", + "- Den Abstand zwischen `1` und dem Nachfolger `nextfloat(1)` nennt man [**Maschinenepsilon**](https://en.wikipedia.org/wiki/Machine_epsilon). \n", + "- Für `Float64` mit einer Mantissenlänge von 52 Bit, ist $\\epsilon=2^{-52}$.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "53a4703b", + "metadata": {}, + "outputs": [], + "source": [ + "@show nextfloat(1.) - 1 2^-52 eps(Float64);" + ] + }, + { + "cell_type": "markdown", + "id": "1b27e5f1", + "metadata": {}, + "source": [ + "- Das Maschinenepsilon ist ein Maß für den relativen Abstand zwischen den Maschinenzahlen und quantifiziert die Aussage: „64-Bit-Gleitkommazahlen haben eine Genauigkeit von etwa 16 Dezimalstellen.“\n", + "- Das Maschinenepsilon ist etwas völlig anderes als die kleinste von Null verschiedene Gleitkommazahl:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6c6247c5", + "metadata": {}, + "outputs": [], + "source": [ + "floatmin(Float64)" + ] + }, + { + "cell_type": "markdown", + "id": "ace02061", + "metadata": {}, + "source": [ + "- Ein Teil der Literatur verwendet eine andere Definition des Maschinenepsilons, die halb so groß ist. \n", + "$$\n", + "\\epsilon' = \\frac{\\epsilon}{2}\\approx 1.1\\times 10^{-16}\n", + "$$ \n", + "ist der maximale relative Fehler, der beim Runden einer reellen Zahl auf die nächste Maschinenzahl entstehen kann.\n", + "- Da Zahlen aus dem Intervall $(1-\\epsilon',1+\\epsilon']$ auf die Maschinenzahl $1$ gerundet werden, kann man $\\epsilon'$ auch definieren als: *die größte Zahl, für die in der Maschinenzahlarithmetik noch gilt: $1+\\epsilon' = 1$.* \n", + "\n", + "Auf diese Weise kann man das Maschinenepsilon auch berechnen:\n", + "\n", + ":::{.ansitight}\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "94351455", + "metadata": {}, + "outputs": [], + "source": [ + "Eps = 1\n", + "while(1 != 1 + Eps)\n", + " Eps /= 2\n", + " println(1+Eps)\n", + "end\n", + "Eps" + ] + }, + { + "cell_type": "markdown", + "id": "ce03b152", + "metadata": {}, + "source": [ + "oder als Bitmuster:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "de6c5e53", + "metadata": {}, + "outputs": [], + "source": [ + "Eps=1\n", + "while 1 != 1 + Eps\n", + " Eps/= 2\n", + " printbitsf64(1+Eps)\n", + "end\n", + "Eps" + ] + }, + { + "cell_type": "markdown", + "id": "23b7914a", + "metadata": {}, + "source": [ + ":::\n", + "\n", + "Die größte und die kleinste positive normalisiert darstellbare Gleitkommazahl eines Gleitkommatyps kann man abfragen:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "10296953", + "metadata": {}, + "outputs": [], + "source": [ + "@show floatmax(Float64)\n", + "printbitsf64(floatmax(Float64))\n", + "\n", + "@show floatmin(Float64)\n", + "printbitsf64(floatmin(Float64))" + ] + }, + { + "cell_type": "markdown", + "id": "ac56b395", + "metadata": {}, + "source": [ + "## Runden auf Maschinenzahlen\n", + "\n", + "- Die Abbildung rd: ℝ $\\rightarrow$ 𝕄 soll zur nächstgelegenen darstellbaren Zahl runden. \n", + "- Standardrundungsregel: _round to nearest, ties to even_ \n", + " Wenn man genau die Mitte zwischen zwei Maschinenzahlen trifft *(tie)*, wählt man die, deren letztes Mantissenbit 0 ist. \n", + "- Begründung: damit wird statistisch in 50% der Fälle auf- und in 50% der Fälle abgerundet und so ein „statistischer Drift“ bei längeren Rechnungen vermieden. \n", + "\n", + "## Maschinenzahlarithmetik\n", + "\n", + "Die Maschinenzahlen sind als Untermenge von ℝ nicht algebraisch abgeschlossen. Schon die Summe zweier Maschinenzahlen wird in der Regel keine Maschinenzahl sein. \n", + "\n", + ":::{.callout-important}\n", + "Der Standard IEEE 754 fordert, dass die Maschinenzahlarithmetik das *gerundete exakte Ergebnis* liefert:\n", + "\n", + "Das Resultat muss gleich demjenigen sein, das bei einer exakten Ausführung der entsprechenden Operation mit anschließender Rundung entsteht.\n", + "$$\n", + " a \\oplus b = \\text{rd}(a + b)\n", + "$$ \n", + "Analoges muss für die Implemetierung der Standardfunktionen wie \n", + "wie `sqrt()`, `log()`, `sin()` ... gelten: Sie liefern ebenfalls die Maschinenzahl, die dem exakten Ergebnis am nächsten kommt.\n", + ":::\n", + "\n", + "\n", + "Die Arithmetik ist *nicht assoziativ*:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dbe01c9d", + "metadata": {}, + "outputs": [], + "source": [ + "1 + 10^-16 + 10^-16 " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cd4dea94", + "metadata": {}, + "outputs": [], + "source": [ + "1 + (10^-16 + 10^-16)" + ] + }, + { + "cell_type": "markdown", + "id": "c5f1bc1c", + "metadata": {}, + "source": [ + "Im ersten Fall (ohne Klammern) wird von links nach rechts ausgewertet:\n", + "$$\n", + "\\begin{aligned}\n", + "1 \\oplus 10^{-16} \\oplus 10^{-16} &=\n", + " (1 \\oplus 10^{-16}) \\oplus 10^{-16} \\\\ &= \n", + "\\text{rd}\\left(\\text{rd}(1 + 10^{-16}) + 10^{-16} \\right)\\\\\n", + "&= \\text{rd}(1 + 10^{-16})\\\\\n", + "&= 1\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Im zweiten Fall erhält man:\n", + "$$\n", + "\\begin{aligned}\n", + "1 \\oplus \\left(10^{-16} \\oplus 10^{-16}\\right) &=\n", + "\\text{rd}\\left(1 + \\text{rd}(10^{-16} + 10^{-16}) \\right)\\\\\n", + "&= \\text{rd}(1 + 2*10^{-16})\\\\\n", + "&= 1.0000000000000002\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "\n", + "Es sei auch daran erinnert, dass sich selbst „einfache“ Dezimalbrüche häufig nicht exakt als Maschinenzahlen darstellen lassen:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "(0.1)_{10} &= (0.000110011001100110011001100...)_2 = (0.000\\overline{1100})_2 \\\\\n", + " (0.3)_{10} &= (0.0100110011001100110011001100..)_2 = (0.0\\overline{1001})_2 \n", + " \\end{aligned}\n", + " $$\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d3d65d23", + "metadata": {}, + "outputs": [], + "source": [ + "printbitsf64(0.1)\n", + "printbitsf64(0.3)" + ] + }, + { + "cell_type": "markdown", + "id": "4941993c", + "metadata": {}, + "source": [ + "Folge:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c2d4306a", + "metadata": {}, + "outputs": [], + "source": [ + "0.1 + 0.1 == 0.2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "92671384", + "metadata": {}, + "outputs": [], + "source": [ + "0.2 + 0.1 == 0.3" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a3ae81f9", + "metadata": {}, + "outputs": [], + "source": [ + "0.2 + 0.1" + ] + }, + { + "cell_type": "markdown", + "id": "2ea75313", + "metadata": {}, + "source": [ + "Bei der Ausgabe einer Maschinenzahl muss der Binärbruch in einen Dezimalbruch entwickelt werden. Man kann sich auch mehr Stellen dieser Dezimalbruchentwicklung anzeigen lassen: \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "17c80acc", + "metadata": {}, + "outputs": [], + "source": [ + "using Printf\n", + "@printf(\"%.30f\", 0.1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3409a939", + "metadata": {}, + "outputs": [], + "source": [ + "@printf(\"%.30f\", 0.3)" + ] + }, + { + "cell_type": "markdown", + "id": "51bd9e73", + "metadata": {}, + "source": [ + "Die Binärbruch-Mantisse einer Maschinenzahl kann eine lange oder sogar unendlich-periodische Dezimalbruchentwicklung haben. Dadurch \n", + "sollte man sich nicht eine „höheren Genauigkeit“ suggerieren lassen! \n", + "\n", + ":::{.callout-important}\n", + "Moral: wenn man `Float`s auf Gleichheit testen will, sollte man fast immer eine dem Problem angemessene realistische Genauigkeit `epsilon` festlegen und \n", + "darauf testen:\n", + "\n", + "```julia\n", + "epsilon = 1.e-10\n", + "\n", + "if abs(x-y) < epsilon\n", + " # ...\n", + "end\n", + "```\n", + ":::\n", + "\n", + "## Normalisierte und Denormalisierte Maschinenzahlen\n", + "\n", + "Zum Verständnis nehmen wir ein einfaches Modell: \n", + "\n", + "- Sei 𝕄(10,4,±5) die Menge der Maschinenzahlen zur Basis 10 mit 4 Mantissenstellen (eine vor dem Komma, 3 Nachkommastellen) und dem Exponentenbereich -5 ≤ E ≤ 5.\n", + "- Dann ist die normalisierte Darstellung (Vorkommastelle ungleich 0)\n", + " von z.B. 1234.0 gleich 1.234e3 und von 0.00789 gleich 7.890e-3.\n", + "- Es ist wichtig, dass die Maschinenzahlen bei jedem Rechenschritt normalisiert gehalten werden. Nur so wird die Mantissenlänge voll ausgenutzt und die Genauigkeit ist maximal.\n", + "- Die kleinste positive normalisierte Zahl in unserem Modell ist `x = 1.000e-5`. Schon `x/2` müsste auf 0 gerundet werden. \n", + "- Hier erweist es sich für viele Anwendungen als günstiger, auch denormalisierte *(subnormal)* Zahlen zuzulassen und `x/2` als `0.500e-5` oder `x/20` als `0.050e-5` darzustellen. \n", + "- Dieser *gradual underflow* ist natürlich mit einem Verlust an gültigen Stellen und damit Genauigkeit verbunden.\n", + "\n", + "\n", + "Im `Float`-Datentyp werden solche *subnormal values* dargestellt durch ein Exponentenfeld, in dem alle Bits gleich Null sind:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4cf6ecae", + "metadata": {}, + "outputs": [], + "source": [ + "#| echo: false\n", + "#| output: false\n", + "flush(stdout)" + ] + }, + { + "cell_type": "markdown", + "id": "baddd014", + "metadata": {}, + "source": [ + ":::{.ansitight}\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1d0377d1", + "metadata": {}, + "outputs": [], + "source": [ + "using Printf\n", + "\n", + "x = 2 * floatmin(Float64) # 2*kleinste normalisierte Gleitkommazahl > 0\n", + "\n", + "while x != 0\n", + " x /= 2\n", + " @printf \"%14.6g \" x\n", + " printbitsf64(x)\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "246e9987", + "metadata": {}, + "source": [ + ":::\n", + "\n", + "## Spezielle Werte\n", + "\n", + "Die Gleitkommaarithmetik kennt einige spezielle Werte:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7a7ad264", + "metadata": {}, + "outputs": [], + "source": [ + "for x ∈ (NaN, Inf, -Inf, -0.0)\n", + " @printf \"%6g \" x\n", + " printbitsf64(x)\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "806100b7", + "metadata": {}, + "source": [ + "- Ein Exponentenüberlauf *(overflow)* führt zum Ergebnis `Inf` oder `-Inf`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c4381f5a", + "metadata": {}, + "outputs": [], + "source": [ + "2/0, -3/0, floatmax(Float64) * 1.01, exp(1300)" + ] + }, + { + "cell_type": "markdown", + "id": "01836c3b", + "metadata": {}, + "source": [ + "- Damit kann weitergerechnet werden:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f6d21942", + "metadata": {}, + "outputs": [], + "source": [ + "-Inf + 20, Inf/30, 23/-Inf, sqrt(Inf), Inf * 0, Inf - Inf" + ] + }, + { + "cell_type": "markdown", + "id": "b8dd245d", + "metadata": {}, + "source": [ + "- `NaN` *(Not a Number)* steht für das Resultat einer Operation, das undefiniert ist. Alle weiteren Operationen mit `NaN` ergeben ebenfalls `NaN`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ed988054", + "metadata": {}, + "outputs": [], + "source": [ + "0/0, Inf - Inf, 2.3NaN, sqrt(NaN)" + ] + }, + { + "cell_type": "markdown", + "id": "a5cdc827", + "metadata": {}, + "source": [ + "- Da `NaN` einen undefinierten Wert repräsentiert, ist es zu nichts gleich, nichtmal zu sich selbst. Das ist sinnvoll, denn wenn zwei Variablen `x` und `y` als `NaN` berechnet wurden, sollte man nicht schlußfolgern, dass sie gleich sind. \n", + "- Zum Testen auf `NaN` gibt es daher die boolsche Funktion `isnan()`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c1fddee9", + "metadata": {}, + "outputs": [], + "source": [ + "x = 0/0\n", + "y = Inf - Inf\n", + "@show x==y NaN==NaN isfinite(NaN) isinf(NaN) isnan(x) isnan(y); " + ] + }, + { + "cell_type": "markdown", + "id": "7620f690", + "metadata": {}, + "source": [ + "- Es gibt eine „minus Null“. Sie signalisiert einen Exponentenunterlauf *(underflow)* einer betragsmäßig zu klein gewordenen *negativen* Größe. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "448f1740", + "metadata": {}, + "outputs": [], + "source": [ + "@show 23/-Inf -2/exp(1200) -0.0==0.0;" + ] + }, + { + "cell_type": "markdown", + "id": "fc1c8f29", + "metadata": {}, + "source": [ + "## Mathematische Funktionen\n", + "\n", + "Julia verfügt über die [üblichen mathematischen Funktionen](https://docs.julialang.org/en/v1/manual/mathematical-operations/#Rounding-functions) \n", + "`sqrt, exp, log, log2, log10, sin, cos,..., asin, acos,..., sinh,..., gcd, lcm, factorial,...,abs, max, min,...`,\n", + "\n", + "darunter z.B. die [Rundungsfunktionen](https://de.wikipedia.org/wiki/Abrundungsfunktion_und_Aufrundungsfunktion)\n", + "\n", + "- `floor(T,x)` = $\\lfloor x \\rfloor$\n", + "- `ceil(T,x)` = $\\lceil x \\rceil$\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a22d5739", + "metadata": {}, + "outputs": [], + "source": [ + "floor(3.4), floor(Int64, 3.5), floor(Int64, -3.5)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "175b33d1", + "metadata": {}, + "outputs": [], + "source": [ + "ceil(3.4), ceil(Int64, 3.5), ceil(Int64, -3.5)" + ] + }, + { + "cell_type": "markdown", + "id": "40ce370d", + "metadata": {}, + "source": [ + "Es sei noch hingewiesen auf `atan(y, x)`, den [Arkustangens mit 2 Argumenten](https://de.wikipedia.org/wiki/Arctan2), Er ist in anderen Programmiersprachen oft als Funktion mit eigenem Namen *atan2* implementiert. \n", + "Dieser löst das Problem der Umrechnung von kartesischen in Polarkoordinaten ohne lästige Fallunterscheidung. \n", + "\n", + "- `atan(y,x)` ist Winkel der Polarkoordinaten von (x,y) im Intervall $(-\\pi,\\pi]$. Im 1. und 4. Quadranten ist er also gleich `atan(y/x)`\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "518c24db", + "metadata": {}, + "outputs": [], + "source": [ + "atan(3, -2), atan(-3, 2), atan(-3/2)" + ] + }, + { + "cell_type": "markdown", + "id": "f61060f4", + "metadata": {}, + "source": [ + "## Umwandlung Strings $\\Longleftrightarrow$ Zahlen\n", + "\n", + "Die Umwandlung ist mit den Funktionen `parse()` und `string()` möglich.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "96490c3b", + "metadata": {}, + "outputs": [], + "source": [ + "parse(Int64, \"1101\", base=2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "814ac0ed", + "metadata": {}, + "outputs": [], + "source": [ + "string(13, base=2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "90b64397", + "metadata": {}, + "outputs": [], + "source": [ + "string(1/7)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fb1ebb4d", + "metadata": {}, + "outputs": [], + "source": [ + "string(77, base=16)" + ] + }, + { + "cell_type": "markdown", + "id": "029d437e", + "metadata": {}, + "source": [ + "Zur Umwandlung der numerischen Typen ineinander kann man die Typnamen verwenden. Typenamen sind auch Konstruktoren:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "df5b20f2", + "metadata": {}, + "outputs": [], + "source": [ + "x = Int8(67)\n", + "@show x typeof(x);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "27314b21", + "metadata": {}, + "outputs": [], + "source": [ + "z = UInt64(3459)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5687c82a", + "metadata": {}, + "outputs": [], + "source": [ + "y = Float64(z)" + ] + }, + { + "cell_type": "markdown", + "id": "075b91d7", + "metadata": {}, + "source": [ + "## Literatur\n", + "\n", + "- D. Goldberg, [What Every Computer Scientist Should Know About Floating-Point Arithmetic](http://www.validlab.com/goldberg/paper.pdf)\n", + "- C. Vuik, [Some Disasters caused by numerical errors](http://ta.twi.tudelft.nl/users/vuik/wi211/disasters.html)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/pcomplex.ipynb b/nb/pcomplex.ipynb new file mode 100644 index 0000000..1d2c72c --- /dev/null +++ b/nb/pcomplex.ipynb @@ -0,0 +1,746 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "3b9e97dc", + "metadata": {}, + "source": [ + "# Ein Fallbeispiel: Der parametrisierte Datentyp PComplex\n", + "\n", + "Wir wollen als neuen numerischen Typen **komplexe Zahlen in Polardarstellung $z=r e^{i\\phi}=(r,ϕ)$** einführen. \n", + "\n", + "- Der Typ soll sich in die Typhierarchie einfügen als Subtyp von 'Number'.\n", + "- $r$ und $\\phi$ sollen Gleitkommazahlen sein. (Im Unterschied zu komplexen Zahlen in 'kartesischen' Koordinaten hat eine Einschränkung auf ganzzahlige Werte von r oder ϕ mathematisch wenig Sinn.)\n", + "\n", + "## Die Definition von `PComplex`\n", + "\n", + "Ein erster Versuch könnte so aussehen:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b00fa817", + "metadata": {}, + "outputs": [], + "source": [ + "struct PComplex1{T <: AbstractFloat} <: Number\n", + " r :: T\n", + " ϕ :: T\n", + "end\n", + "\n", + "z1 = PComplex1(-32.0, 33.0)\n", + "z2 = PComplex1{Float32}(12, 13)\n", + "@show z1 z2;" + ] + }, + { + "cell_type": "markdown", + "id": "00603f51", + "metadata": {}, + "source": [ + "Julia stellt automatisch *default constructors* zur Verfügung:\n", + "\n", + "- den Konstruktor `PComplex1`, bei dem der Typ `T` von den übergebenen Argumenten abgeleitet wird und\n", + "- Konstruktoren `PComplex{Float64},...` mit expliziter Typangabe. Hier wird versucht, die Argumente in den angeforderten Typ zu konvertieren. \n", + "\n", + "------\n", + "\n", + "Wir wollen nun, dass der Konstruktor noch mehr tut. \n", + "In der Polardarstellung soll $0\\le r$ und $0\\le \\phi<2\\pi$ gelten.\n", + "\n", + "Wenn die übergebenen Argumente das nicht erfüllen, sollten sie entsprechend umgerechnet werden.\n", + "\n", + "Dazu definieren wir einen _inner constructor_, der den _default constructor_ ersetzt.\n", + "\n", + "- Ein _inner constructor_ ist eine Funktion innerhalb der `struct`-Definition.\n", + "- In einem _inner constructor_ kann man die spezielle Funktion `new` verwenden, die wie der _default constructor_ wirkt.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d583f845", + "metadata": {}, + "outputs": [], + "source": [ + "struct PComplex{T <: AbstractFloat} <: Number\n", + " r :: T\n", + " ϕ :: T\n", + "\n", + " function PComplex{T}(r::T, ϕ::T) where T<:AbstractFloat\n", + " if r<0 # flip the sign of r and correct phi\n", + " r = -r\n", + " ϕ += π\n", + " end\n", + " if r==0 ϕ=0 end # normalize r=0 case to phi=0 \n", + " ϕ = mod(ϕ, 2π) # map phi into interval [0,2pi)\n", + " new(r, ϕ) # new() ist special function,\n", + " end # available only inside inner constructors\n", + "\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e3d6ada4", + "metadata": {}, + "outputs": [], + "source": [ + "#| echo: false\n", + "#| output: false\n", + "\n", + "#=\n", + "in den ganzen quarto-runs wollen bir hier noch das default-show benutzen\n", + "=#\n", + "zz = @which Base.show(stdout, PComplex{Float64}(2.,3.))\n", + "if zz.module != Base\n", + " Base.delete_method(zz)\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "55f6b7dc", + "metadata": {}, + "outputs": [], + "source": [ + "z1 = PComplex{Float64}(-3.3, 7π+1)" + ] + }, + { + "cell_type": "markdown", + "id": "99f6d6e1", + "metadata": {}, + "source": [ + "Für die explizite Angabe eines *inner constructors* müssen wir allerdings einen Preis zahlen: Die sonst von Julia bereitgestellten *default constructors* fehlen. \n", + "\n", + "Den Konstruktor, der ohne explizite Typangabe in geschweiften Klammern auskommt und den Typ der Argumente übernimmt, wollen wir gerne auch haben:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e6c36f18", + "metadata": {}, + "outputs": [], + "source": [ + "PComplex(r::T, ϕ::T) where {T<:AbstractFloat} = PComplex{T}(r,ϕ)\n", + "\n", + "z2 = PComplex(2.0, 0.3)" + ] + }, + { + "cell_type": "markdown", + "id": "5d77812c", + "metadata": {}, + "source": [ + "## Eine neue Schreibweise\n", + "\n", + "Julia verwendet `//` als Infix-Konstruktor für den Typ `Rational`. Sowas Schickes wollen wir auch. \n", + "\n", + "In der Elektronik/Elektrotechnik werden [Wechselstromgrößen durch komplexe Zahlen beschrieben.](https://de.wikipedia.org/wiki/Komplexe_Wechselstromrechnung). Dabei ist eine Darstellung komplexer Zahlen durch \"Betrag\" und \"Phase\" üblich und sie wird gerne in der sogenannten [Versor-Form](https://de.wikipedia.org/wiki/Versor) (engl. *phasor*) dargestellt:\n", + "$$\n", + " z= r\\enclose{phasorangle}{\\phi} = 3.4\\;\\enclose{phasorangle}{45^\\circ}\n", + "$$\n", + "wobei man in der Regel den Winkel in Grad notiert. \n", + "\n", + ":::{.callout-note .titlenormal collapse=\"true\"}\n", + "\n", + "## Mögliche Infix-Operatoren in Julia\n", + "\n", + "In Julia ist eine große Anzahl von Unicode-Zeichen reserviert für die Verwendung als Operatoren. Die definitive Liste ist im [Quellcode des Parsers.](https://github.com/JuliaLang/julia/blob/eaa2c58aeb12f27c1d8c116ab111773a4fc4495f/src/julia-parser.scm#L13-L31)\n", + "\n", + "Auf Details werden wir in einem späteren Kapitel noch eingehen. \n", + "\n", + "Und ja, der Julia-Parser ist in einem Lisp(genauer: Scheme)-Dialekt geschrieben. In Julia ist ein kleiner Scheme-Interpreter namens [femtolisp](https://github.com/JeffBezanson/femtolisp) integriert. Geschrieben hat ihn einer der \"Väter\" von Julia bevor er mit der Arbeit an Julia begann. \n", + "\n", + ":::\n", + "\n", + "Das Winkel-Zeichen `∠` steht leider nicht als Operatorsymbol zur Verfügung. Wir weichen aus auf `⋖`. Das kann in Julia als als `\\lessdot` eingegeben werden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a4fc6d3c", + "metadata": {}, + "outputs": [], + "source": [ + " ⋖(r::Real, ϕ::Real) = PComplex(r, π*ϕ/180)\n", + "\n", + "z3 = 2. ⋖ 90." + ] + }, + { + "cell_type": "markdown", + "id": "c19f6e25", + "metadata": {}, + "source": [ + "(Die Typ-Annotation -- `Real` statt `AbstractFloat` -- ist ein Vorgriff auf kommende weitere Konstruktoren. Im Moment funktioniert der Operator `⋖` erstmal nur mit `Float`s.)\n", + "\n", + "\n", + "Natürlich wollen wir auch die Ausgabe so schön haben. Details dazu findet man in der [Dokumentation](https://docs.julialang.org/en/v1/manual/types/#man-custom-pretty-printing).\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "13e750ef", + "metadata": {}, + "outputs": [], + "source": [ + "using Printf\n", + "\n", + "function Base.show(io::IO, z::PComplex)\n", + " # wir drucken die Phase in Grad, auf Zehntelgrad gerundet, \n", + " p = z.ϕ * 180/π\n", + " sp = @sprintf \"%.1f\" p\n", + " print(io, z.r, \"⋖\", sp, '°')\n", + "end\n", + "\n", + "@show z3;" + ] + }, + { + "cell_type": "markdown", + "id": "e1c7d6fa", + "metadata": {}, + "source": [ + "## Methoden für `PComplex`\n", + "\n", + "Damit unser Typ ein anständiges Mitglied der von `Number` abstammenden Typfamilie wird, brauchen wir allerdings noch eine ganze Menge mehr. Es müssen Arithmetik, Vergleichsoperatoren, Konvertierungen usw. definiert werden. \n", + "\n", + "\n", + "Wir beschränken uns auf Multiplikation und Quadratwurzeln.\n", + "\n", + "\n", + ":::{.callout-note collapse=\"true\"}\n", + "## Module \n", + "\n", + "- Um die `methods` der existierenden Funktionen und Operationen zu ergänzen, muss man diese mit ihrem 'vollen Namen' ansprechen.\n", + "- Alle Objekte gehören zu einem Namensraum oder `module`.\n", + "- Die meisten Basisfunktionen gehören zum Modul `Base`, welches standardmäßig immer ohne explizites `using ...` geladen wird. \n", + "- Solange man keine eigenen Module definiert, sind die eigenen Definitionen im Modul `Main`.\n", + "- Das Macro `@which`, angewendet auf einen Namen, zeigt an, in welchem Modul der Name definiert wurde. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "373829e0", + "metadata": {}, + "outputs": [], + "source": [ + "f(x) = 3x^3\n", + "@which f" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a4490292", + "metadata": {}, + "outputs": [], + "source": [ + "wp = @which +\n", + "ws = @which(sqrt)\n", + "println(\"Modul für Addition: $wp, Modul für sqrt: $ws\")" + ] + }, + { + "cell_type": "markdown", + "id": "d49ec514", + "metadata": {}, + "source": [ + ":::\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d2186aeb", + "metadata": {}, + "outputs": [], + "source": [ + "qwurzel(z::PComplex) = PComplex(sqrt(z.r), z.ϕ / 2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5d93d3ca", + "metadata": {}, + "outputs": [], + "source": [ + "#| echo: false\n", + "#| output: false\n", + "\n", + "#=\n", + "damit das length(methods(sqrt)) klappt\n", + "=#\n", + "if hasmethod(sqrt, (PComplex,))\n", + " zz = @which Base.sqrt(PComplex{Float64}(1.,1.))\n", + " Base.delete_method(zz)\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "07ed8595", + "metadata": {}, + "source": [ + "Die Funktion `sqrt()` hat schon einige Methoden:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1ecfd1ac", + "metadata": {}, + "outputs": [], + "source": [ + "length(methods(sqrt))" + ] + }, + { + "cell_type": "markdown", + "id": "f619c771", + "metadata": {}, + "source": [ + "Jetzt wird es eine Methode mehr:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "56a4ce0f", + "metadata": {}, + "outputs": [], + "source": [ + "Base.sqrt(z::PComplex) = qwurzel(z)\n", + "\n", + "length(methods(sqrt))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "195204e7", + "metadata": {}, + "outputs": [], + "source": [ + "sqrt(z2)" + ] + }, + { + "cell_type": "markdown", + "id": "c912bcd2", + "metadata": {}, + "source": [ + "und nun zur Multiplikation:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8c648a2d", + "metadata": {}, + "outputs": [], + "source": [ + "Base.:*(x::PComplex, y::PComplex) = PComplex(x.r * y.r, x.ϕ + y.ϕ)\n", + "\n", + "@show z1 * z2;" + ] + }, + { + "cell_type": "markdown", + "id": "79074b01", + "metadata": {}, + "source": [ + "(Da das Operatorsymbol kein normaler Name ist, muss der Doppelpunkt bei der Zusammensetzung mit `Base.` sein.)\n", + "\n", + "Wir können allerdings noch nicht mit anderen numerischen Typen multiplizieren. Dazu könnte man nun eine Vielzahl von entsprechenden Methoden definieren. Julia stellt *für numerische Typen* noch einen weiteren Mechanismus zur Verfügung, der das etwas vereinfacht.\n", + "\n", + "\n", + "## Typ-Promotion und Konversion \n", + "\n", + "In Julia kann man bekanntlich die verschiedensten numerischen Typen nebeneinander verwenden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ff3ee027", + "metadata": {}, + "outputs": [], + "source": [ + "1//3 + 5 + 5.2 + 0xff" + ] + }, + { + "cell_type": "markdown", + "id": "f43ef8c6", + "metadata": {}, + "source": [ + "Wenn man in die zahlreichen Methoden schaut, die z.B. für `+` und `*` definiert sind, findet man u.a. eine Art 'catch-all-Definition'\n", + "\n", + "```julia\n", + "+(x::Number, y::Number) = +(promote(x,y)...)\n", + "*(x::Number, y::Number) = *(promote(x,y)...)\n", + "```\n", + "\n", + "\n", + "\n", + "(Die 3 Punkte sind der splat-Operator, der das von promote() zurückgegebene Tupel wieder in seine Bestandteile zerlegt.)\n", + "\n", + "Da die Methode mit den Typen `(Number, Number)` sehr allgemein ist, wird sie erst verwendet, wenn spezifischere Methoden nicht greifen.\n", + "\n", + "Was passiert hier?\n", + "\n", + "### Die Funktion `promote(x,y,...)`\n", + "\n", + "Diese Funktion versucht, alle Argumente in einen gemeinsamen Typen umzuwandeln, der alle Werte (möglichst) exakt darstellen kann.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8f1d4d57", + "metadata": {}, + "outputs": [], + "source": [ + "promote(12, 34.555, 77/99, 0xff)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "27c2724e", + "metadata": {}, + "outputs": [], + "source": [ + "z = promote(BigInt(33), 27)\n", + "@show z typeof(z);" + ] + }, + { + "cell_type": "markdown", + "id": "8347acad", + "metadata": {}, + "source": [ + "Die Funktion `promote()` verwendet dazu zwei Helfer, die Funktionen\n", + " `promote_type(T1, T2)` und `convert(T, x)`\n", + "\n", + "Wie üblich in Julia, kann man diesen Mechanismus durch [eigene *promotion rules* und `convert(T,x)`-Methoden erweitern.](https://docs.julialang.org/en/v1/manual/conversion-and-promotion/) \n", + "\n", + "\n", + "### Die Funktion `promote_type(T1, T2,...)` \n", + "\n", + "Sie ermittelt, zu welchem Typ umgewandelt werden soll. Argumente sind Typen, nicht Werte.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fe551c95", + "metadata": {}, + "outputs": [], + "source": [ + "@show promote_type(Rational{Int64}, ComplexF64, Float32);" + ] + }, + { + "cell_type": "markdown", + "id": "e4c08732", + "metadata": {}, + "source": [ + "### Die Funktion `convert(T,x)`\n", + "\n", + "Die Methoden von \n", + "`convert(T, x)` wandeln `x` in ein Objekt vom Typ `T` um. Dabei sollte eine solche Umwandlung verlustfrei möglich sein.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5d6aabe4", + "metadata": {}, + "outputs": [], + "source": [ + "z = convert(Float64, 3)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8b5205d2", + "metadata": {}, + "outputs": [], + "source": [ + "z = convert(Int64, 23.00)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0d4b80ce", + "metadata": {}, + "outputs": [], + "source": [ + "z = convert(Int64, 2.3)" + ] + }, + { + "cell_type": "markdown", + "id": "3e3d953b", + "metadata": {}, + "source": [ + "Die spezielle Rolle von `convert()` liegt darin, dass es an verschiedenen Stellen _implizit_ und automatisch eingesetzt wird: \n", + "\n", + "> [The following language constructs call convert](https://docs.julialang.org/en/v1/manual/conversion-and-promotion/#When-is-convert-called?):\n", + "> \n", + " - Assigning to an array converts to the array's element type.\n", + " - Assigning to a field of an object converts to the declared type of the field.\n", + " - Constructing an object with new converts to the object's declared field types.\n", + " - Assigning to a variable with a declared type (e.g. local x::T) converts to that type.\n", + " - A function with a declared return type converts its return value to that type.\n", + "\n", + "-- und natürlich in `promote()`\n", + "\n", + "Für selbstdefinierte Datentypen kann man convert() um weitere Methoden ergänzen.\n", + "\n", + "Für Datentypen innerhalb der Number-Hierarchie gibt es wieder eine 'catch-all-Definition'\n", + "```julia\n", + "convert(::Type{T}, x::Number) where {T<:Number} = T(x)\n", + "```\n", + "\n", + "Also: Wenn für einen Typen `T` aus der Hierarchie `T<:Number` ein Konstruktor `T(x)` mit einem numerischen Argument `x` existiert, dann wird dieser Konstruktor `T(x)` automatisch für Konvertierungen benutzt. (Natürlich können auch speziellere Methoden für `convert()` definiert werden, die dann Vorrang haben.)\n", + "\n", + "\n", + "### Weitere Konstruktoren für `PComplex`\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2f9e1ebe", + "metadata": {}, + "outputs": [], + "source": [ + "## (a) r, ϕ beliebige Reals, z.B. Integers, Rationals\n", + "\n", + "PComplex{T}(r::T1, ϕ::T2) where {T<:AbstractFloat, T1<:Real, T2<: Real} = \n", + " PComplex{T}(convert(T, r), convert(T, ϕ))\n", + "\n", + "PComplex(r::T1, ϕ::T2) where {T1<:Real, T2<: Real} = \n", + " PComplex{promote_type(Float64, T1, T2)}(r, ϕ) \n", + "\n", + "## (b) Zur Umwandlung von Reals: Konstruktor mit \n", + "## nur einem Argument r\n", + "\n", + "PComplex{T}(r::S) where {T<:AbstractFloat, S<:Real} = \n", + " PComplex{T}(convert(T, r), convert(T, 0)) \n", + "\n", + "PComplex(r::S) where {S<:Real} = \n", + " PComplex{promote_type(Float64, S)}(r, 0.0)\n", + "\n", + "## (c) Umwandlung Complex -> PComplex\n", + "\n", + "PComplex{T}(z::Complex{S}) where {T<:AbstractFloat, S<:Real} = \n", + " PComplex{T}(abs(z), angle(z))\n", + "\n", + "PComplex(z::Complex{S}) where {S<:Real} = \n", + " PComplex{promote_type(Float64, S)}(abs(z), angle(z))\n" + ] + }, + { + "cell_type": "markdown", + "id": "c831e4c3", + "metadata": {}, + "source": [ + "Ein Test der neuen Konstruktoren:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8103dc03", + "metadata": {}, + "outputs": [], + "source": [ + "3//5 ⋖ 45, PComplex(Complex(1,1)), PComplex(-13) " + ] + }, + { + "cell_type": "markdown", + "id": "c85b8d7a", + "metadata": {}, + "source": [ + "Wir brauchen nun noch *promotion rules*, die festlegen, welcher Typ bei `promote(x::T1, y::T2)` herauskommen soll. Damit wird `promote_type()` intern um die nötigen weiteren Methoden erweitert. \n", + "\n", + "### *Promotion rules* für `PComplex`\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8e6a1e94", + "metadata": {}, + "outputs": [], + "source": [ + "Base.promote_rule(::Type{PComplex{T}}, ::Type{S}) where {T<:AbstractFloat,S<:Real} = \n", + " PComplex{promote_type(T,S)}\n", + "\n", + "Base.promote_rule(::Type{PComplex{T}}, ::Type{Complex{S}}) where \n", + " {T<:AbstractFloat,S<:Real} = PComplex{promote_type(T,S)}" + ] + }, + { + "cell_type": "markdown", + "id": "4ad30167", + "metadata": {}, + "source": [ + "1. Regel:\n", + ": Wenn ein `PComplex{T}` und ein `S<:Real` zusammentreffen, dann sollen beide zu `PComplex{U}` umgewandelt werden, wobei `U` der Typ ist, zu dem `S` und `T` beide umgewandelt (_promoted_) werden können. \n", + "\n", + "2. Regel\n", + ": Wenn ein `PComplex{T}` und ein `Complex{S}` zusammentreffen, dann sollen beide zu `PComplex{U}` umgewandelt werden, wobei `U` der Typ ist, zu dem `S` und `T` beide umgewandelt werden können. \n", + "\n", + "\n", + "\n", + "Damit klappt nun die Multiplikation mit beliebigen numerischen Typen.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9e72f683", + "metadata": {}, + "outputs": [], + "source": [ + "z3, 3z3" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f0aec53e", + "metadata": {}, + "outputs": [], + "source": [ + "(3.0+2im) * (12⋖30.3), 12sqrt(z2) " + ] + }, + { + "cell_type": "markdown", + "id": "0d881cc4", + "metadata": {}, + "source": [ + ":::{.callout-caution icon=\"false\" collapse=\"true\" .titlenormal}\n", + "\n", + "## Zusammenfassung: unser Typ `PComplex`\n", + "\n", + "```julia\n", + "struct PComplex{T <: AbstractFloat} <: Number\n", + " r :: T\n", + " ϕ :: T\n", + "\n", + " function PComplex{T}(r::T, ϕ::T) where T<:AbstractFloat\n", + " if r<0 # flip the sign of r and correct phi\n", + " r = -r\n", + " ϕ += π\n", + " end\n", + " if r==0 ϕ=0 end # normalize r=0 case to phi=0 \n", + " ϕ = mod(ϕ, 2π) # map phi into interval [0,2pi)\n", + " new(r, ϕ) # new() ist special function,\n", + " end # available only inside inner constructors\n", + "\n", + "end\n", + "\n", + "# additional constructors\n", + "PComplex(r::T, ϕ::T) where {T<:AbstractFloat} = PComplex{T}(r,ϕ)\n", + "\n", + "\n", + "PComplex{T}(r::T1, ϕ::T2) where {T<:AbstractFloat, T1<:Real, T2<: Real} = \n", + " PComplex{T}(convert(T, r), convert(T, ϕ))\n", + "\n", + "PComplex(r::T1, ϕ::T2) where {T1<:Real, T2<: Real} = \n", + " PComplex{promote_type(Float64, T1, T2)}(r, ϕ) \n", + "\n", + "\n", + "PComplex{T}(r::S) where {T<:AbstractFloat, S<:Real} = \n", + " PComplex{T}(convert(T, r), convert(T, 0)) \n", + "\n", + "PComplex(r::S) where {S<:Real} = \n", + " PComplex{promote_type(Float64, S)}(r, 0.0)\n", + "\n", + "\n", + "PComplex{T}(z::Complex{S}) where {T<:AbstractFloat, S<:Real} = \n", + " PComplex{T}(abs(z), angle(z))\n", + "\n", + "PComplex(z::Complex{S}) where {S<:Real} = \n", + " PComplex{promote_type(Float64, S)}(abs(z), angle(z))\n", + "\n", + "# nice input\n", + "⋖(r::Real, ϕ::Real) = PComplex(r, π*ϕ/180)\n", + "\n", + "# nice output\n", + "using Printf\n", + "\n", + "function Base.show(io::IO, z::PComplex)\n", + " # wir drucken die Phase in Grad, auf Zehntelgrad gerundet, \n", + " p = z.ϕ * 180/π\n", + " sp = @sprintf \"%.1f\" p\n", + " print(io, z.r, \"⋖\", sp, '°')\n", + "end\n", + "\n", + "# arithmetic\n", + "Base.sqrt(z::PComplex) = PComplex(sqrt(z.r), z.ϕ / 2)\n", + "\n", + "Base.:*(x::PComplex, y::PComplex) = PComplex(x.r * y.r, x.ϕ + y.ϕ)\n", + "\n", + "# promotion rules\n", + "Base.promote_rule(::Type{PComplex{T}}, ::Type{S}) where \n", + " {T<:AbstractFloat,S<:Real} = PComplex{promote_type(T,S)}\n", + "\n", + "Base.promote_rule(::Type{PComplex{T}}, ::Type{Complex{S}}) where \n", + " {T<:AbstractFloat,S<:Real} = PComplex{promote_type(T,S)}\n", + "```\n", + ":::\n", + "\n", + ":::{.content-hidden unless-format=\"xxx\"}\n", + "\n", + "Jetzt geht sowas wie `PComplex(1, 0)` noch nicht. Wir wollen auch andere reelle Typen für `r` und `ϕ` zulassen. Der Einfachheit halber wandeln wir hier alles nach `Float64` um. Analog verfahren wir auch, wenn nur ein reelles oder komplexes Argument verwendet wird.\n", + "\n", + "```julia\n", + "PComplex(r::Real, ϕ::Real) = PComplex(Float64(r), Float64(ϕ))\n", + "PComplex(r::Real) = PComplex(Float64(r), 0.0)\n", + "PComplex(z::Complex) = PComplex(abs(z), angle(z))\n", + "\n", + "z3 = PComplex(-2); z4 = PComplex(3im)\n", + "@show z3 z4;\n", + "```\n", + "\n", + ":::" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/script1.sh b/nb/script1.sh new file mode 100755 index 0000000..801804c --- /dev/null +++ b/nb/script1.sh @@ -0,0 +1,7 @@ +#!/bin/bash +cp ../chapters/*.ipynb . +for i in *.ipynb + do + echo $i + jupyter nbconvert --inplace --clear-output --to notebook $i + done diff --git a/nb/summary.ipynb b/nb/summary.ipynb new file mode 100644 index 0000000..ba82a9c --- /dev/null +++ b/nb/summary.ipynb @@ -0,0 +1,167 @@ +{ + "cells": [ + { + "cell_type": "raw", + "id": "bb4361d9", + "metadata": {}, + "source": [ + "---\n", + "title: summary\n", + "---" + ] + }, + { + "cell_type": "markdown", + "id": "58e5805d", + "metadata": {}, + "source": [ + "format:\n", + " html:\n", + " include-in-header:\n", + " text: |\n", + " \n", + "\n", + "\n", + "https://github.com/JuliaPlots/PlotlyJS.jl/issues/322\n", + "\n", + "In summary, this book has no content whatsoever.\n", + "\n", + "https://discourse.julialang.org/t/seven-lines-of-julia-examples-sought/50416\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "caf6e3b3", + "metadata": {}, + "outputs": [], + "source": [ + "#| error: false\n", + "using PlotlyJS, Random\n", + "using HypertextLiteral\n", + "using JSON, UUIDs\n", + "using Base64\n", + "\n", + "function IJulia.display_dict(p::PlotlyJS.SyncPlot)\n", + " Dict(\n", + " # \"application/vnd.plotly.v1+json\" => JSON.lower(p),\n", + " # \"text/plain\" => sprint(show, \"text/plain\", p),\n", + " \"text/html\" => let\n", + " buf = IOBuffer()\n", + " show(buf, MIME(\"text/html\"), p)\n", + " String(resize!(buf.data, buf.size))\n", + " end,\n", + " \"image/png\" => let\n", + " buf = IOBuffer()\n", + " buf64 = Base64EncodePipe(buf)\n", + " show(buf64, MIME(\"image/png\"), p)\n", + " String(resize!(buf.data, buf.size))\n", + " end,\n", + "\n", + " )\n", + " end\n", + " \n", + " function Base.show(io::IO, mimetype::MIME\"text/html\", p::PlotlyJS.SyncPlot)\n", + " uuid = string(UUIDs.uuid4())\n", + " show(io,mimetype,@htl(\"\"\"\n", + "
\n", + " \n", + "\"\"\"))\n", + "end " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a6260dc2", + "metadata": {}, + "outputs": [], + "source": [ + "Random.seed!(42)\n", + "\n", + "N = 100\n", + "random_x = range(0, stop=1, length=N)\n", + "random_y0 = randn(N) .+ 5\n", + "random_y1 = randn(N)\n", + "random_y2 = randn(N) .- 5\n", + "\n", + "plot([\n", + " scatter(x=random_x, y=random_y0, mode=\"markers\", name=\"markers\"),\n", + " scatter(x=random_x, y=random_y1, mode=\"lines\", name=\"lines\"),\n", + " scatter(x=random_x, y=random_y2, mode=\"markers+lines\", name=\"markers+lines\")\n", + "])" + ] + }, + { + "cell_type": "markdown", + "id": "dd0a1a29", + "metadata": {}, + "source": [ + "jkjkjkj\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "813b97ce", + "metadata": {}, + "outputs": [], + "source": [ + "#| warning: false\n", + "\n", + "plot([\n", + " scatter(x=random_x, y=random_y0, mode=\"markers\", name=\"markers\") ])" + ] + }, + { + "cell_type": "markdown", + "id": "c271b5dc", + "metadata": {}, + "source": [ + ";;l;l;l\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6cb53248", + "metadata": {}, + "outputs": [], + "source": [ + "#| warning: false\n", + "\n", + "plot([\n", + " scatter(x=random_x, y=random_y2, mode=\"markers\", name=\"markers\") ])" + ] + }, + { + "cell_type": "markdown", + "id": "7df06b26", + "metadata": {}, + "source": [ + "lllklk" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/syntax.ipynb b/nb/syntax.ipynb new file mode 100644 index 0000000..074b2a9 --- /dev/null +++ b/nb/syntax.ipynb @@ -0,0 +1,1185 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "d56a820e", + "metadata": {}, + "source": [ + "# Grundlagen der Syntax\n", + "\n", + "## Namen von Variablen, Funktionen, Typen etc.\n", + "\n", + "- Namen können Buchstaben, Ziffern, den Unterstrich `_` und das Ausrufezeichen `!` enthalten.\n", + "- Das erste Zeichen muss ein Buchstabe oder ein Unterstrich sein.\n", + "- Groß- und Kleinbuchstaben werden unterschieden: `Nmax` und `NMAX` sind verschiedene Variablen.\n", + "- Als Zeichensatz wird [Unicode](https://home.unicode.org/) verwendet. Damit stehen über 150 Schriften und zahlreiche Symbole zur Verfügung.\n", + "- Es gibt eine kurze [Liste reservierter Schlüsselwörter](https://docs.julialang.org/en/v1/base/base/#Keywords): `if, then, function, true, false,...`\n", + "\n", + ":::{.callout-tip} \n", + "## Beispiel\n", + "\n", + "zulässig: `i, x, Ω, x2, DieUnbekannteZahl, neuer_Wert, 🎷, Zähler, лічильник, einself!!!!,...`\n", + "\n", + "unzulässig: `Uwe's_Funktion, 3achsen, A#B, $this_is_not_Perl, true,...` \n", + ":::\n", + "\n", + "----\n", + "\n", + ":::{.callout-note }\n", + "## Anmerkung \n", + "\n", + "Neben den *reserved keywords* der Kernsprache sind zahlreiche weitere Funktionen und Objekte vordefiniert, wie z.B. die mathematischen Funktionen `sqrt(), log(), sin()`.\n", + "Diese Definitionen finden sich in dem Modul `Base`, welches Julia beim Start automatisch lädt. \n", + "Namen aus `Base` können umdefiniert werden, solange sie noch nicht verwendet wurden:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ff07d3b4", + "metadata": {}, + "outputs": [], + "source": [ + "#| error: true \n", + "log = 3\n", + "1 + log" + ] + }, + { + "cell_type": "markdown", + "id": "da69601f", + "metadata": {}, + "source": [ + "Jetzt ist natürlich der Logarithmus kaputt:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "88275d81", + "metadata": {}, + "outputs": [], + "source": [ + "#| error: true\n", + "x = log(10)" + ] + }, + { + "cell_type": "markdown", + "id": "5ecfdec6", + "metadata": {}, + "source": [ + "(siehe auch )\n", + ":::\n", + "\n", + "## Anweisungen\n", + "\n", + "- Im Normalfall enthält eine Zeile eine Anweisung.\n", + "- Wenn eine Anweisung am Zeilenende als unvollständig erkennbar ist durch \n", + " - offene Klammern\n", + " - Operationszeichen,\n", + " \n", + " dann wird die nächste Zeile als Fortsetzung aufgefasst.\n", + "- Mehrere Anweisungen pro Zeile können durch Semikolon getrennt werden.\n", + "- Im interaktiven Betrieb (REPL oder Notebook) unterdrückt ein Semikolon nach der letzten Anweisung die Ausgabe des Ergebnisses dieser Anweisung.\n", + "\n", + ":::{.callout-tip}\n", + "## Beispiel \n", + "\n", + "Im interaktiven Betrieb wird der Wert der letzten Anweisung auch ohne explizites `print()` ausgegeben:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dc76d67e", + "metadata": {}, + "outputs": [], + "source": [ + "println(\"Hallo 🌍!\")\n", + "x = sum([i^2 for i=1:10])" + ] + }, + { + "cell_type": "markdown", + "id": "6b068f1c", + "metadata": {}, + "source": [ + "Das Semikolon unterdrückt das:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "efd01a2c", + "metadata": {}, + "outputs": [], + "source": [ + "println(\"Hallo 🌍!\")\n", + "x = sum([i^2 for i=1:10]);" + ] + }, + { + "cell_type": "markdown", + "id": "18387226", + "metadata": {}, + "source": [ + ":::\n", + "\n", + "---------\n", + "\n", + "\n", + ":::{.callout-warning }\n", + "\n", + "Bei mehrzeiligen Anweisungen muss die fortzusetzende Zeile mit einer offenen Operation oder Klammer enden: \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "41df7f55", + "metadata": {}, + "outputs": [], + "source": [ + "x = sin(π/2) +\n", + " 3 * cos(0)" + ] + }, + { + "cell_type": "markdown", + "id": "61e668f9", + "metadata": {}, + "source": [ + "Also geht das Folgende schief, aber leider **ohne eine Fehlermeldung**!\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "694793eb", + "metadata": {}, + "outputs": [], + "source": [ + "#| error: true\n", + "#| warning: true\n", + "x = sin(π/2)\n", + " + 3 * cos(0)\n", + "println(x)" + ] + }, + { + "cell_type": "markdown", + "id": "88c64cd2", + "metadata": {}, + "source": [ + "Hier wird das `+` in der zweiten Zeile als Präfix-Operator (Vorzeichen) interpretiert. Damit sind 1. und 2. Zeile jeweils für sich vollständige, korrekte Ausdrücke (auch wenn die 2. Zeile natürlich völlig nutzlos ist) und werden auch so abgearbeitet. \n", + "\n", + "Moral: Wenn man längere Ausdrücke auf mehrere Zeilen aufteilen will, sollte man immer eine Klammer aufmachen. Dann ist egal, wo der Zeilenumbruch ist:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8ec8508d", + "metadata": {}, + "outputs": [], + "source": [ + "x = ( sin(π/2) \n", + " + 3 * cos(0) )\n", + "println(x)" + ] + }, + { + "cell_type": "markdown", + "id": "1b323891", + "metadata": {}, + "source": [ + ":::\n", + "\n", + "\n", + "## Kommentare\n", + "\n", + "Julia kennt 2 Arten von Kommentaren im Programmtext:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d733f6a2", + "metadata": {}, + "outputs": [], + "source": [ + "# Einzeilige Kommentare beginnen mit einem Doppelkreuz.\n", + "\n", + "x = 2 # alles vom '#' bis zum Zeilenende ist ein Kommentar und wird ignoriert. x = 3" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cf4ef498", + "metadata": {}, + "outputs": [], + "source": [ + "#= \n", + " Ein- und mehrzeilige Kommentare können zwischen #= ... =# eingeschlossen werden.\n", + " Dabei sind verschachtelte Kommentare möglich. \n", + " #= \n", + " d.h., anders als in C/C++/Java endet der Kommentar nicht mit dem ersten \n", + " Kommentar-Endezeichen, sondern die #=...=# - Paare wirken wie Klammern. \n", + " =# \n", + " Der automatische 'syntax highlighter' weiss das leider noch nicht, wie die wechselnde \n", + " Graufärbung dieses Kommentars zeigt. \n", + "=#\n", + "\n", + "\n", + "x #= das ist ein seltener Variablenname! =# = 3 " + ] + }, + { + "cell_type": "markdown", + "id": "e0fc09d1", + "metadata": {}, + "source": [ + "## Datentypen Teil I \n", + "\n", + "- Julia ist eine [stark typisierte](https://de.wikipedia.org/wiki/Starke_Typisierung) Sprache. Alle Objekte haben einen Typ. Funktionen/Operationen erwarten Argumente mit dem richtigen Typ.\n", + "- Julia ist eine [dynamisch typisierte](https://de.wikipedia.org/wiki/Dynamische_Typisierung) Sprache. Variablen haben keinen Typ. Sie sind Namen, die durch Zuweisung `x = ...` an Objekte gebunden werden können.\n", + "- Wenn man vom „Typ einer Variablen“ spricht, meint man den Typ des Objektes, das der Variablen gerade zugewiesen ist.\n", + "- Funktionen/Operatoren können verschiedene *methods* für verschiedene Argumenttypen implementieren.\n", + "- Abhängig von den konkreten Argumenttypen wird dann bei Verwendung einer Funktion entschieden, welche Methode benutzt wird ([*dynamic dispatch*](https://en.wikipedia.org/wiki/Dynamic_dispatch)).\n", + "\n", + "\n", + "Einfache Basistypen sind z.B.:\n", + "\n", + "```\n", + "Int64, Float64, String, Char, Bool\n", + "```\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0ba7db71", + "metadata": {}, + "outputs": [], + "source": [ + "x = 2\n", + "x, typeof(x), sizeof(x) " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ad90519a", + "metadata": {}, + "outputs": [], + "source": [ + "x = 0.2\n", + "x, typeof(x), sizeof(x) " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e36334d2", + "metadata": {}, + "outputs": [], + "source": [ + "x = \"Hallo!\"\n", + "x, typeof(x), sizeof(x) " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f48d35a6", + "metadata": {}, + "outputs": [], + "source": [ + "x = 'Ω'\n", + "x, typeof(x), sizeof(x) " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0eb5282b", + "metadata": {}, + "outputs": [], + "source": [ + "x = 3 > π\n", + "x, typeof(x), sizeof(x) " + ] + }, + { + "cell_type": "markdown", + "id": "6407ce53", + "metadata": {}, + "source": [ + "- `sizeof()` liefert die Größe eines Objekts oder Typs in Bytes (1 Byte = 8 Bit)\n", + "- 64bit Ganzzahlen und 64bit Gleitkommazahlen entsprechen dem Befehlssatz moderner Prozessoren und sind daher die numerischen Standardtypen.\n", + "- Zeichen/*chars* `'A'` und Zeichenketten/*strings* `\"A\"` der Länge 1 sind verschiedene Objekte. \n", + "\n", + "## Ablaufsteuerung\n", + "\n", + "### `if`-Blöcke\n", + "\n", + "- Ein `if`-Block *kann* **beliebig viele** `elseif`-Zweige und als letztes maximal **einen** `else`-Zweig enthalten.\n", + "- Der Block hat einen Wert, den Wert der letzten ausgeführten Anweisung.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d2c3f6c8", + "metadata": {}, + "outputs": [], + "source": [ + "x = 33\n", + "y = 44\n", + "z = 34\n", + "\n", + "if x < y && z != x # elseif- und else-Blöcke sind optional\n", + " println(\"yes\")\n", + " x += 10\n", + "elseif x < z # beliebig viele elseif-Blöcke\n", + " println(\" x is smaller than z\")\n", + "elseif x == z+1 \n", + " println(\" x is successor of z\")\n", + "else # maximal ein else-Block \n", + " println(\"Alles falsch\")\n", + "end # Wert des gesamten Blocks ist der Wert der \n", + " # letzten ausgeführten Auswertung" + ] + }, + { + "cell_type": "markdown", + "id": "868ae573", + "metadata": {}, + "source": [ + "Kurze Blöcke kann man in eine Zeile schreiben:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "76f17f5f", + "metadata": {}, + "outputs": [], + "source": [ + "if x > 10 println(\"x is larger than 10\") end " + ] + }, + { + "cell_type": "markdown", + "id": "ef1e84b5", + "metadata": {}, + "source": [ + "Der Wert eines `if`-Blocks kann natürlich zugewiesen werden:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "318501e9", + "metadata": {}, + "outputs": [], + "source": [ + "y = 33\n", + "z = if y > 10 \n", + " println(\"y is larger than 10\") \n", + " y += 1 \n", + " end\n", + "z " + ] + }, + { + "cell_type": "markdown", + "id": "0c05b161", + "metadata": {}, + "source": [ + "### Auswahloperator (ternary operator) `test ? exp1 : exp2`\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "40e9db00", + "metadata": {}, + "outputs": [], + "source": [ + "x = 20\n", + "y = 15\n", + "z = x < y ? x+1 : y+1" + ] + }, + { + "cell_type": "markdown", + "id": "48705675", + "metadata": {}, + "source": [ + "ist äquivalent zu\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dadac914", + "metadata": {}, + "outputs": [], + "source": [ + "z = if x < y\n", + " x+1\n", + " else\n", + " y+1\n", + " end" + ] + }, + { + "cell_type": "markdown", + "id": "8d122010", + "metadata": {}, + "source": [ + "## Vergleiche, Tests, Logische Operationen\n", + "\n", + "### Arithmetische Vergleiche\n", + "\n", + "- `==`\n", + "- `!=`, `≠`\n", + "- `>`\n", + "- `>=`, `≥`\n", + "- `<`\n", + "- `<=`, `≤`\n", + "\n", + "Wie üblich, ist der Test auf Gleichheit `==` vom Zuweisungsoperator `=` zu unterscheiden. Vergleichen lässt sich so gut wie alles:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "13005342", + "metadata": {}, + "outputs": [], + "source": [ + "\"Aachen\" < \"Leipzig\", 10 ≤ 10.01, [3,4,5] < [3,6,2]" + ] + }, + { + "cell_type": "markdown", + "id": "dd31f487", + "metadata": {}, + "source": [ + "Nun ja, fast alles:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7491b44b", + "metadata": {}, + "outputs": [], + "source": [ + "3 < \"vier\"" + ] + }, + { + "cell_type": "markdown", + "id": "d5eace21", + "metadata": {}, + "source": [ + "Die Fehlermeldung zeigt ein paar Grundprinzipien von Julia:\n", + "\n", + "- Operatoren sind auch nur Funktionen: `x < y` wird zum Funktionsaufruf `isless(x, y)`.\n", + "- Funktionen (und damit Operatoren) können verschiedene *methods* für verschiedene Argumenttypen implementieren. \n", + "- Abhängig von den konkreten Argumenttypen wird beim Aufruf der Funktion entschieden, welche Methode benutzt wird ([*dynamic dispatch*](https://en.wikipedia.org/wiki/Dynamic_dispatch)).\n", + "\n", + "Man kann sich alle Methoden zu einer Funktion anzeigen lassen. Das gibt einen Einblick in das komplexe Typssystem von Julia:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6538caaf", + "metadata": {}, + "outputs": [], + "source": [ + "methods(<)" + ] + }, + { + "cell_type": "markdown", + "id": "297ce845", + "metadata": {}, + "source": [ + "Zuletzt noch: Vergleiche können gekettet werden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "449eba70", + "metadata": {}, + "outputs": [], + "source": [ + "10 < x ≤ 100 # das ist äquivalent zu\n", + " # 10 < x && x ≤ 100" + ] + }, + { + "cell_type": "markdown", + "id": "9f4b1c41", + "metadata": {}, + "source": [ + "### Tests \n", + "Einge Funktionen vom Typ `f(c::Char) -> Bool`\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "18d77ec1", + "metadata": {}, + "outputs": [], + "source": [ + "isnumeric('a'), isnumeric('7'), isletter('a')" + ] + }, + { + "cell_type": "markdown", + "id": "2dc1c0aa", + "metadata": {}, + "source": [ + "und vom Typ `f(s1::String, s2::String) -> Bool`\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ea9be46e", + "metadata": {}, + "outputs": [], + "source": [ + "contains(\"Lampenschirm\", \"pensch\"), startswith(\"Lampenschirm\", \"Lamb\"), endswith(\"Lampenschirm\", \"rm\")" + ] + }, + { + "cell_type": "markdown", + "id": "af8b3ce6", + "metadata": {}, + "source": [ + "- Die Funktion `in(item, collection) -> Bool` testet, ob `item` in `collection` ist. \n", + "- Sie hat auch das Alias ` ∈(item, collection)` und \n", + "- sowohl `in` als auch `∈` können auch als Infix-Operatoren geschrieben werden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e811c4d8", + "metadata": {}, + "outputs": [], + "source": [ + "x = 3\n", + "x in [1, 2, 3, 4, 5]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "15f8ba27", + "metadata": {}, + "outputs": [], + "source": [ + "x ∈ [1, 2, 33, 4, 5]" + ] + }, + { + "cell_type": "markdown", + "id": "6b811515", + "metadata": {}, + "source": [ + "### Logische Operationen: `&&`, `||`, `!`\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ea9ad7fb", + "metadata": {}, + "outputs": [], + "source": [ + "3 < 4 && !(2 > 8) && !contains(\"aaa\", \"b\")" + ] + }, + { + "cell_type": "markdown", + "id": "a1886e91", + "metadata": {}, + "source": [ + "#### Bedingte Auswertung (_short circuit evaluation_)\n", + "\n", + "- in `a && b` wird `b` nur ausgewertet, wenn `a == true`\n", + "- in `a || b` wird `b` nur ausgewertet, wenn `a == false`\n", + "\n", + "(i) Damit kann `if test statement end` auch als `test && statement` geschrieben werden.\n", + "\n", + "(ii) Damit kann `if !test statement end` als `test || statement` geschrieben werden.\n", + "\n", + "Als Beispiel^[aus der [Julia-Dokumentation](https://docs.julialang.org/en/v1/manual/control-flow/#Short-Circuit-Evaluation)] hier eine Implementierung der Fakultätsfunktion *(factorial)*:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a5ef06bf", + "metadata": {}, + "outputs": [], + "source": [ + "function fact(n::Int)\n", + " n >= 0 || error(\"n must be non-negative\")\n", + " n == 0 && return 1\n", + " n * fact(n-1)\n", + "end\n", + "\n", + "fact(5)" + ] + }, + { + "cell_type": "markdown", + "id": "bb950743", + "metadata": {}, + "source": [ + "Natürlich kann man alle diese Tests auch Variablen vom Typ `Bool` zuordnen und\n", + "diese Variablen können als Tests in `if`- und `while`-Blöcken verwendet werden:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8c44f3bc", + "metadata": {}, + "outputs": [], + "source": [ + "x = 3 < 4\n", + "y = 5 ∈ [1, 2, 5, 7]\n", + "z = x && y\n", + "if z # äquivalent zu: if 3 < 4 && 5 in [1,2,5,7]\n", + " println(\"Stimmt alles!\")\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "b7d1e766", + "metadata": {}, + "source": [ + "- In Julia müssen alle Tests in einem logischen Ausdruck vom Typ `Bool` sein.\n", + "- Es gibt keine implizite Konvertierung à la *\"0 is false and 1 (or anything != 0) is true\"*\n", + "- Wenn `x` ein numerischer Typ ist, dann muss daher das C-Idiom `if(x)` als `if x != 0` geschrieben werden.\n", + "- Es gibt eine Ausnahme zur Unterstützung der _short circuit evaluation_:\n", + " - bei den Konstrukten `a && b && c...` bzw `a || b || c...` muss der letzte Teilausdruck nicht vom Typ `Bool` sein, wenn diese Konstrukte nicht als Tests in `if` oder `while` verwendet werden:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0a46fa2b", + "metadata": {}, + "outputs": [], + "source": [ + "z = 3 < 4 && 10 < 5 && sqrt(3^3)\n", + "z, typeof(z)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f56bbc75", + "metadata": {}, + "outputs": [], + "source": [ + "z = 3 < 4 && 10 < 50 && sqrt(3^3)\n", + "z, typeof(z)" + ] + }, + { + "cell_type": "markdown", + "id": "508cebd9", + "metadata": {}, + "source": [ + "## Schleifen *(loops)*\n", + "\n", + "### Die `while` (\"solange\")-Schleife\n", + "\n", + "\n", + "Syntax:\n", + "```\n", + "while *condition*\n", + " *loop body*\n", + "end\n", + "```\n", + "Eine Reihe von Anweisungen (der Schleifenkörper) wird immer wieder abgearbeitet, solange eine Bedingung erfüllt ist.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d91b98b6", + "metadata": {}, + "outputs": [], + "source": [ + "i = 1 # typischerweise braucht der Test der \n", + " # while-Schleife eine Vorbereitung ...\n", + "while i < 10 \n", + " println(i)\n", + " i += 2 # ... und ein update\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "f7edea21", + "metadata": {}, + "source": [ + "Der Körper einer `while`- und `for`-Schleife kann die Anweisungen `break` und `continue` enthalten. `break` stoppt die Schleife, `continue` überspringt den Rest des Schleifenkörpers und beginnt sofort mit dem nächsten Schleifendurchlauf.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "149c79ac", + "metadata": {}, + "outputs": [], + "source": [ + "i = 0\n", + "\n", + "while i<10\n", + " i += 1\n", + "\n", + " if i == 3\n", + " continue # beginne sofort nächsten Durchlauf,\n", + " end # überspringe Rest des Schleifenkörpers\n", + "\n", + " println(\"i = $i\")\n", + "\n", + " if i ≥ 5\n", + " break # breche Schleife ab\n", + " end\n", + "end\n", + "\n", + "println(\"Fertig!\")" + ] + }, + { + "cell_type": "markdown", + "id": "2e91f7a3", + "metadata": {}, + "source": [ + "Mit `break` kann man auch Endlosschleifen verlassen:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0b1b1ab2", + "metadata": {}, + "outputs": [], + "source": [ + "i = 1\n", + "\n", + "while true\n", + " println(2^i)\n", + " i += 1\n", + " if i > 8 break end\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "d9bc10da", + "metadata": {}, + "source": [ + "### `for`-Schleifen\n", + "\n", + "Syntax:\n", + "\n", + "```\n", + "for *var* in *iterable container*\n", + " *loop body*\n", + "end\n", + "```\n", + "\n", + "Der Schleifenkörper wird für alle Items aus einem Container durchlaufen. \n", + "\n", + "Statt `in` kann immer auch $\\in$ verwendet werden. Im Kopf einer `for`-Schleife kann auch `=` verwendet werden.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "99cd73cb", + "metadata": {}, + "outputs": [], + "source": [ + "for i ∈ [\"Mutter\", \"Vater\", \"Tochter\"]\n", + " println(i)\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "1a17064c", + "metadata": {}, + "source": [ + "Oft benötigt man einen numerischen Schleifenzähler. Dafür gibt es das *range*-Konstrukt. Die einfachsten Formen sind \n", + "`Start:Ende` und `Start:Schrittweite:Ende`. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3177977b", + "metadata": {}, + "outputs": [], + "source": [ + "endwert = 5\n", + "\n", + "for i ∈ 1:endwert\n", + " println(i^2)\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0c859acc", + "metadata": {}, + "outputs": [], + "source": [ + "for i = 1:5.5 print(\" $i\") end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c31d91f6", + "metadata": {}, + "outputs": [], + "source": [ + "for i = 1:2:14 print(\" $i\") end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c35be84d", + "metadata": {}, + "outputs": [], + "source": [ + "for k = 14 : -2.5 : 1 print(\" $k\") end" + ] + }, + { + "cell_type": "markdown", + "id": "19034238", + "metadata": {}, + "source": [ + "#### Geschachtelte Schleifen _(nested loops)_\n", + "\n", + "Ein `break` beendet die innerste Schleife.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9be68ac5", + "metadata": {}, + "outputs": [], + "source": [ + "for i = 1:3\n", + " for j = 1:3\n", + " println( (i,j) )\n", + " if j == 2\n", + " break\n", + " end\n", + " end\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "99328006", + "metadata": {}, + "source": [ + "Man kann *nested loops* auch in einer `for`-Anweisung zusammenfassen. Dann beendet ein `break` die Gesamtschleife.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e437369c", + "metadata": {}, + "outputs": [], + "source": [ + "for i = 1:3, j=1:3 # im Prinzip dasselbe wie oben, aber:\n", + " println( (i,j) )\n", + " if j == 2\n", + " break # break bricht hier die Gesamtschleife ab\n", + " end\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "e995a233", + "metadata": {}, + "source": [ + ":::{.callout-important .titlenormalxx}\n", + "## **Wichtig:** Die Semantik ist völlig anders, als bei C-artigen `for`-Schleifen!\n", + "\n", + "**Bei jedem Schleifendurchlauf wird die Laufvariable neu mit dem nächsten Element aus dem Container initialisiert.**\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2d2e2164", + "metadata": {}, + "outputs": [], + "source": [ + "for i = 1:5\n", + " print(i,\" ... \")\n", + " i += 2\n", + " println(i)\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "6c940891", + "metadata": {}, + "source": [ + "-------\n", + "\n", + "Die C-Semantik von `for(i=1; i<5; i++)` entspricht der `while`-Schleife:\n", + "```\n", + "i = 1\n", + "while i<5\n", + " *loop body* # hier kann auch wirksam an i rumgepfuscht werden\n", + " i += 1\n", + "end\n", + "```\n", + ":::\n", + "\n", + "## Unicode \n", + "\n", + "Julia verwendet Unicode als Zeichensatz. Damit können für Variablen, Funktionen etc auch Bezeichner aus nicht-lateinischen Schriften (zB Kyrillisch, Koreanisch, Sanskrit, Runen,\n", + "Emoji,...) verwendet werden. Die Frage, wie man solche Zeichen in seinem Editor eingeben kann und ob der verwendete Bildschirm-Font sie darstellen kann, ist nicht Julias Problem.\n", + "\n", + "- Einige Unicode-Zeichen, z.B. `≤, ≠, ≥, π, ∈, √`, können anstelle von `<=, !=, >=, pi, in, sqrt` verwendet werden. \n", + "\n", + "- über 3000 Unicode-Zeichen können in Julia in einer LaTeX-ähnlichen Weise mit der Tab-Vervollständigung eingegeben werden. \n", + " - `\\alpha` wird zu `α`, \n", + " - `\\euler` wird zu `ℯ` (Eulersche Zahl `exp(1)`, [spezielles Schreibschrift-e, `U+0212F`](https://www.htmlsymbol.com/unicode-code/212f.html))\n", + " - `\\le` wird zu `≤`,\n", + " - `\\in` wird zu `∈`,\n", + " - `\\:rainbow:` wird zu `🌈` \n", + " [Hier geht es zur Liste.](https://docs.julialang.org/en/v1/manual/unicode-input/)\n", + "\n", + "## Eigenheiten und Stolperfallen der Syntax\n", + "\n", + "- Man kann den Multiplikationsoperator `*` nach einer numerischen Konstanten weglassen, wenn eine Variable, Funktion oder öffnende Klammer folgt.\n", + " ```\n", + " z = 3.4x + 2(x+y) + xy\n", + " ```\n", + "\n", + "ist daher korrektes Julia. Beachte allerdings, dass der Term `xy` als eine Variable mit dem Namen xy interpretiert wird __und nicht__ als Produkt von x und y!\n", + "\n", + "- Diese Regel hat ein paar Tücken:\n", + "\n", + "Das funktioniert wie erwartet:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9d8ee587", + "metadata": {}, + "outputs": [], + "source": [ + "e = 7\n", + "3e " + ] + }, + { + "cell_type": "markdown", + "id": "4a3975ec", + "metadata": {}, + "source": [ + "Hier wird die Eingabe als Gleitkommazahl interpretiert -- und `3E+2` oder `3f+2` (Float32) ebenso. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fa68ebcd", + "metadata": {}, + "outputs": [], + "source": [ + "3e+2 " + ] + }, + { + "cell_type": "markdown", + "id": "d3b54ba7", + "metadata": {}, + "source": [ + "Ein Leerzeichen schafft Eindeutigkeit:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "378e3e06", + "metadata": {}, + "outputs": [], + "source": [ + "3e + 2 " + ] + }, + { + "cell_type": "markdown", + "id": "d23bc72e", + "metadata": {}, + "source": [ + "Das funktioniert:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ab2811f6", + "metadata": {}, + "outputs": [], + "source": [ + "x = 4\n", + "3x + 3 " + ] + }, + { + "cell_type": "markdown", + "id": "c81689d3", + "metadata": {}, + "source": [ + "...und das nicht. `0x`, `0o`, `0b` wird als Anfang einer Hexadezimal-, Oktal- bzw. Binärkonstanten interpretiert.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a5eff7fc", + "metadata": {}, + "outputs": [], + "source": [ + "3y + 0x " + ] + }, + { + "cell_type": "markdown", + "id": "ac739eda", + "metadata": {}, + "source": [ + "- Es gibt noch ein paar andere Fälle, bei denen die sehr kulante Syntax zu Überraschungen führt.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a69f9e83", + "metadata": {}, + "outputs": [], + "source": [ + "Wichtig = 21\n", + "Wichtig! = 42 # Bezeichner können auch ein ! enthalten\n", + "(Wichtig, Wichtig!)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3d9dc81e", + "metadata": {}, + "outputs": [], + "source": [ + "Wichtig!=88" + ] + }, + { + "cell_type": "markdown", + "id": "89722987", + "metadata": {}, + "source": [ + "Julia interpretiert das als Vergleich `Wichtig != 88`.\n", + "\n", + "Leerzeichen helfen:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "87a6cfd7", + "metadata": {}, + "outputs": [], + "source": [ + "Wichtig! = 88\n", + "Wichtig!" + ] + }, + { + "cell_type": "markdown", + "id": "90ae7dac", + "metadata": {}, + "source": [ + "- Operatoren der Form `.*`, `.+`,... haben in Julia eine spezielle Bedeutung (*broadcasting*, d.h., vektorisierte Operationen). \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "538cd36e", + "metadata": {}, + "outputs": [], + "source": [ + "1.+2." + ] + }, + { + "cell_type": "markdown", + "id": "7f39acd9", + "metadata": {}, + "source": [ + "Wieder gilt: Leerzeichen schaffen Klarheit!\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "45ceb4be", + "metadata": {}, + "outputs": [], + "source": [ + "1. + 2." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/nb/types.ipynb b/nb/types.ipynb new file mode 100644 index 0000000..946ff36 --- /dev/null +++ b/nb/types.ipynb @@ -0,0 +1,178 @@ +{ + "cells": [ + { + "cell_type": "raw", + "id": "f1724c85", + "metadata": {}, + "source": [ + "---\n", + "notebook-links: false\n", + "---" + ] + }, + { + "cell_type": "markdown", + "id": "75a11f86", + "metadata": {}, + "source": [ + "# Das Typsystem von Julia\n", + "\n", + "Man kann umfangreiche Programme in Julia schreiben, ohne auch nur eine einzige Typdeklaration verwenden zu müssen. Das ist natürlich Absicht und soll die Arbeit der Anwender vereinfachen.\n", + "\n", + "Wir blicken jetzt trotzdem mal unter die Motorhaube.\n", + "\n", + "## Die Typhierarchie\n", + "\n", + "Das Typsystem hat die Struktur eines Baums, dessen Wurzel der Typ `Any` ist. Mit den Funktionen `subtypes()` und `supertype()` kann man den Baum erforschen. Sie zeigen alle Kinder bzw. die Mutter eines Knotens an.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f3f47e9d", + "metadata": {}, + "outputs": [], + "source": [ + "subtypes(Int64)" + ] + }, + { + "cell_type": "markdown", + "id": "3cb68ade", + "metadata": {}, + "source": [ + "Das Ergebnis ist eine leere Liste von Typen. `Int64` ist ein sogenannter **konkreter Typ** und hat keine Untertypen.\n", + "\n", + "Wir klettern jetzt mal die Typhierarchie auf diesem Ast nach oben bis zur Wurzel (Informatiker-Bäume stehen bekanntlich immer auf dem Kopf).\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c7c10d75", + "metadata": {}, + "outputs": [], + "source": [ + "supertype(Int64)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "15b4e8d6", + "metadata": {}, + "outputs": [], + "source": [ + "supertype(Signed)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2c62f342", + "metadata": {}, + "outputs": [], + "source": [ + "supertype(Integer)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ee7eb511", + "metadata": {}, + "outputs": [], + "source": [ + "supertype(Real)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9ab37b54", + "metadata": {}, + "outputs": [], + "source": [ + "supertype(Number)" + ] + }, + { + "cell_type": "markdown", + "id": "d5fe3447", + "metadata": {}, + "source": [ + "Das wäre übrigens auch schneller gegangen: Die Funktion `supertypes()` (mit Plural-s) zeigt alle Vorfahren an.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "895d4570", + "metadata": {}, + "outputs": [], + "source": [ + "supertypes(Int64)" + ] + }, + { + "cell_type": "markdown", + "id": "79a45ce0", + "metadata": {}, + "source": [ + "Nun kann man sich die Knoten angucken:\n", + "\n", + "\n", + "\n", + "Mit einer kleinen rekursiven Funktion kann man schnell einen ganzen (Unter-)Baum ausdrucken: \n", + "\n", + "\n", + "\n", + "::::{.content-hidden unless-format=\"xxx\"}\n", + "\n", + "...und natürlich gibt es da auch ein Julia-Paket:\n", + "\n", + "\n", + "\n", + ":::\n", + "\n", + "\n", + "::: {.content-visible when-format=\"html\"}\n", + "![](../images/TypeTree2.png)\n", + ":::\n", + "\n", + "::: {.content-visible when-format=\"pdf\"}\n", + "![The type tree of numbers](../images/TypeTree2.png) {width=50%}\n", + ":::\n", + "\n", + "### Abstrakte und Konkrete Typen\n", + "\n", + "- Ein Objekt hat immer einen **konkreten** Typ. \n", + "- Komkrete Typen haben keine Untertypen mehr, sie sind immer „Blätter“ des Baumes.\n", + "- Abstrakte Typen können in der Definition von Funktionstypen, Argumenttypen, Elementtypen von zusammengesetzten Typen,... verwendet werden\n", + "\n", + "https://github.com/carstenbauer/JuliaCologne21/blob/master/Day1/1_types_and_dispatch.ipynb\n", + "\n", + "Zum Deklarieren und Testen der \"Abstammung\" gibt es einen eigenen Operator:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e300c9a9", + "metadata": {}, + "outputs": [], + "source": [ + "Int64 <: Number " + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/nb-types.ipynb b/notebooks/nb-types.ipynb new file mode 100644 index 0000000..b525f3d --- /dev/null +++ b/notebooks/nb-types.ipynb @@ -0,0 +1,182 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "46e9fc16", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "629" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#| label: nb4\n", + "#| echo: true\n", + "length(subtypes(Any))" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "9feb9e06", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number\n", + " Complex\n", + " Real\n", + " AbstractFloat\n", + " BigFloat\n", + " Float16\n", + " Float32\n", + " Float64\n", + " AbstractIrrational\n", + " Irrational\n", + " Integer\n", + " Bool\n", + " Signed\n", + " BigInt\n", + " Int128\n", + " Int16\n", + " Int32\n", + " Int64\n", + " Int8\n", + " Unsigned\n", + " UInt128\n", + " UInt16\n", + " UInt32\n", + " UInt64\n", + " UInt8\n", + " Rational\n" + ] + } + ], + "source": [ + "#| label: nb1\n", + "#| echo: true\n", + "\n", + "function show_subtype_tree(T, i=0)\n", + " println(\" \"^i, T)\n", + " for Ts ∈ subtypes(T)\n", + " show_subtype_tree(Ts, i+1)\n", + " end\n", + "end\n", + "\n", + "show_subtype_tree(Number)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "fe5594b9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number\n", + "├─ Complex\n", + "└─ Real\n", + " ├─ AbstractFloat\n", + " │ ├─ BigFloat\n", + " │ ├─ Float16\n", + " │ ├─ Float32\n", + " │ └─ Float64\n", + " ├─ AbstractIrrational\n", + " │ └─ Irrational\n", + " ├─ Integer\n", + " │ ├─ Bool\n", + " │ ├─ Signed\n", + " │ │ ├─ BigInt\n", + " │ │ ├─ Int128\n", + " │ │ ├─ Int16\n", + " │ │ ├─ Int32\n", + " │ │ ├─ Int64\n", + " │ │ └─ Int8\n", + " │ └─ Unsigned\n", + " │ ├─ UInt128\n", + " │ ├─ UInt16\n", + " │ ├─ UInt32\n", + " │ ├─ UInt64\n", + " │ └─ UInt8\n", + " └─ Rational\n" + ] + } + ], + "source": [ + "#| label: nb2\n", + "#| echo: true\n", + "using AbstractTrees\n", + "\n", + "AbstractTrees.children(x::Type) = subtypes(x)\n", + "print_tree(Number)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "0dcccd86", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4-element Vector{Any}:\n", + " AbstractFloat\n", + " AbstractIrrational\n", + " Integer\n", + " Rational" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#| label: nb3\n", + "#| echo: true\n", + "subtypes(Real)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dfabcc51", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "@webio": { + "lastCommId": null, + "lastKernelId": null + }, + "kernelspec": { + "display_name": "Julia 1.8.5", + "language": "julia", + "name": "julia-1.8" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/nb-types.ipynb.html b/notebooks/nb-types.ipynb.html new file mode 100644 index 0000000..8c3799c --- /dev/null +++ b/notebooks/nb-types.ipynb.html @@ -0,0 +1,615 @@ + + + + + + + + + + Julia für Numerik – nb-types + + + + + + +
+
nb-types.ipynb
+ Download Notebook +
+
+
+ +
+ +
+ + +
+ + + +
+
function show_subtype_tree(T, i=0)
+    println("       "^i, T)
+    for Ts ∈ subtypes(T)
+        show_subtype_tree(Ts, i+1)
+    end
+end
+
+show_subtype_tree(Number)
+
+
Number
+       Complex
+       Real
+              AbstractFloat
+                     BigFloat
+                     Float16
+                     Float32
+                     Float64
+              AbstractIrrational
+                     Irrational
+              Integer
+                     Bool
+                     Signed
+                            BigInt
+                            Int128
+                            Int16
+                            Int32
+                            Int64
+                            Int8
+                     Unsigned
+                            UInt128
+                            UInt16
+                            UInt32
+                            UInt64
+                            UInt8
+              Rational
+
+
+
+
using AbstractTrees
+
+AbstractTrees.children(x::Type) = subtypes(x)
+print_tree(Number)
+
+
Number
+├─ Complex
+└─ Real
+   ├─ AbstractFloat
+   │  ├─ BigFloat
+   │  ├─ Float16
+   │  ├─ Float32
+   │  └─ Float64
+   ├─ AbstractIrrational
+   │  └─ Irrational
+   ├─ Integer
+   │  ├─ Bool
+   │  ├─ Signed
+   │  │  ├─ BigInt
+   │  │  ├─ Int128
+   │  │  ├─ Int16
+   │  │  ├─ Int32
+   │  │  ├─ Int64
+   │  │  └─ Int8
+   │  └─ Unsigned
+   │     ├─ UInt128
+   │     ├─ UInt16
+   │     ├─ UInt32
+   │     ├─ UInt64
+   │     └─ UInt8
+   └─ Rational
+
+
+ + +
+
+
+
+
All content licenced under [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/). +
+
+
+   +
+
+
Created with [Quarto](https://quarto.org/) +
+
+
+
+ + diff --git a/notebooks/nb-types.md b/notebooks/nb-types.md new file mode 100644 index 0000000..6592830 --- /dev/null +++ b/notebooks/nb-types.md @@ -0,0 +1,87 @@ +::: {#nb1 .cell execution_count=1} +``` {.julia .cell-code} +function show_subtype_tree(T, i=0) + println(" "^i, T) + for Ts ∈ subtypes(T) + show_subtype_tree(Ts, i+1) + end +end + +show_subtype_tree(Number) +``` + +::: {.cell-output .cell-output-stdout} +``` +Number + Complex + Real + AbstractFloat + BigFloat + Float16 + Float32 + Float64 + AbstractIrrational + Irrational + Integer + Bool + Signed + BigInt + Int128 + Int16 + Int32 + Int64 + Int8 + Unsigned + UInt128 + UInt16 + UInt32 + UInt64 + UInt8 + Rational +``` +::: +::: + + +::: {#nb2 .cell execution_count=2} +``` {.julia .cell-code} +using AbstractTrees + +AbstractTrees.children(x::Type) = subtypes(x) +print_tree(Number) +``` + +::: {.cell-output .cell-output-stdout} +``` +Number +├─ Complex +└─ Real + ├─ AbstractFloat + │ ├─ BigFloat + │ ├─ Float16 + │ ├─ Float32 + │ └─ Float64 + ├─ AbstractIrrational + │ └─ Irrational + ├─ Integer + │ ├─ Bool + │ ├─ Signed + │ │ ├─ BigInt + │ │ ├─ Int128 + │ │ ├─ Int16 + │ │ ├─ Int32 + │ │ ├─ Int64 + │ │ └─ Int8 + │ └─ Unsigned + │ ├─ UInt128 + │ ├─ UInt16 + │ ├─ UInt32 + │ ├─ UInt64 + │ └─ UInt8 + └─ Rational +``` +::: +::: + + + diff --git a/notebooks/nb1.ipynb b/notebooks/nb1.ipynb new file mode 100644 index 0000000..f9291b7 --- /dev/null +++ b/notebooks/nb1.ipynb @@ -0,0 +1,55 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "8da1eabc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hello!\n" + ] + } + ], + "source": [ + "#| label: cell1\n", + "#| echo: true\n", + "\n", + "\n", + "print(\"Hello!\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8bd33e25", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}

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