master > master: handschrift - woche 15 aktualisiert

justfile

@@ -121,6 +121,17 @@ dist:
     @just build
     @just build-documentation
 
+# exports notebook to format: html, markdown, pdf, latex.
+export name format="pdf" theme="light":
+    @{{PYTHON}} -m jupyter nbconvert \
+        --allow-chromium-download \
+        --HTMLExporter.theme={{theme}} \
+        --TemplateExporter.exclude_input=false \
+        --to {{format}} \
+        --output-dir notes \
+        --ouput "notebook-{{name}}.{{format}}" \
+        notebooks/{{name}}.ipynb
+
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 # TARGETS: run
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

notebooks/week-10.ipynb

@@ -49,7 +49,7 @@
     "u[8] = -0.7\n",
     "u[58] = 1j * sqrt(2);\n",
     "\n",
-    "display_signal(u, 'Beispiel eines Vektors als Signal dargestellt');"
+    "display_signal(u, 'Beispiel eines Vektors in $\\mathbb{C}^{100}$ als Signal über $\\{0,1,2,\\ldots,99\\}$ dargestellt');"
    ]
   },
   {
@@ -101,26 +101,28 @@
     "Für $i\\in\\{0,1,\\ldots,n-1\\}$ ist die $i$-te von $\\mathcal{F}_{n}\\,u_{n,k}$\n",
     "\n",
     "$$\n",
+    "    \\begin{array}{rcl}\n",
     "    (\\mathcal{F}_{n}\\,u_{n,k})_{i}\n",
-    "    = \\sum_{j=0}^{n-1}\n",
+    "    &= &\\displaystyle\\sum_{j=0}^{n-1}\n",
-    "        (\\mathcal{F}_{n})_{ij}\\,(u_{n,k})_{j}\n",
+    "        (\\mathcal{F}_{n})_{ij}\\,(u_{n,k})_{j}\\\\\n",
-    "    = \\sum_{j=0}^{n-1}\n",
+    "    &= &\\displaystyle\\sum_{j=0}^{n-1}\n",
     "        \\tfrac{1}{\\sqrt{n}}\n",
     "        \\exp(-\\imath\\tfrac{2\\pi\\,ij}{n})\n",
     "        \\cdot\n",
     "        \\tfrac{1}{\\sqrt{n}}\n",
-    "        \\exp(\\imath\\tfrac{2\\pi\\,kj}{n})\n",
+    "        \\exp(\\imath\\tfrac{2\\pi\\,kj}{n})\\\\\n",
-    "    = \\frac{1}{n}\\sum_{j=0}^{n-1}\n",
+    "    &= &\\frac{1}{n}\\displaystyle\\sum_{j=0}^{n-1}\n",
     "        \\underbrace{\n",
     "            \\exp(\\imath\\tfrac{2\\pi\\,(k-i)j}{n})\n",
-    "        }_{= r^{j}}\n",
+    "        }_{= r^{j}}\\\\\n",
+    "    \\end{array}\n",
     "$$\n",
     "\n",
-    "wobei $r \\colonequals \\exp(\\imath\\tfrac{2\\pi\\,(k-i)}{n})$.\n",
+    "wobei $r := \\exp(\\imath\\tfrac{2\\pi\\,(k-i)}{n})$.\n",
     "Wir haben, dass\n",
     "    $r = 1$\n",
     "    $\\Leftrightarrow$\n",
-    "        $\\tfrac{k-i}{n} \\in \\Z$\n",
+    "        $\\tfrac{k-i}{n} \\in \\mathbb{Z}$\n",
     "    $\\Leftrightarrow$\n",
     "        $i = k$,\n",
     "da $0\\leq i,k \\leq n-1$.\n",
@@ -130,23 +132,34 @@
     "Aus der o.s. Berechnung erhält man also\n",
     "\n",
     "$$\n",
+    "    \\begin{array}{rcl}\n",
     "    (\\mathcal{F}_{n}\\,u_{n,k})_{i}\n",
-    "    = \\tfrac{1}{n}\\displaystyle\\sum_{j=0}^{n-1}r^{j}\n",
+    "    &= &\\tfrac{1}{n}\\displaystyle\\sum_{j=0}^{n-1}r^{j}\\\\\n",
-    "    = \\tfrac{1}{n}\n",
+    "    &= &\\tfrac{1}{n}\n",
-    "        \\begin{cases}\n",
+    "        \\left\\{\n",
+    "        \\begin{array}{lcl}\n",
     "            \\displaystyle\\sum_{j=0}^{n-1}1 &: &i = k\\\\\n",
-    "            \\frac{1 - r^{n}}{1 - r} &: &\\text{sonst}\\\\\n",
+    "            \\dfrac{1 - r^{n}}{1 - r} &: &\\text{sonst}\\\\\n",
-    "        \\end{cases}\n",
+    "        \\end{array}\n",
-    "    = \\tfrac{1}{n}\n",
+    "        \\right.\\\\\n",
-    "        \\begin{cases}\n",
+    "    &= &\\tfrac{1}{n}\n",
+    "        \\left\\{\n",
+    "        \\begin{array}{lcl}\n",
     "            n &: &i = k\\\\\n",
-    "            \\frac{1 - 1}{1 - r} &: &\\text{sonst}\\\\\n",
+    "            \\dfrac{1 - 1}{1 - r} &: &\\text{sonst}\\\\\n",
-    "        \\end{cases}\n",
+    "        \\end{array}\n",
-    "    = \\delta_{ik}.\n",
+    "        \\right.\\\\\n",
+    "    &= &\\left\\{\n",
+    "        \\begin{array}{lcl}\n",
+    "            1 &: &i = k\\\\\n",
+    "            0 &: &\\text{sonst}\\\\\n",
+    "        \\end{array}\n",
+    "        \\right.\\\\\n",
+    "    &= &\\delta_{ik}.\\\\\n",
+    "    \\end{array}\n",
     "$$\n",
     "\n",
-    "Darum $\n",
+    "Darum $\\mathcal{F}_{n}\\,u_{n,k}\n",
-    "    \\mathcal{F}_{n}\\,u_{n,k}\n",
     "    = \\left(\\begin{matrix}\n",
     "        0\\\\\n",
     "        0\\\\\n",
@@ -163,8 +176,7 @@
     "        \\\\\n",
     "        \\\\\n",
     "    \\end{matrix}\n",
-    "    = \\mathbf{e}_{k}\n",
+    "    = \\mathbf{e}_{k}$.\n"
-    "$.\n"
    ]
   },
   {
@@ -199,16 +211,33 @@
     "# Anzeige der Lösung:\n",
     "display_signal(u_guess, 'Geschätztes Signal');\n",
     "\n",
-    "# Verifikation von Lösung:\n",
+    "# Verifizierung der Lösung:\n",
-    "print(dedent(\n",
+    "display_latex(\n",
     "    f'''\n",
-    "    %error := ‖u_guess –  u‖ / ‖u‖\n",
+    "    $$\n",
-    "            = ‖F_n · (u_guess – u)‖ / ‖F_n · u‖\n",
+    "    \\\\begin{{array}}{{rcl}}\n",
-    "                ... wieso?? [Stichwort: unitär]\n",
+    "        \\\\%\\\\text{{error}}\n",
-    "            = ‖F_n · u_guess –  F_n · u‖ / ‖F_n · u‖\n",
+    "            &\\colonequals\n",
-    "            = {linalg.norm(F_n @ u_guess - F_mal_u)/linalg.norm(F_mal_u):.2%}\n",
+    "                &\\\\dfrac{{\\\\|u_{{\\\\text{{guess}}}} - u\\\\|}}{{\\\\|u\\\\|}}\\\\\\\\\n",
+    "            &=\n",
+    "                &\\\\dfrac{{\n",
+    "                    \\\\|\\\\mathcal{{F}}_{{n}}\\\\,(u_{{\\\\text{{guess}}}} - u)\\\\|\n",
+    "                }}{{\n",
+    "                    \\\\|\\\\mathcal{{F}}_{{n}}\\\\,u\\\\|\n",
+    "                }}\n",
+    "            \\\\quad\\\\text{{\\\\ldots wieso?? [Stichwort: unitär!]}}\\\\\\\\\n",
+    "            &= &\\\\dfrac{{\n",
+    "                    \\\\|\\\\mathcal{{F}}_{{n}}\\\\,u_{{\\\\text{{guess}}}} - \\\\mathcal{{F}}_{{n}}\\\\,u\\\\|\n",
+    "                }}{{\n",
+    "                    \\\\|\\\\mathcal{{F}}_{{n}}\\\\,u\\\\|\n",
+    "                }}\\\\\\\\\n",
+    "            &= &{linalg.norm(F_n @ u_guess - F_mal_u)/linalg.norm(F_mal_u):.2%}\n",
+    "            \\\\%\n",
+    "            \\\\\\\\\n",
+    "    \\\\end{{array}}\n",
+    "    $$\n",
     "    '''\n",
-    "));\n"
+    ");\n"
    ]
   }
  ],

src/thirdparty/render.py

@@ -6,14 +6,47 @@
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 from IPython.display import Latex;
-from IPython.display import display_latex;
-from IPython.display import display_png;
-from IPython.display import display_markdown;
 from IPython.display import display;
+from IPython.display import display_png;
+from IPython.display import display as display_text_ipython;
+from IPython.display import display_latex as display_latex_ipython;
+from IPython.display import display_markdown as display_md_ipython;
 import ipywidgets as widgets;
 # from array_to_latex import to_ltx as array_to_latex; # <- has issues
 from qiskit.visualization import array_to_latex;
 
+from functools import wraps;
+from typing import Callable;
+from typing import TypeVar;
+
+from src.thirdparty.misc import dedent;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# MODIFICATIONS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+T1 = TypeVar('T1');
+T2 = TypeVar('T2');
+
+def display_with_dedent(pre_process: Callable[[str], T1] = lambda x: x):
+    '''
+    Returns a decorator that modifies string -> string methods
+    '''
+    def dec(method: Callable[[T1], T2]) -> Callable[[str], T2]:
+        '''
+        Performs method but dedents first.
+        '''
+        @wraps(method)
+        def wrapped_method(text: str) -> T2:
+            return method(pre_process(dedent(text)));
+        return wrapped_method;
+
+    return dec;
+
+display_latex = display_with_dedent(Latex)(display_latex_ipython);
+display_text = display_with_dedent()(display_text_ipython);
+display_markdown = display_with_dedent()(display_md_ipython);
+
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 # EXPORTS
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~