From 847e7744ff5a7f02bc16185f801e34eaff53c399 Mon Sep 17 00:00:00 2001
From: raj_mathe <raj.dahya@math.uni-leipzig.de>
Date: Thu, 15 Dec 2022 07:05:50 +0100
Subject: [PATCH] =?UTF-8?q?master=20>=20master:=20src=20-=20f=C3=BCr=20not?=
 =?UTF-8?q?ebook=20wk10?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 src/maths/diagrams/__init__.py |  2 ++
 src/maths/diagrams/signal.py   | 48 ++++++++++++++++++++++++++++++++++
 src/thirdparty/maths.py        | 16 +++++++++++-
 src/thirdparty/render.py       |  4 +--
 src/thirdparty/types.py        |  4 +--
 5 files changed, 69 insertions(+), 5 deletions(-)
 create mode 100644 src/maths/diagrams/signal.py

diff --git a/src/maths/diagrams/__init__.py b/src/maths/diagrams/__init__.py
index 6b4eff7..a6b09d0 100644
--- a/src/maths/diagrams/__init__.py
+++ b/src/maths/diagrams/__init__.py
@@ -6,6 +6,7 @@
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 from src.maths.diagrams.sets import *;
+from src.maths.diagrams.signal import *;
 
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 # EXPORTS
@@ -14,4 +15,5 @@ from src.maths.diagrams.sets import *;
 __all__ = [
     'Function',
     'Functions',
+    'display_signal',
 ];
diff --git a/src/maths/diagrams/signal.py b/src/maths/diagrams/signal.py
new file mode 100644
index 0000000..2187df5
--- /dev/null
+++ b/src/maths/diagrams/signal.py
@@ -0,0 +1,48 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# IMPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+from __future__ import annotations;
+
+from src.thirdparty.code import *;
+from src.thirdparty.types import *;
+from src.thirdparty.maths import *;
+from src.thirdparty.plots import *;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# EXPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+__all__ = [
+    'display_signal',
+];
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# CONSTANTS / VARIABLES
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+def display_signal(
+    u: np.ndarray,
+    title: str,
+    max_labels = 10,
+):
+    n = len(u);
+    if n <= max_labels:
+        x_axis = list(range(n));
+    else:
+        skip = int(n/max_labels);
+        x_axis = [ k*skip for k in range(max_labels) ];
+
+    fig, axs = mplot.subplots(1, 1, constrained_layout=True);
+    mplot.title(title);
+    mplot.xlabel('»Zeit« [=Indizes]');
+    mplot.ylabel('Werte [=Einträge]');
+    axs.stem(linspace(0,n-1,n), np.real(u), label='reeller Teil', linefmt='red');
+    axs.stem(linspace(0,n-1,n) + 0.05, np.imag(u), label='imaginärer Teil', linefmt='lime');
+    mplot.legend();
+    axs.set_xticks(x_axis, labels=[ str(index) for index in x_axis]);
+    mplot.show();
+    return;
diff --git a/src/thirdparty/maths.py b/src/thirdparty/maths.py
index 39f3820..debcaff 100644
--- a/src/thirdparty/maths.py
+++ b/src/thirdparty/maths.py
@@ -6,10 +6,17 @@
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 from fractions import Fraction;
+from numpy import cos;
+from numpy import exp;
+from numpy import linalg;
+from numpy import linspace;
+from numpy import pi;
+from numpy import sin;
+from numpy import sqrt;
+from typing import TypeVar;
 import math;
 import numpy as np;
 import random;
-from typing import TypeVar;
 
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 # MODIFICATIONS
@@ -39,8 +46,15 @@ def sample(
 
 __all__ = [
     'Fraction',
+    'cos',
+    'exp',
+    'linalg',
+    'linspace',
     'math',
     'np',
+    'pi',
     'random',
     'sample',
+    'sin',
+    'sqrt',
 ];
diff --git a/src/thirdparty/render.py b/src/thirdparty/render.py
index 33b4893..477c6dc 100644
--- a/src/thirdparty/render.py
+++ b/src/thirdparty/render.py
@@ -19,11 +19,11 @@ from qiskit.visualization import array_to_latex;
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 __all__ = [
+    'Latex',
     'array_to_latex',
+    'display',
     'display_latex',
     'display_markdown',
     'display_png',
-    'display',
-    'Latex',
     'widgets',
 ];
diff --git a/src/thirdparty/types.py b/src/thirdparty/types.py
index 17ec4d3..b9bfd2f 100644
--- a/src/thirdparty/types.py
+++ b/src/thirdparty/types.py
@@ -38,8 +38,8 @@ from typing import Generic;
 from typing import Optional;
 from typing import Type;
 from typing import TypeVar;
-from typing_extensions import Concatenate;
-from typing_extensions import ParamSpec;
+from typing import Concatenate;
+from typing import ParamSpec;
 
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 # EXPORTS