用python代替matlab

一般用Matlab来做数据处理、科学计算、机器学习等，可以用SciPy替代，包含了算法库和数学工具包：

NumPy：提供了数组，以及相关的大量数学函数
Matplotlib：绘图库

参考：

numpy教程 https://www.runoob.com/numpy/numpy-tutorial.html

SciPy Lecture Notes 中文版 https://wizardforcel.gitbooks.io/scipy-lecture-notes/content/index.html

文档： Numpy API： https://numpy.org/doc/stable/reference/ Matplotlib API：https://matplotlib.org/stable/api/index.html

环境布置：anaconda + vscode + jupyter¶

refer: vscode官方博客提到了「文学式编程」「Literate programming」 https://code.visualstudio.com/blogs/2021/08/05/notebooks

//TODO:

jupyter允许你在文档中插入Markdown、代码段，这样就可以轻松地写代码相关的文章，而拿到它的人也能轻松的运行程序观察效果，例如abc.ipynb档，内嵌了Markdown和一段Python程序：

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "这是一段文字"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "import tensorflow as tf\n",
    "\n",
    "mnist = tf.keras.datasets.mnist\n",
    "\n",
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n",
    "x_train, x_test = x_train / 255.0, x_test / 255.0\n",
    "\n",
    "model = tf.keras.models.Sequential([\n",
    "  tf.keras.layers.Flatten(input_shape=(28, 28)),\n",
    "  tf.keras.layers.Dense(128, activation='relu'),\n",
    "  tf.keras.layers.Dropout(0.2),\n",
    "  tf.keras.layers.Dense(10, activation='softmax')\n",
    "])\n",
    "\n",
    "model.compile(optimizer='adam',\n",
    "              loss='sparse_categorical_crossentropy',\n",
    "              metrics=['accuracy'])\n",
    "\n",
    "model.fit(x_train, y_train, epochs=5)\n",
    "\n",
    "model.evaluate(x_test,  y_test, verbose=2)"
   ],
   "outputs": [],
   "metadata": {}
  }
 ],
 "metadata": {
  "orig_nbformat": 4,
  "language_info": {
   "name": "python",
   "version": "3.8.3",
   "mimetype": "text/x-python",
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "pygments_lexer": "ipython3",
   "nbconvert_exporter": "python",
   "file_extension": ".py"
  },
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.8.3 64-bit ('base': conda)"
  },
  "interpreter": {
   "hash": "aaa97bc5370cf97ed399135bd4cca32d07276e3f65c685ca649928a10d743540"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}

实例¶

创建环境：

$ conda create -n math python=3.8
$ conda activate math
$ pip install matplotlib

测试程序：

import numpy as np
import matplotlib.pyplot as plt

scale_val = 256
sample_rate = 16000
sin_freq = 10
half_scale = scale_val/2

x = np.arange(0, 16000)
y = half_scale * np.sin(x*sin_freq*(2*np.pi)/sample_rate) + half_scale
plt.plot(x, y)
plt.show()

pandas¶

https://www.pypandas.cn/docs/getting_started/

强大的 Python 数据分析支持库，主要用于数据处理，比如I/O导入数据（从csv/excel/sql数据库）、合并分组等。

$\begin{align*} y = y(x,t) &= A e^{i\theta} \\ &= A (\cos \theta + i \sin \theta) \\ &= A (\cos(kx - \omega t) + i \sin(kx - \omega t)) \\ &= A\cos(kx - \omega t) + i A\sin(kx - \omega t) \\ &= A\cos \Big(\frac{2\pi}{\lambda}x - \frac{2\pi v}{\lambda} t \Big) + i A\sin \Big(\frac{2\pi}{\lambda}x - \frac{2\pi v}{\lambda} t \Big) \\ &= A\cos \frac{2\pi}{\lambda} (x - v t) + i A\sin \frac{2\pi}{\lambda} (x - v t) \end{align*}$

SymPy符号计算¶

数值计算和符号计算的区别，符号计算在过程中会保留符号，例如计算sin(pi)时，数值计算不保证结果为0，而符号计算最后计算得出0.

参考：

SymPy符号计算-让Python帮我们推公式

SymPy 符号计算基本教程

用SymPy可以帮助展开公式、化简数式.. 比如：

>>> x = symbols('x')
>>> simplify(sin(x)**2)
sin(x)**2
>>> simplify(sin(x)**2+cos(x)**2)
1
>>> simplify(sin(x)**2+cos(x)**2+x)
x + 1

带符号的矩阵计算例子：

>>> a = Matrix([[1, x], [3, 4], [0, 2]])
>>> b = Matrix([[3], [4]])
>>> a*b
Matrix([
[4*x + 3],
[     25],
[      8]])

python音频合成¶

https://pythonaudiosynthesisbasics.com/

这个网站提示了

把声卡当信号发生器
生成正波形文件

matplotlib显示中文¶

plt.rcParams['font.sans-serif']=['NotoSerif'] #用来正常显示中文标签 或者SimHei
plt.rcParams['axes.unicode_minus']=False #用来正常显示负号

python可视化¶

Pyecharts