003_Numpy的常见运算

1.加减乘除幂运算

import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
import math
from matplotlib import cm 
def visual_2D(array, vmax, vmin):
    
    fig_width = math.ceil(array.shape[1] * 0.5)
    fig_length = math.ceil(array.shape[0] * 0.5)
    
    fig, ax = plt.subplots(figsize = (fig_width, fig_length))
    
    sns.heatmap(array,
               vmax = vmax,
               vmin = vmin,
               annot = True,
               fmt = '.0f',
               square = True,
               cmap = 'RdYlBu_r',
               linewidth = .5,
               cbar = False,
               xticklabels = False,
               yticklabels = False,
               ax = ax)

def visual_1D(array):
    fix, ax = plt.subplots()
    
    colors = cm.RdYlBu_r(np.linspace(0, 1, len(array)))
    
    for idx,num in enumerate(array):
        circle_idx = plt.Circle((idx, 0 ), 
                                0.5,
                               facecolor = colors[idx],
                               edgecolor = 'w')
        ax.add_patch(circle_idx)
        ax.text(idx, 0, s = str(array[idx]),
                horizontalalignment = 'center',
                verticalalignment = 'center'
               )
    ax.set_xlim(-0.6, 0.6 + len(array))
    ax.set_ylim(-0.6, 0.6)
    ax.axis('off')
    
    ax.set_aspect('equal', adjustable = 'box')
    
def visual_fx(x_array, y_array, step = False):
    fig, ax = plt.subplots(figsize = (5, 5))
    ax.plot([-5, 5], [-5, 5], c = 'r', ls = '--', lw = 0.5)
    
    if step:
        ax.step(x_array,y_array)
    else:
        ax.plot(x_array,y_array)
    ax.set_xlim(-5, 5)
    ax.set_ylim(-5, 5)
    ax.axvline(0, c = 'b')
    ax.axhline(0, c = 'b')
    ax.set_xlabel('x')
    ax.set_ylabel('f(x)')
    plt.grid(True)
    ax.set_aspect('equal', adjustable = 'box')

a = np.arange(-2,3)
b = np.full(5,2)
print('a + b =',a+b)
print('a - b =',a-b)
print('a * b =',a*b)
print('a / b =',a/b)
print('a **b =',a**b)

a + b = [0 1 2 3 4]
a - b = [-4 -3 -2 -1  0]
a * b = [-4 -2  0  2  4]
a / b = [-1.  -0.5  0.   0.5  1. ]
a **b = [4 1 0 1 4]

注：二维数组和多维数组和一维数组的运算法则一致

2.广播原则

2.1一维数组和标量

a = np.arange(-2,3) 
B = 2
print(f'a = {a} b = {B}')
print('a + 2 =',a+B)
print('a - 2 =',a-B)
print('a * 2 =',a*B)
print('a / 2 =',a/B)
print('a **2 =',a**B)

a = [-2 -1  0  1  2] b = 2
a + 2 = [0 1 2 3 4]
a - 2 = [-4 -3 -2 -1  0]
a * 2 = [-4 -2  0  2  4]
a / 2 = [-1.  -0.5  0.   0.5  1. ]
a **2 = [4 1 0 1 4]

2.2一维数组和列向量

一维数组和列向量相加的过程：
a：

0	1	2	3	4
-2	-1	0	1	2
-2	-1	0	1	2
-2	-1	0	1	2

b

0	1	2	3	4
1	1	1	1	1
2	2	2	2	2
3	3	3	3	3

把两个数组扩充到同一维度再相加

a = np.arange(-2,3) 
b = np.arange(1,4)
b = b[:,np.newaxis]
visual_1D(a)
visual_2D(b,4,1)
visual_2D(a+b,4,1)

2.3二维数组和标量

# 二维数组和标量的乘法久相当于：
a = np.array([[j for j in range(-2,3)] for i in range(3)])
b = 2
c = np.full_like(a,b)   # 构造一个全为 b 的数组 然后和 a 数组做运算

a = np.array([[j for j in range(-2,3)] for i in range(3)])
b = 2
visual_2D(a,2,-2)
visual_2D(a+b,2,-2)
visual_2D(a*b,2,-2)

2.4二维数组和一维数组

a = np.array([[j for j in range(-2,3)] for i in range(3)])
b = np.arange(-2,3) 
visual_1D(b)
visual_2D(a * b,2,-2)

2.4二维数组和列向量

a = np.array([[j for j in range(-2,3)] for i in range(3)])
b = np.arange(0,3) 
b = b[:,np.newaxis]
visual_2D(a, 2, -2)
visual_2D(b, 3,  0)
visual_2D(a + b,2,-2)

3.统计运算

np.random.seed(10)
a = np.random.randint(10,size = (4,5))
visual_2D(a, 10, 0)
a.max() 
visual_1D(a.max(axis = 0))  # axis 用来计算某一个维度最大值
visual_2D(a.max(axis = 1, keepdims = True), 10, 0) # keepdims 用来保持列向量

4.常见函数

幂函数

x = np.linspace(-5,6,100)
y = np.power(x, 2)
visual_fx(x,y)
# y = np.power(x, 3)
# visual_fx(x,y)

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三角函数

x = np.linspace(-5,6,100)
y = np.sin(x)
# y = np.arcsin(x)
# y = np.cos(x)
# y = np.arccos(x)
# y = np.tan(x)
# y = np.arctan(x)
visual_fx(x,y)

绝对值函数

x = np.linspace(-5,6,100)
y = np.abs(x)
visual_fx(x,y)

向下取整

x = np.linspace(-5,6,100)
y = np.floor(x)
visual_fx(x,y,step = False)

向上取整

x = np.linspace(-5,6,100)
y = np.ceil(x)
visual_fx(x,y,step = True)  # 对比step取true和上一个cell step 取 false的区别

指数函数

x = np.linspace(-5,6,100)
y = np.exp(x)
visual_fx(x,y)

对数函数

x = np.linspace(-5,6,100)
y = np.log(x)
visual_fx(x,y)

C:\Users\23991\AppData\Local\Temp\ipykernel_13416\2861088069.py:2: RuntimeWarning: divide by zero encountered in log
  y = np.log(x)
C:\Users\23991\AppData\Local\Temp\ipykernel_13416\2861088069.py:2: RuntimeWarning: invalid value encountered in log
  y = np.log(x)