Numpy

numpy

numpy属性

属性： 形状，数量...

import numpy as np
a = np.arange(9).reshape(3, 3)
print(a)

[[0 1 2]
 [3 4 5]
 [6 7 8]]

# 数组的维度 m*n
print(a.shape)

(3, 3)

# 数组轴的个数
print(a.ndim)

2

b = np.arange(27).reshape(3, 3, 3)
print(b)

[[[ 0  1  2]
  [ 3  4  5]
  [ 6  7  8]]

 [[ 9 10 11]
  [12 13 14]
  [15 16 17]]

 [[18 19 20]
  [21 22 23]
  [24 25 26]]]

print(b.ndim)

3

# 数组元素的总个数
print(b.size)

27

# 一个用来描述数组中元素类型的对象
print(b.dtype)

int32

创建数组

array, zeros, ones

# array([])创建数组
c = np.array([1,2,3,4,5])

print(c.dtype)

int32

# 转换数组中元素的类型
d = np.array([1,2,3,4,5], dtype='float64')

print(d.dtype)

float64

# 创建数值为0的数组
print(np.zeros((3,3,3)))

[[[ 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.]]]

# 创建数值为1的数组
print(np.ones((3,3,3)))

[[[ 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.]]]

基本运算

数组运算，常用函数。

数组运算

e = np.array([20,30,40,50])
f = np.arange(4)

print(e-f)

[20 29 38 47]

print(e*2)

[ 40  60  80 100]

# 返回输入数量的等比间隔，linspace(start, stop, num=50)
g = np.linspace(0,np.pi,3)

常用函数

# 求和
print(g.sum())

4.71238898038

# 累加
print(g.cumsum())

[ 0.          1.57079633  4.71238898]

# 对数
print(np.log(g))

[       -inf  0.45158271  1.14472989]


D:\Anaconda3\lib\site-packages\ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in log

# 指数
print(np.exp(g))

[  1.           4.81047738  23.14069263]

# 开方
print(np.sqrt(g))

[ 0.          1.25331414  1.77245385]

索引，切片和迭代

print(a)

[[0 1 2]
 [3 4 5]
 [6 7 8]]

print(a[:, 1])

[1 4 7]

print(a[1, :])

[3 4 5]

print(a[a>3])

[4 5 6 7 8]

print(b)

[[[ 0  1  2]
  [ 3  4  5]
  [ 6  7  8]]

 [[ 9 10 11]
  [12 13 14]
  [15 16 17]]

 [[18 19 20]
  [21 22 23]
  [24 25 26]]]

print(b[-1][-1][-1])

26

print(b[1:])

[[[ 9 10 11]
  [12 13 14]
  [15 16 17]]

 [[18 19 20]
  [21 22 23]
  [24 25 26]]]

# 迭代
for row in b[0][0]:
    print(row)

0
1
2

# flat数组元素迭代器
for element in b.flat:
    print(element)

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26

更改数组的形状

# 将多维数组降位一维
print(a.ravel())

[0 1 2 3 4 5 6 7 8]

a1 = np.array([9,10,11])

# 横向添加数组
a2 = np.vstack((a,a1))
print(a2)

[[ 0  1  2]
 [ 3  4  5]
 [ 6  7  8]
 [ 9 10 11]]

# 不改变原有数组
print(a2.reshape(2,6))

[[ 0  1  2  3  4  5]
 [ 6  7  8  9 10 11]]

# 改变原有数组
a2.resize(2,6)

print(a2)

[[ 0  1  2  3  4  5]
 [ 6  7  8  9 10 11]]

# 转变形状
print(a2.transpose())

[[ 0  6]
 [ 1  7]
 [ 2  8]
 [ 3  9]
 [ 4 10]
 [ 5 11]]

print(a2)

[[ 0  1  2  3  4  5]
 [ 6  7  8  9 10 11]]

# 垂直切分
print(np.hsplit(a2,3))

[array([[0, 1],
       [6, 7]]), array([[2, 3],
       [8, 9]]), array([[ 4,  5],
       [10, 11]])]

# 生成对角矩阵
print(np.eye(5))

[[ 1.  0.  0.  0.  0.]
 [ 0.  1.  0.  0.  0.]
 [ 0.  0.  1.  0.  0.]
 [ 0.  0.  0.  1.  0.]
 [ 0.  0.  0.  0.  1.]]

矩阵计算基础

矩阵相乘

矩阵A和B必须是相符的矩阵，A的列要等于B的行。

A = np.array([
[1, 2],
[4, 5],
[7, 8]
])
B = np.array([
[4, 4, 2],
[2, 3, 1],
])
print(np.dot(A, B))

[[ 8 10  4]
 [26 31 13]
 [44 52 22]]

逆矩阵

矩阵与逆矩阵相乘为 [[1,0][0,1]]

A=np.array([[2,1],[1,-2]])
# 计算逆矩阵
A_=np.linalg.inv(A)
print(A)
print(A_)
print(np.dot(A,A_))

[[ 2  1]
 [ 1 -2]]
[[ 0.4  0.2]
 [ 0.2 -0.4]]
[[ 1.  0.]
 [ 0.  1.]]

矩阵解线代：

b=np.array([[1],[1]])
z=np.dot(A_,b)
print(z)

[[ 0.6]
 [-0.2]]