numpy

# 约定俗成定义为np
import numpy as np

array

• data type, kind of like a list

one-dimensional array

• only one line
• Equivalent to a line in mathematics

lis = [1, 2, 3]
print(np.array(lis))

[1 2 3]

2D array (most used)

• row and column
• It is equivalent to a surface in mathematics, in which there are multiple lines, that is, multiple one-dimensional arrays are installed

arr = np.array([[1, 2, 3], [4, 5, 6]])
print(arr)

[[1 2 3]
 [4 5 6]]

The difference between np.array and list

1. np.array is multi-dimensional, list is one-dimensional
2. list does some operations on one-dimensional arrays, while numpy operates on multidimensional arrays

Get the rows and columns of a multidimensional array

arr = np.array([[1, 2, 3, 4], [5, 6, 7, 8]])

print(arr.shape)        # 把行和列返回在一个元祖中
print(arr.shape[0])     # 行
print(arr.shape[1])     # 列

(2, 4)
2
4

index of multidimensional array

• Square brackets are indexed, and rows and columns are separated by commas

print(arr)
print('-' * 10)
print(arr[1, 2])     # 第二行第三列
print(arr[0, [0, 1, 2, 3]])    # 第一行所有的值
print(arr[0, :])    # 第一行所有的值切片
print(arr[:, 0])    # 第一列所有的值切片
print(arr[:, :])    # 整个多维数组切片

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

Advanced Features

• Add judgment and filter functions

# 筛选出值大于50的数
arr = np.array([[12, 123, 20], [145, 56, 24], [51, 1, 2]])
print(arr)
print('-' * 20)
print(arr > 50)
print('-' * 20)
print(arr[arr > 50])
print('-' * 20) 

[[ 12 123  20]
 [145  56  24]
 [ 51   1   2]]
--------------------
[[False  True False]
 [ True  True False]
 [ True False False]]
--------------------
[123 145  56  51]
--------------------

Element replacement of multidimensional arrays

arr = np.array([[12, 123, 20], [145, 56, 24], [51, 1, 2]])
print(arr)
print('-' * 20)
arr[1, 2] = 20    # 第二行的第三个元素改为20
print(arr)
print('-' * 20)
arr[1, :] = 20    # 第一行所有元素改为0
print(arr)
print('-' * 20)
arr[arr > 50] = 40  # 大于50的全变为40
print(arr)
print('-' * 20)

[[ 12 123  20]
 [145  56  24]
 [ 51   1   2]]
--------------------
[[ 12 123  20]
 [145  56  20]
 [ 51   1   2]]
--------------------
[[ 12 123  20]
 [ 20  20  20]
 [ 51   1   2]]
--------------------
[[12 40 20]
 [20 20 20]
 [40  1  2]]
--------------------

merging of multidimensional arrays

arr1 = np.array([[1, 2, 3], [4, 5, 6]])
arr2 = np.array([[7, 8, 9], [10, 11, 12]])

• vstack and hstack can only put one parameter, this parameter must be a container

# vstack和hstack
print(np.vstack((arr1, arr2)))  # v:vertical 垂直
print('-' * 20)
print(np.hstack([arr1, arr2]))  # h:horizon 水平
print('-' * 20)

[[ 1  2  3]
 [ 4  5  6]
 [ 7  8  9]
 [10 11 12]]
--------------------
[[ 1  2  3  7  8  9]
 [ 4  5  6 10 11 12]]
--------------------

• ==In numpy, in order to uniformly process, as long as there is an axis parameter, axis=0 is a column, and axis=1 is a row==

# concatenate
print(np.concatenate((arr1, arr2)))   # 默认是垂直
print('-' * 20)
print(np.concatenate((arr1, arr2), axis=0))  # 0是列
print('-' * 20)
print(np.concatenate((arr1, arr2), axis=1))  # 1是行
print('-' * 20)

[[ 1  2  3]
 [ 4  5  6]
 [ 7  8  9]
 [10 11 12]]
--------------------
[[ 1  2  3]
 [ 4  5  6]
 [ 7  8  9]
 [10 11 12]]
--------------------
[[ 1  2  3  7  8  9]
 [ 4  5  6 10 11 12]]
--------------------

Create multidimensional arrays with functional methods

Create a one-dimensional array

• range

print(np.arange(10))
print(np.arange(1, 10, 2))

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

Create a multidimensional array

• zeros

# zeros全是0
print(np.zeros((3, 4)))    
print('-' * 20)
print(np.zeros((2, 4, 3)))     # 3控制一维,(3,4)控制二维,(3,4,5)控制三维

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

• ones

# ones全是1
print(np.ones((3, 4)))

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

• eys

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.]]

Matrix operations

+   两个矩阵对应元素相加
-   两个矩阵对应元素相减
*   两个矩阵对应元素相乘
/   两个矩阵对应元素相除，如果都是整数则取商
%   两个矩阵对应元素相除后取余数
**n 单个矩阵每个元素都取n次方，如**2：每个元素都取平方

# 元素对应相加，可以加一维，但是不要这么做
arr1 = np.array([[1, 2, 3], [4, 5, 6]])
arr2 = np.array([[7, 8, 9], [10, 11, 12]])
print(arr1+arr2)

#...其余方法都大同小异

[[ 8 10 12]
 [14 16 18]]

Dot product, transpose, inversion (understanding, math knowledge)

# 点乘
# 需要一个(m,n)的数组和一个(n,m)的数组
# T可以把数组转置
np.dot(arr1, arr2.T)

array([[ 50,  68],
       [122, 167]])

# 求逆
np.linalg.inv(np.dot(arr1, arr2.T))

array([[ 3.09259259, -1.25925926],
       [-2.25925926,  0.92592593]])

extremum

print(arr1)
print(arr1.max())
print(arr1.min())

[[1 2 3]
 [4 5 6]]
6
1

numpy generates random numbers

np.random.rand(3, 4)

array([[0.95163457, 0.8643344 , 0.86843741, 0.45000529],
       [0.01025429, 0.25391508, 0.28262799, 0.88679772],
       [0.43937459, 0.13525713, 0.13961072, 0.61232842]])

Fix random numbers, make it not random

rs = np.random.RandomState(1)
print(rs.rand(3, 4))

# 和上面作用相同
# np.random.seed(1)
# print(np.random.rand(3, 4))

[[4.17022005e-01 7.20324493e-01 1.14374817e-04 3.02332573e-01]
 [1.46755891e-01 9.23385948e-02 1.86260211e-01 3.45560727e-01]
 [3.96767474e-01 5.38816734e-01 4.19194514e-01 6.85219500e-01]]

3D arrays (understand)

• Multiple faces (2D array)