Common knowledge arrangement of numpy database

Catalog

Array

np.ones()： Create an array

np.array()： Convert to array type

reshape()： Reorganize array

The array performs four operations  

ix_()： Slice the array

  Fusion between arrays ：hstack() and vstack()

save() Data access and load() load

ravel()： Is an array programming one-dimensional array

sort()： Sort by value

argmax()： Get the index of the maximum value  

argmin()： Get the minimum index  

matrix

mat()： Convert to matrix

eye()： Create identity matrix

bmat()： Composite matrix

The transpose of the matrix , Conjugate transpose of matrix  

A matrix can perform four operations  

Inverse matrix

Solve equations ： Where the matrix is the coefficient matrix , Resolve to array

Find eigenvalues and eigenvectors

Find the singular value decomposition of the matrix

Find the value of matrix determinant

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Array

np.ones()： Create an array

>>> import numpy as np
>>> z1=np.ones((3,3))# Create an array 
>>> print(z1)
[[1. 1. 1.]
 [1. 1. 1.]
 [1. 1. 1.]]
<class 'numpy.ndarray'>

np.array()： Convert to array type

>>> d1=[1,2,3,4,5,6,7,8,9]
>>> d11=np.array(d1)# Convert to array type 
>>> s11=d11.shape# View size 
>>> print(type(d11))
<class 'numpy.ndarray'>
>>> print(d11)
[1 2 3 4 5 6 7 8 9]
>>> print(s11)
(9,)

reshape()： Reorganize array

To learn more about the lesson view Python——numpy In the library reshape Usage of _ I am a little monster blog -CSDN Blog

The array performs four operations  

>>> A=np.array([[1,2],[3,4]])
>>> B=np.array([[5,6],[7,8]])
>>> c1=A-B
>>> c2=A*B# Array can perform four operations 
>>> E=np.exp(A)
>>> print(E)
[[ 2.71828183  7.3890561 ]
 [20.08553692 54.59815003]]

ix_()： Slice the array

>>> D=np.array([[1,2,3,4,],[5,6,99,6],[5,6,12,3],[7,8,5,32]])
>>> print(D)
>>> d1=D[np.ix_([1,2],[0,3])]
>>> d2=D[np.ix_(np.arange(3),[1,3])]
>>> d3=D[np.ix_(D[:,1]>5,[2])]
>>> print(d1,d2,d3,sep='\n')

[[ 1  2  3  4]
 [ 5  6 99  6]
 [ 5  6 12  3]
 [ 7  8  5 32]]
[[5 6]
 [5 3]]
[[2 4]
 [6 6]
 [6 3]]
[[99]
 [12]
 [ 5]]

  Fusion between arrays ：hstack() and vstack()

>>> A=np.array([[1,2],[3,4]])
>>> B=np.array([[5,6],[7,8]])
>>> C1=np.hstack((A,B))# The same number of lines is required 
>>> C2=np.vstack((A,B))# The number of columns is required to be the same 
>>> print(C1,C2,sep='\n')
[[1 2 5 6]
 [3 4 7 8]]
[[1 2]
 [3 4]
 [5 6]
 [7 8]]

save() Data access and load() load

# Access to data /// Use save(' file name ', Data name ) Store the data /// Use load(' file name . file type ')
>>> A=np.array([[1,2],[3,4]])
>>> np.save('data',A)
>>> Q=np.load('data.npy')
>>> print(Q)
[[1 2]
 [3 4]]

ravel()： Is an array programming one-dimensional array

>>> arr=np.arange(12)
>>> arr1=arr.reshape((3,4))
>>> arr2=arr1.ravel()
>>> print(arr,arr1,arr2,sep='\n')
[ 0  1  2  3  4  5  6  7  8  9 10 11]
[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]]
[ 0  1  2  3  4  5  6  7  8  9 10 11]

sort()： Sort by value

argmax()： Get the index of the maximum value  

argmin()： Get the minimum index  

>>> arrs=np.array([516,1,132,15,19,561,56,1616,16,16,65,13,651,16,12])
>>> arrs_1=np.sort(arrs)
>>> print(arrs_1)
[   1   12   13   15   16   16   16   19   56   65  132  516  561  651
 1616]
>>> arrs_2=arrs.reshape(3,5)
>>> print(arrs_2)
[[ 516    1  132   15   19]
 [ 561   56 1616   16   16]
 [  65   13  651   16   12]]
>>> maxindex=np.argmax(arrs)# Get the index of the maximum value 
>>> minindex=np.argmin(arrs)# Get the minimum index 
>>> maxindex_1=np.argmax(arrs_2,axis=0)
>>> minindex_1=np.argmin(arrs_2,axis=1)
>>> print(maxindex,minindex,maxindex_1,minindex_1,sep='\n')
7
1
[1 1 1 1 0]
[1 3 4]

matrix

mat()： Convert to matrix

>>> mat1=np.mat('1,5,9;,5,6,4;,6,8,7')# Convert to matrix 
>>> mat2=np.mat(arrs_2)
>>> print(mat1,arrs_2,sep='\n')
[[1 5 9]
 [5 6 4]
 [6 8 7]]
[[ 516    1  132   15   19]
 [ 561   56 1616   16   16]
 [  65   13  651   16   12]]

eye()： Create identity matrix

bmat()： Composite matrix

The transpose of the matrix , Conjugate transpose of matrix  

>>> arr1=np.eye(3)# Create identity matrix 
>>> arr2=arr1*4
>>> arr3=arr1*6
>>> mat_s=np.bmat('arr1 arr2 arr3;arr1 arr3 arr2;arr3 arr1 arr2')
>>> print(mat_s,end='\n')
[[1. 0. 0. 4. 0. 0. 6. 0. 0.]
 [0. 1. 0. 0. 4. 0. 0. 6. 0.]
 [0. 0. 1. 0. 0. 4. 0. 0. 6.]
 [1. 0. 0. 6. 0. 0. 4. 0. 0.]
 [0. 1. 0. 0. 6. 0. 0. 4. 0.]
 [0. 0. 1. 0. 0. 6. 0. 0. 4.]
 [6. 0. 0. 1. 0. 0. 4. 0. 0.]
 [0. 6. 0. 0. 1. 0. 0. 4. 0.]
 [0. 0. 6. 0. 0. 1. 0. 0. 4.]]
>>> print(mat_s.T,end='\n')# Transposition 
[[1. 0. 0. 1. 0. 0. 6. 0. 0.]
 [0. 1. 0. 0. 1. 0. 0. 6. 0.]
 [0. 0. 1. 0. 0. 1. 0. 0. 6.]
 [4. 0. 0. 6. 0. 0. 1. 0. 0.]
 [0. 4. 0. 0. 6. 0. 0. 1. 0.]
 [0. 0. 4. 0. 0. 6. 0. 0. 1.]
 [6. 0. 0. 4. 0. 0. 4. 0. 0.]
 [0. 6. 0. 0. 4. 0. 0. 4. 0.]
 [0. 0. 6. 0. 0. 4. 0. 0. 4.]]
>>> print(mat_s.H,end='\n')# Conjugate transpose 
[[1. 0. 0. 1. 0. 0. 6. 0. 0.]
 [0. 1. 0. 0. 1. 0. 0. 6. 0.]
 [0. 0. 1. 0. 0. 1. 0. 0. 6.]
 [4. 0. 0. 6. 0. 0. 1. 0. 0.]
 [0. 4. 0. 0. 6. 0. 0. 1. 0.]
 [0. 0. 4. 0. 0. 6. 0. 0. 1.]
 [6. 0. 0. 4. 0. 0. 4. 0. 0.]
 [0. 6. 0. 0. 4. 0. 0. 4. 0.]
 [0. 0. 6. 0. 0. 4. 0. 0. 4.]]
>>> print(mat_s.I,end='\n')# Inverse matrix 
[[-0.18181818  0.          0.          0.09090909  0.          0.
   0.18181818  0.          0.        ]
 [ 0.         -0.18181818  0.          0.          0.09090909  0.
   0.          0.18181818  0.        ]
 [ 0.          0.         -0.18181818  0.          0.          0.09090909
   0.          0.          0.18181818]
 [-0.18181818  0.          0.          0.29090909  0.          0.
  -0.01818182  0.          0.        ]
 [ 0.         -0.18181818  0.          0.          0.29090909  0.
   0.         -0.01818182  0.        ]
 [ 0.          0.         -0.18181818  0.          0.          0.29090909
   0.          0.         -0.01818182]
 [ 0.31818182  0.          0.         -0.20909091  0.          0.
  -0.01818182  0.          0.        ]
 [ 0.          0.31818182  0.          0.         -0.20909091  0.
   0.         -0.01818182  0.        ]
 [ 0.          0.          0.31818182  0.          0.         -0.20909091
   0.          0.         -0.01818182]]

A matrix can perform four operations  

# A matrix can perform four operations , According to the matrix algorithm in mathematics 
>>> mat1=np.mat('1,2,3;4,5,6;5,6,8')
>>> mat2=mat1*3
>>> mat3=mat1*mat2
>>> mat4=np.multiply(mat1,mat2)# Point multiplication 
>>> print(mat1,mat2,mat3,mat4,sep='\n')
[[1 2 3]
 [4 5 6]
 [5 6 8]]
[[ 3  6  9]
 [12 15 18]
 [15 18 24]]
[[ 72  90 117]
 [162 207 270]
 [207 264 345]]
[[  3  12  27]
 [ 48  75 108]
 [ 75 108 192]]

Inverse matrix

>>> mat=np.mat('1,1,1;1,2,3;,1,3,6')
>>> inverse=np.linalg.inv(mat)# Calculate the inverse matrix 
>>> print(mat)
[[1 1 1]
 [1 2 3]
 [1 3 6]]
>>> print(inverse)
[[ 3. -3.  1.]
 [-3.  5. -2.]
 [ 1. -2.  1.]]

Solve equations ： Where the matrix is the coefficient matrix , Resolve to array

>>> # Solve equations 
>>> A=np.mat('1,-1,1;2,1,0;,2,1,-1')
>>> b=np.array([4,3,-1])
>>> x=np.linalg.solve(A,b)
>>> print(x)
[1. 1. 4.]

Find eigenvalues and eigenvectors

>>> # Solve eigenvalues and eigenvectors 
>>> A=np.mat('1,0,2;0,3,0;2,0,1')
>>> print(np.linalg.eigvals(A))# The eigenvalue can be obtained directly 
[ 3. -1.  3.]
>>> a_value,a_vector=np.linalg.eig(A)
>>> print(a_value,a_vector,sep='\n')
[ 3. -1.  3.]
[[ 0.70710678 -0.70710678  0.        ]
 [ 0.          0.          1.        ]
 [ 0.70710678  0.70710678  0.        ]]

Find the singular value decomposition of the matrix

>>> A=np.mat('4.0,11.0,14.0;8.0,7.0,-2.0')
>>> u,s,v=np.linalg.svd(A,full_matrices=False)# Find the singular value decomposition of a matrix 
>>> print(u,s,v,sep='\n')
[[-0.9486833  -0.31622777]
 [-0.31622777  0.9486833 ]]
[18.97366596  9.48683298]
[[-0.33333333 -0.66666667 -0.66666667]
 [ 0.66666667  0.33333333 -0.66666667]]

Find the value of matrix determinant

>>> A=np.mat('1,-1,1;2,1,0;,2,1,-1')# Solve the value of matrix determinant 
>>> print(np.linalg.det(A))
-2.9999999999999996