numpy 行列の積: 備忘録

初めに

einsumを使うため、行列の演算を整理しておく。

基本操作

matrix generation

import numpy as np
mat = np.array([[1,2],
                [3,4],
                [5,6]])

array([[1, 2],
       [3, 4],
       [5, 6]])

inverse matrix

mat = np.array([[1,2],
                [3,4],
                ])
mat_inv = np.linalg.inv(mat)

array([[-2. ,  1. ],
       [ 1.5, -0.5]])

pseudo inverser matrix

mat = np.array([[1,2],
                [3,4],
                ])
mat_inv2 = np.linalg.pinv(mat)

array([[-2. ,  1. ],
       [ 1.5, -0.5]])

transpose

mat = np.array([[1,2],
                [3,4],
                ])
mat_t = mat.T
array([[1, 3],
       [2, 4]])

積 Product

element-wise multiplication

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

[[1 2]
 [3 4]]

[[5 6]
 [7 8]]

matAB = np.multiply(matA, matB)

[[ 5 12]
 [21 32]]

inner product (dot product)

matA_dot_matB = np.dot(matA,matB)

[[19 22]
 [43 50]]

matmul()

matA_matmul_matB = np.matmul(matA, matB)

[[19, 22],
  [43, 50]]

outer product (cross product)

np.cross(matA, matB)
[-4, -4]