没有numpy的矩阵求幂

Question

我需要编写一个函数来执行矩阵的常用幂运算

def matrix_power(a, power):
    rows, columns = len(a), len(a[0])
    result = np.zeros((rows, columns))
    b = a
    for step in range(1, power):
        for i in range(0, rows):
            for j in range(0, columns):
                for m in range(0, rows):
                    result[i][j] += a[i][m] * b[m][j]
        a = result
    return result
matrix_power(matrix, 3)

但出于某种原因，它给出了与np.linalg.matrix_power(matrix, 3)不同的答案可能是什么问题？

Answer 1

看到这个：

>>> import numpy as np
>>> result = np.zeros((3, 3))
>>> result
array([[0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.]])
>>> a = result
>>> result[1][0] += 42
>>> result
array([[ 0.,  0.,  0.],
       [42.,  0.,  0.],
       [ 0.,  0.,  0.]])
>>> a
array([[ 0.,  0.,  0.],
       [42.,  0.,  0.],
       [ 0.,  0.,  0.]])

您的代码中的问题是您没有将result复制到a并且当您稍后在循环中改变result时，您同时改变a 。

要制作副本，请将您的作业替换为：

a = result.copy()

Answer 2

def matrix_power(a, power):
    rows, columns = len(a), len(a[0])
    result = np.zeros((rows, columns))
    b = a
    for step in range(1, power):
        result = np.zeros((rows, columns)) # reset result to all zeroes matrix here
        for i in range(0, rows):
            for j in range(0, columns):
                for m in range(0, rows):
                    result[i][j] += a[i][m] * b[m][j]
        
        a = result
    for val in result:
        print(val)
    return result