[英]custom matrix multiplication with numpy
我想要一個奇怪的點積用於numpy中的矩陣乘法。 對於線[1,2,3]
矩陣的A
和列[4,5,6]
為基質B
,我想使用的“產品” min(1+4, 2+5, 3+6)
用於獲得矩陣積AB
。
In [498]: A = np.arange(12).reshape(4,3)
In [499]: B = np.arange(4,10).reshape(3,2)
In [500]: A
Out[500]:
array([[ 0, 1, 2],
[ 3, 4, 5],
[ 6, 7, 8],
[ 9, 10, 11]])
In [501]: B
Out[501]:
array([[4, 5],
[6, 7],
[8, 9]])
參考迭代解決方案:
In [504]: res = np.zeros((A.shape[0],B.shape[1]), A.dtype)
...: for i,row in enumerate(A):
...: for j,col in enumerate(B.T):
...: res[i,j] = np.min(row+col)
...:
In [505]: res
Out[505]:
array([[ 4, 5],
[ 7, 8],
[10, 11],
[13, 14]])
使用廣播的更快版本:
In [506]: np.min(A[:,:,None]+B[None,:,:], axis=1)
Out[506]:
array([[ 4, 5],
[ 7, 8],
[10, 11],
[13, 14]])
===
證明等效於矩陣乘積:
In [507]: np.dot(A,B)
Out[507]:
array([[ 22, 25],
[ 76, 88],
[130, 151],
[184, 214]])
In [508]: np.sum(A[:,:,None]*B[None,:,:], axis=1)
Out[508]:
array([[ 22, 25],
[ 76, 88],
[130, 151],
[184, 214]])
您可以使用循環和numpy來構建自己的自定義乘法函數,如下所示:
import numpy as np
x = np.array([[1, 2, 3],
[4 ,5, 6],
[7 ,8, 9]])
y = np.array([[4, 0, 6],
[5, 7, 3],
[6, 5, 9]])
def custom_multiply(x, y):
return np.array([min(row*column) for row in x for column in y.T]).reshape(x.shape[0], y.shape[1])
print(custom_multiply(x, y))
輸出:
[[ 4 0 6]
[16 0 15]
[28 0 24]]
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