如何计算numpy中两个矩阵的外积? [英] How to compute the outer product of two matrices in numpy?

问题描述

我有两个分别为NxK和MxK的矩阵A和B.我希望计算大小为NxMxK的张量C，使得C(i，j，k)= A(i，k)* B(j，k).

如何在numpy中有效地实现这一点? 所有尺寸都很大，因此不能选择循环.

解决方案

使用循环版本中迭代器的文字翻译作为np.einsum的字符串表示法，我们将获得解决方案-

np.einsum('ik,jk->ijk',A,B)

样品运行-

In [2]: N,K,M = 3,4,5

In [3]: A = np.random.rand(N,K)

In [4]: B = np.random.rand(M,K)

In [5]: np.einsum('ik,jk->ijk',A,B).shape
Out[5]: (3, 5, 4)

In [6]: (N,M,K)
Out[6]: (3, 5, 4)

I have two matrices A and B of size NxK and MxK respectively. I wish to compute a tensor C of size NxMxK such that C(i,j,k) = A(i,k)*B(j,k).

How can I implement this efficiently in numpy? All the dimensions are large, and hence, looping isn't an option.

解决方案

Using a literal translation of the iterators from the loopy version as string notation with np.einsum, we would have the solution -

np.einsum('ik,jk->ijk',A,B)

Sample run -

In [2]: N,K,M = 3,4,5

In [3]: A = np.random.rand(N,K)

In [4]: B = np.random.rand(M,K)

In [5]: np.einsum('ik,jk->ijk',A,B).shape
Out[5]: (3, 5, 4)

In [6]: (N,M,K)
Out[6]: (3, 5, 4)

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