产品和总和,无需额外的内存分配

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英文:

Product and sum without addtional memory allocation

问题

在这个示例中,当计算C时,会创建一个大小为10x10x10x10x10的中间矩阵,然后立即折叠它。在NumPy中有没有办法避免这种情况?

英文:

Is there away to multiply two arrays and sum along an axis (or multiple axes) without allocating extra memory?

In this example:

import numpy as np

A = np.random.random((10, 10, 10))
B = np.random.random((10, 10, 10))

C = np.sum(A[:, None, :, :, None] * B[None, :, None, :, :], axis=(-1,-2))

When computing C, an intermediate matrix of size 10x10x10x10x10 is created only to be collapsed immediately. Is there a way to avoid this in numpy?

答案1

得分: 4

这看起来像是对第二个数组的转置进行的点积:

C = A @ B.T

注意:原始问题中的操作是:C = np.sum(A[:, None, :] * B[None, :, :], axis=-1)

快速检查:

C1 = np.sum(A[:, None, :] * B[None, :, :], axis=-1)
C2 = A @ B.T

assert np.allclose(C1, C2)

您还可以使用 einsum 进行泛化:

np.einsum('ikl,jlm->ijk', A, B)

快速检查:

A = np.random.random((2, 3, 4))
B = np.random.random((2, 4, 5))

#             i    j   k  l    m         i   j    k   l  m
C1 = np.sum(A[:, None, :, :, None] * B[None, :, None, :, :], axis=(-1,-2))
C2 = np.einsum('ikl,jlm->ijk', A, B)

assert np.allclose(C1, C2)
英文:

This looks like a dot product with the transpose of the second array:

C = A @ B.T

NB. The operation in the original question was: C = np.sum(A[:, None, :] * B[None, :, :], axis=-1).

Quick check:

C1 = np.sum(A[:, None, :] * B[None, :, :], axis=-1)
C2 = A @ B.T

assert np.allclose(C1, C2)

You can generalize with einsum:

np.einsum('ikl,jlm->ijk', A, B)

Quick check:

A = np.random.random((2, 3, 4))
B = np.random.random((2, 4, 5))

#             i    j   k  l    m         i   j    k   l  m
C1 = np.sum(A[:, None, :, :, None] * B[None, :, None, :, :], axis=(-1,-2))
C2 = np.einsum('ikl,jlm->ijk', A, B)

assert np.allclose(C1, C2)

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  • 本文由 发表于 2023年4月6日 22:33:14
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