矩阵和向量的元素明智点积 [英] Element wise dot product of matrices and vectors
问题描述
此处,此处, 注意:我的实际情况比matrix1
和matrix2
对于np.einsum
,您可以使用:
np.einsum("ijk,ki->ji", matrices, vectors)
#array([[ 1., 5.],
# [ 1., 5.],
# [ 1., 5.],
# [ 1., 5.],
# [ 1., 5.]])
There are really similar questions here, here, here, but I don't really understand how to apply them to my case precisely.
I have an array of matrices and an array of vectors and I need element-wise dot product. Illustration:
In [1]: matrix1 = np.eye(5)
In [2]: matrix2 = np.eye(5) * 5
In [3]: matrices = np.array((matrix1,matrix2))
In [4]: matrices
Out[4]:
array([[[ 1., 0., 0., 0., 0.],
[ 0., 1., 0., 0., 0.],
[ 0., 0., 1., 0., 0.],
[ 0., 0., 0., 1., 0.],
[ 0., 0., 0., 0., 1.]],
[[ 5., 0., 0., 0., 0.],
[ 0., 5., 0., 0., 0.],
[ 0., 0., 5., 0., 0.],
[ 0., 0., 0., 5., 0.],
[ 0., 0., 0., 0., 5.]]])
In [5]: vectors = np.ones((5,2))
In [6]: vectors
Out[6]:
array([[ 1., 1.],
[ 1., 1.],
[ 1., 1.],
[ 1., 1.],
[ 1., 1.]])
In [9]: np.array([m @ v for m,v in zip(matrices, vectors.T)]).T
Out[9]:
array([[ 1., 5.],
[ 1., 5.],
[ 1., 5.],
[ 1., 5.],
[ 1., 5.]])
This last line is my desired output. Unfortunately it is very inefficient, for instance doing matrices @ vectors
that computes unwanted dot products due to broadcasting (if I understand well, it returns the first matrix dot the 2 vectors and the second matrix dot the 2 vectors) is actually faster.
I guess np.einsum
or np.tensordot
might be helpful here but all my attempts have failed:
In [30]: np.einsum("i,j", matrices, vectors)
ValueError: operand has more dimensions than subscripts given in einstein sum, but no '...' ellipsis provided to broadcast the extra dimensions.
In [34]: np.tensordot(matrices, vectors, axes=(0,1))
Out[34]:
array([[[ 6., 6., 6., 6., 6.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.]],
[[ 0., 0., 0., 0., 0.],
[ 6., 6., 6., 6., 6.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.]],
[[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 6., 6., 6., 6., 6.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.]],
[[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 6., 6., 6., 6., 6.],
[ 0., 0., 0., 0., 0.]],
[[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 6., 6., 6., 6., 6.]]])
NB: my real-case scenario use more complicated matrices than matrix1
and matrix2
With np.einsum
, you might use:
np.einsum("ijk,ki->ji", matrices, vectors)
#array([[ 1., 5.],
# [ 1., 5.],
# [ 1., 5.],
# [ 1., 5.],
# [ 1., 5.]])
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