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I get two 3d matrix A (32x3x3) and B(32x3x3), and I want to get matrix C with dimension 32x3x3. The calculation can be done using loop like:
a = numpy.random.rand(32, 3, 3)
b = numpy.random.rand(32, 3, 3)
c = numpy.random.rand(32, 3, 3)
for i in range(32):
c[i] = numpy.dot(a[i], b[i])
I believe there must be a more efficient one-line solution to this problem. Can anybody help, thanks.
880
multidimensional matrices are as follows: 1. The number of elements in the second dimension being multiplied in the first multidimensional matrix must equal the number of elements in the first dimension being multiplied of the second multidimensional matrix. That is, Ndb(A) = Nda(B).
A 3D matrix is nothing but a collection (or a stack) of many 2D matrices, just like how a 2D matrix is a collection/stack of many 1D vectors. So, matrix multiplication of 3D matrices involves multiple multiplications of 2D matrices, which eventually boils down to a dot product between their row/column vectors.
To multiply two matrices use the dot() function of NumPy. It takes only 2 arguments and returns the product of two matrices.
You could do this using np.einsum:
In [142]: old = orig(a,b)
In [143]: new = np.einsum('ijk,ikl->ijl', a, b)
In [144]: np.allclose(old, new)
Out[144]: True
One advantage of using einsum is that you can almost read off what it's doing from the indices: leave the first axis alone (i), and perform a matrix multiplication on the last two (jk,kl->jl)).
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