python - numpy - matrix multiple 3x3 and 100x100x3 arrays?

Question

I have the following:

import numpy as np

XYZ_to_sRGB_mat_D50 = np.asarray([
    [3.1338561, -1.6168667, -0.4906146],
    [-0.9787684, 1.9161415, 0.0334540],
    [0.0719453, -0.2289914, 1.4052427],
])

XYZ_1 = np.asarray([0.25, 0.4, 0.1])
XYZ_2 = np.random.rand(100,100,3)

np.matmul(XYZ_to_sRGB_mat_D50, XYZ_1) # valid operation
np.matmul(XYZ_to_sRGB_mat_D50, XYZ_2) # makes no sense mathematically

How do I perform the same operation on XYZ_2 that I would on XYZ_2? Do I somehow reshape the array first?

Answer 1

It seems you are trying to sum-reduce the last axis of XYZ_to_sRGB_mat_D50 (axis=1) with the last one of XYZ_2 (axis=2). So, you can use np.tensordot like so -

np.tensordot(XYZ_2, XYZ_to_sRGB_mat_D50, axes=((2),(1)))

Related post to understand tensordot.

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For completeness, we can surely use np.matmul too after swappping last two axes of XYZ_2, like so -

np.matmul(XYZ_to_sRGB_mat_D50, XYZ_2.swapaxes(1,2)).swapaxes(1,2)

This won't be as efficient as tensordot one.

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Runtime test -

In [158]: XYZ_to_sRGB_mat_D50 = np.asarray([
     ...:     [3.1338561, -1.6168667, -0.4906146],
     ...:     [-0.9787684, 1.9161415, 0.0334540],
     ...:     [0.0719453, -0.2289914, 1.4052427],
     ...: ])
     ...: 
     ...: XYZ_1 = np.asarray([0.25, 0.4, 0.1])
     ...: XYZ_2 = np.random.rand(100,100,3)

# @Julien's soln
In [159]: %timeit XYZ_2.dot(XYZ_to_sRGB_mat_D50.T)
1000 loops, best of 3: 450 μs per loop

In [160]: %timeit np.tensordot(XYZ_2, XYZ_to_sRGB_mat_D50, axes=((2),(1)))
10000 loops, best of 3: 73.1 μs per loop

Generally speaking, when it comes to sum-reductions on tensors, tensordot is much more efficient. Since, the axis of sum-reduction is just one, we can make the tensor a 2D array by reshaping, use np.dot, get the result and reshape back to 3D.