Python Numpy matrix multiplication using loop to multiply multiple matrices together

Question

I have written code which creates matrices with name matrixi, where i is replaced with the current loop number:

for i in range(len(node2)):
    if sOrP[i] == 'S':
        #print('series connection')
        matrixTemplate = numpy.array([[1.0, 0.0], [0.0, 1.0]])  #Got to put 1.0 else it doesnt work
        matrixTemplate[0][1] = frequenciesList[0][i]
        globals()['matrix%s' % i] = matrixTemplate
        #print(matrixTemplate)
    elif sOrP[i] == 'P':
        #print('parallel connection')
        matrixTemplate = numpy.array([[1.0, 0.0], [0.0, 1.0]])
        matrixTemplate[1][0] = 1 / frequenciesList[0][i]
        globals()['matrix%s' % i] = matrixTemplate
        #print(matrixTemplate)

I then need to multiply the created matrices together:

Ty = matrix0 @ matrix1 @ matrix2 @ matrix3 @ matrix4 @ matrix5 @ matrix6 @ matrix7 @ matrix8 @ matrix9

This works but the code has to be able to take multiple inputs with potentially more or fewer matrices being created. In that case it wouldn't work.

Would it be possible to do the multiplication part using a loop or function?

dzang · Accepted Answer · 2020-04-06 15:19:50Z

3

You could use a list (or a dictionary) to hold your matrices:

matrices = []

for i in range(len(node2)):

    if (sOrP[i] == 'S'):
        #print('series connection')
        matrixTemplate = numpy.array([[1.0, 0.0],[0.0, 1.0]]) #Got to put 1.0 else it doesnt work

        matrixTemplate[0][1] = frequenciesList[0][i]

        matrices.append(matrixTemplate)

        #print(matrixTemplate)

    elif (sOrP[i] == 'P'):
        #print('parallel connection')
        matrixTemplate = numpy.array([[1.0, 0.0],[0.0, 1.0]])

        matrixTemplate[1][0] = 1/frequenciesList[0][i]

        matrices.append(matrixTemplate)

        #print(matrixTemplate)

And then use reduce and numpy.matmul to compute your total matrix product:

from functools import reduce

Ty = reduce(numpy.matmul, matrices)

edited Apr 6, 2020 at 15:19

answered Apr 6, 2020 at 15:14

dzang

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Comments

Mathieu · Accepted Answer · 2020-04-06 15:33:41Z

0

You can use either a loop or a numpy function.

Loop implementation:

matrixes = [M1, M2, ..., Mn]
A = matrixes[0]
for i in range(1, len(matrixes)):
    B = matrixes[i]
    A = np.dot(A, B)

First iteration: A = M1, B = M2; M1.M2

Second iteration: A = M1.M2, B = M3; M1.M2.M3

...

Numpy function: numpy.linalg.multi_dot(matrixes)

edited Apr 6, 2020 at 15:33

answered Apr 6, 2020 at 15:14

Mathieu

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1 Comment

Mathieu Over a year ago

By the way, np.linalg.multi_dot does exactly the same think as described by dzang, but with np.dot instead of np.matmul. If you want to know the differences between dot and matmul, you can look at this post.

bkraines · Accepted Answer · 2020-08-17 17:55:42Z

Setting the variables you have done is a pretty terrible way if doing it, as you seem to realize already. If your matrices are all nice and square, you only need one variable to hold the entire stack, shaped (len(node2), 2, 2).

Another point is your indexing. Numpy arrays are not lists. Your indices should look like [1, 0], not [1][0]. Answers like the following shameless plug explain why: https://stackoverflow.com/a/60919478/2988730.

Let's assume that sOrP and frequenciesList are numpy arrays. If they aren't, wrap them in a call to np.array. You can make the stack like this:

matrices = np.broadcast_to([[[1, 0], [0, 1]]], (len(node2), 2, 2)).copy()
maskS = (sOrP == 'S')
maskP = (sOrP == 'P')
matrices[maskS, 0, 1] = frequenciesList[maskS]
matrices[maskP, 1, 0] = 1 / frequenciesList[maskP]

You can verify that matrices[i] is equivalent to matrixi in your original construction.

The simple way to multiply all the matrices together would be using a loop:

Ty = np.eye(2)
for mat in matrices:
    Ty @= mat

But numpy is all about vectorization. As it happens, np.linalg.multidot was made to optimize this exact operation:

Ty = np.linalg.multidot(matrices)

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