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Kronecker Power of sparse matrices problem

asked 2020-05-02 22:36:12 +0100

SYLA gravatar image

updated 2020-05-12 13:10:53 +0100

Why the following code does not work? I try it also in loops.

import numpy

from scipy import sparse

from scipy.sparse import coo_matrix

def SparseMatrixPower(A,p):
    if p == 1: 
    elif Mod(p,2):
        return(SparseMatrixPower(A,SparseMatrixProduct(A,A)), (p - 1) / 2)  
        return(SparseMatrixPower(SparseMatrixProduct(A,A), p / 2))

def SparseMatrixProduct(A,B):

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answered 2020-05-03 00:06:12 +0100

tmonteil gravatar image

updated 2020-05-03 14:43:57 +0100

It seems you are confusing calls to SparseMatrixProduct and SparseMatrixPower. Indeed, SparseMatrixPower(A,A) is meaningless (the second argument should be an integer not a matrix).

When p is odd, your code try to make two steps at once (see the (p-1)/2). To understand the algorithm that is behind your code, I would suggest to separate the add/multiply (p -> p-1) part and the double/squaring (p -> p/2) part as follows :

sage: def SparseMatrixPower(A, p):
....:     if p == 1: 
....:         return(A)
....:     elif Mod(p, 2):
....:         return SparseMatrixProduct(A, SparseMatrixPower(A, p-1))
....:     else:
....:         return SparseMatrixPower(SparseMatrixProduct(A, A), p/2)

That said, if you plan to play a lot with twose objects, I would suggest to define a class for them and define a __mul__method to define the product. Then Sage has generic double-and-add (or multiply-and-square) to automatically define the power, see for example

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Yes, this is typo, I repaired my code. It does not work as well.

SYLA gravatar imageSYLA ( 2020-05-12 13:10:38 +0100 )edit

It is not completely fixed:


does not makes sense since the second argument of SparseMatrixPower should be a number, not a matrix.

tmonteil gravatar imagetmonteil ( 2020-05-12 15:31:56 +0100 )edit

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Asked: 2020-05-02 22:36:12 +0100

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Last updated: May 12 '20