scipy.sparse.linalg.

matrix_power#

scipy.sparse.linalg.matrix_power(A, power)[source]#

Raise a square matrix to the integer power, power.

For non-negative integers, A**power is computed using repeated matrix multiplications. Negative integers are not supported.

Parameters:

A(M, M) square sparse array or matrix: sparse array that will be raised to power power
powerint: Exponent used to raise sparse array A

Returns:

A**power(M, M) sparse array or matrix: The output matrix will be the same shape as A, and will preserve the class of A, but the format of the output may be changed.

Notes

This uses a recursive implementation of the matrix power. For computing the matrix power using a reasonably large power, this may be less efficient than computing the product directly, using A @ A @ … @ A. This is contingent upon the number of nonzero entries in the matrix.

Added in version 1.12.0.

Examples

>>> from scipy import sparse
>>> A = sparse.csc_array([[0,1,0],[1,0,1],[0,1,0]])
>>> A.todense()
array([[0, 1, 0],
       [1, 0, 1],
       [0, 1, 0]])
>>> (A @ A).todense()
array([[1, 0, 1],
       [0, 2, 0],
       [1, 0, 1]])
>>> A2 = sparse.linalg.matrix_power(A, 2)
>>> A2.todense()
array([[1, 0, 1],
       [0, 2, 0],
       [1, 0, 1]])
>>> A4 = sparse.linalg.matrix_power(A, 4)
>>> A4.todense()
array([[2, 0, 2],
       [0, 4, 0],
       [2, 0, 2]])