`scipy.sparse._construct:kronsum`

source: /scipy/sparse/_construct.py :843

Signature

def kronsum ( A , B , format = None )

Summary

Kronecker sum of square sparse matrices A and B

Extended Summary

Kronecker sum of two sparse matrices is a sum of two Kronecker products kron(I_n,A) + kron(B,I_m) where A has shape (m, m) and B has shape (n, n) and I_m and I_n are identity matrices of shape (m, m) and (n, n), respectively.

Parameters

A : sparse matrix or array: Square matrix
B : sparse array or array: Square matrix
format : str: format of the result (e.g. "csr")

Returns

: sparse matrix or array: kronecker sum in a sparse format. Returns a sparse matrix unless either A or B is a sparse array in which case returns a sparse array.

Examples

`kronsum` can be used to construct a finite difference discretization of the 2D Laplacian from a 1D discretization.

from scipy.sparse import diags_array, kronsum
from matplotlib import pyplot as plt
import numpy as np
ex = np.ones(10)
D_x = diags_array([ex, -ex[1:]], offsets=[0, -1])  # 1D first derivative
D_xx = D_x.T @ D_x  # 1D second derivative
L = kronsum(D_xx, D_xx)  # 2D Laplacian

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plt.spy(L.toarray())

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plt.show()

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