PyKronecker is a library for manipulating matrices which have a Kronecker product structure. Systems involving Kronecker products arise in many areas of applied mathematics and statistics. The aim of this library is to provide a clean interface for dealing with such systems, combining lazy evaluation and algebraic tricks to deliver large savings in terms of both memory and execution time.
Quickstart
Create a KroneckerProduct operator from two or more square arrays. These may be real or complex-valued.
import numpy as np
from pykronecker import KroneckerProduct
Ns = [30, 40, 50]
As = [np.random.normal(size=(Ni, Ni)) for Ni in Ns]
A = KroneckerProduct(As)
This object can be multiplied onto a vector of shape (30 * 40 * 50, ) or a tensor of shape (30, 40, 50) using the @ syntax for matrix multiplication. The returned array will be the same size as the input array.
X = np.random.normal(size=(30 * 40 * 50))
x = np.random.normal(size=(30, 40, 50))
print(A @ X, A @ x)
A KroneckerSum operator can be created and used in much the same way.
from pykronecker import KroneckerSum
B = KroneckerSum(As)
print(A @ X, A @ x)
These objects can be added, scaled, and transposed arbitrarily to create new composite operators.
C = 2 * A - 0.5 * B.T
print(C @ X, C @ x)