misc.kronColumnwise: new method

+misc/kronColumnwise.m

+function C = kronColumnwise(A, B, AcolumnSize, BcolumnSize)
+% misc.kronColumnwise calculates a modified Kronecker product for block matrices defined by
+%			[kron(A_11, B_1)	kron(A_12, B_2)		...		kron(A_1r, B_r)	]
+%		C = [	...					...				...			...			]
+%			[kron(A_r1, B_1)	kron(A_r2, B_2)		...		kron(A_rr, B_r)	]
+%
+% or equally
+%		C = [kron(A_1, B_1)		kron(A_2, B_2)		...		kron(A_r, B_r)	]
+%
+% Therein, 
+%		   r: number of blocks, i.e. r = numel(AcolumnSize) = numel(BcolumnSize)
+%		 A_i: The sub-matrix of A resulting by evaluating its
+%					columns sum(AcolumnSize(i-1) + (1:AcolumnSize(i)
+%			 -> A = [ A_1	A_2	...	A_r ]
+%		 B_i: The sub-matrix of B resulting by evaluating its
+%					columns sum(BcolumnSize(i-1) + (1:BcolumnSize(i)
+%			 -> B = [ B_1	B_2	...	B_r ]
+%
+%	C = misc.kronColumnwise(A, B, AcolumnSize, BcolumnSize) calculates the product defined above. 
+%		AcolumnSize, and BcolumnSize resepectivly, define how many columns AcolumnSize(i) belong to
+%		the i-th componenent A_i.
+%	
+%	C = misc.kronColumnwise(A, B) calculates the usual Kronecker product
+%	
+%%
+% Example
+%	A = [1, 2; 3, 4]
+%	B = [1, 2, 3]
+%	C = misc.kronColumnwise(A, B, [1, 1], [1, 2])
+
+arguments
+	A (:, :);
+	B (:, :);
+	AcolumnSize (:, 1) double = size(A, 2);
+	BcolumnSize (:, 1) double = size(B, 2);
+end % arguments
+
+assert(sum(AcolumnSize) == size(A, 2), ...
+	"The sum of AcolumnSize must be equal to the number of columns of A");
+assert(sum(BcolumnSize) == size(B, 2), ...
+	"The sum of BcolumnSize must be equal to the number of columns of B");
+assert(isequal(numel(AcolumnSize), numel(BcolumnSize)), ...
+	"AcolumnSize and BcolumnSize must have same number of elements, because there need to be "...
+	+ "same number of sub-matrices for A and B");
+
+Ccell = cell(size(AcolumnSize));
+for it = 1 : numel(AcolumnSize)
+	Ccell{it} = kron(...
+		A(:, sum(AcolumnSize(1:it-1)) + (1 : AcolumnSize(it))), ...
+		B(:, sum(BcolumnSize(1:it-1)) + (1 : BcolumnSize(it))));
+end % for it = 1 : numel(AcolumnSize)
+C = cat(2, Ccell{:});
+end % misc.kronColumnwise()
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+unittests/+misc/testKronColumnwise.m

+function [tests] = testKronColumnwise()
+	tests = functiontests(localfunctions);
+end
+
+function testKron(tc)
+A = 1:1:(2^2); A = reshape(A, sqrt(numel(A)) * [1, 1]);
+B = magic(2);
+tc.verifyEqual(misc.kronColumnwise(A, B), kron(A, B));
+end % testKron()
+
+function testBVector(tc)
+A = [1, 2; 3, 4];
+A11 = A(1, 1);
+A12 = A(1, 2);
+A21 = A(2, 1);
+A22 = A(2, 2);
+
+B = [1, 2, 3];
+B1 = B(1, 1);
+B2 = B(1, [2, 3]);
+tc.verifyEqual(misc.kronColumnwise(A, B, [1, 1], [1, 2]), ...
+	[kron(A11, B1), kron(A12, B2); kron(A21, B1), kron(A22, B2)])
+end % testBVector()
+
+function testMatrix(tc)
+A = 1:1:(4^2); A = reshape(A, sqrt(numel(A)) * [1, 1]);
+A11 = A(1:2, 1:2);
+A12 = A(1:2, 3:4);
+A21 = A(3:4, 1:2);
+A22 = A(3:4, 3:4);
+
+B = [1, 2, 3; 4, 5, 6]+2;
+B1 = B(:, 1);
+B2 = B(:, [2, 3]);
+tc.verifyEqual(misc.kronColumnwise(A, B, [2, 2], [1, 2]), ...
+	[kron(A11, B1), kron(A12, B2); kron(A21, B1), kron(A22, B2)])
+end % testMatrix()
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