Is there an equivalent function to the "kron(x,y)" that uses subtraction as its operation rather than multiplication?

For example,

say we have two matrices as follows:

>> A = [1 2;3 4]

A =

       1     2
       3     4

>> B = [5 6;7 8]

B =

       5     6
       7     8

>> kron(A,B)

ans =

       5     6    10    12
       7     8    14    16
      15    18    20    24
      21    24    28    32

However I want a matrix that will subtract every component of matrix A by every component of matrix B, yielding a 4x4 matrix as follows:

A - B = 
  [-4 -5 -3 -4;-6 -7 -5 -6;-2 -3 -1 -2;-4 -5 -3 -4]

Note that I switched the multiplication function with subtraction BY HAND here. I need to do this with two 100x100 matrices, so it wouldn't be so easy. Thanks

Answer 1

[Azzi Abdelmalek]

A = [1 2;3 4]
B = [5 6;7 8]
C=cell2mat(arrayfun(@(x) x-B,A,'un',0))

Answer 2

[Matt J]

Using the function below

result=tensorfun(@minus,A,B)

It is an easy modification of kron.m, but more efficient since it uses bsxfun.

function X = tensorfun(op,A,B)
%TENSORFUN
%
%   X = tensorfun(operation,A,B)
%
%Generalization of KRON (as modified, e.g., by Laurent Sorber, Bruno Luong, and others)
%
%Creates matrix X consisting of blocks X_ij=bsxfun(operation,a(i,j),B).
%Note that "operation" must preserve the size of B.

[I J] = size(A);
[K L] = size(B);
if ~issparse(A) && ~issparse(B)
    A = reshape(A,[1 I 1 J]);
    B = reshape(B,[K 1 L 1]);
    X = reshape(bsxfun(op,A,B),[I*K J*L]);
else

      [ia,ja,sa] = find(A); ia=ia(:); ja=ja(:); sa=sa(:);
      [ib,jb,sb] = find(B); ib=ib(:); jb=jb(:); sb=sb(:);

      ix = bsxfun(op,K*(ia-1).',ib);
      jx = bsxfun(op,L*(ja-1).',jb);

      X = sparse(ix,jx,bsxfun(op,sb,sa.'),I*K,J*L);

end

Answer 3

[Matt J]

I need to do this with two 100x100 matrices, so it wouldn't be so easy.

Does that mean you plan to construct a 10000x10000 matrix? I don't know exactly what you're doing, but constructing A matrix that large could be greatly inefficient. Suppose you wanted to multiply the desired matrix in your example

 T=[-4 -5 -3 -4;-6 -7 -5 -6;-2 -3 -1 -2;-4 -5 -3 -4]

by a 4x1 vector c, so as to obtain y=T*c. Then it can be done equivalently, as

 C=reshape(c,2,2);
 result=ones(2)*C*A.'-B*C*ones(2);
  y=result(:);

which involves only 2x2 matrix operations instead of the 4x4 matrix T.

For the 2x2 case, the difference is of little consequence, but when the matrices grow to be 100x100, the saving both in speed and memory is significant.