multiply a matrix into every block matrix in a big matrix

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Tony Cheng
Tony Cheng 2024-11-27
评论： Tony Cheng 2024-11-28
Hi there,
Here I want to multiply a matrix H into every block matrix Aij in the matrix A, i.e.,
Are there any codes can realize this? so I do not need to repeat the manipulation of the multiplication.
Best regards

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采纳的回答

Matt J
Matt J 2024-11-27
编辑：Matt J 2024-11-27
You can download this package,
https://www.mathworks.com/matlabcentral/fileexchange/115340-block-transposition-permutation-and-reshaping-of-arrays
Example:
Hc=[1,2;3,4];
A=kron(ones(3),eye(2)); %2x2 blocks Aij
dims=[2,2]; %block dims
tmp=Hc*blkColonTranspose(A,dims);
result=blkReshape(tmp,dims,blkSize(A,dims))
result =
1 2 1 2 1 2
3 4 3 4 3 4
1 2 1 2 1 2
3 4 3 4 3 4
1 2 1 2 1 2
3 4 3 4 3 4
  3 个评论
显示 1更早的评论
Matt J
Matt J 2024-11-27
编辑：Matt J 2024-11-27
My other answer will handle this case as is, or you could do,
tmp=Hc*blkColonTranspose(A,[12,12]);
result=blkReshape(tmp,[6,12],blkSize(A,[12,12]))
Tony Cheng
Tony Cheng 2024-11-28
Matt, you are so excellent! I just wonder how I can be as skilled as U in Matlab!

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更多回答（2 个）

Matt J
Matt J 2024-11-27
编辑：Matt J 2024-11-27
Ran in:
Hc=[1,2;3,4];
A=kron(ones(3),eye(2)); %2x2 blocks Aij
blockheight=2;
result=reshape( Hc*reshape(A,blockheight,[]) , [],width(A))
result = 6×6
1 2 1 2 1 2 3 4 3 4 3 4 1 2 1 2 1 2 3 4 3 4 3 4 1 2 1 2 1 2 3 4 3 4 3 4
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Paul
Paul 2024-11-27
Ran in:
Check out blockproc.
Example data
H = [1,2;3,4];
rng(100);
A = rand(4,6);
Result
R = blockproc(A,[2 2],@(B) H*B.data)
R = 4×6
1.1001 0.2479 1.2869 0.4021 1.1556 2.3118 2.7437 0.5004 2.7105 0.9895 3.1228 5.0552 2.1141 2.3225 1.3097 2.1769 1.3644 1.4899 4.6527 5.3157 3.5108 4.5736 3.5450 3.7974
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Check
isequal(R,[H*A(1:2,1:2),H*A(1:2,3:4),H*A(1:2,5:6);H*A(3:4,1:2),H*A(3:4,3:4),H*A(3:4,5:6)])
ans = logical
1
  1 个评论
Matt J
Matt J 2024-11-27
编辑：Matt J 2024-11-27
Ran in:
blockproc is quite slow, and is usually inadvisable.
H = [1,2;3,4];
rng(100);
A = randi(10,400,600);
tic;
R1 = blockproc(A,[2 2],@(B) H*B.data);
toc
Elapsed time is 0.490280 seconds.
tic;
R2=reshape( H*reshape(A,2,[]) , [],width(A));
toc;
Elapsed time is 0.001811 seconds.
Even cellfun would be better:
tic;
Acell=mat2cell(A,ones(200,1)*2,ones(300,1)*2);
R3=cell2mat(cellfun(@(B) H*B ,Acell,'uni',0));
toc
Elapsed time is 0.226868 seconds.
isequal(R1,R2,R3)
ans = logical
1

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