multiply a matrix into every block matrix in a big matrix

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

[Tony Cheng]

u are so smart man! great!

Answer 1

[Matt J]

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

[Tony Cheng]

Hi Matt,

Now I tried another case where Hc is not square：

Hc = rand( 6 , 12 ) ;

A = kron( ones( 6 ) , eye( 12 ) ) ; %2x2 blocks Aij

dims=[ 12 , 12 ] ; %block dims

tmp=Hc*blkColonTranspose(A,dims)

result=blkReshape(tmp,dims,blkSize(A,dims))

Then in the command window, it says

The input array does not divide evenly into tiles of the specified size.

So how to handle this issue?

Many thanks!

Stanley

[Matt J]

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]

Matt, you are so excellent! I just wonder how I can be as skilled as U in Matlab!

Answer 2

[Matt J]

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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Answer 3

[Paul]

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

[Matt J]

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