Build matrix with other matrices.

Perhaps this is a simple question, but I need an answer.

If I want to build a 6x8 matrix with help of 6 other matrices, is there a smart command or function to do that? I have only built matrix with vectors so far.

Anyhow, here is my attempt so far:

A=[3 4 2; 7 2 1]
B=[2 2 1; 5 2 8]
C=[4 2 1; 3 1 2; 0 7 1]
D=[1 2 4]
F=[3; 2; 1]
G=[2; 1; 4]

blkdiag(A,B,C,D,F,G)
ans =

Columns 1 through 6

     3     4     2     0     0     0
     7     2     1     0     0     0
     0     0     0     2     2     1
     0     0     0     5     2     8
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0

Columns 7 through 12

     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0
     4     2     1     0     0     0
     3     1     2     0     0     0
     0     7     1     0     0     0
     0     0     0     1     2     4
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0

Columns 13 through 14

     0     0
     0     0
     0     0
     0     0
     0     0
     0     0
     0     0
     0     0
     3     0
     2     0
     1     0
     0     2
     0     1
     0     4

>>

I got answer, but I wonder if this is correct or not.

I would be glad if you can help me

Best regards Cillian

[Sean de Wolski]

What result do you expect for the above? Demonstrate it with just two or three matrices.

[Daniel Shub]

I have a hard time seeing a reasonable way of combing your matrices A-G and getting a 6x8 matrix.

[Sean de Wolski]

@Daniel: The only way I see it

X = zeros(6,8);

X(1:size(A,1),1:size(A,2)) = X(1:size(A,1),1:size(A,2))+A;

X(1:size(B,1),1:size(B,2)) = X(1:size(B,1),1:size(B,2))+B;

...

[Cillian]

Thank you Sean, but can you please describe in words how it works for me. I don't quite understand it.

Like this one; " X(1:size(A,1),1:size(A,2)) = X(1:size(A,1),1:size(A,2))+A; "

[Daniel Shub]

Both Sean and I are confused about what you are asking. Does Sean's "answer" give you the result you are looking for?

[Cillian]

Yes, Sean's answer give me what I am looking for. I just don't quite understand how his code works. Can you or Sean describe for me in words, please.

Answer 1

[Daniel Shub]

Following on from Sean's comment, I was curious if I could do his calculation in a "cleaner" way that also uses blkdiag which Cillian seems to think is needed.

x = {A,B,C,D,F,G};
sum(reshape(cell2mat(cellfun(@(y)(blkdiag(y, zeros(6-size(y, 1), 8-size(y, 2)))), x, 'UniformOutput', false)), 6, 8, 6), 3)

    15    10     8     0     0     0     0     0
    18     5    11     0     0     0     0     0
     5     7     1     0     0     0     0     0
     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0

EDIT The high level over view of the code is I make a 6x8xN matrix, where N is 6 because you have 6 vectors you are working with. I then sum across the 3rd dimension to get the answer. So working inside out with the code:

blkdiag(y, zeros(6-size(y, 1), 8-size(y, 2)))

produces a 6x8 matrix for any y matrix (that has size less than 6x8) where the values of y are in the top left corner of the matrix and zeros are in the remaining slots.

 cellfun(@(y)(blkdiag(y, zeros(6-size(y, 1), 8-size(y, 2)))), x, 'UniformOutput', false)

produces a 1x6 cell array with each element of the cell array is a 6x8 version of the corresponding input matrices A, B, C, D, F.

 cell2mat(cellfun(@(y)(blkdiag(y, zeros(6-size(y, 1), 8-size(y, 2)))), x, 'UniformOutput', false))

then converts the 1x6 cell array into a 6x48 matrix where the first 6x8 elements are from the 6x8 version of A and the next 6x8 elements are from the 6x8 version of B ...

Finally

reshape(cell2mat(cellfun(@(y)(blkdiag(y, zeros(6-size(y, 1), 8-size(y, 2)))), x, 'UniformOutput', false)), 6, 8, 6)

produces the desired 6x8x6 matrix and the final sum does the summation.

[Andrei Bobrov]

+1

Answer 2

[Andrei Bobrov]

z = {A,B,C,D,F,G};
out = zeros(6,8);
for jj = 1:numel(z)
    [i1 j1] = size(z{jj});
    out(1:i1,1:j1) = out(1:i1,1:j1) + z{jj};
end

or:

[I, J, c] = cellfun(@(x)find(x),z,'un',0);
k = reshape(cellfun(@(x)x(:),[I, J, c],'un',0),[],3);
out = accumarray(cell2mat(k(:,1:2)),cat(1,k{:,3}),[6, 8]);

[Daniel Shub]

But you didn't use BLKDIAG. You do get points for using ACCUMARRAY, but I don't think the tag was there when I posted my answer.