Transforming a array of matrices into a single large matrix with these matrices on the diagonal.

Hi,

I have an array of length z with different n times m matrices. Now I would like to put all these matrices on the diagonal of some large sparse matrix. If the matrices were all identical, I would simply write:

kron(speye(z,z),A)

Unfortunately, in my case they are not. So the above doesn't really work. Is there a simple elegant way to solve my problem?

Regards, Laurent

Answer 1

[Laurent]

I think this does the trick:

function B = MatsDiag(A)
[ l c m ] = size(A)
B = sparse( ...
  reshape(repmat(reshape(1:m*l,l,[]),c,1),[],1), ...
  kron(1:m*c,ones(1,l))', ...
  reshape(A(:,:),[],1), ...
  m*l,m*c);
end

where I assume that A(:,:,i) is the i-th matrix with size l times c. I shortly tested it with a small number of parameter choices and it seems to work, but I guess there quite some room for optimisation left.

Regards, Laurent

[Walter Roberson]

Looks like it is possibly messier than it needs to be, but please explain what exactly how your input A is structured.

[Laurent]

Consider the following code

l = 4;

c = 2;

m = 3;

A = zeros(l,c,m);

for i=1:m

for j = 1:l

for k = 1:c

A(j,k,i)=i*100+j*10+k;

end

end

end

In that case A(:,:,i) will be a 4 times 2 matrix for i=1,...,3, e.g. A is an array of length 3 of 4 times 2 matrices. If you check the output from the code above, then the entries will be of the form 'abc' where a is the matrix, b its line and c its column.

I hope this makes the structure of A a bit clearer.

As for my proposed solution, I played around with it little more and think it's working in all the cases where I need it.

Regards,

Laurent

Answer 2

[Walter Roberson]

See blkdiag()

This will, I know, produce a full matrix instead of a sparse matrix, but it will at least get the elements positioned as you would like.

You might consider the less direct use of spconvert()

[Laurent]

If I understand the documentation for blkdiag() correctly, you have to specify explicitly all the matrices, e.g.

blkdiag(A,B,C,D)

returns the desired result, but if I have an array V that contains the matrices A, B, C and D, then

blkdiag(V)

will result in an error. Since I'm trying to write a function, I can't really state all the matrices explicitly. Correct me if I'm wrong on this subject.

Regards,

Laurent

[Walter Roberson]

What does it mean to say that you have an array that contains matrices? Does it mean that your array is a cell array? If so then,

blkdiag(V{:})

[Jan]

@Walter: BLKDIAG replies a sparse array if any input is sparse.