Thread Subject: Biulding a diagonal matrix from submatrices

Hi,
I am trying to build up a diagonal matrix (A) of 3x(nxn) dimension,where n is the number of paths. Each path (p) is represented by a 3x3 matrix.
Example: Let's assume we have three paths (n=3).
p1=[1 1 1;1 1 1;1 1 1];
p2=[2 2 2;2 2 2;2 2 2];
p3=[3 3 3;3 3 3;3 3 3];

The diagonal matrix (A) would look like:
A =

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

Note the number of paths could be any number.
I really appreciate your help.

"Jal" <jal@mathworks.com> wrote in message <hntu7g$plp$1@fred.mathworks.com>...
> Hi,
> I am trying to build up a diagonal matrix (A) of 3x(nxn) dimension,where n is the number of paths. Each path (p) is represented by a 3x3 matrix.
> Example: Let's assume we have three paths (n=3).
> p1=[1 1 1;1 1 1;1 1 1];
> p2=[2 2 2;2 2 2;2 2 2];
> p3=[3 3 3;3 3 3;3 3 3];
>
> The diagonal matrix (A) would look like:
> A =
>
> 1 1 1 0 0 0 0 0 0
> 1 1 1 0 0 0 0 0 0
> 1 1 1 0 0 0 0 0 0
> 0 0 0 2 2 2 0 0 0
> 0 0 0 2 2 2 0 0 0
> 0 0 0 2 2 2 0 0 0
> 0 0 0 0 0 0 3 3 3
> 0 0 0 0 0 0 3 3 3
> 0 0 0 0 0 0 3 3 3
>
> Note the number of paths could be any number.
> I really appreciate your help.

Here is one way:

% your data, stored as cell arrays (see the FAQ)
  p{1} = ones(3) ;
  p{2} = p{1}+1 ;
  p{3} = p{1}+2 ;

%engine
  c = repmat({zeros(numel(p))},size(p{1})) ;
  [c{eye(numel(p))==1}] = deal(p{:}) ;
  D = cell2mat(c)

hth
Jos

"Jal" <jal@mathworks.com> wrote in message <hntu7g$plp$1@fred.mathworks.com>...
> Hi,
> I am trying to build up a diagonal matrix (A) of 3x(nxn) dimension,where n is the number of paths. Each path (p) is represented by a 3x3 matrix.
> Example: Let's assume we have three paths (n=3).
> p1=[1 1 1;1 1 1;1 1 1];
> p2=[2 2 2;2 2 2;2 2 2];
> p3=[3 3 3;3 3 3;3 3 3];

Do the p matrices always consist of identical values, and are they always consecutive integers, as in your example? If so, a lazy way to construct this is by taking Kronecker products

A=kron(sparse(diag(1:n)),ones(3));

However, it is rare to find an application where you would want to construct such a Kronecker product matrix explicitly. It's a very large matrix with a lot of redundant information. I created this FEX tool as a more efficient alternative,

http://www.mathworks.com/matlabcentral/fileexchange/25969-efficient-object-oriented-kronecker-product-manipulation

A = blkdiag(p1,p2,p3)

Bruno

"Jal" <jal@mathworks.com> wrote in message <hntu7g$plp$1@fred.mathworks.com>...
> Hi,
> I am trying to build up a diagonal matrix (A) of 3x(nxn) dimension,where n is the number of paths. Each path (p) is represented by a 3x3 matrix.
> Example: Let's assume we have three paths (n=3).
> p1=[1 1 1;1 1 1;1 1 1];
> p2=[2 2 2;2 2 2;2 2 2];
> p3=[3 3 3;3 3 3;3 3 3];
>
> The diagonal matrix (A) would look like:
> A =
>
> 1 1 1 0 0 0 0 0 0
> 1 1 1 0 0 0 0 0 0
> 1 1 1 0 0 0 0 0 0
> 0 0 0 2 2 2 0 0 0
> 0 0 0 2 2 2 0 0 0
> 0 0 0 2 2 2 0 0 0
> 0 0 0 0 0 0 3 3 3
> 0 0 0 0 0 0 3 3 3
> 0 0 0 0 0 0 3 3 3
>
> Note the number of paths could be any number.
> I really appreciate your help.

Hi guys,
Thanks a lot for your reply. i will try blkdiag function. I do not know if there is any a better way to do it ,because this function consumes time. As for the matrices entries,they could be complex numbers.

For such matrix, you might want to store in sparse format.

for i=1:10000
  p{i}=sparse(i*eye(3));
end

A = blkdiag(p{:});

Bruno