How to create sparse matrix with blkdiag ?

Hello guys,

I have a matrix "param" of size (N,3,3) with N being relatively large. I want to create a sparse 3*N*N square matrix whose diagonals are param(1,:,:) which are 3x3 matrix. Here is what I do:

paramC=num2cell(param,[2 3]);
DiagMatrix=blkdiag(paramC{:});

But, when I try to do that I have a memory problem when calling blkdiag, arguing that the matrix is too large (3*N*N square matrix). But the matrix should be really sparse as it is a tridiagonal matrix.

I have tried multiple way to make matlab understand that this is a sparse matrix include:

paramC=num2cell(sparse(param),[2 3]);
DiagMatrix=blkdiag(paramC{:});
paramC=num2cell(param,[2 3]);
DiagMatrix=blkdiag(sparse(paramC{:}));

but everytime I get the error:

Undefined function 'sparse' for input arguments of type 'double' and attributes 'full 3d real'.

Do you have a way to fix this issue ?

Thanks a lot !

Answer 1

[John D'Errico]

A sparse tridiagonal matrix, built directly from the diagonal elements is one of the things that my blktridiag can build. It is on the file exchange.

It is a bit unclear if your goal is to build a block diagonal matrix or a tridiagonal matrix, or exactly what. For example, you can use spdiags to build a sparse tridiagonal matrix. And you CAN use blkdiag to build a sparse block diagonal matrix. You need to force each block to be itself sparse.

C = {sparse(rand(3)),sparse(rand(3)),sparse(rand(3))};
A = blkdiag(C{:});
whos A
Name      Size            Bytes  Class     Attributes
A         9x9               512  double    sparse    

spy(A)

Answer 2

[Walter Roberson]

You face the fundamental problem that in MATLAB, only 2D sparse matrices are supported, not 3D.

http://www.mathworks.com/help/matlab/ref/sparse.html#moreabout

"accumarray groups data into bins using n-dimensional subscripts, but sparse groups data into bins using 2-D subscripts."