block matrix multiplication for solving large linear equation systems

hello all

i am working with a huge matrix and trying to do matrix computations in blocks.

i am trying to derive a matrix from my original matrix and then i want to multiply the new matrix with my original matrix and store it in another matrix.

i start out by first generating my original matrix using a function in matlab and then use that matrix to get the new matrix. however as my matrices are big, i have to do block multiplication.

however i cannot figure out how to calculate all the blocks.

i use 2 for loops but the code only generates the block multiplication data for the first column ad the code ends

i tried to implement the code for a smaller part of the data(5blocks*5blocks) which if successful i could implement for the whole data(48*48), but it did not work. --- each block is a 1000*1000 matrix in itself ---

please suggest something

[Cedric]

Is it a block matrix or a block-diagonal matrix? Or did I misunderstand and you are not dealing with a block(-diagonal) matrix, but a completely dense matrix, and you want to implement an approach by block?

[Analyst]

It is a sparse positive definite symmetric matrix.. sparse as value are really close to zero but not zero

[Cedric]

Sparse implies elements identically equal to zero, which are not stored in memory at all. This is why I asked if it was a block, block-diagonal or dense matrix. If it were a block-diagonal matrix with 48 blocks of 1000x1000 non-zero elements on the diagonal, you could easily store it and compute with it (it would take a little less than 800MB of RAM when stored as a 48e3x48e3 sparse matrix with 48e6 non-zero elements). But I suspect that you are not dealing with a block-diagonal matrix, otherwise you could solve 48 small independent systems.

[Analyst]

No i cannot generate the complete matrix at once.

[Nick Hobbs]

I understand that you want to multiply two large matrices in MATLAB. Have you considered using the function matfile. The documentation for 'matfile' says that you can write and read from a MAT-file without loading the entire variable into memory. You could then save each of your two matrices as MAT-files, and then solve for each entry in your final matrix and save it directly into a final MAT-file as you solve for the values.