How much memory a Sparse Matrix created using SPRAND, with given number of rows, columns and density consume in MATLAB 7.14 (R2012a)?

If I know the number of rows (say m) and the number of columns (say n) of a sparse matrix, to be created using SPRAND with density (say rho). How much is the memory consumed with such a matrix and also are there any guidelines as to when use SPARSE matrices compared to standard matrix?

Answer 1

[MathWorks Support Team]

In MathWorks documentation, there exists a formula to compute this :

Strategies for Efficient Use of Memory:

https://www.mathworks.com/help/matlab/matlab_prog/strategies-for-efficient-use-of-memory.html

Sub-Topic : Make Arrays Sparse When Possible

Basic calculation for memory consumption :

In general, for a sparse double array with nnz nonzero elements and ncol columns, the memory required is

- 16 * nnz + 8 * ncol + 8 bytes (on a 64 bit machine)

- 12 * nnz + 4 * ncol + 4 bytes (on a 32 bit machine)

where

nnz = Number of non-zeros

ncol = Number of columns of the Sparse Matrix

Also, note SPARSE matrices are stored in a different fashion compared to standard matrices in MATLAB, hence under certain circumstances SPARSE matrices may consume more memory compared to standard matrices.

As a guideline you can follow this :

* If the memory consumption (computed using the formula above) > 8*NumOfRows*NumOfColumns => then it is not recommended.

The memory consumption and the proper usage of Sparse Matrices can be written as a MATLAB function as :

function tdensity(m,n,rho)

if nargin == 3
    nnzS = m * n * rho
    bytesS64 = 16*nnzS + 8*(n+1)
%     bytesS32 = 12*nnzS + 4*(n+1)
    bytesA = 8 * m * n
    
    if bytesS64 > bytesA
        disp('It is not worthwhile to store your matrix in sparse format, on 64-bit platforms')
    else
        disp('It is worthwhile to store your matrix in sparse format, on 64-bit platforms')
    end
else
    maxnnzS64 = (8*m*n - 8*(n+1)) / 16
    disp(sprintf('The maximum number of nonzeros to make it worthwhile to store your matrix in sparse format on 64-bit platforms is %d',maxnnzS64))
end