How can I specify a symmetric matrix so that MATLAB does not need to create and store the redundant symmetric part?

I have an N-by-N symmetric matrix that is very large and requires a large amount of memory to store. However, of the "N^2" elements in the matrix, "N*(N - 1)/2" are redundant. I would like to be able to create and operate on this symmetric matrix without ever having to create and store the entire N-by-N matrix.

LAPACK supports this type of matrix storage, and is referred to as a "packed" matrix.

I also have another sparse symmetric matrix and would like to store only half of it as opposed to the entire matrix.

Answer 1

[MathWorks Support Team]

The ability to store and operate on only the significant part of a symmetric or a sparse symmetric matrix is not available in MATLAB.

The following symmat2vec.m function extracts and stores the significant part of an N-by-N symmetric matrix within a "N*(N + 1)/2"-by-1 vector. However, you will not be able to operate on this vector as a symmetric matrix without recreating the entire N-by-N symmetric matrix using the following vec2symmat.m function.

function V = symmat2vec(A)

% Converts a symmetric matrix "A" to a vector "V" of its significant part 

N = size(A, 1); 

V = zeros(N/2*(N + 1), 1); 

I = [0 cumsum(1:N)];

for m = 1:N

      V(I(m)+1:I(m + 1)) = A(1:m, m);

end

function A = vec2symmat(V)

% Converts vector "V" to an N-by-N matrix "A" 

n = length(V); 

N = (-1 + sqrt(1 + 8*n))/2; 

A = zeros(N); 

I = [0 cumsum(1:N)];

for m = 1:N

      A(1:m, m) = V(I(m)+1:I(m + 1));

end

% Insert symmetric part

for m = 1:N-1

      A(m+1:N, m) = A(m, m+1:N).';

end