To optimize the computation of the large matrix sizes and the sparsity of MAT, you should consider the following approaches:
- Use Sparse Matrices: If you haven't already, convert MAT to a sparse matrix format in MATLAB using sparse(MAT). This will significantly speed up matrix-vector multiplications for large, sparse matrices.
- Precompute Static Values: If exp(-k*dt) does not change over iterations, compute it once before the loop and reuse the result.
- Avoid Growing Arrays in a Loop: Preallocate the full size of g before the loop to avoid dynamically resizing it during each iteration, which is costly.
Given these points, your revised code snippet would look something like this:
% Assuming MAT is already defined and is sparse
% Convert MAT to sparse format if not already
% MAT = sparse(MAT); % Uncomment if MAT is not already sparse
% Precompute constants
exp_neg_kdt = exp(-k*dt);
% Preallocate g
g = zeros(m, n+1);
g(:,1) = g0; % Initial condition
% Time evolution loop
for i = 1:n
g(:,i+1) = (g(:,i) + dt*MAT*g(:,i)) .* exp_neg_kdt;
end
I hope this helps!
Animesh
