Speed up sparse matrix calculations

Question

John Doe 2013-5-12

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https://ww2.mathworks.cn/matlabcentral/answers/75506-speed-up-sparse-matrix-calculations

Is it possible to speed up large sparse matrix calculations by e.g. placing parantheses optimally?

What I'm asking is: Can I speed up the following code by forcing Matlab to do the operations in a specified order (for instance "from right to left" or something similar)?

I have a sparse square symmetric matrix H (4000x4000), that previously has been factorized, and a sparse vector M with length equal to the dimension of H. What I want to do is the following:

k = 0;
cList = 1:3500     % List of contingecies to study
nc = length(cList);
nb = size(bus,1); % bus is a matrix with information about buses in the system
resVa = zeros(nb,nc);
[L U P] = lu(H);      % H is sparse (thus also L, U and P). Dimension = nbxnb
while k < nc
  k = k + 1;
  cont = cList(k);
    bf = branch(cont,1);  % branch is a matrix with information about branches
    bt = branch(cont,2);  % Col 1 = from-bus, col 2 = to-bus
    dy = -H(bf,bt);      % 
    M = sparse([bf,bt],1,[1,-1],nb,1);
    z = -M'*(U \ (L \ (P * M)));
    c = (1/dy + z)^-1;
    % V = Vm*exp(j*Va); - A complex vector of dimension nbx1
    % Sbus is a complex vector of dimension nbx1
    % Ybus is a complec matrix of dimension nbxnb
    mis = (V .*conj((Ybus)*V) - Sbus) ./ Vm;
    P_mis = real(mis);  
    converged = 0;
    i = 0;
    while (~converged && i < max_it)
       i = i + 1;
       %%The lines I hope to optimize:
       dVa = - (U \ (L \ (P * P_mis))); 
       dVaComp = (U \ (L \ (P * M * c * M' * dVa)));
       Va = Va + dVa + dVaComp;
       V = Vm .* exp(1j * Va);
       mis = (V .*conj((Ybus)*V) - Sbus) ./ Vm;    
       P_mis = real(mis);
       normP = norm(P, inf);
       if normP < tol
         converged = 1;
         break;
       end
    end
  resVa(:,k) = Va * 180 / pi;
end

Some additional information regarding the matrices:

All diagonal elements of H are non-zeros (it's still square, sparse and symmetrical).

Ybus and H have the same structure, but Ybus is complex and H is real.

Vm is updated using the imaginary part of mis, and some other matrices, but I've left it out for simplicity.

EDIT:

I achieved almost 75% reduction in computation time by using the extended syntax for lu when factorizing H.

[L U P Q] = lu(H);

Please let me know if any additional savings are possible to achieve.

Thanks!

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Jan 2013-5-13

编辑：Jan 2013-5-13

在 MATLAB Online 中打开

@Robert P: It would be much more convenient and useful to post the Matlab code instead of a mathematical notation. Instead of optimizing your code, we have to write it from scratch. On one hand this is more work for us, on the other hand the created code will not necessarily match your one sufficiently. So please post the code, which you want to get optimized.

You mathematical notation is even not clear:

start loop # 2 (10 iterations)
  dVa = - (U \ (L \ (P * P))); 
  dVaComp = (U \ (L \ (P * M * c * M' * dVa)));
end loop # 2

It is not specified, what is changed in the iterations. Then it is not meaningful to run the loop 10 times at all.

Calculating the inverse explicitly is not useful in general: it is slower and less accurate compared to solving the corresponding linear equation system.

John Doe 2013-5-13

编辑：John Doe 2013-5-13

Thanks for the hints Jan! I have updated the question, please let me know if I should do further changes, or provide additional information.

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Speed up sparse matrix calculations

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Speed up sparse matrix calculations

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