trdsdsmat

 compute trace(A*S1*B*S2) where A,B are dense symmetric matrices, S1,S2 are sparse
 typically, it would be: trdsdsmat(pZUZ, Akdix, invZ, Akdjx)

0001 % compute trace(A*S1*B*S2) where A,B are dense symmetric matrices, S1,S2 are sparse
0002 % typically, it would be: trdsdsmat(pZUZ, Akdix, invZ, Akdjx)
0003 function [tr]=trdsdsmat(A,S1,B,S2)
0004 
0005   %tic;
0006   %S1BS2=S1*B*S2;
0007   %tr = trace(A*S1BS2);
0008   %toc
0009 
0010   %tic;
0011   %S1BS2=sparse(S1*(full(B)*S2)); % or sparse(full(B)*S2)...?
0012   %tr = trace(A*S1BS2);
0013   %toc
0014 
0015   % USE ME (if not mex)!   % -->7.5s (sparse), ?? (dense)
0016   %tic;
0017   S1BS2=S1*(B*S2); % or sparse(full(B)*S2)...?
0018   tr = A(:)'*S1BS2(:);
0019   %toc
0020 
0021   % or use mex
0022   %tr=mextrdsdsmat(A,S1,full(B),S2);  % very slow... --> 15s
0023   %%tr=mextrdsdsmat(A,S1,B,S2);  % with full one above --> ~6s
0024 
0025   %S1BS2=S1*sparse((full(B)*S2)); % or sparse(full(B)*S2)...?
0026   %tr = A(:)'*S1BS2(:);
0027 
0028   % rather list the elements...?
0029   % zkusit tr(A,B) = sum A_ij * B_ij = svec(A)'svec(B)
0030   % careful about svec on symmetric matrices (sqrt(2)...)
0031 
0032