64 lines
2.1 KiB
Mathematica
64 lines
2.1 KiB
Mathematica
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function [V,D,permutation,failure] = dmpermblockeig(X,switchtosparse)
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[permutation,aux1,aux2,blocks] = dmperm(X+speye(length(X)));
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Xpermuted = X(permutation,permutation);
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V = [];
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D = [];
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V = zeros(size(X,1),1);
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top = 1;
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left = 1;
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anycholfail = 0;
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failure = 0;
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for i = 1:length(blocks)-1
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Xi = Xpermuted(blocks(i):blocks(i+1)-1,blocks(i):blocks(i+1)-1);
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[R,fail] = chol(Xi);
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anycholfail = anycholfail | fail;
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if fail
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if length(Xi) >= switchtosparse
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[vi,di,eigfail] = eigs(Xi,5,'SA');
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if eigfail || isempty(di)
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res = 0;
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for j = 1:size(vi,2)
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res(j) = norm(Xi*vi(:,j)-vi(:,j)*di(j,j));
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end
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% We only trust these
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notfailed = abs(res) <= 1e-12;
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vi = vi(:,notfailed);
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di = di(notfailed,notfailed);
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if length(vi) == 0
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[vi,di,eigfail] = eigs(sparse(Xi),25,'SA');
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if eigfail
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res = 0;
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for j = 1:size(vi,2)
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res(j) = norm(Xi*vi(:,j)-vi(:,j)*di(j,j));
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end
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% We only trust these
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notfailed = abs(res) <= 1e-12;
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vi = vi(:,notfailed);
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di = di(notfailed,notfailed);
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end
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end
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end
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else
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[vi,di] = eig(full(Xi));
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end
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for j = 1:length(di)
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if di(j,j)<=0
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V(top:top+length(Xi)-1,left)=vi(:,j);
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left = left + 1;
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D = blkdiag(D,di(j,j));
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end
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end
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end
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top = top + length(Xi);
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end
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if (anycholfail && isempty(V)) || (anycholfail && all(diag(D)>0))
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% OK, we have a problem. The Cholesky factorization failed for some of
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% the matrices, but yet no eigenvalue decomposition revealed a negative
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% eigenvalue (due to convergence issues in the sparse eigs)
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failure = 1;
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end
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