wehub-resource-sync
33 lines
934 B
Matlab
Executable File
33 lines
934 B
Matlab
Executable File
% function [L, D] = ld(X)
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% % LD factorization produces LDL'=X*X' which is the same as [L,D] = ldl(X*X');
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% % the underlying algorithm is Gram-Schmidt orthogonalization
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% [d,n] = size(X);
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% m = min(d,n);
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% L = eye(d,m);
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% Q = zeros(m,n);
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% D = zeros(m,1);
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% for i = 1:m
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% L(i,1:i-1) = X(i,:)*bsxfun(@times,Q(1:i-1,:),1./D(1:i-1))';
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% Q(i,:) = X(i,:)-L(i,1:i-1)*Q(1:i-1,:);
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% D(i) = dot(Q(i,:),Q(i,:));
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% end
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% L(m+1:d,:) = X(m+1:d,:)*bsxfun(@times,Q,1./D)';
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function [L, D] = ld(X)
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% LD factorization produces LDL'=X*X' which is the same as [L,D] = ldl(X*X');
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% the underlying algorithm is modified Gram-Schmidt orthogonalization
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[d,n] = size(X);
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m = min(d,n);
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L = eye(d,m);
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Q = zeros(m,n);
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D = zeros(m,1);
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for i = 1:m
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v = X(i,:);
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for j = 1:i-1
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L(i,j) = v*Q(j,:)'/D(j);
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v = v-L(i,j)*Q(j,:);
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end
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Q(i,:) = v;
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D(i) = dot(Q(i,:),Q(i,:));
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end
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L(m+1:d,:) = X(m+1:d,:)*bsxfun(@times,Q,1./D)'; |