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