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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ldldown.m %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% function [L,d]=ldldown(L,d,j)
% downdates LDL^T factorization when j-th row and column are replaced 
% by j-th unit vector
%
% d contains diag(D) and is assumed positive
%
function [L,d]=ldldown(L,d,j);

n=size(d,1);

test=0;
if test,
  disp('enter ldldown')
  A=L*diag(d)*L';A(:,j)=zeros(n,1);A(j,:)=zeros(1,n);A(j,j)=1; 
end;

if j<n,
  I=1:j-1;K=j+1:n;
  [LKK,d(K)]=ldlrk1(L(K,K),d(K),d(j),L(K,j));
  % work around expensive sparse L(K,K)=LKK
  L=[L(I,:);
     sparse(1,n);
     L(K,I),sparse(n-j,1),LKK];
  L(j,j)=1;
else
  L(n,1:n-1)=sparse(1,n-1);
end;
d(j)=1;

if test, 
  A1=L*diag(d)*L',A 
  quot=norm(A1-A,1)/norm(A,1), 
  disp('leave ldldown')
end;