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function [L, w] = chol_downdate (L, w)
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%CHOL_DOWNDATE downdate a Cholesky factorization.
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% [L, w] = chol_downdate (L, w)
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% Copyright 2006-2007, Timothy A. Davis.
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% http://www.cise.ufl.edu/research/sparse
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alpha = w (j) / L (j,j) ;
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beta2 = sqrt (beta^2 - alpha^2) ;
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error ('not positive definite') ;
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gamma = alpha / (beta2 * beta) ;
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delta = beta2 / beta ;
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L (j,j) = delta * L (j,j) ;
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w (j+1:n) = w (j+1:n) - alpha * L (j+1:n,j) ;
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L (j+1:n,j) = delta * L (j+1:n,j) - gamma * w (j+1:n) ;