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function [L, w] = chol_updown2 (L, sigma, w)
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%CHOL_UPDOWN2 Cholesky update/downdate (real and complex)
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% [L, w] = chol_updown2 (L, sigma, w)
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% Copyright 2006-2007, Timothy A. Davis, William W. Hager
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% http://www.cise.ufl.edu/research/sparse
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L = sqrt (L*L'+sigma*w*w') ;
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alpha = w(k) / L(k,k) ;
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beta2 = sqrt (beta*beta + sigma*alpha*conj(alpha)) ;
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gamma = sigma * conj(alpha) / (beta2 * beta) ;
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delta = beta / beta2 ;
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L (k,k) = delta * L (k,k) + gamma * w (k) ;
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phase = abs (L (k, k))/L (k, k) ;
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L (k, k) = phase*L (k, k) ;
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w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
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L (k+1:n,k) = phase * (delta * L (k+1:n,k) + gamma * w1) ;
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delta = beta2 / beta ;
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L (k,k) = delta * L (k,k) ;
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phase = abs (L (k, k))/L (k, k) ;
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L (k, k) = phase*L (k, k) ;
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w (k+1:n) = w (k+1:n) - alpha * L (k+1:n,k) ;
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L (k+1:n,k) = phase * (delta * L (k+1:n,k) + gamma * w (k+1:n)) ;