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#include "cs.h"
/* sparse Cholesky update/downdate, L*L' + sigma*w*w' (sigma = +1 or -1) */
CS_INT cs_updown (cs *L, CS_INT sigma, const cs *C, const CS_INT *parent)
{
CS_INT n, p, f, j, *Lp, *Li, *Cp, *Ci ;
CS_ENTRY *Lx, *Cx, alpha, gamma, w1, w2, *w ;
double beta = 1, beta2 = 1, delta ;
#ifdef CS_COMPLEX
cs_complex_t phase ;
#endif
if (!CS_CSC (L) || !CS_CSC (C) || !parent) return (0) ; /* check inputs */
Lp = L->p ; Li = L->i ; Lx = L->x ; n = L->n ;
Cp = C->p ; Ci = C->i ; Cx = C->x ;
if ((p = Cp [0]) >= Cp [1]) return (1) ; /* return if C empty */
w = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get workspace */
if (!w) return (0) ; /* out of memory */
f = Ci [p] ;
for ( ; p < Cp [1] ; p++) f = CS_MIN (f, Ci [p]) ; /* f = min (find (C)) */
for (j = f ; j != -1 ; j = parent [j]) w [j] = 0 ; /* clear workspace w */
for (p = Cp [0] ; p < Cp [1] ; p++) w [Ci [p]] = Cx [p] ; /* w = C */
for (j = f ; j != -1 ; j = parent [j]) /* walk path f up to root */
{
p = Lp [j] ;
alpha = w [j] / Lx [p] ; /* alpha = w(j) / L(j,j) */
beta2 = beta*beta + sigma*alpha*CS_CONJ(alpha) ;
if (beta2 <= 0) break ; /* not positive definite */
beta2 = sqrt (beta2) ;
delta = (sigma > 0) ? (beta / beta2) : (beta2 / beta) ;
gamma = sigma * CS_CONJ(alpha) / (beta2 * beta) ;
Lx [p] = delta * Lx [p] + ((sigma > 0) ? (gamma * w [j]) : 0) ;
beta = beta2 ;
#ifdef CS_COMPLEX
phase = CS_ABS (Lx [p]) / Lx [p] ; /* phase = abs(L(j,j))/L(j,j)*/
Lx [p] *= phase ; /* L(j,j) = L(j,j) * phase */
#endif
for (p++ ; p < Lp [j+1] ; p++)
{
w1 = w [Li [p]] ;
w [Li [p]] = w2 = w1 - alpha * Lx [p] ;
Lx [p] = delta * Lx [p] + gamma * ((sigma > 0) ? w1 : w2) ;
#ifdef CS_COMPLEX
Lx [p] *= phase ; /* L(i,j) = L(i,j) * phase */
#endif
}
}
cs_free (w) ;
return (beta2 > 0) ;
}