1 #include "cs.h"
2 /* sparse Cholesky update/downdate, L*L' + sigma*w*w' (sigma = +1 or -1) */
cs_updown(cs * L,CS_INT sigma,const cs * C,const CS_INT * parent)3 CS_INT cs_updown (cs *L, CS_INT sigma, const cs *C, const CS_INT *parent)
4 {
5 CS_INT n, p, f, j, *Lp, *Li, *Cp, *Ci ;
6 CS_ENTRY *Lx, *Cx, alpha, gamma, w1, w2, *w ;
7 double beta = 1, beta2 = 1, delta ;
8 #ifdef CS_COMPLEX
9 cs_complex_t phase ;
10 #endif
11 if (!CS_CSC (L) || !CS_CSC (C) || !parent) return (0) ; /* check inputs */
12 Lp = L->p ; Li = L->i ; Lx = L->x ; n = L->n ;
13 Cp = C->p ; Ci = C->i ; Cx = C->x ;
14 if ((p = Cp [0]) >= Cp [1]) return (1) ; /* return if C empty */
15 w = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get workspace */
16 if (!w) return (0) ; /* out of memory */
17 f = Ci [p] ;
18 for ( ; p < Cp [1] ; p++) f = CS_MIN (f, Ci [p]) ; /* f = min (find (C)) */
19 for (j = f ; j != -1 ; j = parent [j]) w [j] = 0 ; /* clear workspace w */
20 for (p = Cp [0] ; p < Cp [1] ; p++) w [Ci [p]] = Cx [p] ; /* w = C */
21 for (j = f ; j != -1 ; j = parent [j]) /* walk path f up to root */
22 {
23 p = Lp [j] ;
24 alpha = w [j] / Lx [p] ; /* alpha = w(j) / L(j,j) */
25 beta2 = beta*beta + sigma*alpha*CS_CONJ(alpha) ;
26 if (beta2 <= 0) break ; /* not positive definite */
27 beta2 = sqrt (beta2) ;
28 delta = (sigma > 0) ? (beta / beta2) : (beta2 / beta) ;
29 gamma = sigma * CS_CONJ(alpha) / (beta2 * beta) ;
30 Lx [p] = delta * Lx [p] + ((sigma > 0) ? (gamma * w [j]) : 0) ;
31 beta = beta2 ;
32 #ifdef CS_COMPLEX
33 phase = CS_ABS (Lx [p]) / Lx [p] ; /* phase = abs(L(j,j))/L(j,j)*/
34 Lx [p] *= phase ; /* L(j,j) = L(j,j) * phase */
35 #endif
36 for (p++ ; p < Lp [j+1] ; p++)
37 {
38 w1 = w [Li [p]] ;
39 w [Li [p]] = w2 = w1 - alpha * Lx [p] ;
40 Lx [p] = delta * Lx [p] + gamma * ((sigma > 0) ? w1 : w2) ;
41 #ifdef CS_COMPLEX
42 Lx [p] *= phase ; /* L(i,j) = L(i,j) * phase */
43 #endif
44 }
45 }
46 cs_free (w) ;
47 return (beta2 > 0) ;
48 }
49