EVSL  1.1.0
EigenValues Slicing Library
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cs_updown.c
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1 #include "cs.h"
2 /* sparse Cholesky update/downdate, L*L' + sigma*w*w' (sigma = +1 or -1) */
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 }
void * cs_free(void *p)
Definition: cs_malloc.c:22
#define cs
Definition: cs.h:637
#define CS_CONJ(x)
Definition: cs.h:649
#define CS_ENTRY
Definition: cs.h:635
#define cs_complex_t
Definition: cs.h:41
#define CS_ABS(x)
Definition: cs.h:650
#define CS_CSC(A)
Definition: cs.h:659
#define CS_INT
Definition: cs.h:627
#define CS_MIN(a, b)
Definition: cs.h:654
void * cs_malloc(CS_INT n, size_t size)
Definition: cs_malloc.c:10
CS_INT cs_updown(cs *L, CS_INT sigma, const cs *C, const CS_INT *parent)
Definition: cs_updown.c:3