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#include "cs.h"
/* L = chol (A, [pinv parent cp]), pinv is optional */
csn *cs_chol (const cs *A, const css *S)
{
CS_ENTRY d, lki, *Lx, *x, *Cx ;
CS_INT top, i, p, k, n, *Li, *Lp, *cp, *pinv, *s, *c, *parent, *Cp, *Ci ;
cs *L, *C, *E ;
csn *N ;
if (!CS_CSC (A) || !S || !S->cp || !S->parent) return (NULL) ;
n = A->n ;
N = cs_calloc (1, sizeof (csn)) ; /* allocate result */
c = cs_malloc (2*n, sizeof (CS_INT)) ; /* get CS_INT workspace */
x = cs_malloc (n, sizeof (CS_ENTRY)) ; /* get CS_ENTRY workspace */
cp = S->cp ; pinv = S->pinv ; parent = S->parent ;
C = pinv ? cs_symperm (A, pinv, 1) : ((cs *) A) ;
E = pinv ? C : NULL ; /* E is alias for A, or a copy E=A(p,p) */
if (!N || !c || !x || !C) return (cs_ndone (N, E, c, x, 0)) ;
s = c + n ;
Cp = C->p ; Ci = C->i ; Cx = C->x ;
N->L = L = cs_spalloc (n, n, cp [n], 1, 0) ; /* allocate result */
if (!L) return (cs_ndone (N, E, c, x, 0)) ;
Lp = L->p ; Li = L->i ; Lx = L->x ;
for (k = 0 ; k < n ; k++) Lp [k] = c [k] = cp [k] ;
for (k = 0 ; k < n ; k++) /* compute L(k,:) for L*L' = C */
{
/* --- Nonzero pattern of L(k,:) ------------------------------------ */
top = cs_ereach (C, k, parent, s, c) ; /* find pattern of L(k,:) */
x [k] = 0 ; /* x (0:k) is now zero */
for (p = Cp [k] ; p < Cp [k+1] ; p++) /* x = full(triu(C(:,k))) */
{
if (Ci [p] <= k) x [Ci [p]] = Cx [p] ;
}
d = x [k] ; /* d = C(k,k) */
x [k] = 0 ; /* clear x for k+1st iteration */
/* --- Triangular solve --------------------------------------------- */
for ( ; top < n ; top++) /* solve L(0:k-1,0:k-1) * x = C(:,k) */
{
i = s [top] ; /* s [top..n-1] is pattern of L(k,:) */
lki = x [i] / Lx [Lp [i]] ; /* L(k,i) = x (i) / L(i,i) */
x [i] = 0 ; /* clear x for k+1st iteration */
for (p = Lp [i] + 1 ; p < c [i] ; p++)
{
x [Li [p]] -= Lx [p] * lki ;
}
d -= lki * CS_CONJ (lki) ; /* d = d - L(k,i)*L(k,i) */
p = c [i]++ ;
Li [p] = k ; /* store L(k,i) in column i */
Lx [p] = CS_CONJ (lki) ;
}
/* --- Compute L(k,k) ----------------------------------------------- */
if (CS_REAL (d) <= 0 || CS_IMAG (d) != 0)
return (cs_ndone (N, E, c, x, 0)) ; /* not pos def */
p = c [k]++ ;
Li [p] = k ; /* store L(k,k) = sqrt (d) in column k */
Lx [p] = sqrt (d) ;
}
Lp [n] = cp [n] ; /* finalize L */
return (cs_ndone (N, E, c, x, 1)) ; /* success: free E,s,x; return N */
}