int main (void)
{
cs_cl *T, *A, *Eye, *AT, *C, *D ;
cs_long_t i, m ;
T = cs_cl_load (stdin) ; /* load triplet matrix T from stdin */
printf ("T:\n") ; cs_cl_print (T, 0) ; /* print T */
A = cs_cl_compress (T) ; /* A = compressed-column form of T */
printf ("A:\n") ; cs_cl_print (A, 0) ; /* print A */
cs_cl_spfree (T) ; /* clear T */
AT = cs_cl_transpose (A, 1) ; /* AT = A' */
printf ("AT:\n") ; cs_cl_print (AT, 0) ; /* print AT */
m = A ? A->m : 0 ; /* m = # of rows of A */
T = cs_cl_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */
for (i = 0 ; i < m ; i++) cs_cl_entry (T, i, i, 1) ;
Eye = cs_cl_compress (T) ; /* Eye = speye (m) */
cs_cl_spfree (T) ;
C = cs_cl_multiply (A, AT) ; /* C = A*A' */
D = cs_cl_add (C, Eye, 1, cs_cl_norm (C)) ; /* D = C + Eye*norm (C,1) */
printf ("D:\n") ; cs_cl_print (D, 0) ; /* print D */
cs_cl_spfree (A) ; /* clear A AT C D Eye */
cs_cl_spfree (AT) ;
cs_cl_spfree (C) ;
cs_cl_spfree (D) ;
cs_cl_spfree (Eye) ;
return (0) ;
}
/* Cholesky update/downdate */
cs_long_t demo3 (problem *Prob)
{
cs_cl *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ;
cs_long_t n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ;
cs_complex_t *b, *x, *resid, *y = NULL, *Lx, *Wx, s ;
double t, t1 ;
cs_cls *S = NULL ;
cs_cln *N = NULL ;
if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ;
A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
n = A->n ;
if (!Prob->sym || n == 0) return (1) ;
rhs (x, b, n) ; /* compute right-hand side */
printf ("\nchol then update/downdate ") ;
print_order (1) ;
y = cs_cl_malloc (n, sizeof (cs_complex_t)) ;
t = tic () ;
S = cs_cl_schol (1, C) ; /* symbolic Chol, amd(A+A') */
printf ("\nsymbolic chol time %8.2f\n", toc (t)) ;
t = tic () ;
N = cs_cl_chol (C, S) ; /* numeric Cholesky */
printf ("numeric chol time %8.2f\n", toc (t)) ;
if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ;
t = tic () ;
cs_cl_ipvec (S->pinv, b, y, n) ; /* y = P*b */
cs_cl_lsolve (N->L, y) ; /* y = L\y */
cs_cl_ltsolve (N->L, y) ; /* y = L'\y */
cs_cl_pvec (S->pinv, y, x, n) ; /* x = P'*y */
printf ("solve chol time %8.2f\n", toc (t)) ;
printf ("original: ") ;
print_resid (1, C, x, b, resid) ; /* print residual */
k = n/2 ; /* construct W */
W = cs_cl_spalloc (n, 1, n, 1, 0) ;
if (!W) return (done3 (0, S, N, y, W, E, p)) ;
Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ;
Wp = W->p ; Wi = W->i ; Wx = W->x ;
Wp [0] = 0 ;
p1 = Lp [k] ;
Wp [1] = Lp [k+1] - p1 ;
s = Lx [p1] ;
srand (1) ;
for ( ; p1 < Lp [k+1] ; p1++)
{
p2 = p1 - Lp [k] ;
Wi [p2] = Li [p1] ;
Wx [p2] = s * rand () / ((double) RAND_MAX) ;
}
t = tic () ;
ok = cs_cl_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */
t1 = toc (t) ;
printf ("update: time: %8.2f\n", t1) ;
if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
t = tic () ;
cs_cl_ipvec (S->pinv, b, y, n) ; /* y = P*b */
cs_cl_lsolve (N->L, y) ; /* y = L\y */
cs_cl_ltsolve (N->L, y) ; /* y = L'\y */
cs_cl_pvec (S->pinv, y, x, n) ; /* x = P'*y */
t = toc (t) ;
p = cs_cl_pinv (S->pinv, n) ;
W2 = cs_cl_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */
WT = cs_cl_transpose (W2,1) ;
WW = cs_cl_multiply (W2, WT) ;
cs_cl_spfree (WT) ;
cs_cl_spfree (W2) ;
E = cs_cl_add (C, WW, 1, 1) ;
cs_cl_spfree (WW) ;
if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ;
printf ("update: time: %8.2f (incl solve) ", t1+t) ;
print_resid (1, E, x, b, resid) ; /* print residual */
cs_cl_nfree (N) ; /* clear N */
t = tic () ;
N = cs_cl_chol (E, S) ; /* numeric Cholesky */
if (!N) return (done3 (0, S, N, y, W, E, p)) ;
cs_cl_ipvec (S->pinv, b, y, n) ; /* y = P*b */
cs_cl_lsolve (N->L, y) ; /* y = L\y */
cs_cl_ltsolve (N->L, y) ; /* y = L'\y */
cs_cl_pvec (S->pinv, y, x, n) ; /* x = P'*y */
t = toc (t) ;
printf ("rechol: time: %8.2f (incl solve) ", t) ;
print_resid (1, E, x, b, resid) ; /* print residual */
t = tic () ;
ok = cs_cl_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */
t1 = toc (t) ;
if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
printf ("downdate: time: %8.2f\n", t1) ;
t = tic () ;
cs_cl_ipvec (S->pinv, b, y, n) ; /* y = P*b */
cs_cl_lsolve (N->L, y) ; /* y = L\y */
cs_cl_ltsolve (N->L, y) ; /* y = L'\y */
cs_cl_pvec (S->pinv, y, x, n) ; /* x = P'*y */
t = toc (t) ;
printf ("downdate: time: %8.2f (incl solve) ", t1+t) ;
print_resid (1, C, x, b, resid) ; /* print residual */
return (done3 (1, S, N, y, W, E, p)) ;
}
