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) ;
}
/* cs_updown: sparse Cholesky update/downdate (rank-1 or multiple rank) */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
CS_INT ignore, j, k, n, lnz, *parent, sigma = 1, cp [2], ok ;
char sigma_string [20] ;
if (nargout > 1 || nargin < 3 || nargin > 4)
{
mexErrMsgTxt ("Usage: L = cs_updown(L,C,parent,sigma)") ;
}
if (nargin > 3 && mxIsChar (pargin [3]))
{
mxGetString (pargin [3], sigma_string, 8) ;
sigma = (sigma_string [0] == '-') ? (-1) : 1 ;
}
n = mxGetN (pargin [0]) ;
parent = cs_dl_mex_get_int (n, pargin [2], &ignore, 0) ; /* get parent*/
if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
{
#ifndef NCOMPLEX
cs_cl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ;
/* get input L, and copy MATLAB complex to C complex type */
Lin = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ;
/* make a copy of L (this can take more work than updating L itself) */
lnz = Lin->p [n] ;
L = cs_cl_spalloc (n, n, lnz, 0, 0) ;
for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ;
for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ;
/* complex values already copied into Lin->x, use shallow copy for L */
L->x = Lin->x ;
cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */
C = cs_cl_mex_get_sparse (&Cmatrix, 0, pargin [1]) ;
/* do the update one column at a time */
Cvec = &Cvector ;
Cvec->m = n ;
Cvec->n = 1 ;
Cvec->p = cp ;
Cvec->nz = -1 ;
cp [0] = 0 ;
for (k = 0 ; k < C->n ; k++)
{
/* extract C(:,k) */
cp [1] = C->p [k+1] - C->p [k] ;
Cvec->nzmax = cp [1] ;
Cvec->i = C->i + C->p [k] ;
Cvec->x = C->x + C->p [k] ;
/* update/downdate */
ok = cs_cl_updown (L, sigma, Cvec, parent) ;
if (!ok) mexErrMsgTxt ("matrix is not positive definite") ;
}
/* return new L */
pargout [0] = cs_cl_mex_put_sparse (&L) ;
cs_free (C->x) ; /* free complex copy of C */
#else
mexErrMsgTxt ("complex matrices not supported") ;
#endif
}
else
{
cs_dl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ;
/* get input L */
Lin = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;
/* make a copy of L (this can take more work than updating L itself) */
lnz = Lin->p [n] ;
L = cs_dl_spalloc (n, n, lnz, 1, 0) ;
for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ;
for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ;
for (k = 0 ; k < lnz ; k++) L->x [k] = Lin->x [k] ;
cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */
C = cs_dl_mex_get_sparse (&Cmatrix, 0, 1, pargin [1]) ;
/* do the update one column at a time */
Cvec = &Cvector ;
Cvec->m = n ;
Cvec->n = 1 ;
Cvec->p = cp ;
Cvec->nz = -1 ;
cp [0] = 0 ;
for (k = 0 ; k < C->n ; k++)
{
/* extract C(:,k) */
cp [1] = C->p [k+1] - C->p [k] ;
Cvec->nzmax = cp [1] ;
Cvec->i = C->i + C->p [k] ;
Cvec->x = C->x + C->p [k] ;
/* update/downdate */
ok = cs_dl_updown (L, sigma, Cvec, parent) ;
if (!ok) mexErrMsgTxt ("matrix is not positive definite") ;
}
/* return new L */
pargout [0] = cs_dl_mex_put_sparse (&L) ;
}
}
/* 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)) ;
}