int main (int argc, char **argv)
{
/* ---------------------------------------------------------------------- */
/* get the file containing the input matrix */
/* ---------------------------------------------------------------------- */
FILE *ff = NULL ;
FILE *fb = NULL ;
if (argc <= 1)
{
printf("Usage is: cholmod_simple A.tri [B.txt (dense)]\n");
exit(0);
}
if (argc > 1)
ff = fopen(argv[1],"r");
if (argc > 2)
fb = fopen(argv[2], "r");
cholmod_sparse *A ;
cholmod_dense *x, *b, *r ;
cholmod_factor *L ;
double one [2] = {1,0}, m1 [2] = {-1,0} ; // basic scalars
cholmod_common c ;
cholmod_start (&c) ; /* start CHOLMOD */
A = cholmod_read_sparse (ff, &c) ; /* read in a matrix */
cholmod_print_sparse (A, (char *)"A", &c) ; /* print the matrix */
if (A->dtype) printf("A is float\n");
else printf("A is double\n");
if (A == NULL || A->stype == 0) /* A must be symmetric */
{
cholmod_free_sparse (&A, &c) ;
cholmod_finish (&c) ;
if (ff) fclose(ff);
if (fb) fclose(fb);
return (0) ;
}
if (fb)
b = cholmod_read_dense(fb, &c);
else
b = cholmod_ones (A->nrow, 1, A->xtype, &c) ; /* b = ones(n,1) */
double t0 = CPUTIME;
L = cholmod_analyze (A, &c) ; /* analyze */
cholmod_factorize (A, L, &c) ; /* factorize */
x = cholmod_solve (CHOLMOD_A, L, b, &c) ; /* solve Ax=b */
double t1 = CPUTIME;
if (c.dtype) printf("Compute is float\n");
else printf("Compute is double\n");
printf("Time: %12.4f \n", t1-t0);
r = cholmod_copy_dense (b, &c) ; /* r = b */
cholmod_sdmult (A, 0, m1, one, x, r, &c) ; /* r = r-Ax */
printf ("norm(b-Ax) %8.1e\n",
cholmod_norm_dense (r, 0, &c)) ; /* print norm(r) */
cholmod_free_factor (&L, &c) ; /* free matrices */
cholmod_free_sparse (&A, &c) ;
cholmod_free_dense (&r, &c) ;
cholmod_free_dense (&x, &c) ;
cholmod_free_dense (&b, &c) ;
cholmod_finish (&c) ; /* finish CHOLMOD */
return (0) ;
}
int main (void)
{
cholmod_sparse *A ;
cholmod_dense *x, *b, *r ;
cholmod_factor *L ;
double one [2] = {1,0}, m1 [2] = {-1,0} ; /* basic scalars */
cholmod_common c ;
cholmod_start (&c) ; /* start CHOLMOD */
A = cholmod_read_sparse (stdin, &c) ; /* read in a matrix */
cholmod_print_sparse (A, "A", &c) ; /* print the matrix */
if (A == NULL || A->stype == 0) /* A must be symmetric */
{
cholmod_free_sparse (&A, &c) ;
cholmod_finish (&c) ;
return (0) ;
}
b = cholmod_ones (A->nrow, 1, A->xtype, &c) ; /* b = ones(n,1) */
L = cholmod_analyze (A, &c) ; /* analyze */
cholmod_factorize (A, L, &c) ; /* factorize */
x = cholmod_solve (CHOLMOD_A, L, b, &c) ; /* solve Ax=b */
r = cholmod_copy_dense (b, &c) ; /* r = b */
cholmod_sdmult (A, 0, m1, one, x, r, &c) ; /* r = r-Ax */
printf ("norm(b-Ax) %8.1e\n",
cholmod_norm_dense (r, 0, &c)) ; /* print norm(r) */
cholmod_free_factor (&L, &c) ; /* free matrices */
cholmod_free_sparse (&A, &c) ;
cholmod_free_dense (&r, &c) ;
cholmod_free_dense (&x, &c) ;
cholmod_free_dense (&b, &c) ;
cholmod_finish (&c) ; /* finish CHOLMOD */
return (0) ;
}
int main() {
// define variable
cholmod_dense *A;
cholmod_common c ;
cholmod_start(&c) ; // start CHOLMOD
A = cholmod_ones(3, 3, CHOLMOD_REAL, &c) ; // A = ones(3,3)
std::cout << "norm(A): " << cholmod_norm_dense(A, 0, &c) << std::endl;
cholmod_finish (&c) ; // finish CHOLMOD
}
int main (int argc, char **argv)
{
double resid, t, ta, tf, ts, tot, bnorm, xnorm, anorm, rnorm, fl, anz,
axbnorm, rnorm2, resid2 ;
FILE *f ;
cholmod_sparse *A ;
cholmod_dense *X, *B, *W, *R ;
double one [2], zero [2], minusone [2], beta [2], xlnz ;
cholmod_common Common, *cm ;
cholmod_factor *L ;
double *Bx, *Rx, *Xx ;
int i, n, isize, xsize, ordering, xtype, s, ss, lnz ;
/* ---------------------------------------------------------------------- */
/* get the file containing the input matrix */
/* ---------------------------------------------------------------------- */
ff = NULL ;
if (argc > 1)
{
if ((f = fopen (argv [1], "r")) == NULL)
{
my_handler (CHOLMOD_INVALID, __FILE__, __LINE__,
"unable to open file") ;
}
ff = f ;
}
else
{
f = stdin ;
}
/* ---------------------------------------------------------------------- */
/* start CHOLMOD and set parameters */
/* ---------------------------------------------------------------------- */
cm = &Common ;
cholmod_start (cm) ;
/* use default parameter settings, except for the error handler. This
* demo program terminates if an error occurs (out of memory, not positive
* definite, ...). It makes the demo program simpler (no need to check
* CHOLMOD error conditions). This non-default parameter setting has no
* effect on performance. */
cm->error_handler = my_handler ;
/* Note that CHOLMOD will do a supernodal LL' or a simplicial LDL' by
* default, automatically selecting the latter if flop/nnz(L) < 40. */
/* ---------------------------------------------------------------------- */
/* create basic scalars */
/* ---------------------------------------------------------------------- */
zero [0] = 0 ;
zero [1] = 0 ;
one [0] = 1 ;
one [1] = 0 ;
minusone [0] = -1 ;
minusone [1] = 0 ;
beta [0] = 1e-6 ;
beta [1] = 0 ;
/* ---------------------------------------------------------------------- */
/* read in a matrix */
/* ---------------------------------------------------------------------- */
printf ("\n---------------------------------- cholmod_demo:\n") ;
A = cholmod_read_sparse (f, cm) ;
if (ff != NULL) fclose (ff) ;
anorm = cholmod_norm_sparse (A, 0, cm) ;
xtype = A->xtype ;
printf ("norm (A,inf) = %g\n", anorm) ;
printf ("norm (A,1) = %g\n", cholmod_norm_sparse (A, 1, cm)) ;
cholmod_print_sparse (A, "A", cm) ;
if (A->nrow > A->ncol)
{
/* Transpose A so that A'A+beta*I will be factorized instead */
cholmod_sparse *C = cholmod_transpose (A, 2, cm) ;
cholmod_free_sparse (&A, cm) ;
A = C ;
printf ("transposing input matrix\n") ;
}
/* ---------------------------------------------------------------------- */
/* create an arbitrary right-hand-side */
/* ---------------------------------------------------------------------- */
n = A->nrow ;
B = cholmod_zeros (n, 1, xtype, cm) ;
Bx = B->x ;
#if GHS
{
/* b = A*ones(n,1), used by Gould, Hu, and Scott in their experiments */
cholmod_dense *X0 ;
X0 = cholmod_ones (A->ncol, 1, xtype, cm) ;
cholmod_sdmult (A, 0, one, zero, X0, B, cm) ;
cholmod_free_dense (&X0, cm) ;
}
#else
if (xtype == CHOLMOD_REAL)
{
/* real case */
for (i = 0 ; i < n ; i++)
{
double x = n ;
Bx [i] = 1 + i / x ;
}
}
else
{
/* complex case */
for (i = 0 ; i < n ; i++)
{
double x = n ;
Bx [2*i ] = 1 + i / x ; /* real part of B(i) */
Bx [2*i+1] = (x/2 - i) / (3*x) ; /* imag part of B(i) */
}
}
#endif
cholmod_print_dense (B, "B", cm) ;
bnorm = cholmod_norm_dense (B, 0, cm) ; /* max norm */
printf ("bnorm %g\n", bnorm) ;
/* ---------------------------------------------------------------------- */
/* analyze, factorize, and solve */
/* ---------------------------------------------------------------------- */
t = CPUTIME ;
L = cholmod_analyze (A, cm) ;
ta = CPUTIME - t ;
ta = MAX (ta, 0) ;
printf ("Analyze: flop %g lnz %g\n", cm->fl, cm->lnz) ;
if (A->stype == 0)
{
printf ("Factorizing A*A'+beta*I\n") ;
t = CPUTIME ;
cholmod_factorize_p (A, beta, NULL, 0, L, cm) ;
tf = CPUTIME - t ;
tf = MAX (tf, 0) ;
}
else
{
printf ("Factorizing A\n") ;
t = CPUTIME ;
cholmod_factorize (A, L, cm) ;
tf = CPUTIME - t ;
tf = MAX (tf, 0) ;
}
t = CPUTIME ;
X = cholmod_solve (CHOLMOD_A, L, B, cm) ;
ts = CPUTIME - t ;
ts = MAX (ts, 0) ;
tot = ta + tf + ts ;
/* ---------------------------------------------------------------------- */
/* compute the residual */
/* ---------------------------------------------------------------------- */
if (A->stype == 0)
{
/* (AA'+beta*I)x=b is the linear system that was solved */
/* W = A'*X */
W = cholmod_allocate_dense (A->ncol, 1, A->ncol, xtype, cm) ;
cholmod_sdmult (A, 2, one, zero, X, W, cm) ;
/* R = B - beta*X */
R = cholmod_zeros (n, 1, xtype, cm) ;
Rx = R->x ;
Xx = X->x ;
if (xtype == CHOLMOD_REAL)
{
for (i = 0 ; i < n ; i++)
{
Rx [i] = Bx [i] - beta [0] * Xx [i] ;
}
}
else
{
/* complex case */
for (i = 0 ; i < n ; i++)
{
Rx [2*i ] = Bx [2*i ] - beta [0] * Xx [2*i ] ;
Rx [2*i+1] = Bx [2*i+1] - beta [0] * Xx [2*i+1] ;
}
}
/* R = A*W - R */
cholmod_sdmult (A, 0, one, minusone, W, R, cm) ;
cholmod_free_dense (&W, cm) ;
}
else
{
/* Ax=b was factorized and solved, R = B-A*X */
R = cholmod_copy_dense (B, cm) ;
cholmod_sdmult (A, 0, minusone, one, X, R, cm) ;
}
rnorm = cholmod_norm_dense (R, 0, cm) ; /* max abs. entry */
xnorm = cholmod_norm_dense (X, 0, cm) ; /* max abs. entry */
axbnorm = (anorm * xnorm + bnorm + ((n == 0) ? 1 : 0)) ;
resid = rnorm / axbnorm ;
/* ---------------------------------------------------------------------- */
/* iterative refinement (real symmetric case only) */
/* ---------------------------------------------------------------------- */
resid2 = -1 ;
if (A->stype != 0 && A->xtype == CHOLMOD_REAL)
{
cholmod_dense *R2 ;
/* R2 = A\(B-A*X) */
R2 = cholmod_solve (CHOLMOD_A, L, R, cm) ;
/* compute X = X + A\(B-A*X) */
Xx = X->x ;
Rx = R2->x ;
for (i = 0 ; i < n ; i++)
{
Xx [i] = Xx [i] + Rx [i] ;
}
cholmod_free_dense (&R2, cm) ;
cholmod_free_dense (&R, cm) ;
/* compute the new residual, R = B-A*X */
R = cholmod_copy_dense (B, cm) ;
cholmod_sdmult (A, 0, minusone, one, X, R, cm) ;
rnorm2 = cholmod_norm_dense (R, 0, cm) ;
resid2 = rnorm2 / axbnorm ;
}
cholmod_free_dense (&R, cm) ;
/* ---------------------------------------------------------------------- */
/* print results */
/* ---------------------------------------------------------------------- */
cholmod_print_factor (L, "L", cm) ;
/* determine the # of integers's and reals's in L. See cholmod_free */
if (L->is_super)
{
s = L->nsuper + 1 ;
xsize = L->xsize ;
ss = L->ssize ;
isize =
n /* L->Perm */
+ n /* L->ColCount, nz in each column of 'pure' L */
+ s /* L->pi, column pointers for L->s */
+ s /* L->px, column pointers for L->x */
+ s /* L->super, starting column index of each supernode */
+ ss ; /* L->s, the pattern of the supernodes */
}
else
{
/* this space can increase if you change parameters to their non-
* default values (cm->final_pack, for example). */
lnz = L->nzmax ;
xsize = lnz ;
isize =
n /* L->Perm */
+ n /* L->ColCount, nz in each column of 'pure' L */
+ n+1 /* L->p, column pointers */
+ lnz /* L->i, integer row indices */
+ n /* L->nz, nz in each column of L */
+ n+2 /* L->next, link list */
+ n+2 ; /* L->prev, link list */
}
anz = cm->anz ;
for (i = 0 ; i < CHOLMOD_MAXMETHODS ; i++)
{
fl = cm->method [i].fl ;
xlnz = cm->method [i].lnz ;
cm->method [i].fl = -1 ;
cm->method [i].lnz = -1 ;
ordering = cm->method [i].ordering ;
if (fl >= 0)
{
printf ("Ordering: ") ;
if (ordering == CHOLMOD_POSTORDERED) printf ("postordered ") ;
if (ordering == CHOLMOD_NATURAL) printf ("natural ") ;
if (ordering == CHOLMOD_GIVEN) printf ("user ") ;
if (ordering == CHOLMOD_AMD) printf ("AMD ") ;
if (ordering == CHOLMOD_METIS) printf ("METIS ") ;
if (ordering == CHOLMOD_NESDIS) printf ("NESDIS ") ;
if (xlnz > 0)
{
printf ("fl/lnz %10.1f", fl / xlnz) ;
}
if (anz > 0)
{
printf (" lnz/anz %10.1f", xlnz / anz) ;
}
printf ("\n") ;
}
}
printf ("ints in L: %d, doubles in L: %d\n", isize, xsize) ;
printf ("factor flops %g nnz(L) %15.0f (w/no amalgamation)\n",
cm->fl, cm->lnz) ;
if (A->stype == 0)
{
printf ("nnz(A): %15.0f\n", cm->anz) ;
}
else
{
printf ("nnz(A*A'): %15.0f\n", cm->anz) ;
}
if (cm->lnz > 0)
{
printf ("flops / nnz(L): %8.1f\n", cm->fl / cm->lnz) ;
}
if (anz > 0)
{
printf ("nnz(L) / nnz(A): %8.1f\n", cm->lnz / cm->anz) ;
}
printf ("analyze cputime: %12.4f\n", ta) ;
printf ("factor cputime: %12.4f mflop: %8.1f\n", tf,
(tf == 0) ? 0 : (1e-6*cm->fl / tf)) ;
printf ("solve cputime: %12.4f mflop: %8.1f\n", ts,
(ts == 0) ? 0 : (1e-6*4*cm->lnz / ts)) ;
printf ("overall cputime: %12.4f mflop: %8.1f\n",
tot, (tot == 0) ? 0 : (1e-6 * (cm->fl + 4 * cm->lnz) / tot)) ;
printf ("peak memory usage: %12.0f (MB)\n",
(double) (cm->memory_usage) / 1048576.) ;
printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))\n", resid) ;
if (resid2 >= 0)
{
printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))"
" after iterative refinement\n", resid2) ;
}
printf ("rcond %8.1e\n\n", cholmod_rcond (L, cm)) ;
cholmod_free_factor (&L, cm) ;
cholmod_free_dense (&X, cm) ;
/* ---------------------------------------------------------------------- */
/* free matrices and finish CHOLMOD */
/* ---------------------------------------------------------------------- */
cholmod_free_sparse (&A, cm) ;
cholmod_free_dense (&B, cm) ;
cholmod_finish (cm) ;
return (0) ;
}
int main (int argc, char **argv)
{
double resid [4], t, ta, tf, ts [3], tot, bnorm, xnorm, anorm, rnorm, fl,
anz, axbnorm, rnorm2, resid2, rcond ;
FILE *f ;
cholmod_sparse *A ;
cholmod_dense *X = NULL, *B, *W, *R ;
double one [2], zero [2], minusone [2], beta [2], xlnz ;
cholmod_common Common, *cm ;
cholmod_factor *L ;
double *Bx, *Rx, *Xx ;
int i, n, isize, xsize, ordering, xtype, s, ss, lnz ;
int trial, method, L_is_super ;
int ver [3] ;
ts[0] = 0.;
ts[1] = 0.;
ts[2] = 0.;
/* ---------------------------------------------------------------------- */
/* get the file containing the input matrix */
/* ---------------------------------------------------------------------- */
ff = NULL ;
if (argc > 1)
{
if ((f = fopen (argv [1], "r")) == NULL)
{
my_handler (CHOLMOD_INVALID, __FILE__, __LINE__,
"unable to open file") ;
}
ff = f ;
}
else
{
f = stdin ;
}
/* ---------------------------------------------------------------------- */
/* start CHOLMOD and set parameters */
/* ---------------------------------------------------------------------- */
cm = &Common ;
cholmod_start (cm) ;
CHOLMOD_FUNCTION_DEFAULTS (cm) ; /* just for testing (not required) */
/* use default parameter settings, except for the error handler. This
* demo program terminates if an error occurs (out of memory, not positive
* definite, ...). It makes the demo program simpler (no need to check
* CHOLMOD error conditions). This non-default parameter setting has no
* effect on performance. */
cm->error_handler = my_handler ;
/* Note that CHOLMOD will do a supernodal LL' or a simplicial LDL' by
* default, automatically selecting the latter if flop/nnz(L) < 40. */
/* ---------------------------------------------------------------------- */
/* create basic scalars */
/* ---------------------------------------------------------------------- */
zero [0] = 0 ;
zero [1] = 0 ;
one [0] = 1 ;
one [1] = 0 ;
minusone [0] = -1 ;
minusone [1] = 0 ;
beta [0] = 1e-6 ;
beta [1] = 0 ;
/* ---------------------------------------------------------------------- */
/* read in a matrix */
/* ---------------------------------------------------------------------- */
printf ("\n---------------------------------- cholmod_demo:\n") ;
cholmod_version (ver) ;
printf ("cholmod version %d.%d.%d\n", ver [0], ver [1], ver [2]) ;
SuiteSparse_version (ver) ;
printf ("SuiteSparse version %d.%d.%d\n", ver [0], ver [1], ver [2]) ;
A = cholmod_read_sparse (f, cm) ;
if (ff != NULL)
{
fclose (ff) ;
ff = NULL ;
}
anorm = cholmod_norm_sparse (A, 0, cm) ;
xtype = A->xtype ;
printf ("norm (A,inf) = %g\n", anorm) ;
printf ("norm (A,1) = %g\n", cholmod_norm_sparse (A, 1, cm)) ;
cholmod_print_sparse (A, "A", cm) ;
if (A->nrow > A->ncol)
{
/* Transpose A so that A'A+beta*I will be factorized instead */
cholmod_sparse *C = cholmod_transpose (A, 2, cm) ;
cholmod_free_sparse (&A, cm) ;
A = C ;
printf ("transposing input matrix\n") ;
}
/* ---------------------------------------------------------------------- */
/* create an arbitrary right-hand-side */
/* ---------------------------------------------------------------------- */
n = A->nrow ;
B = cholmod_zeros (n, 1, xtype, cm) ;
Bx = B->x ;
#if GHS
{
/* b = A*ones(n,1), used by Gould, Hu, and Scott in their experiments */
cholmod_dense *X0 ;
X0 = cholmod_ones (A->ncol, 1, xtype, cm) ;
cholmod_sdmult (A, 0, one, zero, X0, B, cm) ;
cholmod_free_dense (&X0, cm) ;
}
#else
if (xtype == CHOLMOD_REAL)
{
/* real case */
for (i = 0 ; i < n ; i++)
{
double x = n ;
Bx [i] = 1 + i / x ;
}
}
else
{
/* complex case */
for (i = 0 ; i < n ; i++)
{
double x = n ;
Bx [2*i ] = 1 + i / x ; /* real part of B(i) */
Bx [2*i+1] = (x/2 - i) / (3*x) ; /* imag part of B(i) */
}
}
#endif
cholmod_print_dense (B, "B", cm) ;
bnorm = cholmod_norm_dense (B, 0, cm) ; /* max norm */
printf ("bnorm %g\n", bnorm) ;
/* ---------------------------------------------------------------------- */
/* analyze and factorize */
/* ---------------------------------------------------------------------- */
t = CPUTIME ;
L = cholmod_analyze (A, cm) ;
ta = CPUTIME - t ;
ta = MAX (ta, 0) ;
printf ("Analyze: flop %g lnz %g\n", cm->fl, cm->lnz) ;
if (A->stype == 0)
{
printf ("Factorizing A*A'+beta*I\n") ;
t = CPUTIME ;
cholmod_factorize_p (A, beta, NULL, 0, L, cm) ;
tf = CPUTIME - t ;
tf = MAX (tf, 0) ;
}
else
{
printf ("Factorizing A\n") ;
t = CPUTIME ;
cholmod_factorize (A, L, cm) ;
tf = CPUTIME - t ;
tf = MAX (tf, 0) ;
}
cholmod_print_factor (L, "L", cm) ;
/* determine the # of integers's and reals's in L. See cholmod_free */
if (L->is_super)
{
s = L->nsuper + 1 ;
xsize = L->xsize ;
ss = L->ssize ;
isize =
n /* L->Perm */
+ n /* L->ColCount, nz in each column of 'pure' L */
+ s /* L->pi, column pointers for L->s */
+ s /* L->px, column pointers for L->x */
+ s /* L->super, starting column index of each supernode */
+ ss ; /* L->s, the pattern of the supernodes */
}
else
{
/* this space can increase if you change parameters to their non-
* default values (cm->final_pack, for example). */
lnz = L->nzmax ;
xsize = lnz ;
isize =
n /* L->Perm */
+ n /* L->ColCount, nz in each column of 'pure' L */
+ n+1 /* L->p, column pointers */
+ lnz /* L->i, integer row indices */
+ n /* L->nz, nz in each column of L */
+ n+2 /* L->next, link list */
+ n+2 ; /* L->prev, link list */
}
/* solve with Bset will change L from simplicial to supernodal */
rcond = cholmod_rcond (L, cm) ;
L_is_super = L->is_super ;
/* ---------------------------------------------------------------------- */
/* solve */
/* ---------------------------------------------------------------------- */
for (method = 0 ; method <= 3 ; method++)
{
double x = n ;
if (method == 0)
{
/* basic solve, just once */
t = CPUTIME ;
X = cholmod_solve (CHOLMOD_A, L, B, cm) ;
ts [0] = CPUTIME - t ;
ts [0] = MAX (ts [0], 0) ;
}
else if (method == 1)
{
/* basic solve, many times, but keep the last one */
t = CPUTIME ;
for (trial = 0 ; trial < NTRIALS ; trial++)
{
cholmod_free_dense (&X, cm) ;
Bx [0] = 1 + trial / x ; /* tweak B each iteration */
X = cholmod_solve (CHOLMOD_A, L, B, cm) ;
}
ts [1] = CPUTIME - t ;
ts [1] = MAX (ts [1], 0) / NTRIALS ;
}
else if (method == 2)
{
/* solve with reused workspace */
cholmod_dense *Ywork = NULL, *Ework = NULL ;
cholmod_free_dense (&X, cm) ;
t = CPUTIME ;
for (trial = 0 ; trial < NTRIALS ; trial++)
{
Bx [0] = 1 + trial / x ; /* tweak B each iteration */
cholmod_solve2 (CHOLMOD_A, L, B, NULL, &X, NULL,
&Ywork, &Ework, cm) ;
}
cholmod_free_dense (&Ywork, cm) ;
cholmod_free_dense (&Ework, cm) ;
ts [2] = CPUTIME - t ;
ts [2] = MAX (ts [2], 0) / NTRIALS ;
}
else
{
/* solve with reused workspace and sparse Bset */
cholmod_dense *Ywork = NULL, *Ework = NULL ;
cholmod_dense *X2 = NULL, *B2 = NULL ;
cholmod_sparse *Bset, *Xset = NULL ;
int *Bsetp, *Bseti, *Xsetp, *Xseti, xlen, j, k, *Lnz ;
double *X1x, *X2x, *B2x, err ;
FILE *timelog = fopen ("timelog.m", "w") ;
if (timelog) fprintf (timelog, "results = [\n") ;
B2 = cholmod_zeros (n, 1, xtype, cm) ;
B2x = B2->x ;
Bset = cholmod_allocate_sparse (n, 1, 1, FALSE, TRUE, 0,
CHOLMOD_PATTERN, cm) ;
Bsetp = Bset->p ;
Bseti = Bset->i ;
Bsetp [0] = 0 ; /* nnz(B) is 1 (it can be anything) */
Bsetp [1] = 1 ;
resid [3] = 0 ;
for (i = 0 ; i < MIN (100,n) ; i++)
{
/* B (i) is nonzero, all other entries are ignored
(implied to be zero) */
Bseti [0] = i ;
if (xtype == CHOLMOD_REAL)
{
B2x [i] = 3.1 * i + 0.9 ;
}
else
{
B2x [2*i ] = i + 0.042 ;
B2x [2*i+1] = i - 92.7 ;
}
/* first get the entire solution, to compare against */
cholmod_solve2 (CHOLMOD_A, L, B2, NULL, &X, NULL,
&Ywork, &Ework, cm) ;
/* now get the sparse solutions; this will change L from
supernodal to simplicial */
if (i == 0)
{
/* first solve can be slower because it has to allocate
space for X2, Xset, etc, and change L.
So don't time it */
cholmod_solve2 (CHOLMOD_A, L, B2, Bset, &X2, &Xset,
&Ywork, &Ework, cm) ;
}
t = CPUTIME ;
for (trial = 0 ; trial < NTRIALS ; trial++)
{
/* solve Ax=b but only to get x(i).
b is all zero except for b(i).
This takes O(xlen) time */
cholmod_solve2 (CHOLMOD_A, L, B2, Bset, &X2, &Xset,
&Ywork, &Ework, cm) ;
}
t = CPUTIME - t ;
t = MAX (t, 0) / NTRIALS ;
/* check the solution and log the time */
Xsetp = Xset->p ;
Xseti = Xset->i ;
xlen = Xsetp [1] ;
X1x = X->x ;
X2x = X2->x ;
Lnz = L->nz ;
/*
printf ("\ni %d xlen %d (%p %p)\n", i, xlen, X1x, X2x) ;
*/
if (xtype == CHOLMOD_REAL)
{
fl = 2 * xlen ;
for (k = 0 ; k < xlen ; k++)
{
j = Xseti [k] ;
fl += 4 * Lnz [j] ;
err = X1x [j] - X2x [j] ;
err = ABS (err) ;
resid [3] = MAX (resid [3], err) ;
}
}
else
{
fl = 16 * xlen ;
for (k = 0 ; k < xlen ; k++)
{
j = Xseti [k] ;
fl += 16 * Lnz [j] ;
err = X1x [2*j ] - X2x [2*j ] ;
err = ABS (err) ;
resid [3] = MAX (resid [3], err) ;
err = X1x [2*j+1] - X2x [2*j+1] ;
err = ABS (err) ;
resid [3] = MAX (resid [3], err) ;
}
}
if (timelog) fprintf (timelog, "%g %g %g %g\n",
(double) i, (double) xlen, fl, t);
/* clear B for the next test */
if (xtype == CHOLMOD_REAL)
{
B2x [i] = 0 ;
}
else
{
B2x [2*i ] = 0 ;
B2x [2*i+1] = 0 ;
}
}
if (timelog)
{
fprintf (timelog, "] ; resid = %g ;\n", resid [3]) ;
fprintf (timelog, "lnz = %g ;\n", cm->lnz) ;
fprintf (timelog, "t = %g ; %% dense solve time\n", ts [2]) ;
fclose (timelog) ;
}
resid [3] = resid [3] / cholmod_norm_dense (X, 1, cm) ;
cholmod_free_dense (&Ywork, cm) ;
cholmod_free_dense (&Ework, cm) ;
cholmod_free_dense (&X2, cm) ;
cholmod_free_dense (&B2, cm) ;
cholmod_free_sparse (&Xset, cm) ;
cholmod_free_sparse (&Bset, cm) ;
}
/* ------------------------------------------------------------------ */
/* compute the residual */
/* ------------------------------------------------------------------ */
if (method < 3)
{
if (A->stype == 0)
{
/* (AA'+beta*I)x=b is the linear system that was solved */
/* W = A'*X */
W = cholmod_allocate_dense (A->ncol, 1, A->ncol, xtype, cm) ;
cholmod_sdmult (A, 2, one, zero, X, W, cm) ;
/* R = B - beta*X */
R = cholmod_zeros (n, 1, xtype, cm) ;
Rx = R->x ;
Xx = X->x ;
if (xtype == CHOLMOD_REAL)
{
for (i = 0 ; i < n ; i++)
{
Rx [i] = Bx [i] - beta [0] * Xx [i] ;
}
}
else
{
/* complex case */
for (i = 0 ; i < n ; i++)
{
Rx [2*i ] = Bx [2*i ] - beta [0] * Xx [2*i ] ;
Rx [2*i+1] = Bx [2*i+1] - beta [0] * Xx [2*i+1] ;
}
}
/* R = A*W - R */
cholmod_sdmult (A, 0, one, minusone, W, R, cm) ;
cholmod_free_dense (&W, cm) ;
}
else
{
/* Ax=b was factorized and solved, R = B-A*X */
R = cholmod_copy_dense (B, cm) ;
cholmod_sdmult (A, 0, minusone, one, X, R, cm) ;
}
rnorm = cholmod_norm_dense (R, 0, cm) ; /* max abs. entry */
xnorm = cholmod_norm_dense (X, 0, cm) ; /* max abs. entry */
axbnorm = (anorm * xnorm + bnorm + ((n == 0) ? 1 : 0)) ;
resid [method] = rnorm / axbnorm ;
}
}
tot = ta + tf + ts [0] ;
/* ---------------------------------------------------------------------- */
/* iterative refinement (real symmetric case only) */
/* ---------------------------------------------------------------------- */
resid2 = -1 ;
if (A->stype != 0 && A->xtype == CHOLMOD_REAL)
{
cholmod_dense *R2 ;
/* R2 = A\(B-A*X) */
R2 = cholmod_solve (CHOLMOD_A, L, R, cm) ;
/* compute X = X + A\(B-A*X) */
Xx = X->x ;
Rx = R2->x ;
for (i = 0 ; i < n ; i++)
{
Xx [i] = Xx [i] + Rx [i] ;
}
cholmod_free_dense (&R2, cm) ;
cholmod_free_dense (&R, cm) ;
/* compute the new residual, R = B-A*X */
R = cholmod_copy_dense (B, cm) ;
cholmod_sdmult (A, 0, minusone, one, X, R, cm) ;
rnorm2 = cholmod_norm_dense (R, 0, cm) ;
resid2 = rnorm2 / axbnorm ;
}
cholmod_free_dense (&R, cm) ;
/* ---------------------------------------------------------------------- */
/* print results */
/* ---------------------------------------------------------------------- */
anz = cm->anz ;
for (i = 0 ; i < CHOLMOD_MAXMETHODS ; i++)
{
fl = cm->method [i].fl ;
xlnz = cm->method [i].lnz ;
cm->method [i].fl = -1 ;
cm->method [i].lnz = -1 ;
ordering = cm->method [i].ordering ;
if (fl >= 0)
{
printf ("Ordering: ") ;
if (ordering == CHOLMOD_POSTORDERED) printf ("postordered ") ;
if (ordering == CHOLMOD_NATURAL) printf ("natural ") ;
if (ordering == CHOLMOD_GIVEN) printf ("user ") ;
if (ordering == CHOLMOD_AMD) printf ("AMD ") ;
if (ordering == CHOLMOD_METIS) printf ("METIS ") ;
if (ordering == CHOLMOD_NESDIS) printf ("NESDIS ") ;
if (xlnz > 0)
{
printf ("fl/lnz %10.1f", fl / xlnz) ;
}
if (anz > 0)
{
printf (" lnz/anz %10.1f", xlnz / anz) ;
}
printf ("\n") ;
}
}
printf ("ints in L: %15.0f, doubles in L: %15.0f\n",
(double) isize, (double) xsize) ;
printf ("factor flops %g nnz(L) %15.0f (w/no amalgamation)\n",
cm->fl, cm->lnz) ;
if (A->stype == 0)
{
printf ("nnz(A): %15.0f\n", cm->anz) ;
}
else
{
printf ("nnz(A*A'): %15.0f\n", cm->anz) ;
}
if (cm->lnz > 0)
{
printf ("flops / nnz(L): %8.1f\n", cm->fl / cm->lnz) ;
}
if (anz > 0)
{
printf ("nnz(L) / nnz(A): %8.1f\n", cm->lnz / cm->anz) ;
}
printf ("analyze cputime: %12.4f\n", ta) ;
printf ("factor cputime: %12.4f mflop: %8.1f\n", tf,
(tf == 0) ? 0 : (1e-6*cm->fl / tf)) ;
printf ("solve cputime: %12.4f mflop: %8.1f\n", ts [0],
(ts [0] == 0) ? 0 : (1e-6*4*cm->lnz / ts [0])) ;
printf ("overall cputime: %12.4f mflop: %8.1f\n",
tot, (tot == 0) ? 0 : (1e-6 * (cm->fl + 4 * cm->lnz) / tot)) ;
printf ("solve cputime: %12.4f mflop: %8.1f (%d trials)\n", ts [1],
(ts [1] == 0) ? 0 : (1e-6*4*cm->lnz / ts [1]), NTRIALS) ;
printf ("solve2 cputime: %12.4f mflop: %8.1f (%d trials)\n", ts [2],
(ts [2] == 0) ? 0 : (1e-6*4*cm->lnz / ts [2]), NTRIALS) ;
printf ("peak memory usage: %12.0f (MB)\n",
(double) (cm->memory_usage) / 1048576.) ;
printf ("residual (|Ax-b|/(|A||x|+|b|)): ") ;
for (method = 0 ; method <= 3 ; method++)
{
printf ("%8.2e ", resid [method]) ;
}
printf ("\n") ;
if (resid2 >= 0)
{
printf ("residual %8.1e (|Ax-b|/(|A||x|+|b|))"
" after iterative refinement\n", resid2) ;
}
printf ("rcond %8.1e\n\n", rcond) ;
if (L_is_super)
{
cholmod_gpu_stats (cm) ;
}
cholmod_free_factor (&L, cm) ;
cholmod_free_dense (&X, cm) ;
/* ---------------------------------------------------------------------- */
/* free matrices and finish CHOLMOD */
/* ---------------------------------------------------------------------- */
cholmod_free_sparse (&A, cm) ;
cholmod_free_dense (&B, cm) ;
cholmod_finish (cm) ;
return (0) ;
}
