int main (void)
{
KLU_common Common ;
cholmod_sparse *A, *A2 ;
cholmod_dense *X, *B ;
cholmod_common ch ;
Int *Ap, *Ai, *Puser, *Quser, *Gunk ;
double *Ax, *Bx, *Xx, *A2x ;
double one [2], zero [2], xsave, maxerr ;
Int n, i, j, nz, save, isreal, k, nan ;
KLU_symbolic *Symbolic, *Symbolic2 ;
KLU_numeric *Numeric ;
one [0] = 1 ;
one [1] = 0 ;
zero [0] = 0 ;
zero [1] = 0 ;
printf ("klu test: -------------------------------------------------\n") ;
OK (klu_defaults (&Common)) ;
CHOLMOD_start (&ch) ;
ch.print = 0 ;
normal_memory_handler (&Common) ;
/* ---------------------------------------------------------------------- */
/* read in a sparse matrix from stdin */
/* ---------------------------------------------------------------------- */
A = CHOLMOD_read_sparse (stdin, &ch) ;
if (A->nrow != A->ncol || A->stype != 0)
{
fprintf (stderr, "error: only square unsymmetric matrices handled\n") ;
CHOLMOD_free_sparse (&A, &ch) ;
return (0) ;
}
if (!(A->xtype == CHOLMOD_REAL || A->xtype == CHOLMOD_COMPLEX))
{
fprintf (stderr, "error: only real or complex matrices hanlded\n") ;
CHOLMOD_free_sparse (&A, &ch) ;
return (0) ;
}
n = A->nrow ;
Ap = A->p ;
Ai = A->i ;
Ax = A->x ;
nz = Ap [n] ;
isreal = (A->xtype == CHOLMOD_REAL) ;
/* ---------------------------------------------------------------------- */
/* construct random permutations */
/* ---------------------------------------------------------------------- */
Puser = randperm (n, n) ;
Quser = randperm (n, n) ;
/* ---------------------------------------------------------------------- */
/* select known solution to Ax=b */
/* ---------------------------------------------------------------------- */
X = CHOLMOD_allocate_dense (n, NRHS, n, A->xtype, &ch) ;
Xx = X->x ;
for (j = 0 ; j < NRHS ; j++)
{
for (i = 0 ; i < n ; i++)
{
if (isreal)
{
Xx [i] = 1 + ((double) i) / ((double) n) + j * 100;
}
else
{
Xx [2*i ] = 1 + ((double) i) / ((double) n) + j * 100 ;
Xx [2*i+1] = - ((double) i+1) / ((double) n + j) ;
if (j == NRHS-1)
{
Xx [2*i+1] = 0 ; /* zero imaginary part */
}
else if (j == NRHS-2)
{
Xx [2*i] = 0 ; /* zero real part */
}
}
}
Xx += isreal ? n : 2*n ;
}
/* B = A*X */
B = CHOLMOD_allocate_dense (n, NRHS, n, A->xtype, &ch) ;
CHOLMOD_sdmult (A, 0, one, zero, X, B, &ch) ;
Bx = B->x ;
/* ---------------------------------------------------------------------- */
/* test KLU */
/* ---------------------------------------------------------------------- */
test_memory_handler (&Common) ;
maxerr = do_solves (A, B, X, Puser, Quser, &Common, &ch, &nan) ;
/* ---------------------------------------------------------------------- */
/* basic error checking */
/* ---------------------------------------------------------------------- */
FAIL (klu_defaults (NULL)) ;
FAIL (klu_extract (NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
NULL, NULL, NULL, NULL, NULL, NULL, NULL)) ;
FAIL (klu_extract (NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
NULL, NULL, NULL, NULL, NULL, NULL, &Common)) ;
FAIL (klu_z_extract (NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL)) ;
FAIL (klu_z_extract (NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, &Common)) ;
FAIL (klu_analyze (0, NULL, NULL, NULL)) ;
FAIL (klu_analyze (0, NULL, NULL, &Common)) ;
FAIL (klu_analyze_given (0, NULL, NULL, NULL, NULL, NULL)) ;
FAIL (klu_analyze_given (0, NULL, NULL, NULL, NULL, &Common)) ;
FAIL (klu_cholmod (0, NULL, NULL, NULL, NULL)) ;
FAIL (klu_factor (NULL, NULL, NULL, NULL, NULL)) ;
FAIL (klu_factor (NULL, NULL, NULL, NULL, &Common)) ;
FAIL (klu_z_factor (NULL, NULL, NULL, NULL, NULL)) ;
FAIL (klu_z_factor (NULL, NULL, NULL, NULL, &Common)) ;
FAIL (klu_refactor (NULL, NULL, NULL, NULL, NULL, NULL)) ;
FAIL (klu_refactor (NULL, NULL, NULL, NULL, NULL, &Common)) ;
FAIL (klu_z_refactor (NULL, NULL, NULL, NULL, NULL, NULL)) ;
FAIL (klu_z_refactor (NULL, NULL, NULL, NULL, NULL, &Common)) ;
FAIL (klu_rgrowth (NULL, NULL, NULL, NULL, NULL, NULL)) ;
FAIL (klu_rgrowth (NULL, NULL, NULL, NULL, NULL, &Common)) ;
FAIL (klu_z_rgrowth (NULL, NULL, NULL, NULL, NULL, NULL)) ;
FAIL (klu_z_rgrowth (NULL, NULL, NULL, NULL, NULL, &Common)) ;
FAIL (klu_condest (NULL, NULL, NULL, NULL, NULL)) ;
FAIL (klu_condest (NULL, NULL, NULL, NULL, &Common)) ;
FAIL (klu_z_condest (NULL, NULL, NULL, NULL, NULL)) ;
FAIL (klu_z_condest (NULL, NULL, NULL, NULL, &Common)) ;
FAIL (klu_flops (NULL, NULL, NULL)) ;
FAIL (klu_flops (NULL, NULL, &Common)) ;
FAIL (klu_z_flops (NULL, NULL, NULL)) ;
FAIL (klu_z_flops (NULL, NULL, &Common)) ;
FAIL (klu_rcond (NULL, NULL, NULL)) ;
FAIL (klu_rcond (NULL, NULL, &Common)) ;
FAIL (klu_z_rcond (NULL, NULL, NULL)) ;
FAIL (klu_z_rcond (NULL, NULL, &Common)) ;
FAIL (klu_free_symbolic (NULL, NULL)) ;
OK (klu_free_symbolic (NULL, &Common)) ;
FAIL (klu_free_numeric (NULL, NULL)) ;
OK (klu_free_numeric (NULL, &Common)) ;
FAIL (klu_z_free_numeric (NULL, NULL)) ;
OK (klu_z_free_numeric (NULL, &Common)) ;
FAIL (klu_scale (0, 0, NULL, NULL, NULL, NULL, NULL, NULL)) ;
FAIL (klu_scale (0, 0, NULL, NULL, NULL, NULL, NULL, &Common)) ;
OK (klu_scale (-1, 0, NULL, NULL, NULL, NULL, NULL, &Common)) ;
FAIL (klu_z_scale (0, 0, NULL, NULL, NULL, NULL, NULL, NULL)) ;
FAIL (klu_z_scale (0, 0, NULL, NULL, NULL, NULL, NULL, &Common)) ;
OK (klu_z_scale (-1, 0, NULL, NULL, NULL, NULL, NULL, &Common)) ;
FAIL (klu_solve (NULL, NULL, 0, 0, NULL, NULL)) ;
FAIL (klu_solve (NULL, NULL, 0, 0, NULL, &Common)) ;
FAIL (klu_z_solve (NULL, NULL, 0, 0, NULL, NULL)) ;
FAIL (klu_z_solve (NULL, NULL, 0, 0, NULL, &Common)) ;
FAIL (klu_tsolve (NULL, NULL, 0, 0, NULL, NULL)) ;
FAIL (klu_tsolve (NULL, NULL, 0, 0, NULL, &Common)) ;
FAIL (klu_z_tsolve (NULL, NULL, 0, 0, NULL, 0, NULL)) ;
FAIL (klu_z_tsolve (NULL, NULL, 0, 0, NULL, 0, &Common)) ;
FAIL (klu_malloc (0, 0, NULL)) ;
FAIL (klu_malloc (0, 0, &Common)) ;
FAIL (klu_malloc (Int_MAX, 1, &Common)) ;
FAIL (klu_realloc (0, 0, 0, NULL, NULL)) ;
FAIL (klu_realloc (0, 0, 0, NULL, &Common)) ;
FAIL (klu_realloc (Int_MAX, 1, 0, NULL, &Common)) ;
Gunk = (Int *) klu_realloc (1, 0, sizeof (Int), NULL, &Common) ;
OK (Gunk) ;
OK (klu_realloc (Int_MAX, 1, sizeof (Int), Gunk, &Common)) ;
OK (Common.status == KLU_TOO_LARGE) ;
klu_free (Gunk, 1, sizeof (Int), &Common) ;
/* ---------------------------------------------------------------------- */
/* mangle the matrix, and other error checking */
/* ---------------------------------------------------------------------- */
printf ("\nerror handling:\n") ;
Symbolic = klu_analyze (n, Ap, Ai, &Common) ;
OK (Symbolic) ;
Xx = X->x ;
if (nz > 0)
{
/* ------------------------------------------------------------------ */
/* row index out of bounds */
/* ------------------------------------------------------------------ */
save = Ai [0] ;
Ai [0] = -1 ;
FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
if (isreal)
{
FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
}
else
{
FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
}
Ai [0] = save ;
/* ------------------------------------------------------------------ */
/* row index out of bounds */
/* ------------------------------------------------------------------ */
save = Ai [0] ;
Ai [0] = Int_MAX ;
FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
if (isreal)
{
FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
}
else
{
FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
}
Ai [0] = save ;
/* ------------------------------------------------------------------ */
/* column pointers mangled */
/* ------------------------------------------------------------------ */
save = Ap [n] ;
Ap [n] = -1 ;
FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
if (isreal)
{
FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
}
else
{
FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
}
Ap [n] = save ;
/* ------------------------------------------------------------------ */
/* column pointers mangled */
/* ------------------------------------------------------------------ */
save = Ap [n] ;
Ap [n] = Ap [n-1] - 1 ;
FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
if (isreal)
{
FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
}
else
{
FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
}
Ap [n] = save ;
/* ------------------------------------------------------------------ */
/* duplicates */
/* ------------------------------------------------------------------ */
if (n > 1 && Ap [1] - Ap [0] > 1)
{
save = Ai [1] ;
Ai [1] = Ai [0] ;
FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
if (isreal)
{
FAIL (klu_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
}
else
{
FAIL (klu_z_scale (1, n, Ap, Ai, Ax, Xx, Puser, &Common)) ;
}
Ai [1] = save ;
}
/* ------------------------------------------------------------------ */
/* invalid ordering */
/* ------------------------------------------------------------------ */
save = Common.ordering ;
Common.ordering = 42 ;
FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
Common.ordering = save ;
/* ------------------------------------------------------------------ */
/* invalid ordering (klu_cholmod, with NULL user_ordering) */
/* ------------------------------------------------------------------ */
save = Common.ordering ;
Common.user_order = NULL ;
Common.ordering = 3 ;
FAIL (klu_analyze (n, Ap, Ai, &Common)) ;
Common.ordering = save ;
}
/* ---------------------------------------------------------------------- */
/* tests with valid symbolic factorization */
/* ---------------------------------------------------------------------- */
Common.halt_if_singular = FALSE ;
Common.scale = 0 ;
Numeric = NULL ;
if (nz > 0)
{
/* ------------------------------------------------------------------ */
/* Int overflow */
/* ------------------------------------------------------------------ */
if (n == 100)
{
Common.ordering = 2 ;
Symbolic2 = klu_analyze (n, Ap, Ai, &Common) ;
OK (Symbolic2) ;
Common.memgrow = Int_MAX ;
if (isreal)
{
Numeric = klu_factor (Ap, Ai, Ax, Symbolic2, &Common) ;
}
else
{
Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic2, &Common) ;
}
Common.memgrow = 1.2 ;
Common.ordering = 0 ;
klu_free_symbolic (&Symbolic2, &Common) ;
klu_free_numeric (&Numeric, &Common) ;
}
/* ------------------------------------------------------------------ */
/* Int overflow again */
/* ------------------------------------------------------------------ */
Common.initmem = Int_MAX ;
Common.initmem_amd = Int_MAX ;
if (isreal)
{
Numeric = klu_factor (Ap, Ai, Ax, Symbolic, &Common) ;
}
else
{
Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, &Common) ;
}
Common.initmem = 10 ;
Common.initmem_amd = 1.2 ;
klu_free_numeric (&Numeric, &Common) ;
/* ------------------------------------------------------------------ */
/* mangle the matrix */
/* ------------------------------------------------------------------ */
save = Ai [0] ;
Ai [0] = -1 ;
if (isreal)
{
Numeric = klu_factor (Ap, Ai, Ax, Symbolic, &Common) ;
}
else
{
Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, &Common) ;
}
FAIL (Numeric) ;
Ai [0] = save ;
/* ------------------------------------------------------------------ */
/* nan and inf handling */
/* ------------------------------------------------------------------ */
xsave = Ax [0] ;
Ax [0] = one [0] / zero [0] ;
if (isreal)
{
Numeric = klu_factor (Ap, Ai, Ax, Symbolic, &Common) ;
klu_rcond (Symbolic, Numeric, &Common) ;
klu_condest (Ap, Ax, Symbolic, Numeric, &Common) ;
}
else
{
Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, &Common) ;
klu_z_rcond (Symbolic, Numeric, &Common) ;
klu_z_condest (Ap, Ax, Symbolic, Numeric, &Common) ;
}
printf ("Nan case: rcond %g condest %g\n",
Common.rcond, Common.condest) ;
OK (Numeric) ;
Ax [0] = xsave ;
/* ------------------------------------------------------------------ */
/* mangle the matrix again */
/* ------------------------------------------------------------------ */
save = Ai [0] ;
Ai [0] = -1 ;
if (isreal)
{
FAIL (klu_refactor (Ap, Ai, Ax, Symbolic, Numeric, &Common)) ;
}
else
{
FAIL (klu_z_refactor (Ap, Ai, Ax, Symbolic, Numeric, &Common)) ;
}
Ai [0] = save ;
/* ------------------------------------------------------------------ */
/* all zero */
/* ------------------------------------------------------------------ */
A2 = CHOLMOD_copy_sparse (A, &ch) ;
A2x = A2->x ;
for (k = 0 ; k < nz * (isreal ? 1:2) ; k++)
{
A2x [k] = 0 ;
}
for (Common.halt_if_singular = 0 ; Common.halt_if_singular <= 1 ;
Common.halt_if_singular++)
{
for (Common.scale = -1 ; Common.scale <= 2 ; Common.scale++)
{
if (isreal)
{
klu_refactor (Ap, Ai, A2x, Symbolic, Numeric, &Common) ;
klu_condest (Ap, A2x, Symbolic, Numeric, &Common) ;
}
else
{
klu_z_refactor (Ap, Ai, A2x, Symbolic, Numeric, &Common) ;
klu_z_condest (Ap, A2x, Symbolic, Numeric, &Common) ;
}
OK (Common.status = KLU_SINGULAR) ;
}
}
CHOLMOD_free_sparse (&A2, &ch) ;
/* ------------------------------------------------------------------ */
/* all one, or all 1i for complex case */
/* ------------------------------------------------------------------ */
A2 = CHOLMOD_copy_sparse (A, &ch) ;
A2x = A2->x ;
for (k = 0 ; k < nz ; k++)
{
if (isreal)
{
A2x [k] = 1 ;
}
else
{
A2x [2*k ] = 0 ;
A2x [2*k+1] = 1 ;
}
}
Common.halt_if_singular = 0 ;
Common.scale = 0 ;
if (isreal)
{
klu_refactor (Ap, Ai, A2x, Symbolic, Numeric, &Common) ;
klu_condest (Ap, A2x, Symbolic, Numeric, &Common) ;
}
else
{
klu_z_refactor (Ap, Ai, A2x, Symbolic, Numeric, &Common) ;
klu_z_condest (Ap, A2x, Symbolic, Numeric, &Common) ;
}
OK (Common.status = KLU_SINGULAR) ;
CHOLMOD_free_sparse (&A2, &ch) ;
}
klu_free_symbolic (&Symbolic, &Common) ;
if (isreal)
{
klu_free_numeric (&Numeric, &Common) ;
}
else
{
klu_z_free_numeric (&Numeric, &Common) ;
}
/* ---------------------------------------------------------------------- */
/* free problem and quit */
/* ---------------------------------------------------------------------- */
CHOLMOD_free_dense (&X, &ch) ;
CHOLMOD_free_dense (&B, &ch) ;
CHOLMOD_free_sparse (&A, &ch) ;
free (Puser) ;
free (Quser) ;
CHOLMOD_finish (&ch) ;
fprintf (stderr, " maxerr %10.3e", maxerr) ;
printf (" maxerr %10.3e", maxerr) ;
if (maxerr < 1e-8)
{
fprintf (stderr, " test passed") ;
printf (" test passed") ;
}
else
{
fprintf (stderr, " test FAILED") ;
printf (" test FAILED") ;
}
if (nan)
{
fprintf (stderr, " *") ;
printf (" *") ;
}
fprintf (stderr, "\n") ;
printf ("\n-----------------------------------------------------------\n") ;
return (0) ;
}
/*
Setup KLU for a linear solve. This function factors the Jacobian matrix
before handing off the factors for a back solve. Optionally, this function also
computes a new fill-reducing ordering (using KLU) in the case that the matrix
graph has been updated.
*/
int SetupKINKlu(KINMem kin_memory){
//get the KINKlu memory block
KINKluMem kin_klu_mem=(KINKluMem)kin_memory->kin_lmem;
if(!kin_klu_mem) return 1;
//grab appropriate klu objects
cs_di *jac=kin_klu_mem->jac;
klu_symbolic *symb=kin_klu_mem->symbolic;
klu_numeric *numeric=kin_klu_mem->numeric;
klu_common *comm=&(kin_klu_mem->klu_comm);
int n=kin_klu_mem->n, update_fr_order=0;
//call the jacobian evaluation function
kin_klu_mem->jac_fun(n, kin_memory->kin_uu, kin_memory->kin_fval, jac, kin_memory->kin_user_data, &update_fr_order, kin_memory->kin_vtemp1, kin_memory->kin_vtemp2);
/*
if a new fill-reducing ordering has been requested, or if the graph and values have been specified but no ordering has been computed yet, perform the computation
*/
if(update_fr_order){
//if a symbolic object already exists, free it
if(symb){
klu_free_symbolic(&symb, comm);
kin_klu_mem->symbolic=NULL;
}
//perform the fill-reducing ordering
symb=klu_analyze(n, jac->p, jac->i, comm);
if(!symb) return 1;
kin_klu_mem->symbolic=symb;
/*
now we need to perform a numeric factorization. first, free an existing
numeric factorization if there is one.
*/
if(numeric){
klu_free_numeric(&numeric, comm);
kin_klu_mem->numeric=NULL;
}
//perform the factorization
numeric=klu_factor(jac->p, jac->i, jac->x, symb, comm);
/*
check if the factorization was successful and return if not
*/
if(!numeric){
klu_free_symbolic(&symb, comm);
kin_klu_mem->symbolic=NULL;
return 1;
}
kin_klu_mem->numeric=numeric;
//otherwise, the factorization was a success and we can return
return(KINDLS_SUCCESS);
}
/*
if a new fill-reducing ordering is not necessary, we can proceed with factorization. first, check if a numeric factorization exists. if not, compute it
*/
if(!numeric)
{
//perform the factorization
numeric=klu_factor(jac->p, jac->i, jac->x, symb, comm);
/*
check if the factorization was successful and return if not
*/
if(!numeric) return 1;
kin_klu_mem->numeric=numeric;
return(KINDLS_SUCCESS);
}
/*
if a symbolic and numeric factorization already exist, try a refactor using the old numeric factorization. this is much faster than a full numeric factorization and requires no new memory
*/
klu_refactor(jac->p, jac->i, jac->x, symb, numeric, comm);
#ifdef _VERBOSE
/*
check the pivot growth factor. i confess that i dont understand what this
factor means, but a small value is supposed to indicate numerical
instability for testing i'm going to compute it and do a full numerical
factorization if it's too small.
*/
klu_rgrowth(jac->p, jac->i, jac->x, symb, numeric, comm);
/*
print the growth factor to the console for testing
*/
printf("Reciprocal pivot growth after refactor: %1.5e\n\n", kin_klu_mem->klu_comm.rgrowth);
#endif
//return
return(KINDLS_SUCCESS);
};
static double do_1_solve (cholmod_sparse *A, cholmod_dense *B,
cholmod_dense *Xknown, Int *Puser, Int *Quser,
KLU_common *Common, cholmod_common *ch, Int *nan)
{
Int *Ai, *Ap ;
double *Ax, *Bx, *Xknownx, *Xx, *Ax2, *Axx ;
KLU_symbolic *Symbolic = NULL ;
KLU_numeric *Numeric = NULL ;
cholmod_dense *X = NULL, *R = NULL ;
cholmod_sparse *AT = NULL, *A2 = NULL, *AT2 = NULL ;
double one [2], minusone [2],
rnorm, anorm, bnorm, xnorm, relresid, relerr, err = 0. ;
Int i, j, nrhs2, isreal, n, nrhs, transpose, step, k, save, tries ;
printf ("\ndo_1_solve: btf "ID" maxwork %g scale "ID" ordering "ID" user: "******" P,Q: %d halt: "ID"\n",
Common->btf, Common->maxwork, Common->scale, Common->ordering,
Common->user_data ? (*((Int *) Common->user_data)) : -1,
(Puser != NULL || Quser != NULL), Common->halt_if_singular) ;
fflush (stdout) ;
fflush (stderr) ;
CHOLMOD_print_sparse (A, "A", ch) ;
CHOLMOD_print_dense (B, "B", ch) ;
Ap = A->p ;
Ai = A->i ;
Ax = A->x ;
n = A->nrow ;
isreal = (A->xtype == CHOLMOD_REAL) ;
Bx = B->x ;
Xknownx = Xknown->x ;
nrhs = B->ncol ;
one [0] = 1 ;
one [1] = 0 ;
minusone [0] = -1 ;
minusone [1] = 0 ;
/* ---------------------------------------------------------------------- */
/* symbolic analysis */
/* ---------------------------------------------------------------------- */
Symbolic = NULL ;
my_tries = 0 ;
for (tries = 0 ; Symbolic == NULL && my_tries == 0 ; tries++)
{
my_tries = tries ;
if (Puser != NULL || Quser != NULL)
{
Symbolic = klu_analyze_given (n, Ap, Ai, Puser, Quser, Common) ;
}
else
{
Symbolic = klu_analyze (n, Ap, Ai, Common) ;
}
}
printf ("sym try "ID" btf "ID" ordering "ID"\n",
tries, Common->btf, Common->ordering) ;
if (Symbolic == NULL)
{
printf ("Symbolic is null\n") ;
return (998) ;
}
my_tries = -1 ;
/* create a modified version of A */
A2 = CHOLMOD_copy_sparse (A, ch) ;
Ax2 = A2->x ;
my_srand (42) ;
for (k = 0 ; k < Ap [n] * (isreal ? 1:2) ; k++)
{
Ax2 [k] = Ax [k] *
(1 + 1e-4 * ((double) my_rand ( )) / ((double) MY_RAND_MAX)) ;
}
AT = isreal ? NULL : CHOLMOD_transpose (A, 1, ch) ;
AT2 = isreal ? NULL : CHOLMOD_transpose (A2, 1, ch) ;
/* ---------------------------------------------------------------------- */
/* factorize then solve */
/* ---------------------------------------------------------------------- */
for (step = 1 ; step <= 3 ; step++)
{
printf ("step: "ID"\n", step) ;
fflush (stdout) ;
/* ------------------------------------------------------------------ */
/* factorization or refactorization */
/* ------------------------------------------------------------------ */
/* step 1: factor
step 2: refactor with same A
step 3: refactor with modified A, and scaling forced on
and solve each time
*/
if (step == 1)
{
/* numeric factorization */
Numeric = NULL ;
my_tries = 0 ;
for (tries = 0 ; Numeric == NULL && my_tries == 0 ; tries++)
{
my_tries = tries ;
if (isreal)
{
Numeric = klu_factor (Ap, Ai, Ax, Symbolic, Common) ;
}
else
{
Numeric = klu_z_factor (Ap, Ai, Ax, Symbolic, Common) ;
}
}
printf ("num try "ID" btf "ID"\n", tries, Common->btf) ;
my_tries = -1 ;
if (Common->status == KLU_OK ||
(Common->status == KLU_SINGULAR && !Common->halt_if_singular))
{
OK (Numeric) ;
}
else
{
FAIL (Numeric) ;
}
if (Common->status < KLU_OK)
{
printf ("factor failed: "ID"\n", Common->status) ;
}
}
else if (step == 2)
{
/* numeric refactorization with same values, same scaling */
if (isreal)
{
klu_refactor (Ap, Ai, Ax, Symbolic, Numeric, Common) ;
}
else
{
klu_z_refactor (Ap, Ai, Ax, Symbolic, Numeric, Common) ;
}
}
else
{
/* numeric refactorization with different values */
save = Common->scale ;
if (Common->scale == 0)
{
Common->scale = 1 ;
}
for (tries = 0 ; tries <= 1 ; tries++)
{
my_tries = tries ;
if (isreal)
{
klu_refactor (Ap, Ai, Ax2, Symbolic, Numeric, Common) ;
}
else
{
klu_z_refactor (Ap, Ai, Ax2, Symbolic, Numeric, Common) ;
}
}
my_tries = -1 ;
Common->scale = save ;
}
if (Common->status == KLU_SINGULAR)
{
printf ("# singular column : "ID"\n", Common->singular_col) ;
}
/* ------------------------------------------------------------------ */
/* diagnostics */
/* ------------------------------------------------------------------ */
Axx = (step == 3) ? Ax2 : Ax ;
if (isreal)
{
klu_rgrowth (Ap, Ai, Axx, Symbolic, Numeric, Common) ;
klu_condest (Ap, Axx, Symbolic, Numeric, Common) ;
klu_rcond (Symbolic, Numeric, Common) ;
klu_flops (Symbolic, Numeric, Common) ;
}
else
{
klu_z_rgrowth (Ap, Ai, Axx, Symbolic, Numeric, Common) ;
klu_z_condest (Ap, Axx, Symbolic, Numeric, Common) ;
klu_z_rcond (Symbolic, Numeric, Common) ;
klu_z_flops (Symbolic, Numeric, Common) ;
}
printf ("growth %g condest %g rcond %g flops %g\n",
Common->rgrowth, Common->condest, Common->rcond, Common->flops) ;
ludump (Symbolic, Numeric, isreal, ch, Common) ;
if (Numeric == NULL || Common->status < KLU_OK)
{
continue ;
}
/* ------------------------------------------------------------------ */
/* solve */
/* ------------------------------------------------------------------ */
/* forward/backsolve to solve A*X=B or A'*X=B */
for (transpose = (isreal ? 0 : -1) ; transpose <= 1 ; transpose++)
{
for (nrhs2 = 1 ; nrhs2 <= nrhs ; nrhs2++)
{
/* mangle B so that it has only nrhs2 columns */
B->ncol = nrhs2 ;
X = CHOLMOD_copy_dense (B, ch) ;
CHOLMOD_print_dense (X, "X before solve", ch) ;
Xx = X->x ;
if (isreal)
{
if (transpose)
{
/* solve A'x=b */
klu_tsolve (Symbolic, Numeric, n, nrhs2, Xx, Common) ;
}
else
{
/* solve A*x=b */
klu_solve (Symbolic, Numeric, n, nrhs2, Xx, Common) ;
}
}
else
{
if (transpose)
{
/* solve A'x=b (if 1) or A.'x=b (if -1) */
klu_z_tsolve (Symbolic, Numeric, n, nrhs2, Xx,
(transpose == 1), Common) ;
}
else
{
/* solve A*x=b */
klu_z_solve (Symbolic, Numeric, n, nrhs2, Xx, Common) ;
}
}
CHOLMOD_print_dense (X, "X", ch) ;
/* compute the residual, R = B-A*X, B-A'*X, or B-A.'*X */
R = CHOLMOD_copy_dense (B, ch) ;
if (transpose == -1)
{
/* R = B-A.'*X (use A.' explicitly) */
CHOLMOD_sdmult ((step == 3) ? AT2 : AT,
0, minusone, one, X, R, ch) ;
}
else
{
/* R = B-A*X or B-A'*X */
CHOLMOD_sdmult ((step == 3) ? A2 :A,
transpose, minusone, one, X, R, ch) ;
}
CHOLMOD_print_dense (R, "R", ch) ;
/* compute the norms of R, A, X, and B */
rnorm = CHOLMOD_norm_dense (R, 1, ch) ;
anorm = CHOLMOD_norm_sparse ((step == 3) ? A2 : A, 1, ch) ;
xnorm = CHOLMOD_norm_dense (X, 1, ch) ;
bnorm = CHOLMOD_norm_dense (B, 1, ch) ;
CHOLMOD_free_dense (&R, ch) ;
/* relative residual = norm (r) / (norm (A) * norm (x)) */
relresid = rnorm ;
if (anorm > 0)
{
relresid /= anorm ;
}
if (xnorm > 0)
{
relresid /= xnorm ;
}
if (SCALAR_IS_NAN (relresid))
{
*nan = TRUE ;
}
else
{
err = MAX (err, relresid) ;
}
/* relative error = norm (x - xknown) / norm (xknown) */
/* overwrite X with X - Xknown */
if (transpose || step == 3)
{
/* not computed */
relerr = -1 ;
}
else
{
for (j = 0 ; j < nrhs2 ; j++)
{
for (i = 0 ; i < n ; i++)
{
if (isreal)
{
Xx [i+j*n] -= Xknownx [i+j*n] ;
}
else
{
Xx [2*(i+j*n) ] -= Xknownx [2*(i+j*n) ] ;
Xx [2*(i+j*n)+1] -= Xknownx [2*(i+j*n)+1] ;
}
}
}
relerr = CHOLMOD_norm_dense (X, 1, ch) ;
xnorm = CHOLMOD_norm_dense (Xknown, 1, ch) ;
if (xnorm > 0)
{
relerr /= xnorm ;
}
if (SCALAR_IS_NAN (relerr))
{
*nan = TRUE ;
}
else
{
err = MAX (relerr, err) ;
}
}
CHOLMOD_free_dense (&X, ch) ;
printf (ID" "ID" relresid %10.3g relerr %10.3g %g\n",
transpose, nrhs2, relresid, relerr, err) ;
B->ncol = nrhs ; /* restore B */
}
}
}
/* ---------------------------------------------------------------------- */
/* free factorization and temporary matrices, and return */
/* ---------------------------------------------------------------------- */
klu_free_symbolic (&Symbolic, Common) ;
if (isreal)
{
klu_free_numeric (&Numeric, Common) ;
}
else
{
klu_z_free_numeric (&Numeric, Common) ;
}
CHOLMOD_free_sparse (&A2, ch) ;
CHOLMOD_free_sparse (&AT, ch) ;
CHOLMOD_free_sparse (&AT2, ch) ;
fflush (stdout) ;
fflush (stderr) ;
return (err) ;
}
