GLOBAL Int UMFPACK_report_vector
(
Int n,
const double Xx [ ],
#ifdef COMPLEX
const double Xz [ ],
#endif
const double Control [UMFPACK_CONTROL]
)
{
Int prl ;
#ifndef COMPLEX
double *Xz = (double *) NULL ;
#endif
prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
if (prl <= 2)
{
return (UMFPACK_OK) ;
}
return (UMF_report_vector (n, Xx, Xz, prl, TRUE, FALSE)) ;
}
GLOBAL Int UMFPACK_report_numeric
(
void *NumericHandle,
const double Control [UMFPACK_CONTROL]
)
{
Int prl, *W, nn, n_row, n_col, n_inner, num_fixed_size, numeric_size,
npiv ;
NumericType *Numeric ;
prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ;
if (prl <= 2)
{
return (UMFPACK_OK) ;
}
PRINTF (("Numeric object: ")) ;
Numeric = (NumericType *) NumericHandle ;
if (!UMF_valid_numeric (Numeric))
{
PRINTF (("ERROR: LU factors invalid\n\n")) ;
return (UMFPACK_ERROR_invalid_Numeric_object) ;
}
n_row = Numeric->n_row ;
n_col = Numeric->n_col ;
nn = MAX (n_row, n_col) ;
n_inner = MIN (n_row, n_col) ;
npiv = Numeric->npiv ;
DEBUG1 (("n_row "ID" n_col "ID" nn "ID" n_inner "ID" npiv "ID"\n",
n_row, n_col, nn, n_inner, npiv)) ;
/* size of Numeric object, except Numeric->Memory and Numeric->Upattern */
/* see also UMF_set_stats */
num_fixed_size =
UNITS (NumericType, 1) /* Numeric structure */
+ UNITS (Entry, n_inner+1) /* D */
+ UNITS (Int, n_row+1) /* Rperm */
+ UNITS (Int, n_col+1) /* Cperm */
+ 6 * UNITS (Int, npiv+1) /* Lpos, Uilen, Uip, Upos, Lilen, Lip */
+ ((Numeric->scale != UMFPACK_SCALE_NONE) ?
UNITS (Entry, n_row) : 0) ; /* Rs */
DEBUG1 (("num fixed size: "ID"\n", num_fixed_size)) ;
DEBUG1 (("Numeric->size "ID"\n", Numeric->size)) ;
DEBUG1 (("ulen units "ID"\n", UNITS (Int, Numeric->ulen))) ;
/* size of Numeric->Memory is Numeric->size */
/* size of Numeric->Upattern is Numeric->ulen */
numeric_size = num_fixed_size + Numeric->size
+ UNITS (Int, Numeric->ulen) ;
DEBUG1 (("numeric total size "ID"\n", numeric_size)) ;
if (prl >= 4)
{
PRINTF (("\n n_row: "ID" n_col: "ID"\n", n_row, n_col)) ;
PRINTF ((" relative pivot tolerance used: %g\n",
Numeric->relpt)) ;
PRINTF ((" relative symmetric pivot tolerance used: %g\n",
Numeric->relpt2)) ;
PRINTF ((" matrix scaled: ")) ;
if (Numeric->scale == UMFPACK_SCALE_NONE)
{
PRINTF (("no")) ;
}
else if (Numeric->scale == UMFPACK_SCALE_SUM)
{
PRINTF (("yes (divided each row by sum abs value in each row)\n")) ;
PRINTF ((" minimum sum (abs (rows of A)): %.5e\n",
Numeric->rsmin)) ;
PRINTF ((" maximum sum (abs (rows of A)): %.5e",
Numeric->rsmax)) ;
}
else if (Numeric->scale == UMFPACK_SCALE_MAX)
{
PRINTF (("yes (divided each row by max abs value in each row)\n")) ;
PRINTF ((" minimum max (abs (rows of A)): %.5e\n",
Numeric->rsmin)) ;
PRINTF ((" maximum max (abs (rows of A)): %.5e",
Numeric->rsmax)) ;
}
PRINTF (("\n")) ;
PRINTF ((" initial allocation parameter used: %g\n",
Numeric->alloc_init)) ;
PRINTF ((" frontal matrix allocation parameter used: %g\n",
Numeric->front_alloc_init)) ;
PRINTF ((" final total size of Numeric object (Units): "ID"\n",
numeric_size)) ;
PRINTF ((" final total size of Numeric object (MBytes): %.1f\n",
MBYTES (numeric_size))) ;
PRINTF ((" peak size of variable-size part (Units): "ID"\n",
Numeric->max_usage)) ;
PRINTF ((" peak size of variable-size part (MBytes): %.1f\n",
MBYTES (Numeric->max_usage))) ;
PRINTF ((" largest actual frontal matrix size: "ID"\n",
Numeric->maxfrsize)) ;
PRINTF ((" memory defragmentations: "ID"\n",
Numeric->ngarbage)) ;
PRINTF ((" memory reallocations: "ID"\n",
Numeric->nrealloc)) ;
PRINTF ((" costly memory reallocations: "ID"\n",
Numeric->ncostly)) ;
PRINTF ((" entries in compressed pattern (L and U): "ID"\n",
Numeric->isize)) ;
PRINTF ((" number of nonzeros in L (excl diag): "ID"\n",
Numeric->lnz)) ;
PRINTF ((" number of entries stored in L (excl diag): "ID"\n",
Numeric->nLentries)) ;
PRINTF ((" number of nonzeros in U (excl diag): "ID"\n",
Numeric->unz)) ;
PRINTF ((" number of entries stored in U (excl diag): "ID"\n",
Numeric->nUentries)) ;
PRINTF ((" factorization floating-point operations: %g\n",
Numeric->flops)) ;
PRINTF ((" number of nonzeros on diagonal of U: "ID"\n",
Numeric->nnzpiv)) ;
PRINTF ((" min abs. value on diagonal of U: %.5e\n",
Numeric->min_udiag)) ;
PRINTF ((" max abs. value on diagonal of U: %.5e\n",
Numeric->max_udiag)) ;
PRINTF ((" reciprocal condition number estimate: %.2e\n",
Numeric->rcond)) ;
}
W = (Int *) UMF_malloc (nn, sizeof (Int)) ;
if (!W)
{
PRINTF ((" ERROR: out of memory to check Numeric object\n\n")) ;
return (UMFPACK_ERROR_out_of_memory) ;
}
if (Numeric->Rs)
{
#ifndef NRECIPROCAL
if (Numeric->do_recip)
{
PRINTF4 (("\nScale factors applied via multiplication\n")) ;
}
else
#endif
{
PRINTF4 (("\nScale factors applied via division\n")) ;
}
PRINTF4 (("Scale factors, Rs: ")) ;
(void) UMF_report_vector (n_row, Numeric->Rs, (double *) NULL,
prl, FALSE, TRUE) ;
}
else
{
PRINTF4 (("Scale factors, Rs: (not present)\n")) ;
}
PRINTF4 (("\nP: row ")) ;
if (UMF_report_perm (n_row, Numeric->Rperm, W, prl, 0) != UMFPACK_OK)
{
(void) UMF_free ((void *) W) ;
return (UMFPACK_ERROR_invalid_Numeric_object) ;
}
PRINTF4 (("\nQ: column ")) ;
if (UMF_report_perm (n_col, Numeric->Cperm, W, prl, 0) != UMFPACK_OK)
{
(void) UMF_free ((void *) W) ;
return (UMFPACK_ERROR_invalid_Numeric_object) ;
}
if (!report_L (Numeric, W, prl))
{
(void) UMF_free ((void *) W) ;
PRINTF ((" ERROR: L factor invalid\n\n")) ;
return (UMFPACK_ERROR_invalid_Numeric_object) ;
}
if (!report_U (Numeric, W, prl))
{
(void) UMF_free ((void *) W) ;
PRINTF ((" ERROR: U factor invalid\n\n")) ;
return (UMFPACK_ERROR_invalid_Numeric_object) ;
}
/* The diagonal of U is in "merged" (Entry) form, not "split" form. */
PRINTF4 (("\ndiagonal of U: ")) ;
(void) UMF_report_vector (n_inner, (double *) Numeric->D, (double *) NULL,
prl, FALSE, FALSE) ;
(void) UMF_free ((void *) W) ;
PRINTF4 ((" Numeric object: ")) ;
PRINTF (("OK\n\n")) ;
return (UMFPACK_OK) ;
}
PRIVATE Int do_step /* return TRUE if iterative refinement done */
(
double omega [3],
Int step, /* which step of iterative refinement to do */
const double B2 [ ], /* abs (B) */
Entry X [ ],
const Entry W [ ],
const double Y [ ],
const double Z2 [ ],
Entry S [ ],
Int n,
double Info [UMFPACK_INFO]
)
{
double last_omega [3], tau, nctau, d1, wd1, d2, wd2, xi, yix, wi, xnorm ;
Int i ;
/* DBL_EPSILON is a standard ANSI C term defined in <float.h> */
/* It is the smallest positive x such that 1.0+x != 1.0 */
nctau = 1000 * n * DBL_EPSILON ;
DEBUG0 (("do_step start: nctau = %30.20e\n", nctau)) ;
ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
FALSE, FALSE) == UMFPACK_OK) ;
/* for approximate flop count, assume d1 > tau is always true */
/* flops += (2*ABS_FLOPS + 5) * n ; (done in UMF_solve, above) */
/* ---------------------------------------------------------------------- */
/* save the last iteration in case we need to reinstate it */
/* ---------------------------------------------------------------------- */
last_omega [0] = omega [0] ;
last_omega [1] = omega [1] ;
last_omega [2] = omega [2] ;
/* ---------------------------------------------------------------------- */
/* compute sparse backward errors: omega [1] and omega [2] */
/* ---------------------------------------------------------------------- */
/* xnorm = ||x|| maxnorm */
xnorm = 0.0 ;
for (i = 0 ; i < n ; i++)
{
/* xi = ABS (X [i]) ; */
ABS (xi, X [i]) ;
if (SCALAR_IS_NAN (xi))
{
xnorm = xi ;
break ;
}
/* no NaN's to consider here: */
xnorm = MAX (xnorm, xi) ;
}
omega [1] = 0. ;
omega [2] = 0. ;
for (i = 0 ; i < n ; i++)
{
yix = Y [i] * xnorm ;
tau = (yix + B2 [i]) * nctau ;
d1 = Z2 [i] + B2 [i] ;
/* wi = ABS (W [i]) ; */
ABS (wi, W [i]) ;
if (SCALAR_IS_NAN (d1))
{
omega [1] = d1 ;
omega [2] = d1 ;
break ;
}
if (SCALAR_IS_NAN (tau))
{
omega [1] = tau ;
omega [2] = tau ;
break ;
}
if (d1 > tau) /* a double relop, but no NaN's here */
{
wd1 = wi / d1 ;
omega [1] = MAX (omega [1], wd1) ;
}
else if (tau > 0.0) /* a double relop, but no NaN's here */
{
d2 = Z2 [i] + yix ;
wd2 = wi / d2 ;
omega [2] = MAX (omega [2], wd2) ;
}
}
omega [0] = omega [1] + omega [2] ;
Info [UMFPACK_OMEGA1] = omega [1] ;
Info [UMFPACK_OMEGA2] = omega [2] ;
/* ---------------------------------------------------------------------- */
/* stop the iterations if the backward error is small, or NaN */
/* ---------------------------------------------------------------------- */
Info [UMFPACK_IR_TAKEN] = step ;
Info [UMFPACK_IR_ATTEMPTED] = step ;
if (SCALAR_IS_NAN (omega [0]))
{
DEBUG0 (("omega[0] is NaN - done.\n")) ;
ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
FALSE, FALSE) == UMFPACK_OK) ;
return (TRUE) ;
}
if (omega [0] < DBL_EPSILON) /* double relop, but no NaN case here */
{
DEBUG0 (("omega[0] too small - done.\n")) ;
ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
FALSE, FALSE) == UMFPACK_OK) ;
return (TRUE) ;
}
/* ---------------------------------------------------------------------- */
/* stop if insufficient decrease in omega */
/* ---------------------------------------------------------------------- */
/* double relop, but no NaN case here: */
if (step > 0 && omega [0] > last_omega [0] / 2)
{
DEBUG0 (("stop refinement\n")) ;
if (omega [0] > last_omega [0])
{
/* last iteration better than this one, reinstate it */
DEBUG0 (("last iteration better\n")) ;
for (i = 0 ; i < n ; i++)
{
X [i] = S [i] ;
}
Info [UMFPACK_OMEGA1] = last_omega [1] ;
Info [UMFPACK_OMEGA2] = last_omega [2] ;
}
Info [UMFPACK_IR_TAKEN] = step - 1 ;
ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
FALSE, FALSE) == UMFPACK_OK) ;
return (TRUE) ;
}
/* ---------------------------------------------------------------------- */
/* save current solution in case we need to reinstate */
/* ---------------------------------------------------------------------- */
for (i = 0 ; i < n ; i++)
{
S [i] = X [i] ;
}
/* ---------------------------------------------------------------------- */
/* iterative refinement continues */
/* ---------------------------------------------------------------------- */
ASSERT (UMF_report_vector (n, (double *) X, (double *) NULL, UMF_debug,
FALSE, FALSE) == UMFPACK_OK) ;
return (FALSE) ;
}