//=============================================================================
void Epetra_BLAS::GEMV(const char TRANS, const int M, const int N,
const double ALPHA, const double * A, const int LDA, const double * X,
const double BETA, double * Y, const int INCX, const int INCY) const {
DGEMV_F77(CHAR_MACRO(TRANS), &M, &N, &ALPHA,
A, &LDA, X, &INCX, &BETA, Y, &INCY);
}
void AZ_pgmresr(double b[], double x[],double weight[], int options[],
double params[], int proc_config[], double status[], AZ_MATRIX *Amat,
AZ_PRECOND *precond, struct AZ_CONVERGE_STRUCT *convergence_info)
/*******************************************************************************
This routine uses Saad's restarted Genralized Minimum Residual method to solve
the nonsymmetric matrix problem Ax = b.
IMPORTANT NOTE: While the 2-norm of the gmres residual is available, the
actual residual is not normally computed as part of the gmres algorithm. Thus,
if the user uses a convergence condition (see AZ_gmres_global_scalars()) that
is based on the 2-norm of the residual there is no need to compute the
residual (i.e. r_avail = AZ_FALSE). However, if another norm of r is
requested, AZ_gmres_global_scalars() sets r_avail = AZ_TRUE and the algorithm
computes the residual.
Author: John N. Shadid, SNL, 1421
=======
Return code: void
============
Parameter list:
===============
Amat: Structure used for DMSR and DVBR sparse matrix storage (see
file Aztec User's Guide).
b: Right hand side of linear system.
x: On input, contains the initial guess. On output contains the
solution to the linear system.
weight: Vector of weights for convergence norm #4.
options: Determines specific solution method and other parameters.
params: Drop tolerance and convergence tolerance info.
data_org: Array containing information on the distribution of the
matrix to this processor as well as communication parameters
(see file Aztec User's Guide).
proc_config: Machine configuration. proc_config[AZ_node] is the node
number. proc_config[AZ_N_procs] is the number of processors.
status: On output, indicates termination status:
0: terminated normally.
-1: maximum number of iterations taken without achieving
convergence.
-2: Breakdown. The algorithm can not proceed due to
numerical difficulties (usually a divide by zero).
-3: Internal residual differs from the computed residual due
to a significant loss of precision.
Amat: Structure used to represent the matrix (see file az_aztec.h
and Aztec User's Guide).
*******************************************************************************/
{
/* local variables */
register int k;
int i, N, NN, converged, one = 1, iter, r_avail = AZ_FALSE;
int print_freq, proc, kspace;
double **UU, **CC, *dots, *tmp, *res;
double dble_tmp, r_2norm = 1.0, epsilon;
double rec_residual, scaled_r_norm, true_scaled_r=0.0;
double actual_residual = -1.0, minus_alpha, alpha;
double *dummy = (double *) 0;
double *UUblock, *CCblock;
int mm, ii;
char label[64],suffix[32], prefix[64];
int *data_org, str_leng, first_time = AZ_TRUE;
double doubleone = 1.0, minusone = -1.0, init_time = 0.0;
char *T = "T";
char *T2 = "N";
/**************************** execution begins ******************************/
sprintf(suffix," in gmresr%d",options[AZ_recursion_level]);
/* set string that will be used */
/* for manage_memory label */
/* set prefix for printing */
str_leng = 0;
for (i = 0; i < 16; i++) prefix[str_leng++] = ' ';
for (i = 0 ; i < options[AZ_recursion_level]; i++ ) {
prefix[str_leng++] = ' '; prefix[str_leng++] = ' '; prefix[str_leng++] = ' ';
prefix[str_leng++] = ' '; prefix[str_leng++] = ' ';
}
prefix[str_leng] = '\0';
data_org = Amat->data_org;
/* pull needed values out of parameter arrays */
N = data_org[AZ_N_internal] + data_org[AZ_N_border];
epsilon = params[AZ_tol];
proc = proc_config[AZ_node];
print_freq = options[AZ_print_freq];
kspace = options[AZ_kspace];
/* Initialize some values in convergence info struct */
convergence_info->print_info = print_freq;
convergence_info->iteration = 0;
convergence_info->sol_updated = 0; /* GMRES seldom updates solution */
convergence_info->epsilon = params[AZ_tol];
/* allocate memory for required vectors */
NN = kspace + 1;
/* +1: make sure everybody allocates something */
sprintf(label,"dots%s",suffix);
dots = AZ_manage_memory(2*NN*sizeof(double), AZ_ALLOC,AZ_SYS+az_iterate_id,label,&i);
tmp = &(dots[NN]);
sprintf(label,"CC%s",suffix);
CC = (double **) AZ_manage_memory(2*NN*sizeof(double *),
AZ_ALLOC,AZ_SYS+az_iterate_id,label,&i);
UU = &(CC[NN]);
NN = N + data_org[AZ_N_external];
if (NN == 0) NN++; /* make sure everybody allocates something */
NN = NN + (NN%2); /* make sure things are aligned for intel */
sprintf(label,"UUblock%s",suffix);
UUblock = AZ_manage_memory(2*NN*kspace*sizeof(double),
AZ_ALLOC, AZ_SYS+az_iterate_id,label, &i);
for (k = 0; k < kspace; k++) UU[k] = &(UUblock[k*NN]);
CCblock = &(UUblock[kspace*NN]);
for (k = 0; k < kspace; k++) CC[k] = &(CCblock[k*NN]);
sprintf(label,"res%s",suffix);
res = AZ_manage_memory(NN*sizeof(double),AZ_ALLOC,AZ_SYS+az_iterate_id,label,&i);
AZ_compute_residual(b, x, res, proc_config, Amat);
/*
* Compute a few global scalars:
* 1) ||r|| corresponding to options[AZ_conv]
* 2) scaled ||r|| corresponding to options[AZ_conv]
*/
r_2norm = DDOT_F77(&N, res, &one, res, &one);
AZ_gdot_vec(1, &r_2norm, &rec_residual, proc_config);
r_2norm = sqrt(r_2norm);
rec_residual = r_2norm;
AZ_compute_global_scalars(Amat, x, b, res,
weight, &rec_residual, &scaled_r_norm, options,
data_org, proc_config, &r_avail, NULL, NULL, NULL,
convergence_info);
r_2norm = rec_residual;
converged = scaled_r_norm < epsilon;
if ( (options[AZ_output] != AZ_none) &&
(options[AZ_output] != AZ_last) &&
(options[AZ_output] != AZ_summary) &&
(options[AZ_output] != AZ_warnings) && (proc == 0) )
(void) AZ_printf_out("%siter: 0 residual = %e\n",
prefix,scaled_r_norm);
iter = 0;
/*rst change while (!converged && iter < options[AZ_max_iter]) { */
while (!(convergence_info->converged) && iter < options[AZ_max_iter] && !(convergence_info->isnan)) {
convergence_info->iteration = iter;
i = 0;
/*rst change while (i < kspace && !converged && iter < options[AZ_max_iter]) { */
while (i < kspace && !(convergence_info->converged) && iter < options[AZ_max_iter]
&& !(convergence_info->isnan)) {
iter++;
convergence_info->iteration = iter;
/* v_i+1 = A M^-1 v_i */
DCOPY_F77(&N, res , &one, UU[i], &one);
if (iter == 1) init_time = AZ_second();
#ifdef AZ_ENABLE_TIMEMONITOR
#ifdef HAVE_AZTECOO_TEUCHOS
/* Start timer. */
static int precID = -1;
precID = Teuchos_startTimer( "AztecOO: Operation Prec*x", precID );
#endif
#endif
precond->prec_function(UU[i],options,proc_config,params,Amat,precond);
#ifdef AZ_ENABLE_TIMEMONITOR
#ifdef HAVE_AZTECOO_TEUCHOS
/* Stop timer. */
Teuchos_stopTimer( precID );
#endif
#endif
if (iter == 1) status[AZ_first_precond] = AZ_second() - init_time;
#ifdef AZ_ENABLE_TIMEMONITOR
#ifdef HAVE_AZTECOO_TEUCHOS
/* Start timer. */
static int matvecID = -1;
matvecID = Teuchos_startTimer( "AztecOO: Operation Op*x", matvecID );
#endif
#endif
Amat->matvec(UU[i], CC[i], Amat, proc_config);
#ifdef AZ_ENABLE_TIMEMONITOR
#ifdef HAVE_AZTECOO_TEUCHOS
/* Stop timer. */
Teuchos_stopTimer( matvecID );
#endif
#endif
#ifdef AZ_ENABLE_TIMEMONITOR
#ifdef HAVE_AZTECOO_TEUCHOS
/* Start the timer. */
static int orthoID = -1;
orthoID = Teuchos_startTimer( "AztecOO: Orthogonalization", orthoID );
#endif
#endif
/* Gram-Schmidt orthogonalization */
if (!options[AZ_orthog]) { /* classical (stabilized) */
for (ii = 0 ; ii < 2 ; ii++ ) {
dble_tmp = 0.0; mm = i;
if (N == 0) for (k = 0 ; k < i ; k++) dots[k] = 0.0;
#ifdef AZ_ENABLE_TIMEMONITOR
#ifdef HAVE_AZTECOO_TEUCHOS
/* Start the timer. */
static int orthoInnerProdID = -1;
orthoInnerProdID = Teuchos_startTimer( "AztecOO: Ortho (Inner Product)", orthoInnerProdID );
#endif
#endif
DGEMV_F77(CHAR_MACRO(T[0]), &N, &mm, &doubleone, CCblock, &NN, CC[i],
&one, &dble_tmp, dots, &one);
AZ_gdot_vec(i, dots, tmp, proc_config);
#ifdef AZ_ENABLE_TIMEMONITOR
#ifdef HAVE_AZTECOO_TEUCHOS
Teuchos_stopTimer( orthoInnerProdID );
#endif
#endif
#ifdef AZ_ENABLE_TIMEMONITOR
#ifdef HAVE_AZTECOO_TEUCHOS
/* Start the timer. */
static int orthoUpdateID = -1;
orthoUpdateID = Teuchos_startTimer( "AztecOO: Ortho (Update)", orthoUpdateID );
#endif
#endif
DGEMV_F77(CHAR_MACRO(T2[0]), &N, &mm, &minusone, CCblock, &NN, dots,
&one, &doubleone, CC[i], &one);
DGEMV_F77(CHAR_MACRO(T2[0]), &N, &mm, &minusone, UUblock, &NN, dots,
&one, &doubleone, UU[i], &one);
#ifdef AZ_ENABLE_TIMEMONITOR
#ifdef HAVE_AZTECOO_TEUCHOS
Teuchos_stopTimer( orthoUpdateID );
#endif
#endif
}
}
else { /* modified */
for (k = 0; k < i; k++) {
alpha = AZ_gdot(N, CC[k], CC[i], proc_config);
minus_alpha = -alpha;
DAXPY_F77(&N, &minus_alpha, CC[k], &one, CC[i], &one);
DAXPY_F77(&N, &minus_alpha, UU[k], &one, UU[i], &one);
}
}
/* normalize vector */
#ifdef AZ_ENABLE_TIMEMONITOR
#ifdef HAVE_AZTECOO_TEUCHOS
static int orthoNormID = -1;
orthoNormID = Teuchos_startTimer( "AztecOO: Ortho (Norm)", orthoNormID );
#endif
#endif
dble_tmp = sqrt(AZ_gdot(N, CC[i], CC[i], proc_config));
#ifdef AZ_ENABLE_TIMEMONITOR
#ifdef HAVE_AZTECOO_TEUCHOS
Teuchos_stopTimer( orthoNormID );
#endif
#endif
if (dble_tmp > DBL_EPSILON*r_2norm)
dble_tmp = 1.0 / dble_tmp;
else
dble_tmp = 0.0;
DSCAL_F77(&N, &dble_tmp, CC[i], &one);
DSCAL_F77(&N, &dble_tmp, UU[i], &one);
dble_tmp = AZ_gdot(N, CC[i], res, proc_config);
DAXPY_F77(&N, &dble_tmp, UU[i], &one, x, &one);
dble_tmp = -dble_tmp;
DAXPY_F77(&N, &dble_tmp, CC[i], &one, res, &one);
#ifdef AZ_ENABLE_TIMEMONITOR
#ifdef HAVE_AZTECOO_TEUCHOS
/* Stop the timer. */
Teuchos_stopTimer( orthoID );
#endif
#endif
/* determine residual norm & test convergence */
r_2norm = sqrt(AZ_gdot(N, res, res, proc_config));
rec_residual = r_2norm;
/*
* Compute a few global scalars:
* 1) ||r|| corresponding to options[AZ_conv]
* 2) scaled ||r|| corresponding to options[AZ_conv]
* NOTE: if r_avail = AZ_TRUE or AZ_FIRST is passed in, we perform
* step 1), otherwise ||r|| is taken as rec_residual.
*/
AZ_compute_global_scalars(Amat, x, b, res,
weight, &rec_residual, &scaled_r_norm, options,
data_org, proc_config, &r_avail, dummy, dummy,
dummy, convergence_info);
converged = scaled_r_norm < epsilon;
/*rst change if ( (iter%print_freq == 0) && proc == 0) */
if ( (iter%print_freq == 0) &&
(options[AZ_conv]!=AZTECOO_conv_test) && proc == 0)
(void) AZ_printf_out("%siter: %4d residual = %e\n",prefix,iter,
scaled_r_norm);
i++; /* subspace dim. counter dim(K) = i - 1 */
#ifdef out
if (options[AZ_check_update_size] & converged)
converged = AZ_compare_update_vs_soln(N, -1.,dble_tmp, UU[i-1], x,
params[AZ_update_reduction],
options[AZ_output], proc_config, &first_time);
if (converged) {
/* compute true residual using 'v[kspace]' as a temporary vector */
AZ_scale_true_residual(x, b,
res, weight, &actual_residual, &true_scaled_r,
options, data_org, proc_config, Amat,
convergence_info);
converged = true_scaled_r < params[AZ_tol];
if (!converged && (AZ_get_new_eps(&epsilon, scaled_r_norm,
true_scaled_r,
options, proc_config) == AZ_QUIT)) {
/*
* Computed residual has converged, actual residual has not
* converged, AZ_get_new_eps() has decided that it is time to quit.
*/
AZ_terminate_status_print(AZ_loss, iter, status, rec_residual, params,
true_scaled_r, actual_residual, options,
proc_config);
return;
}
}
#endif
}
}
if ( (iter%print_freq != 0) && (proc == 0) && (options[AZ_output] != AZ_none)
&& (options[AZ_output] != AZ_warnings))
(void) AZ_printf_out("%siter: %4d residual = %e\n",
prefix,iter, scaled_r_norm);
if (convergence_info->converged) {
i = AZ_normal;
scaled_r_norm = true_scaled_r;
}
else if (convergence_info->isnan) i = AZ_breakdown;
else i = AZ_maxits;
AZ_terminate_status_print(i, iter, status, rec_residual, params,
scaled_r_norm, actual_residual, options,
proc_config);
#ifdef out
/* check if we exceeded maximum number of iterations */
if (converged) {
i = AZ_normal;
scaled_r_norm = true_scaled_r;
}
else
i = AZ_maxits;
AZ_terminate_status_print(i, iter, status, rec_residual, params,
scaled_r_norm, actual_residual, options,
proc_config);
#endif
} /* AZ_pgmres */
void BLAS<int, double>::GEMV(ETransp trans, const int m, const int n, const double alpha, const double* A, const int lda, const double* x, const int incx, const double beta, double* y, const int incy) const
{ DGEMV_F77(CHAR_MACRO(ETranspChar[trans]), &m, &n, &alpha, A, &lda, x, &incx, &beta, y, &incy); }
void AZ_pcg_f(double b[], double x[], double weight[], int options[],
double params[], int proc_config[],double status[],
AZ_MATRIX *Amat, AZ_PRECOND *precond,
struct AZ_CONVERGE_STRUCT *convergence_info)
/*******************************************************************************
Conjugate Gradient algorithm to solve the symmetric matrix problem Ax = b.
Author: John N. Shadid, SNL, 1421
=======
Return code: void
============
Parameter list:
===============
b: Right hand side of linear system.
x: On input, contains the initial guess. On output contains the
solution to the linear system.
weight: Vector of weights for convergence norm #4.
options: Determines specific solution method and other parameters.
params: Drop tolerance and convergence tolerance info.
proc_config: Machine configuration. proc_config[AZ_node] is the node
number. proc_config[AZ_N_procs] is the number of processors.
status: On output, indicates termination status:
0: terminated normally.
-1: maximum number of iterations taken without achieving
convergence.
-2: Breakdown. The algorithm can not proceed due to
numerical difficulties (usually a divide by zero).
-3: Internal residual differs from the computed residual due
to a significant loss of precision.
Amat: Structure used to represent the matrix (see file az_aztec.h
and Aztec User's Guide).
precond: Structure used to represent the preconditioner
(see file az_aztec.h and Aztec User's Guide).
*******************************************************************************/
{
/* local variables */
register int i;
int N, NN, one = 1, iter = 1, r_avail = AZ_TRUE, j;
int precond_flag, print_freq, proc, brkdown_will_occur = AZ_FALSE;
double alpha, beta = 0.0, nalpha, true_scaled_r=-1.0;
double *r, *z, *p, *ap, actual_residual = -1.0;
double r_z_dot, r_z_dot_old, p_ap_dot, rec_residual=-1.0;
double scaled_r_norm=-1.0, brkdown_tol = DBL_EPSILON;
int *data_org, str_leng, first_time = AZ_TRUE;
char label[64],suffix[32], prefix[64];
double **saveme, *ptap;
int *kvec_sizes = NULL, current_kept = 0;
double *dots;
double doubleone = 1., dzero = 0.;
char *T = "T";
char *T2 = "N";
double *block;
/**************************** execution begins ******************************/
sprintf(suffix," in cg%d",options[AZ_recursion_level]); /* set string that will be used */
/* for manage_memory label */
/* set prefix for printing */
str_leng = 0;
for (i = 0; i < 16; i++) prefix[str_leng++] = ' ';
for (i = 0 ; i < options[AZ_recursion_level]; i++ ) {
prefix[str_leng++] = ' '; prefix[str_leng++] = ' '; prefix[str_leng++] = ' ';
prefix[str_leng++] = ' '; prefix[str_leng++] = ' ';
}
prefix[str_leng] = '\0';
/* pull needed values out of parameter arrays */
data_org = Amat->data_org;
N = data_org[AZ_N_internal] + data_org[AZ_N_border];
precond_flag = options[AZ_precond];
proc = proc_config[AZ_node];
print_freq = options[AZ_print_freq];
/* Initialize some values in convergence info struct */
convergence_info->print_info = print_freq;
convergence_info->iteration = 0;
convergence_info->sol_updated = 1; /* CG always updates solution */
convergence_info->epsilon = params[AZ_tol]; /* Test against this */
/* allocate space for necessary vectors */
NN = N + data_org[AZ_N_external];
if (NN == 0) NN++; /* make sure everybody allocates something */
NN = NN + (NN%2); /* make sure things are aligned for assembly */
/* matvec on paragon. */
sprintf(label,"z%s",suffix);
p = (double *) AZ_manage_memory(4*NN*sizeof(double),AZ_ALLOC,
AZ_SYS+az_iterate_id, label, &j);
r = &(p[1*NN]);
z = &(p[2*NN]);
ap = &(p[3*NN]);
AZ_compute_residual(b, x, r, proc_config, Amat);
if (options[AZ_apply_kvecs]) {
AZ_compute_global_scalars(Amat, x, b, r,
weight, &rec_residual, &scaled_r_norm, options,
data_org, proc_config, &r_avail,NULL, NULL, &r_z_dot,
convergence_info);
AZ_space_for_kvecs(AZ_OLD_ADDRESS, &kvec_sizes, &saveme,
&ptap, options, data_org, suffix,
proc_config[AZ_node], &block);
dots = (double *) AZ_allocate(2*kvec_sizes[AZ_Nkept]*sizeof(double));
if (dots == NULL) {
printf("Not space to apply vectors in CG\n");
exit(1);
}
DGEMV_F77(CHAR_MACRO(T[0]),&N,&(kvec_sizes[AZ_Nkept]),&doubleone,block,&N, r, &one, &dzero, dots, &one);
AZ_gdot_vec(kvec_sizes[AZ_Nkept], dots, &(dots[kvec_sizes[AZ_Nkept]]), proc_config);
for (i = 0; i < kvec_sizes[AZ_Nkept]; i++) dots[i] = dots[i]/ptap[i];
DGEMV_F77(CHAR_MACRO(T2[0]), &N, &(kvec_sizes[AZ_Nkept]), &doubleone, block, &N, dots, &one, &doubleone,
x, &one);
AZ_free(dots);
AZ_compute_residual(b, x, r, proc_config, Amat);
if ((options[AZ_output] != AZ_none) && (proc == 0))
printf("\t\tApplied Previous Krylov Vectors ... \n\n");
}
if (options[AZ_keep_kvecs] > 0)
AZ_space_for_kvecs(AZ_NEW_ADDRESS, &kvec_sizes, &saveme,
&ptap, options, data_org, suffix,
proc_config[AZ_node], &block);
/* z = M r */
/* p = 0 */
DCOPY_F77(&N, r, &one, z, &one);
status[AZ_first_precond] = AZ_second();
if (precond_flag)
precond->prec_function(z,options,proc_config,params,Amat,precond);
status[AZ_first_precond] = AZ_second() - status[AZ_first_precond];
for (i = 0; i < N; i++ ) p[i] = 0.0;
/* compute a few global scalars: */
/* 1) ||r|| corresponding to options[AZ_conv] */
/* 2) scaled ||r|| corresponding to options[AZ_conv] */
/* 3) r_z_dot = <z, r> */
AZ_compute_global_scalars(Amat, x, b, r,
weight, &rec_residual, &scaled_r_norm, options,
data_org, proc_config, &r_avail,r, z, &r_z_dot,
convergence_info);
true_scaled_r = scaled_r_norm;
if ((options[AZ_output] != AZ_none) &&
(options[AZ_output] != AZ_last) &&
(options[AZ_output] != AZ_warnings) &&
(options[AZ_output] != AZ_summary) &&
(options[AZ_conv]!=AZTECOO_conv_test) && (proc == 0))
{
(void) AZ_printf_out("%siter: 0 residual = %e\n",
prefix,scaled_r_norm);
AZ_flush_out();
}
for (iter = 1; iter <= options[AZ_max_iter] && !(convergence_info->converged) &&
!(convergence_info->isnan); iter++ ) {
convergence_info->iteration = iter;
/* p = z + beta * p */
/* ap = A p */
for (i = 0; i < N; i++) p[i] = z[i] + beta * p[i];
Amat->matvec(p, ap, Amat, proc_config);
if ((options[AZ_orth_kvecs]) && (kvec_sizes != NULL)) {
for (i = 0; i < current_kept; i++) {
alpha = -AZ_gdot(N, ap, saveme[i], proc_config)/ptap[i];
DAXPY_F77(&N, &alpha, saveme[i], &one, p, &one);
}
if (current_kept > 0) Amat->matvec(p, ap, Amat, proc_config);
}
p_ap_dot = AZ_gdot(N, p, ap, proc_config);
if (p_ap_dot < brkdown_tol) {
/* possible problem */
if (p_ap_dot < 0 || AZ_breakdown_f(N, p, ap, p_ap_dot, proc_config)) {
/* something wrong */
AZ_scale_true_residual(x, b, ap,
weight, &actual_residual, &true_scaled_r,
options, data_org, proc_config, Amat,
convergence_info);
AZ_terminate_status_print(AZ_breakdown, iter, status, rec_residual,
params, true_scaled_r, actual_residual,
options, proc_config);
return;
}
else brkdown_tol = 0.1 * p_ap_dot;
}
alpha = r_z_dot / p_ap_dot;
nalpha = -alpha;
/* x = x + alpha*p */
/* r = r - alpha*Ap */
/* z = M^-1 r */
DAXPY_F77(&N, &alpha, p, &one, x, &one);
if (iter <= options[AZ_keep_kvecs]) {
DCOPY_F77(&N, p, &one, saveme[iter-1], &one);
ptap[iter-1] = p_ap_dot ;
kvec_sizes[AZ_Nkept]++;
current_kept = kvec_sizes[AZ_Nkept];
}
/*
else {
i = (iter-1)%options[AZ_keep_kvecs];
DCOPY_F77(&N, p, &one, saveme[i], &one);
ptap[i] = p_ap_dot ;
}
*/
DAXPY_F77(&N, &nalpha, ap, &one, r, &one);
DCOPY_F77(&N, r, &one, z, &one);
if (precond_flag) precond->prec_function(z,options,proc_config,params,Amat,precond);
r_z_dot_old = r_z_dot;
/* compute a few global scalars: */
/* 1) ||r|| corresponding to options[AZ_conv] */
/* 2) scaled ||r|| corresponding to options[AZ_conv] */
/* 3) r_z_dot = <z, r> */
AZ_compute_global_scalars(Amat, x, b, r,
weight, &rec_residual, &scaled_r_norm, options,
data_org, proc_config, &r_avail, r, z, &r_z_dot,
convergence_info);
if (brkdown_will_occur) {
AZ_scale_true_residual( x, b, ap,
weight, &actual_residual, &true_scaled_r, options,
data_org, proc_config, Amat,convergence_info);
AZ_terminate_status_print(AZ_breakdown, iter, status, rec_residual,
params, true_scaled_r, actual_residual, options,
proc_config);
return;
}
beta = r_z_dot / r_z_dot_old;
if (fabs(r_z_dot) < brkdown_tol) {
/* possible problem */
if (AZ_breakdown_f(N, r, z, r_z_dot, proc_config))
brkdown_will_occur = AZ_TRUE;
else
brkdown_tol = 0.1 * fabs(r_z_dot);
}
if ( (iter%print_freq == 0) && (options[AZ_conv]!=AZTECOO_conv_test) && proc == 0 )
{
(void) AZ_printf_out("%siter: %4d residual = %e\n", prefix, iter,
scaled_r_norm);
AZ_flush_out();
}
/* convergence tests */
if (options[AZ_check_update_size] & convergence_info->converged)
convergence_info->converged = AZ_compare_update_vs_soln(N, -1.,alpha, p, x,
params[AZ_update_reduction],
options[AZ_output], proc_config, &first_time);
if (convergence_info->converged) {
AZ_scale_true_residual(x, b, ap,
weight, &actual_residual, &true_scaled_r, options,
data_org, proc_config, Amat, convergence_info);
/*
* Note: epsilon and params[AZ_tol] may not be equal due to a previous
* call to AZ_get_new_eps().
*/
if (!(convergence_info->converged) && options[AZ_conv]!=AZTECOO_conv_test) {
if (AZ_get_new_eps(&(convergence_info->epsilon), scaled_r_norm, true_scaled_r,
options, proc_config) == AZ_QUIT) {
/*
* Computed residual has converged, actual residual has not converged,
* AZ_get_new_eps() has decided that it is time to quit.
*/
AZ_terminate_status_print(AZ_loss, iter, status, rec_residual, params,
true_scaled_r, actual_residual, options,
proc_config);
return;
}
}
}
}
iter--;
if ( (iter%print_freq != 0) && (proc == 0) && (options[AZ_output] != AZ_none)
&& (options[AZ_output] != AZ_warnings) &&
(options[AZ_conv]!=AZTECOO_conv_test) )
{
(void) AZ_printf_out("%siter: %4d residual = %e\n", prefix, iter,
scaled_r_norm);
AZ_flush_out();
}
/* check if we exceeded maximum number of iterations */
if (convergence_info->converged) {
i = AZ_normal; scaled_r_norm = true_scaled_r; }
else if (convergence_info->isnan) i = AZ_breakdown;
else
i = AZ_maxits;
AZ_terminate_status_print(i, iter, status, rec_residual, params,
scaled_r_norm, actual_residual, options,
proc_config);
} /* AZ_pcg */
void dvbr_sparax_basic(int m, double *val, int *bindx, int *rpntr,
int *cpntr, int *bpntr, double *b, double *c,
int exchange_flag, int *data_org, int *proc_config)
/******************************************************************************
c = Ab:
Sparse (square) matrix-vector multiply, using the variable block row (VBR)
data structure (A = val).
Author: Scott A. Hutchinson, SNL, 1421
=======
Return code: void
============
Parameter list:
===============
m: Number of (block) rows in A.
val: Array containing the entries of the matrix. The matrix is
stored block-row-by-block-row. Each block entry is dense and
stored by columns (VBR).
bindx,
rpntr,
cpntr,
bpntr: Arrays used for DMSR and DVBR sparse matrix storage (see
Aztec User's Guide).
b: Right hand side of linear system.
c: On output contains the solution to the linear system.
exchange_flag: Flag which controls call to AZ_exchange_bdry() (ignored in
serial implementation).
data_org: Array containing information on the distribution of the
matrix to this processor as well as communication parameters
(see Aztec User's Guide).
******************************************************************************/
{
/* local variables */
register double *x;
register double *c_pntr;
register int iblk_row, j, jblk, iblk_size;
int m1, ib1, n1;
int bpoff, rpoff;
int ione = 1;
int irpntr, irpntr_next;
int ibpntr, ibpntr_next = 0;
double one = 1.0;
double *val_pntr;
char *N = "N";
/**************************** execution begins *****************************/
/* exchange boundary info */
if (exchange_flag) AZ_exchange_bdry(b, data_org, proc_config);
/* offset of the first block */
bpoff = *bpntr;
rpoff = *rpntr;
/* zero the result vector */
for (j = 0; j < rpntr[m] - rpoff; c[j++] = 0.0);
val_pntr = val;
irpntr_next = *rpntr++;
bpntr++;
c -= rpoff;
/* loop over block rows */
for (iblk_row = 0; iblk_row < m; iblk_row++) {
irpntr = irpntr_next;
irpntr_next = *rpntr++;
ibpntr = ibpntr_next;
ibpntr_next = *bpntr++ - bpoff;
/* set result pointer */
c_pntr = c + irpntr;
/* number of rows in the current row block */
m1 = irpntr_next - irpntr;
/* loop over each block in the current row block */
for (j = ibpntr; j < ibpntr_next; j++) {
jblk = *(bindx+j);
/* the starting point column index of the current block */
ib1 = *(cpntr+jblk);
/* number of columns in the current block */
n1 = cpntr[jblk + 1] - ib1;
iblk_size = m1*n1;
/****************** Dense matrix-vector multiplication *****************/
/*
* Get base addresses
*/
x = b + ib1;
/*
* Special case the m1 = n1 = 1 case
*/
if (iblk_size == 1)
*c_pntr += *val_pntr * *x;
else if (m1 == n1) {
/*
* Inline small amounts of work
*/
switch (m1) {
case 2:
c_pntr[0] += val_pntr[0]*x[0] + val_pntr[2]*x[1];
c_pntr[1] += val_pntr[1]*x[0] + val_pntr[3]*x[1];
break;
case 3:
c_pntr[0] += val_pntr[0]*x[0] + val_pntr[3]*x[1] + val_pntr[6]*x[2];
c_pntr[1] += val_pntr[1]*x[0] + val_pntr[4]*x[1] + val_pntr[7]*x[2];
c_pntr[2] += val_pntr[2]*x[0] + val_pntr[5]*x[1] + val_pntr[8]*x[2];
break;
case 4:
c_pntr[0] += val_pntr[0]*x[0] + val_pntr[4]*x[1] + val_pntr[8] *x[2]
+ val_pntr[12]*x[3];
c_pntr[1] += val_pntr[1]*x[0] + val_pntr[5]*x[1] + val_pntr[9] *x[2]
+ val_pntr[13]*x[3];
c_pntr[2] += val_pntr[2]*x[0] + val_pntr[6]*x[1] + val_pntr[10]*x[2]
+ val_pntr[14]*x[3];
c_pntr[3] += val_pntr[3]*x[0] + val_pntr[7]*x[1] + val_pntr[11]*x[2]
+ val_pntr[15]*x[3];
break;
case 5:
c_pntr[0] += val_pntr[0]*x[0] + val_pntr[5]*x[1] + val_pntr[10]*x[2]
+ val_pntr[15]*x[3] + val_pntr[20]*x[4];
c_pntr[1] += val_pntr[1]*x[0] + val_pntr[6]*x[1] + val_pntr[11]*x[2]
+ val_pntr[16]*x[3] + val_pntr[21]*x[4];
c_pntr[2] += val_pntr[2]*x[0] + val_pntr[7]*x[1] + val_pntr[12]*x[2]
+ val_pntr[17]*x[3] + val_pntr[22]*x[4];
c_pntr[3] += val_pntr[3]*x[0] + val_pntr[8]*x[1] + val_pntr[13]*x[2]
+ val_pntr[18]*x[3] + val_pntr[23]*x[4];
c_pntr[4] += val_pntr[4]*x[0] + val_pntr[9]*x[1] + val_pntr[14]*x[2]
+ val_pntr[19]*x[3] + val_pntr[24]*x[4];
break;
case 6:
c_pntr[0] += val_pntr[0]*x[0] + val_pntr[6] *x[1] + val_pntr[12]*x[2]
+ val_pntr[18]*x[3] + val_pntr[24]*x[4] + val_pntr[30]*x[5];
c_pntr[1] += val_pntr[1]*x[0] + val_pntr[7] *x[1] + val_pntr[13]*x[2]
+ val_pntr[19]*x[3] + val_pntr[25]*x[4] + val_pntr[31]*x[5];
c_pntr[2] += val_pntr[2]*x[0] + val_pntr[8] *x[1] + val_pntr[14]*x[2]
+ val_pntr[20]*x[3] + val_pntr[26]*x[4] + val_pntr[32]*x[5];
c_pntr[3] += val_pntr[3]*x[0] + val_pntr[9] *x[1] + val_pntr[15]*x[2]
+ val_pntr[21]*x[3] + val_pntr[27]*x[4] + val_pntr[33]*x[5];
c_pntr[4] += val_pntr[4]*x[0] + val_pntr[10]*x[1] + val_pntr[16]*x[2]
+ val_pntr[22]*x[3] + val_pntr[28]*x[4] + val_pntr[34]*x[5];
c_pntr[5] += val_pntr[5]*x[0] + val_pntr[11]*x[1] + val_pntr[17]*x[2]
+ val_pntr[23]*x[3] + val_pntr[29]*x[4] + val_pntr[35]*x[5];
break;
default:
/*
* For most computers, a really well-optimized assembly-coded level 2
* blas for small blocks sizes doesn't exist. It's better to
* optimize your own version, and take out all the overhead from the
* regular dgemv call. For large block sizes, it's also a win to
* check for a column of zeroes; this is what dgemv_ does. The
* routine dgemvnsqr_() is a fortran routine that contains optimized
* code for the hp, created from the optimizing preprocessor. Every
* workstation will probably have an entry here eventually, since
* this is a key optimization location.
*/
/* #ifdef AZ_PA_RISC */
/* dgemvnsqr_(&m1, val_pntr, x, c_pntr); */
/* #else */
if (m1 < 10)
AZ_dgemv2(m1, n1, val_pntr, x, c_pntr);
else
DGEMV_F77(CHAR_MACRO(N[0]), &m1, &n1, &one, val_pntr, &m1, x, &ione, &one, c_pntr,
&ione);
/* #endif */
}
}
/* nonsquare cases */
else {
if (m1 < 10)
AZ_dgemv2(m1, n1, val_pntr, x, c_pntr);
else
DGEMV_F77(CHAR_MACRO(N[0]), &m1, &n1, &one, val_pntr, &m1, x, &ione, &one, c_pntr,
&ione);
}
val_pntr += iblk_size;
}
}
} /* dvbr_sparax_basic */
