int inner_solve_dprimme(double *x, double *r, double *rnorm,
double *evecs, double *evecsHat, double *UDU, int *ipivot,
double *xKinvx, double *Lprojector, double *RprojectorQ,
double *RprojectorX, int sizeLprojector, int sizeRprojectorQ,
int sizeRprojectorX, double *sol, double eval, double shift,
double eresTol, double aNormEstimate, double machEps, double *rwork,
int rworkSize, primme_params *primme) {
int i; /* loop variable */
int workSpaceSize; /* Size of local work array. */
int numIts; /* Number of inner iterations */
int ret; /* Return value used for error checking. */
int maxIterations; /* The maximum # iterations allowed. Depends on primme */
double *workSpace; /* Workspace needed by UDU routine */
/* QMR parameters */
double *g, *d, *delta, *w, *ptmp;
double alpha_prev, beta, rho_prev, rho;
double Theta_prev, Theta, c, sigma_prev, tau_init, tau_prev, tau;
double ztmp;
/* Parameters used to dynamically update eigenpair */
double Beta, Delta, Psi, Beta_prev, Delta_prev, Psi_prev, eta;
double dot_sol, eval_updated, eval_prev, eres2_updated, eres_updated, R;
double Gamma_prev, Phi_prev;
double Gamma, Phi;
double gamma;
/* The convergence criteria of the inner linear system must satisfy: */
/* || current residual || <= relativeTolerance * || initial residual || */
/* + absoluteTol */
double relativeTolerance;
double absoluteTolerance;
double LTolerance, ETolerance;
/* Some constants */
double tpone = +1.0e+00, tzero = +0.0e+00;
/* -------------------------------------------*/
/* Subdivide the workspace into needed arrays */
/* -------------------------------------------*/
g = rwork;
d = g + primme->nLocal;
delta = d + primme->nLocal;
w = delta + primme->nLocal;
workSpace = w + primme->nLocal; /* This needs at least 2*numOrth+NumEvals) */
workSpaceSize = rworkSize - (workSpace - rwork);
/* -----------------------------------------*/
/* Set up convergence criteria by Tolerance */
/* -----------------------------------------*/
if (primme->aNorm <= 0.0L) {
absoluteTolerance = aNormEstimate*machEps;
eresTol = eresTol*aNormEstimate;
}
else {
absoluteTolerance = primme->aNorm*machEps;
}
tau_prev = tau_init = *rnorm; /* Assumes zero initial guess */
LTolerance = eresTol;
/* Andreas: note that eigenresidual tol may not be achievable, because we */
/* iterate on P(A-s)P not (A-s). But tau reflects linSys on P(A-s)P. */
if (primme->correctionParams.convTest == primme_adaptive) {
ETolerance = max(eresTol/1.8L, absoluteTolerance);
LTolerance = ETolerance;
}
else if (primme->correctionParams.convTest == primme_adaptive_ETolerance) {
LTolerance = max(eresTol/1.8L, absoluteTolerance);
ETolerance = max(tau_init*0.1L, LTolerance);
}
else if (primme->correctionParams.convTest == primme_decreasing_LTolerance) {
relativeTolerance = pow(primme->correctionParams.relTolBase,
(double)-primme->stats.numOuterIterations);
LTolerance = relativeTolerance * tau_init
+ absoluteTolerance + eresTol;
/*printf(" RL %e INI %e abso %e LToler %e aNormEstimate %e \n", */
/*relativeTolerance, tau_init, absoluteTolerance,LTolerance,aNormEstimate);*/
}
/* --------------------------------------------------------*/
/* Set up convergence criteria by max number of iterations */
/* --------------------------------------------------------*/
/* compute first total number of remaining matvecs */
maxIterations = primme->maxMatvecs - primme->stats.numMatvecs;
/* Perform primme.maxInnerIterations, but do not exceed total remaining */
if (primme->correctionParams.maxInnerIterations > 0) {
maxIterations = min(primme->correctionParams.maxInnerIterations,
maxIterations);
}
/* --------------------------------------------------------*/
/* Rest of initializations */
/* --------------------------------------------------------*/
/* Assume zero initial guess */
Num_dcopy_dprimme(primme->nLocal, r, 1, g, 1);
ret = apply_projected_preconditioner(g, evecs, RprojectorQ,
x, RprojectorX, sizeRprojectorQ, sizeRprojectorX,
xKinvx, UDU, ipivot, d, workSpace, primme);
if (ret != 0) {
primme_PushErrorMessage(Primme_inner_solve,
Primme_apply_projected_preconditioner, ret, __FILE__, __LINE__,
primme);
return APPLYPROJECTEDPRECONDITIONER_FAILURE;
}
Theta_prev = 0.0L;
eval_prev = eval;
rho_prev = dist_dot(g, 1, d, 1, primme);
/* Initialize recurrences used to dynamically update the eigenpair */
Beta_prev = Delta_prev = Psi_prev = 0.0L;
Gamma_prev = Phi_prev = 0.0L;
/* other initializations */
for (i = 0; i < primme->nLocal; i++) {
delta[i] = tzero;
sol[i] = tzero;
}
numIts = 0;
/*----------------------------------------------------------------------*/
/*------------------------ Begin Inner Loop ----------------------------*/
/*----------------------------------------------------------------------*/
while (numIts < maxIterations) {
apply_projected_matrix(d, shift, Lprojector, sizeLprojector,
w, workSpace, primme);
sigma_prev = dist_dot(d, 1, w, 1, primme);
if (sigma_prev == 0.0L) {
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile,"Exiting because SIGMA %e\n",sigma_prev);
}
break;
}
alpha_prev = rho_prev/sigma_prev;
if (fabs(alpha_prev) < machEps || fabs(alpha_prev) > 1.0L/machEps){
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile,"Exiting because ALPHA %e\n",alpha_prev);
}
break;
}
Num_axpy_dprimme(primme->nLocal, -alpha_prev, w, 1, g, 1);
Theta = dist_dot(g, 1, g, 1, primme);
Theta = sqrt(Theta);
Theta = Theta/tau_prev;
c = 1.0L/sqrt(1+Theta*Theta);
tau = tau_prev*Theta*c;
gamma = c*c*Theta_prev*Theta_prev;
eta = alpha_prev*c*c;
for (i = 0; i < primme->nLocal; i++) {
delta[i] = gamma*delta[i] + eta*d[i];
sol[i] = delta[i]+sol[i];
}
numIts++;
if (fabs(rho_prev) == 0.0L ) {
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile,"Exiting because abs(rho) %e\n",
fabs(rho_prev));
}
break;
}
if (tau < LTolerance) {
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile, " tau < LTol %e %e\n",tau, LTolerance);
}
break;
}
else if (primme->correctionParams.convTest == primme_adaptive_ETolerance
|| primme->correctionParams.convTest == primme_adaptive) {
/* --------------------------------------------------------*/
/* Adaptive stopping based on dynamic monitoring of eResid */
/* --------------------------------------------------------*/
/* Update the Ritz value and eigenresidual using the */
/* following recurrences. */
Delta = gamma*Delta_prev + eta*rho_prev;
Beta = Beta_prev - Delta;
Phi = gamma*gamma*Phi_prev + eta*eta*sigma_prev;
Psi = gamma*Psi_prev + gamma*Phi_prev;
Gamma = Gamma_prev + 2.0L*Psi + Phi;
/* Perform the update: update the eigenvalue and the square of the */
/* residual norm. */
dot_sol = dist_dot(sol, 1, sol, 1, primme);
eval_updated = shift + (eval - shift + 2*Beta + Gamma)/(1 + dot_sol);
eres2_updated = (tau*tau)/(1 + dot_sol) +
((eval - shift + Beta)*(eval - shift + Beta))/(1 + dot_sol) -
(eval_updated - shift)*(eval_updated - shift);
/* If numerical problems, let eres about the same as tau */
if (eres2_updated < 0){
eres_updated = sqrt( (tau*tau)/(1 + dot_sol) );
}
else
eres_updated = sqrt(eres2_updated);
/* --------------------------------------------------------*/
/* Stopping criteria */
/* --------------------------------------------------------*/
R = max(0.9878, sqrt(tau/tau_prev))*sqrt(1+dot_sol);
if ( tau <= R*eres_updated || eres_updated <= tau*R ) {
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile, " tau < R eres \n");
}
break;
}
if (primme->target == primme_smallest && eval_updated > eval_prev) {
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile, "eval_updated > eval_prev\n");
}
break;
}
else if (primme->target == primme_largest && eval_updated < eval_prev){
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile, "eval_updated < eval_prev\n");
}
break;
}
if (eres_updated < ETolerance) { /* tau < LTol has been checked */
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile, "eres < eresTol %e \n",eres_updated);
}
break;
}
eval_prev = eval_updated;
if (primme->printLevel >= 4 && primme->procID == 0) {
fprintf(primme->outputFile,
"INN MV %d Sec %e Eval %e Lin|r| %.3e EV|r| %.3e\n", primme->stats.
numMatvecs, primme_wTimer(0), eval_updated, tau, eres_updated);
fflush(primme->outputFile);
}
/* --------------------------------------------------------*/
} /* End of if adaptive JDQMR section */
/* --------------------------------------------------------*/
else if (primme->printLevel >= 4 && primme->procID == 0) {
/* Report for non adaptive inner iterations */
fprintf(primme->outputFile,
"INN MV %d Sec %e Lin|r| %e\n", primme->stats.numMatvecs,
primme_wTimer(0),tau);
fflush(primme->outputFile);
}
if (numIts < maxIterations) {
ret = apply_projected_preconditioner(g, evecs, RprojectorQ,
x, RprojectorX, sizeRprojectorQ, sizeRprojectorX,
xKinvx, UDU, ipivot, w, workSpace, primme);
if (ret != 0) {
primme_PushErrorMessage(Primme_inner_solve,
Primme_apply_projected_preconditioner, ret, __FILE__, __LINE__,
primme);
ret = APPLYPROJECTEDPRECONDITIONER_FAILURE;
break;
}
rho = dist_dot(g, 1, w, 1, primme);
beta = rho/rho_prev;
Num_axpy_dprimme(primme->nLocal, beta, d, 1, w, 1);
/* Alternate between w and d buffers in successive iterations
* This saves a memory copy. */
ptmp = d; d = w; w = ptmp;
rho_prev = rho;
tau_prev = tau;
Theta_prev = Theta;
Delta_prev = Delta;
Beta_prev = Beta;
Phi_prev = Phi;
Psi_prev = Psi;
Gamma_prev = Gamma;
}
/* --------------------------------------------------------*/
} /* End of QMR main while loop */
/* --------------------------------------------------------*/
*rnorm = eres_updated;
return 0;
}
static int apply_skew_projector(double *Q, double *Qhat, double *UDU,
int *ipivot, int numCols, double *v, double *rwork,
primme_params *primme) {
int count;
double tpone = +1.0e+00, tzero = +0.0e+00, tmone = -1.0e+00;
if (numCols > 0) { /* there is a projector to be applied */
int ret;
double *overlaps; /* overlaps of v with columns of Q */
double *workSpace; /* Used for computing local overlaps */
overlaps = rwork;
workSpace = overlaps + numCols;
/* --------------------------------------------------------*/
/* Treat the one vector case with BLAS 1 calls */
/* --------------------------------------------------------*/
if (numCols == 1) {
/* Compute workspace = Q'*v */
overlaps[0] = dist_dot(Q, 1, v, 1, primme);
/* Backsolve only if there is a skew projector */
if (UDU != NULL) {
if (UDU[0] == 0.0L) {
return UDUSOLVE_FAILURE;
}
overlaps[0] = overlaps[0]/UDU[0];
}
/* Compute v=v-Qhat*overlaps */
Num_axpy_dprimme(primme->nLocal, -overlaps[0], Qhat, 1, v, 1);
}
else {
/* ------------------------------------------------------*/
/* More than one vectors. Use BLAS 2. */
/* ------------------------------------------------------*/
/* Compute workspace = Q'*v */
Num_gemv_dprimme("C", primme->nLocal, numCols, tpone, Q,
primme->nLocal, v, 1, tzero, workSpace, 1);
/* Global sum: overlaps = Q'*v */
count = numCols;
(*primme->globalSumDouble)(workSpace, overlaps, &count, primme);
/* --------------------------------------------*/
/* Backsolve only if there is a skew projector */
/* --------------------------------------------*/
if (UDU != NULL) {
/* Solve (Q'Qhat)^{-1}*workSpace = overlaps = Q'*v for alpha by */
/* backsolving with the UDU decomposition. */
ret = UDUSolve_dprimme(UDU, ipivot, numCols, overlaps, workSpace);
if (ret != 0) {
primme_PushErrorMessage(Primme_apply_skew_projector,
Primme_udusolve, ret, __FILE__, __LINE__, primme);
return UDUSOLVE_FAILURE;
}
/* Compute v=v-Qhat*workspace */
Num_gemv_dprimme("N", primme->nLocal, numCols, tmone, Qhat,
primme->nLocal, workSpace, 1, tpone, v, 1);
}
else {
/* Compute v=v-Qhat*overlaps */
Num_gemv_dprimme("N", primme->nLocal, numCols, tmone, Qhat,
primme->nLocal, overlaps, 1, tpone, v, 1);
} /* UDU==null */
} /* numCols != 1 */
} /* numCols > 0 */
return 0;
}
static int apply_skew_projector(Complex_Z *Q, Complex_Z *Qhat, Complex_Z *UDU,
int *ipivot, int numCols, Complex_Z *v, Complex_Z *rwork,
primme_params *primme) {
int count;
Complex_Z ztmp;
Complex_Z tpone = {+1.0e+00,+0.0e00}, tzero = {+0.0e+00,+0.0e00}, tmone = {-1.0e+00,+0.0e00};
if (numCols > 0) { /* there is a projector to be applied */
int ret;
Complex_Z *overlaps; /* overlaps of v with columns of Q */
Complex_Z *workSpace; /* Used for computing local overlaps */
overlaps = rwork;
workSpace = overlaps + numCols;
/* --------------------------------------------------------*/
/* Treat the one vector case with BLAS 1 calls */
/* --------------------------------------------------------*/
if (numCols == 1) {
/* Compute workspace = Q'*v */
overlaps[0] = dist_dot(Q, 1, v, 1, primme);
/* Backsolve only if there is a skew projector */
if (UDU != NULL) {
if ( z_eq_primme(UDU[0], tzero) ) {
return UDUSOLVE_FAILURE;
}
z_div_primme(&overlaps[0], &overlaps[0], &UDU[0]);
}
/* Compute v=v-Qhat*overlaps */
ztmp.r = - overlaps[0].r;
ztmp.i = - overlaps[0].i;
Num_axpy_zprimme(primme->nLocal, ztmp, Qhat, 1, v, 1);
}
else {
/* ------------------------------------------------------*/
/* More than one vectors. Use BLAS 2. */
/* ------------------------------------------------------*/
/* Compute workspace = Q'*v */
Num_gemv_zprimme("C", primme->nLocal, numCols, tpone, Q,
primme->nLocal, v, 1, tzero, workSpace, 1);
/* Global sum: overlaps = Q'*v */
// In Complex, the size of the array to globalSum is twice as large
count = 2*numCols;
(*primme->globalSumDouble)(workSpace, overlaps, &count, primme);
/* --------------------------------------------*/
/* Backsolve only if there is a skew projector */
/* --------------------------------------------*/
if (UDU != NULL) {
/* Solve (Q'Qhat)^{-1}*workSpace = overlaps = Q'*v for alpha by */
/* backsolving with the UDU decomposition. */
ret = UDUSolve_zprimme(UDU, ipivot, numCols, overlaps, workSpace);
if (ret != 0) {
primme_PushErrorMessage(Primme_apply_skew_projector,
Primme_udusolve, ret, __FILE__, __LINE__, primme);
return UDUSOLVE_FAILURE;
}
/* Compute v=v-Qhat*workspace */
Num_gemv_zprimme("N", primme->nLocal, numCols, tmone, Qhat,
primme->nLocal, workSpace, 1, tpone, v, 1);
}
else {
/* Compute v=v-Qhat*overlaps */
Num_gemv_zprimme("N", primme->nLocal, numCols, tmone, Qhat,
primme->nLocal, overlaps, 1, tpone, v, 1);
} // UDU==null
} // numCols != 1
} // numCols > 0
return 0;
}