int Zconjugate(Complex_Z a, Complex_Z b, double epsi)
{
double ia = a.i;
double ib = b.i;
double ra = a.r;
double rb = b.r;
int flag = 0;
Complex_Z sum;
double sum_abs;
sum.r = a.r+b.r; sum.i=a.i+b.i;
sum_abs = z_abs_primme(sum);
if ( ia*ib < 0 )
if ( (fabs(ia+ib)/sum_abs) < epsi)
if ( (fabs(ra-rb)/sum_abs) < epsi)
flag = 1;
return flag;
}
static void Olsen_preconditioner_block(Complex_Z *r, Complex_Z *x,
int blockSize, Complex_Z *rwork, primme_params *primme) {
int blockIndex, count;
Complex_Z alpha;
Complex_Z *Kinvx, *xKinvx, *xKinvr, *xKinvx_local, *xKinvr_local;
Complex_Z ztmp;
Complex_Z tzero = {+0.0e+00,+0.0e00};
//------------------------------------------------------------------
// Subdivide workspace
//------------------------------------------------------------------
Kinvx = rwork;
xKinvx_local = Kinvx + primme->nLocal*blockSize;
xKinvr_local = xKinvx_local + blockSize;
xKinvx = xKinvr_local + blockSize;
xKinvr = xKinvx + blockSize;
//------------------------------------------------------------------
// Compute K^{-1}x for block x. Kinvx memory requirement (blockSize*nLocal)
//------------------------------------------------------------------
apply_preconditioner_block(x, Kinvx, blockSize, primme );
//------------------------------------------------------------------
// Compute local x^TK^{-1}x and x^TK^{-1}r = (K^{-1}x)^Tr for each vector
//------------------------------------------------------------------
for (blockIndex = 0; blockIndex < blockSize; blockIndex++) {
xKinvx_local[blockIndex] =
Num_dot_zprimme(primme->nLocal, &x[primme->nLocal*blockIndex],1,
&Kinvx[primme->nLocal*blockIndex],1);
xKinvr_local[blockIndex] =
Num_dot_zprimme(primme->nLocal, &Kinvx[primme->nLocal*blockIndex],1,
&r[primme->nLocal*blockIndex],1);
}
count = 4*blockSize;
(*primme->globalSumDouble)(xKinvx_local, xKinvx, &count, primme);
//------------------------------------------------------------------
// Compute K^{-1}r
//------------------------------------------------------------------
apply_preconditioner_block(r, x, blockSize, primme );
//------------------------------------------------------------------
// Compute K^(-1)r - ( xKinvr/xKinvx ) K^(-1)r for each vector
//------------------------------------------------------------------
for (blockIndex = 0; blockIndex < blockSize; blockIndex++) {
if (z_abs_primme(xKinvx[blockIndex]) > 0.0L)
{
ztmp.r = -xKinvr[blockIndex].r;
ztmp.i = -xKinvr[blockIndex].i;
z_div_primme(&alpha, &ztmp, &xKinvx[blockIndex]);
}
else
alpha = tzero;
Num_axpy_zprimme(primme->nLocal,alpha,&Kinvx[primme->nLocal*blockIndex],
1, &x[primme->nLocal*blockIndex],1);
} //for
} // of Olsen_preconditiner_block
int inner_solve_zprimme(Complex_Z *x, Complex_Z *r, double *rnorm,
Complex_Z *evecs, Complex_Z *evecsHat, Complex_Z *UDU, int *ipivot,
Complex_Z *xKinvx, Complex_Z *Lprojector, Complex_Z *RprojectorQ,
Complex_Z *RprojectorX, int sizeLprojector, int sizeRprojectorQ,
int sizeRprojectorX, Complex_Z *sol, double eval, double shift,
double eresTol, double aNormEstimate, double machEps, Complex_Z *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 */
Complex_Z *workSpace; /* Workspace needed by UDU routine */
/* QMR parameters */
Complex_Z *g, *d, *delta, *w;
Complex_Z alpha_prev, beta, rho_prev, rho;
Complex_Z ztmp;
double Theta_prev, Theta, c, sigma_prev, tau_init, tau_prev, tau;
/* Parameters used to dynamically update eigenpair */
Complex_Z Beta, Delta, Psi, Beta_prev, Delta_prev, Psi_prev;
Complex_Z 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 */
Complex_Z tpone = {+1.0e+00,+0.0e00}, tzero = {+0.0e+00,+0.0e00};
/* -------------------------------------------*/
/* 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_zcopy_zprimme(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 = tzero;
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);
ztmp = dist_dot(d, 1, w, 1, primme);
sigma_prev = ztmp.r;
if (sigma_prev == 0.0L) {
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile,"Exiting because SIGMA %e\n",sigma_prev);
}
break;
}
zd_mult_primme(alpha_prev, rho_prev, 1.0L/sigma_prev);
if (z_abs_primme(alpha_prev) < machEps || z_abs_primme(alpha_prev) > 1.0L/machEps){
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile,"Exiting because ALPHA %e\n",alpha_prev);
}
break;
}
ztmp.r = -alpha_prev.r;
ztmp.i = -alpha_prev.i;
Num_axpy_zprimme(primme->nLocal, ztmp, w, 1, g, 1);
ztmp = dist_dot(g, 1, g, 1, primme);
Theta = ztmp.r;
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;
{ztmp.r = gamma; ztmp.i = 0.0L;}
zd_mult_primme(eta, alpha_prev, c*c);
Num_scal_zprimme(primme->nLocal, ztmp, delta, 1);
Num_axpy_zprimme(primme->nLocal, eta, d, 1, delta, 1);
Num_axpy_zprimme(primme->nLocal, tpone, delta, 1, sol, 1);
numIts++;
if (z_abs_primme(rho_prev) == 0.0L ) {
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile,"Exiting because abs(rho) %e\n",
z_abs_primme(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. */
zd_mult_primme(Delta, Delta_prev, gamma);
zz_mult_primme(ztmp, eta, rho_prev);
z_add_primme(Delta, Delta, ztmp);
z_sub_primme(Beta, Beta_prev, Delta);
Phi = gamma*gamma*Phi_prev + z_abs_primme(eta)*z_abs_primme(eta)*sigma_prev;
zd_mult_primme(Psi, Psi_prev, gamma);
{ztmp.r = gamma*Phi_prev; ztmp.i = 0.0L;}
z_add_primme(Psi, Psi, ztmp);
Gamma = Gamma_prev + 2.0L*Psi.r + Phi;
/* Perform the update: update the eigenvalue and the square of the */
/* residual norm. */
ztmp = dist_dot(sol, 1, sol, 1, primme);
dot_sol = ztmp.r;
eval_updated = shift + (eval - shift + 2*Beta.r + Gamma)/(1 + dot_sol);
eres2_updated = (tau*tau)/(1 + dot_sol)
+ ((eval - shift)*(eval - shift) + z_abs_primme(Beta)*z_abs_primme(Beta)
+ 2.0L*(eval - shift)*Beta.r)/(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);
z_div_primme(&beta, &rho, &rho_prev);
Num_scal_zprimme(primme->nLocal, beta, d, 1);
Num_axpy_zprimme(primme->nLocal, tpone, w, 1, d, 1);
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;
}