int UDUSolve_dprimme(double *UDU, int *ipivot, int dim, double *rhs,
double *sol) {
int info;
if (dim == 1) {
*sol = *rhs/(*UDU);
info = 0;
}
else {
Num_dcopy_dprimme(dim, rhs, 1, sol, 1);
Num_dsytrs_dprimme("U", dim, 1, UDU, dim, ipivot, sol, dim, &info);
}
return info;
}
static int apply_projected_preconditioner(double *v, double *Q,
double *RprojectorQ, double *x, double *RprojectorX,
int sizeRprojectorQ, int sizeRprojectorX, double *xKinvx,
double *UDU, int *ipivot, double *result, double *rwork,
primme_params *primme) {
int ONE = 1;
int ret;
if (primme->correctionParams.precondition) {
/* Place K^{-1}v in result */
(*primme->applyPreconditioner)(v, result, &ONE, primme);
primme->stats.numPreconds += 1;
}
else {
Num_dcopy_dprimme(primme->nLocal, v, 1, result, 1);
}
ret = apply_skew_projector(Q, RprojectorQ, UDU, ipivot, sizeRprojectorQ,
result, rwork, primme);
if (ret != 0) {
primme_PushErrorMessage(Primme_apply_projected_preconditioner,
Primme_apply_skew_projector, ret, __FILE__, __LINE__, primme);
return APPLYSKEWPROJECTOR_FAILURE;
}
apply_skew_projector(x, RprojectorX, xKinvx, ipivot, sizeRprojectorX,
result, rwork, primme);
if (ret != 0) {
primme_PushErrorMessage(Primme_apply_projected_preconditioner,
Primme_apply_skew_projector, ret, __FILE__, __LINE__, primme);
return APPLYSKEWPROJECTOR_FAILURE;
}
return 0;
}
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;
}
int lock_vectors_dprimme(double tol, double *aNormEstimate, double *maxConvTol,
int *basisSize, int *numLocked, int *numGuesses, int *nextGuess,
double *V, double *W, double *H, double *evecsHat, double *M,
double *UDU, int *ipivot, double *hVals, double *hVecs,
double *evecs, double *evals, int *perm, double machEps,
double *resNorms, int *numPrevRitzVals, double *prevRitzVals,
int *flag, double *rwork, int rworkSize, int *iwork,
int *LockingProblem, primme_params *primme) {
int i; /* Loop counter */
int numCandidates; /* Number of targeted Ritz vectors converged before */
/* restart. */
int newStart; /* Index in evecs where the locked vectors were added */
int numNewVectors; /* Number of vectors added to the basis to replace */
/* locked vectors. */
int candidate; /* Index of Ritz vector to be checked for convergence */
int numDeflated; /* The number of vectors actually locked */
int numReplaced; /* The number of locked vectors that were replaced by */
/* initial guesses. */
int numRecentlyLocked; /* Number of vectors locked. */
int evecsSize; /* The number of orthogonalization constraints plus */
/* the number of locked vectors. */
int ret; /* Used to store return values. */
int workinW; /* Flag whether an active W vector is used as tempwork*/
int entireSpace = (*basisSize+*numLocked >= primme->n); /* bool if entire*/
/* space is built, so current ritzvecs are accurate. */
double *norms, *tnorms; /* Array of residual norms, and temp array */
double attainableTol; /* Used to verify a practical convergence problem*/
double *residual; /* Stores residual vector */
double ztmp; /* temp variable */
/* ----------------------------------------*/
/* Assign temporary work space for residual*/
/* ----------------------------------------*/
if (*basisSize < primme->maxBasisSize) {
/* compute residuals in the next open slot of W */
residual = &W[*basisSize*primme->nLocal];
workinW = 0;
}
else {
/* This basiSize==maxBasisSize, immediately after restart, can only occur
* if the basisSize + numLocked = n (at which case we lock everything)
* OR if (numConverged + restartSize + numPrevRetain > basisSize), ie.
* too many converged. Since we do not know which evec will be locked
* we use the W[LAST] as temporary space, but only after W[LAST] has
* been used to compute residual(LAST) -the while loop starts from LAST.
* After all lockings, if the LAST evec was not locked, we must
* recompute W[LAST]=Av. This matvec event is extremely infrequent */
residual = &W[(*basisSize-1)*primme->nLocal];
workinW = 1;
}
/* -------------------------------------*/
/* Set the tolerance, and attainableTol */
/* -------------------------------------*/
if (primme->aNorm <= 0.0L) {
tol = tol * (*aNormEstimate);
}
attainableTol=max(tol,sqrt(primme->numOrthoConst+*numLocked)*(*maxConvTol));
/* -------------------------------------------------------- */
/* Determine how many Ritz vectors converged before restart */
/* -------------------------------------------------------- */
i = *basisSize - 1;
while ((flag[i] == LOCK_IT ||flag[i] == UNCONDITIONAL_LOCK_IT) && i >= 0) {
i--;
}
numCandidates = *basisSize - i - 1;
if (numCandidates == 0) {
return 0;
}
/* --------------------------------- */
/* Compute residuals and their norms */
/* --------------------------------- */
tnorms = (double *) rwork;
norms = tnorms + numCandidates;
for (i = *basisSize-1, candidate = numCandidates-1;
i >= *basisSize-numCandidates; i--, candidate--) {
Num_dcopy_dprimme(primme->nLocal, &W[primme->nLocal*i], 1, residual, 1);
ztmp = -hVals[i];
Num_axpy_dprimme(primme->nLocal, ztmp, &V[primme->nLocal*i],1,residual,1);
tnorms[candidate] = Num_dot_dprimme(primme->nLocal,residual,1,residual,1);
}
/* Global sum the dot products */
(*primme->globalSumDouble)(tnorms, norms, &numCandidates, primme);
numRecentlyLocked = 0;
/* ------------------------------------------------------------------- */
/* Check the convergence of each residual norm. If the Ritz vector is */
/* converged, then lock it. */
/* ------------------------------------------------------------------- */
for (i = *basisSize - numCandidates, candidate = 0; i < *basisSize; i++,
candidate++) {
norms[candidate] = sqrt(norms[candidate]);
/* If the vector has become (regularly or practically) unconverged, */
/* then flag it, else lock it and replace it with an initial guess, */
/* if one is available. Exception: If the entire space is spanned, */
/* we can't do better, so lock it. */
if ((flag[i]!=UNCONDITIONAL_LOCK_IT && norms[candidate] >= tol
&& !entireSpace ) ||
(flag[i]==UNCONDITIONAL_LOCK_IT && norms[candidate] >= attainableTol
&& !entireSpace )) {
flag[i] = UNCONVERGED;
}
else {
/* If an unconditional lock has become converged, show it and */
/* record the max converged tolerance accordingly */
if (norms[candidate]<tol) {
flag[i]=LOCK_IT;
*maxConvTol = max(*maxConvTol, tol);
}
else {
*maxConvTol = max(*maxConvTol, norms[candidate]);
*LockingProblem = 1;
}
if (primme->printLevel >= 2 && primme->procID == 0) {
fprintf(primme->outputFile,
"Lock epair[ %d ]= %e norm %.4e Mvecs %d Time %.4e Flag %d\n",
*numLocked+1, hVals[i], norms[candidate],
primme->stats.numMatvecs,primme_wTimer(0),flag[i]);
fflush(primme->outputFile);
}
/* Copy the converged Ritz vector to the evecs array and */
/* insert the converged Ritz value in sorted order within */
/* the evals array. */
Num_dcopy_dprimme(primme->nLocal, &V[primme->nLocal*i], 1,
&evecs[primme->nLocal*(primme->numOrthoConst + *numLocked)], 1);
insertionSort(hVals[i], evals, norms[candidate], resNorms, perm,
*numLocked, primme);
/* If there are any initial guesses remaining, then copy it */
/* into the basis, else flag the vector as locked so it may */
/* be discarded later. */
if (*numGuesses > 0) {
Num_dcopy_dprimme(primme->nLocal,
&evecs[primme->nLocal*(*nextGuess)], 1, &V[primme->nLocal*i], 1);
flag[i] = INITIAL_GUESS;
*numGuesses = *numGuesses - 1;
*nextGuess = *nextGuess + 1;
}
else {
flag[i] = LOCKED;
}
*numLocked = *numLocked + 1;
numRecentlyLocked++;
}
}
evecsSize = primme->numOrthoConst + *numLocked;
/* -------------------------------------------------------------------- */
/* If a W vector was used as workspace for residual AND its evec has */
/* not been locked out, recompute it, W = A*v. This is rare. */
/* -------------------------------------------------------------------- */
if (workinW && flag[*basisSize-1] != LOCKED) {
update_W_dprimme(V, W, *basisSize-1, 1, primme);
}
/* -------------------------------------------------------------------- */
/* Return IF all target Ritz vectors have been locked, ELSE update the */
/* evecsHat array by applying the preconditioner (if preconditioning is */
/* needed, and JDQMR with right, skew Q projector is applied */
/* -------------------------------------------------------------------- */
if (*numLocked >= primme->numEvals) {
return 0;
}
else if (UDU != NULL) {
/* Compute K^{-1}x for all newly locked eigenvectors */
newStart = primme->nLocal*(evecsSize - numRecentlyLocked);
(*primme->applyPreconditioner)( &evecs[newStart], &evecsHat[newStart],
&numRecentlyLocked, primme);
primme->stats.numPreconds += numRecentlyLocked;
/* Update the projection evecs'*evecsHat now that evecs and evecsHat */
/* have been expanded by numRecentlyLocked columns. Required */
/* workspace is numLocked*numEvals. The most ever needed would be */
/* maxBasisSize*numEvals. */
update_projection_dprimme(evecs, evecsHat, M,
evecsSize-numRecentlyLocked, primme->numOrthoConst+primme->numEvals,
numRecentlyLocked, rwork, primme);
ret = UDUDecompose_dprimme(M, UDU, ipivot, evecsSize, rwork,
rworkSize, primme);
if (ret != 0) {
primme_PushErrorMessage(Primme_lock_vectors, Primme_ududecompose, ret,
__FILE__, __LINE__, primme);
return UDUDECOMPOSE_FAILURE;
}
}
/* --------------------------------------------------------------------- */
/* Swap, towards the end of the basis, vectors that were locked but not */
/* replaced by new initial guesses. */
/* --------------------------------------------------------------------- */
numDeflated = swap_flagVecs_toEnd(*basisSize, LOCKED, V, W, H, hVals, flag,
primme);
/* --------------------------------------------------------------------- */
/* Reduce the basis size by numDeflated and swap the new initial guesses */
/* towards the end of the basis. */
/* --------------------------------------------------------------------- */
numReplaced = swap_flagVecs_toEnd(*basisSize-numDeflated, INITIAL_GUESS,
V, W, H, hVals, flag, primme);
*basisSize = *basisSize - (numDeflated + numReplaced);
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile, "numDeflated: %d numReplaced: %d \
basisSize: %d\n", numDeflated, numReplaced, *basisSize);
}
int check_convergence_dprimme(double *V, double *W, double *hVecs,
double *hVals, int *flags, int basisSize, int *iev, int *ievMax,
double *blockNorms, int *blockSize, int numConverged, int numLocked,
double *evecs, double tol, double maxConvTol, double aNormEstimate,
double *rwork, primme_params *primme) {
int i; /* Loop variable */
int left, right; /* Range of block vectors to be checked for convergence */
int start; /* starting index in block of converged/tobeProject vecs*/
int numVacancies; /* Number of vacant positions between left and right */
int recentlyConverged; /* The number of Ritz values declared converged */
/* since the last iteration */
int numToProject; /* Number of vectors with potential accuracy problem*/
double attainableTol; /* Used in locking to check near convergence problem*/
/* -------------------------------------------- */
/* Tolerance based on our dynamic norm estimate */
/* -------------------------------------------- */
if (primme->aNorm <= 0.0L) {
tol = tol * aNormEstimate;
}
/* ---------------------------------------------------------------------- */
/* If locking, set tol beyond which we need to check for accuracy problem */
/* ---------------------------------------------------------------------- */
if (primme->locking) {
attainableTol = sqrt(primme->numOrthoConst+numLocked)*maxConvTol;
}
/* --------------------------------------------------------------- */
/* Compute each Ritz vector and its corresponding residual vector. */
/* The Ritz vector and residual are stored temporarily in V and W */
/* respectively. For each Ritz vector, determine if it has */
/* converged. If it has, try to replace it with one that hasn't. */
/* --------------------------------------------------------------- */
recentlyConverged = 0;
left = 0;
right = *blockSize - 1;
numVacancies = 1;
while (numVacancies > 0 &&
(numConverged + recentlyConverged) < primme->numEvals) {
/* Consider the newly added vectors in the block and reset counters */
numVacancies = 0;
numToProject = 0;
/* Copy needed hvecs into the front of the work array. */
for (i=left; i <= right; i++) {
Num_dcopy_dprimme(basisSize, &hVecs[basisSize*iev[i]], 1,
&rwork[basisSize*(i-left)], 1);
}
/* ----------------------------------------------------------------- */
/* Compute the Ritz vectors, residuals, and norms for the next */
/* blockSize unconverged Ritz vectors. The Ritz vectors will be */
/* placed from V(0,lft) to V(0,rgt) and the residual vectors from */
/* W(0,lft) to W(0,rgt). */
/* ----------------------------------------------------------------- */
/* rwork must be maxBasisSize*maxBlockSize + maxBlockSize in size, */
/* maxBasisSize*maxBlockSize holds selected hVecs to facilitate */
/* blocking, and maxBlockSize to hold the residual norms */
/* ----------------------------------------------------------------- */
compute_resnorms(V, W, rwork, hVals, basisSize, blockNorms,
iev, left, right, &rwork[basisSize*(right-left+1)], primme);
print_residuals(hVals, blockNorms, numConverged, numLocked, iev,
left, right, primme);
/* ----------------------------------------------------------------- */
/* Determine which Ritz vectors have converged < tol and flag them. */
/* ----------------------------------------------------------------- */
for (i=left; i <= right; i++) {
/* ------------------------------------*/
/* If the vector is converged, flag it */
/* ------------------------------------*/
if (blockNorms[i] < tol) {
flags[iev[i]] = CONVERGED;
numVacancies++;
if ((!primme->locking && iev[i] < primme->numEvals) ||
(primme->locking && ((numLocked + iev[i]) < primme->numEvals))) {
recentlyConverged++;
if (!primme->locking && primme->procID == 0 &&
primme->printLevel >= 2) { fprintf(primme->outputFile,
"#Converged %d eval[ %d ]= %e norm %e Mvecs %d Time %g\n",
numConverged+recentlyConverged, iev[i], hVals[iev[i]],
blockNorms[i], primme->stats.numMatvecs,primme_wTimer(0));
fflush(primme->outputFile);
} /* printf */
} /*if */
} /*if converged */
/* ---------------------------------------------------------------- */
/* If locking there may be an accuracy problem close to convergence */
/* Check if there is danger and set these Ritz vecs for projection */
/* ---------------------------------------------------------------- */
else if (primme->locking && numLocked > 0 &&
blockNorms[i] < attainableTol ) {
flags[iev[i]] = TO_BE_PROJECTED;
numToProject++;
}
} /* for */
/* ---------------------------------------------------------------- */
/* If some of the Ritz vectors in the block have converged, or need */
/* to be projected against evecs, move those flagged Ritz vectors */
/* and residuals towards the end of the block [left,right]. Also */
/* swap iev, and blockNorms for the targeted block. */
/* ---------------------------------------------------------------- */
if (numVacancies > 0 || numToProject > 0) {
swap_UnconvVecs(V, W, primme->nLocal, basisSize, iev, flags,
blockNorms, primme->numOrthoConst + numLocked, *blockSize, left);
}
/* --------------------------------------------------------------- */
/* Project the TO_BE_PROJECTED residuals and check for practical */
/* convergence among them. Those practically converged evecs are */
/* swapped just before the converged ones at the end of the block. */
/* numVacancies and recentlyConverged are also updated */
/* --------------------------------------------------------------- */
if (numToProject > 0) {
start = *blockSize - numVacancies - numToProject;
check_practical_convergence(V, W, evecs, numLocked, basisSize,
*blockSize, start, numToProject, iev, flags, blockNorms, tol,
&recentlyConverged, &numVacancies, rwork, primme);
}
/* ---------------------------------------------------------------- */
/* Replace the vacancies, with as many unconverged vectors beyond */
/* ievMax as possible. If not enough are available reduce blockSize */
/* ---------------------------------------------------------------- */
if (numVacancies > 0) {
replace_vectors(iev, flags, *blockSize, basisSize, numVacancies,
&left, &right, ievMax);
numVacancies = right - left + 1;
*blockSize = left + numVacancies;
}
} /* while there are vacancies */
return recentlyConverged;
}
static void swap_UnconvVecs(double *V, double *W, int nLocal,
int basisSize, int *iev, int *flags, double *blockNorms, int dimEvecs,
int blockSize, int left) {
int right; /* holds the right swapping position */
int temp; /* used to swap integers */
double dtemp; /* used to swap doubles */
/* Search from left to right within the block looking for flagged */
/* Ritz vectors. If a flagged one is found, find also an unconverged */
/* Ritz vector from the right side of the block. If the flagged was */
/* converged, replace it with the unconverged, otherwise if it was */
/* was flagged TO_BE_PROJECTED, swap it with the unconverged vector. */
while (left < blockSize) {
/* If block vector left is unconverged, move left one vector. */
if (flags[iev[left]] == UNCONVERGED) {
left++;
}
else {
/* If block vector left is converged, find an unconverged */
/* vector somewhere between left+1 and blockSize. */
right = left + 1;
/* If the end of the block has been reached, there are */
/* no more unconverged vectors left. If not, keep */
/* searching right for another unconverged vector to */
/* perform the replacement. */
while (right < blockSize && flags[iev[right]] != UNCONVERGED) {
right++;
}
/* No unconverged block vector could be found */
if (right == blockSize) {
return;
}
/* An unconverged Ritz vector was found and should */
/* replace or be swapped with block vector left. */
if (flags[iev[left]] != TO_BE_PROJECTED) {
/* replace */
Num_dcopy_dprimme(nLocal, &V[nLocal*(basisSize+right)], 1,
&V[nLocal*(basisSize+left)], 1);
Num_dcopy_dprimme(nLocal, &W[nLocal*(basisSize+right)], 1,
&W[nLocal*(basisSize+left)], 1);
temp = iev[left];
iev[left] = iev[right];
iev[right] = temp;
blockNorms[left] = blockNorms[right];
}
else { /* swap */
Num_swap_dprimme(nLocal, &V[nLocal*(basisSize+left)], 1,
&V[nLocal*(basisSize+right)], 1);
Num_swap_dprimme(nLocal, &W[nLocal*(basisSize+left)], 1,
&W[nLocal*(basisSize+right)], 1);
temp = iev[left];
iev[left] = iev[right];
iev[right] = temp;
dtemp = blockNorms[left];
blockNorms[left] = blockNorms[right];
blockNorms[right] = dtemp;
} /* end of swaps */
left++;
} /* looking for replacement */
} /* while left < blockSize */
}
static int init_block_krylov(double *V, double *W, int dv1, int dv2,
double *locked, int numLocked, double machEps, double *rwork,
int rworkSize, primme_params *primme) {
int i; /* Loop variables */
int numNewVectors; /* Number of vectors to be generated */
int ret; /* Return code. */
int ONE = 1; /* Used for passing it by reference in matrixmatvec */
numNewVectors = dv2 - dv1 + 1;
/*----------------------------------------------------------------------*/
/* Generate a single Krylov space if there are only a few vectors to be */
/* generated, else generate a block Krylov space with */
/* primme->maxBlockSize as the block Size. */
/*----------------------------------------------------------------------*/
if (numNewVectors <= primme->maxBlockSize) {
/* Create and orthogonalize the inital vectors */
Num_larnv_dprimme(2, primme->iseed,primme->nLocal,&V[primme->nLocal*dv1]);
ret = ortho_dprimme(V, primme->nLocal, dv1, dv1, locked,
primme->nLocal, numLocked, primme->nLocal, primme->iseed, machEps,
rwork, rworkSize, primme);
if (ret < 0) {
primme_PushErrorMessage(Primme_init_block_krylov, Primme_ortho, ret,
__FILE__, __LINE__, primme);
return ORTHO_FAILURE;
}
/* Generate the remainder of the Krylov space. */
for (i = dv1; i < dv2; i++) {
(*primme->matrixMatvec)
(&V[primme->nLocal*i], &V[primme->nLocal*(i+1)], &ONE, primme);
Num_dcopy_dprimme(primme->nLocal, &V[primme->nLocal*(i+1)], 1,
&W[primme->nLocal*i], 1);
ret = ortho_dprimme(V, primme->nLocal, i+1, i+1, locked,
primme->nLocal, numLocked, primme->nLocal, primme->iseed, machEps,
rwork, rworkSize, primme);
if (ret < 0) {
primme_PushErrorMessage(Primme_init_block_krylov, Primme_ortho,
ret, __FILE__, __LINE__, primme);
return ORTHO_FAILURE;
}
}
primme->stats.numMatvecs += dv2-dv1;
update_W_dprimme(V, W, dv2, 1, primme);
}
else {
/*----------------------------------------------------------------------*/
/* Generate the initial vectors. */
/*----------------------------------------------------------------------*/
Num_larnv_dprimme(2, primme->iseed, primme->nLocal*primme->maxBlockSize,
&V[primme->nLocal*dv1]);
ret = ortho_dprimme(V, primme->nLocal, dv1,
dv1+primme->maxBlockSize-1, locked, primme->nLocal, numLocked,
primme->nLocal, primme->iseed, machEps, rwork, rworkSize, primme);
/* Generate the remaining vectors in the sequence */
for (i = dv1+primme->maxBlockSize; i <= dv2; i++) {
(*primme->matrixMatvec)(&V[primme->nLocal*(i-primme->maxBlockSize)],
&V[primme->nLocal*i], &ONE, primme);
Num_dcopy_dprimme(primme->nLocal, &V[primme->nLocal*i], 1,
&W[primme->nLocal*(i-primme->maxBlockSize)], 1);
ret = ortho_dprimme(V, primme->nLocal, i, i, locked,
primme->nLocal, numLocked, primme->nLocal, primme->iseed, machEps,
rwork, rworkSize, primme);
if (ret < 0) {
primme_PushErrorMessage(Primme_init_block_krylov, Primme_ortho,
ret, __FILE__, __LINE__, primme);
return ORTHO_FAILURE;
}
}
primme->stats.numMatvecs += dv2-(dv1+primme->maxBlockSize)+1;
update_W_dprimme(V, W, dv2-primme->maxBlockSize+1, primme->maxBlockSize,
primme);
}
return 0;
}
int init_basis_dprimme(double *V, double *W, double *evecs,
double *evecsHat, double *M, double *UDU, int *ipivot,
double machEps, double *rwork, int rworkSize, int *basisSize,
int *nextGuess, int *numGuesses, double *timeForMV,
primme_params *primme) {
int ret; /* Return value */
int currentSize;
/*-----------------------------------------------------------------------*/
/* Orthogonalize the orthogonalization constraints provided by the user. */
/* If a preconditioner is given and inner iterations are to be */
/* performed, then initialize M. */
/*-----------------------------------------------------------------------*/
if (primme->numOrthoConst > 0) {
ret = ortho_dprimme(evecs, primme->nLocal, 0,
primme->numOrthoConst - 1, NULL, 0, 0, primme->nLocal,
primme->iseed, machEps, rwork, rworkSize, primme);
/* Push an error message onto the stack trace if an error occured */
if (ret < 0) {
primme_PushErrorMessage(Primme_init_basis, Primme_ortho, ret,
__FILE__, __LINE__, primme);
return ORTHO_FAILURE;
}
/* Initialize evecsHat, M, and its factorization UDU,ipivot. This */
/* allows the orthogonalization constraints to be included in the */
/* projector (I-QQ'). Only needed if there is preconditioning, and */
/* JDqmr inner iterations with a right, skew projector. Only in */
/* that case, is UDU not NULL */
if (UDU != NULL) {
(*primme->applyPreconditioner)
(evecs, evecsHat, &primme->numOrthoConst, primme);
primme->stats.numPreconds += primme->numOrthoConst;
update_projection_dprimme(evecs, evecsHat, M, 0,
primme->numOrthoConst+primme->numEvals, primme->numOrthoConst,
rwork, primme);
ret = UDUDecompose_dprimme(M, UDU, ipivot, primme->numOrthoConst,
rwork, rworkSize, primme);
if (ret != 0) {
primme_PushErrorMessage(Primme_init_basis, Primme_ududecompose, ret,
__FILE__, __LINE__, primme);
return UDUDECOMPOSE_FAILURE;
}
} /* if evecsHat and M=evecs'evecsHat, UDU are needed */
} /* if numOrthoCont >0 */
/*-----------------------------------------------------------------------*/
/* No locking */
/*-----------------------------------------------------------------------*/
if (!primme->locking) {
/* Handle case when no initial guesses are provided by the user */
if (primme->initSize == 0) {
ret = init_block_krylov(V, W, 0, primme->minRestartSize - 1, evecs,
primme->numOrthoConst, machEps, rwork, rworkSize, primme);
/* Push an error message onto the stack trace if an error occured */
if (ret < 0) {
primme_PushErrorMessage(Primme_init_basis, Primme_init_block_krylov,
ret, __FILE__, __LINE__, primme);
return INIT_BLOCK_KRYLOV_FAILURE;
}
*basisSize = primme->minRestartSize;
}
else {
/* Handle case when some or all initial guesses are provided by */
/* the user */
/* Copy over the initial guesses provided by the user */
Num_dcopy_dprimme(primme->nLocal*primme->initSize,
&evecs[primme->numOrthoConst*primme->nLocal], 1, V, 1);
/* Orthonormalize the guesses provided by the user */
ret = ortho_dprimme(V, primme->nLocal, 0, primme->initSize-1,
evecs, primme->nLocal, primme->numOrthoConst, primme->nLocal,
primme->iseed, machEps, rwork, rworkSize, primme);
/* Push an error message onto the stack trace if an error occured */
if (ret < 0) {
primme_PushErrorMessage(Primme_init_basis, Primme_ortho, ret,
__FILE__, __LINE__, primme);
return ORTHO_FAILURE;
}
update_W_dprimme(V, W, 0, primme->initSize, primme);
/* An insufficient number of initial guesses were provided by */
/* the user. Generate a block Krylov space to fill the */
/* remaining vacancies. */
if (primme->initSize < primme->minRestartSize) {
ret = init_block_krylov(V, W, primme->initSize,
primme->minRestartSize - 1, evecs, primme->numOrthoConst,
machEps, rwork, rworkSize, primme);
/* Push an error message onto the stack trace if an error occured */
if (ret < 0) {
primme_PushErrorMessage(Primme_init_basis,
Primme_init_block_krylov, ret, __FILE__, __LINE__, primme);
return INIT_KRYLOV_FAILURE;
}
*basisSize = primme->minRestartSize;
}
else {
*basisSize = primme->initSize;
}
}
*numGuesses = 0;
*nextGuess = 0;
}
else {
/*-----------------------------------------------------------------------*/
/* Locking */
/*-----------------------------------------------------------------------*/
*numGuesses = primme->initSize;
*nextGuess = primme->numOrthoConst;
/* If some initial guesses are available, copy them to the basis */
/* and orthogonalize them against themselves and the orthogonalization */
/* constraints. */
if (primme->initSize > 0) {
currentSize = min(primme->initSize, primme->minRestartSize);
Num_dcopy_dprimme(primme->nLocal*currentSize,
&evecs[primme->numOrthoConst*primme->nLocal], 1, V, 1);
ret = ortho_dprimme(V, primme->nLocal, 0, currentSize-1, evecs,
primme->nLocal, primme->numOrthoConst, primme->nLocal,
primme->iseed, machEps, rwork, rworkSize, primme);
if (ret < 0) {
primme_PushErrorMessage(Primme_init_basis, Primme_ortho, ret,
__FILE__, __LINE__, primme);
return ORTHO_FAILURE;
}
update_W_dprimme(V, W, 0, currentSize, primme);
*numGuesses = *numGuesses - currentSize;
*nextGuess = *nextGuess + currentSize;
}
else {
currentSize = 0;
}
/* If an insufficient number of guesses was provided, then fill */
/* the remaining vacancies with a block Krylov space. */
if (currentSize < primme->minRestartSize) {
ret = init_block_krylov(V, W, currentSize, primme->minRestartSize - 1,
evecs, primme->numOrthoConst, machEps, rwork, rworkSize, primme);
if (ret < 0) {
primme_PushErrorMessage(Primme_init_basis, Primme_init_block_krylov,
ret, __FILE__, __LINE__, primme);
return INIT_BLOCK_KRYLOV_FAILURE;
}
}
*basisSize = primme->minRestartSize;
}
/* ----------------------------------------------------------- */
/* If time measurements are needed, waste one MV + one Precond */
/* Put dummy results in the first open space of W (currentSize)*/
/* ----------------------------------------------------------- */
if (primme->dynamicMethodSwitch) {
currentSize = primme->nLocal*(*basisSize);
ret = 1;
*timeForMV = primme_wTimer(0);
(*primme->matrixMatvec)(V, &W[currentSize], &ret, primme);
*timeForMV = primme_wTimer(0) - *timeForMV;
primme->stats.numMatvecs += 1;
}
return 0;
}
