void primme_seq_globalSumDouble(void *sendBuf, void *recvBuf, int *count,
primme_params *params) {
Num_dcopy_primme(*count, (double *) sendBuf, 1, (double *) recvBuf, 1);
}
int solve_correction_zprimme(Complex_Z *V, Complex_Z *W, Complex_Z *evecs,
Complex_Z *evecsHat, Complex_Z *UDU, int *ipivot, double *lockedEvals,
int numLocked, int numConvergedStored, double *ritzVals,
double *prevRitzVals, int *flags, int basisSize, double *blockNorms,
int *iev, int blockSize, double eresTol, double machEps,
double aNormEstimate, Complex_Z *rwork, int *iwork, int rworkSize,
primme_params *primme) {
int blockIndex; /* Loop index. Ranges from 0..blockSize-1. */
int ritzIndex; /* Ritz value index blockIndex corresponds to. */
/* Possible values range from 0..basisSize-1. */
int sortedIndex; /* Ritz value index in sortedRitzVals, blockIndex */
/* corresponds to. Range 0..numLocked+basisSize-1 */
int neededRsize; /* Needed size for rwork. If not enough return */
int linSolverRWorkSize; /* Size of the linSolverRWork array. */
int *ilev; /* Array of size blockSize. Maps the target Ritz */
/* values to their positions in the sortedEvals */
/* array. */
int sizeLprojector; /* Sizes of the various left/right projectors */
int sizeRprojectorQ; /* These will be 0/1/or numOrthConstr+numLocked */
int sizeRprojectorX; /* or numOrthConstr+numConvergedStored w/o locking*/
static int numPrevRitzVals = 0; /* Size of prevRitzVals */
int ret; /* Return code. */
Complex_Z *r, *x, *sol; /* Residual, Ritz vector, and correction. */
Complex_Z *linSolverRWork;/* Workspace needed by linear solver. */
double *sortedRitzVals; /* Sorted array of current and converged Ritz */
/* values. Size of array is numLocked+basisSize. */
double *blockOfShifts; /* Shifts for (A-shiftI) or (if needed) (K-shiftI)*/
double *approxOlsenEps; /* Shifts for approximate Olsen implementation */
Complex_Z *Kinvx; /* Workspace to store K^{-1}x */
Complex_Z *Lprojector; /* Q pointer for (I-Q*Q'). Usually points to evecs*/
Complex_Z *RprojectorQ; /* May point to evecs/evecsHat depending on skewQ */
Complex_Z *RprojectorX; /* May point to x/Kinvx depending on skewX */
Complex_Z xKinvx; /* Stores x'*K^{-1}x if needed */
double eval, shift, robustShift; /* robust shift values. */
Complex_Z tmpShift; /* Temp shift for daxpy */
//------------------------------------------------------------
// Subdivide the workspace with pointers, and figure out
// the total amount of needed real workspace (neededRsize)
//------------------------------------------------------------
/* needed worksize */
neededRsize = 0;
Kinvx = rwork;
/* Kinvx will have nonzero size if precond and both RightX and SkewX */
if (primme->correctionParams.precondition &&
primme->correctionParams.projectors.RightX &&
primme->correctionParams.projectors.SkewX ) {
/* OLSEN's method requires a block, but JDQMR is vector by vector */
if (primme->correctionParams.maxInnerIterations == 0) {
sol = Kinvx + primme->nLocal*blockSize;
neededRsize = neededRsize + primme->nLocal*blockSize;
}
else {
sol = Kinvx + primme->nLocal;
neededRsize = neededRsize + primme->nLocal;
}
}
else {
sol = Kinvx + 0;
}
if (primme->correctionParams.maxInnerIterations == 0) {
linSolverRWork = sol + 0; /* sol not needed for GD */
linSolverRWorkSize = 0; /* No inner solver used */
}
else {
linSolverRWork = sol + primme->nLocal; /* sol needed in innerJD */
neededRsize = neededRsize + primme->nLocal;
linSolverRWorkSize = /* Inner solver worksize */
4*primme->nLocal + 2*(primme->numOrthoConst+primme->numEvals);
neededRsize = neededRsize + linSolverRWorkSize;
}
sortedRitzVals = (double *)(linSolverRWork + linSolverRWorkSize);
blockOfShifts = sortedRitzVals + (numLocked+basisSize);
approxOlsenEps = blockOfShifts + blockSize;
neededRsize = neededRsize + numLocked+basisSize + 2*blockSize;
if (neededRsize > rworkSize) {
return(neededRsize);
}
// Subdivide also the integer work space
ilev = iwork; // of size blockSize
//------------------------------------------------------------
// Figuring out preconditioning shifts (robust, Olsen, etc)
//------------------------------------------------------------
/* blockOfShifts will contain the preconditioning shifts: */
/* either Ritz values or robustShifts computed below. These shifts */
/* will be used in the correction equations or in inverting (K-sigma I) */
/* approxOlsenEps will contain error approximations for eigenavalues */
/* to be used for Olsen's method (when innerIterations =0). */
if (primme->locking) {
/* Combine the sorted list of locked Ritz values with the sorted */
/* list of current Ritz values, ritzVals. The merging of the two */
/* lists lockedEvals and ritzVals is stored in sortedRitzVals. */
mergeSort(lockedEvals, numLocked, ritzVals, flags, basisSize,
sortedRitzVals, ilev, blockSize, primme);
}
else {
/* Then the sorted evals are simply the ritzVals, targeted as iev */
sortedRitzVals = ritzVals;
ilev = iev;
}
/*-----------------------------------------------------------------*/
/* For interior eigenpairs, use the user provided shifts */
/*-----------------------------------------------------------------*/
if (primme->target != primme_smallest && primme->target != primme_largest) {
for (blockIndex = 0; blockIndex < blockSize; blockIndex++) {
sortedIndex = ilev[blockIndex];
blockOfShifts[blockIndex] =
primme->targetShifts[ min(primme->numTargetShifts-1, sortedIndex) ];
if (sortedIndex < numPrevRitzVals) {
approxOlsenEps[blockIndex] =
fabs(prevRitzVals[sortedIndex] - sortedRitzVals[sortedIndex]);
}
else {
approxOlsenEps[blockIndex] = blockNorms[blockIndex];
}
} /* for loop */
} /* user provided shifts */
else {
/*-----------------------------------------------------------------*/
/* else it is primme_smallest or primme_largest */
/*-----------------------------------------------------------------*/
if (primme->correctionParams.robustShifts) {
/*----------------------------------------------------*/
/* Subtract/add a robust shift from/to the Ritz value */
/*----------------------------------------------------*/
/* Find the robust shift for each block vector */
for (blockIndex = 0; blockIndex < blockSize; blockIndex++) {
sortedIndex = ilev[blockIndex];
eval = sortedRitzVals[sortedIndex];
robustShift = computeRobustShift(blockIndex,
blockNorms[blockIndex], prevRitzVals, numPrevRitzVals,
sortedRitzVals, &approxOlsenEps[blockIndex],
numLocked+basisSize, ilev, primme);
/* Subtract/add the shift if looking for the smallest/largest */
/* eigenvalues, Do not go beyond the previous computed eigval */
if (primme->target == primme_smallest) {
blockOfShifts[blockIndex] = eval - robustShift;
if (sortedIndex > 0) blockOfShifts[blockIndex] =
max(blockOfShifts[blockIndex], sortedRitzVals[sortedIndex-1]);
}
else {
blockOfShifts[blockIndex] = eval + robustShift;
if (sortedIndex > 0) blockOfShifts[blockIndex] =
min(blockOfShifts[blockIndex], sortedRitzVals[sortedIndex-1]);
} // robust shifting
} /* for loop */
} /* endif robust shifts */
else {
/*--------------------------------------------------------------*/
/* Otherwise, the shifts for both preconditioner and correction */
/* equation should be just the Ritz values. For Olsen's method, */
/* the shifts for r-eps*x, are chosen as the difference in Ritz */
/* value between successive iterations. */
/*--------------------------------------------------------------*/
for (blockIndex = 0; blockIndex < blockSize; blockIndex++) {
ritzIndex = iev[blockIndex];
sortedIndex = ilev[blockIndex];
blockOfShifts[blockIndex] = ritzVals[ritzIndex];
if (sortedIndex < numPrevRitzVals) {
approxOlsenEps[blockIndex] =
fabs(prevRitzVals[sortedIndex] - sortedRitzVals[sortedIndex]);
}
else {
approxOlsenEps[blockIndex] = blockNorms[blockIndex];
}
} /* for loop */
} /* else no robust shifts */
} /* else primme_smallest or primme_largest */
/* Remember the previous ritz values*/
numPrevRitzVals = numLocked+basisSize;
Num_dcopy_primme(numPrevRitzVals, sortedRitzVals, 1, prevRitzVals, 1);
// Equip the primme struct with the blockOfShifts, in case the user
// wants to precondition (K-sigma_i I)^{-1} with a different shift
// for each vector
primme->ShiftsForPreconditioner = blockOfShifts;
//------------------------------------------------------------
// Generalized Davidson variants -- No inner iterations
//------------------------------------------------------------
if (primme->correctionParams.maxInnerIterations == 0) {
// This is Generalized Davidson or approximate Olsen's method.
// Perform block preconditioning (with or without projections)
r = &W[primme->nLocal*basisSize]; // All the block residuals
x = &V[primme->nLocal*basisSize]; // All the block Ritz vectors
if ( primme->correctionParams.projectors.RightX &&
primme->correctionParams.projectors.SkewX ) {
// Compute exact Olsen's projected preconditioner. This is
// expensive and rarely improves anything! Included for completeness.
Olsen_preconditioner_block(r, x, blockSize, Kinvx, primme);
}
else {
if ( primme->correctionParams.projectors.RightX ) {
// Compute a cheap approximation to OLSENS, where (x'Kinvr)/xKinvx
// is approximated by e: Kinvr-e*Kinvx=Kinv(r-e*x)=Kinv(I-ct*x*x')r
for (blockIndex = 0; blockIndex < blockSize; blockIndex++) {
// Compute r_i = r_i - err_i * x_i
{tmpShift.r = -approxOlsenEps[blockIndex]; tmpShift.i = 0.0L;}
Num_axpy_zprimme(primme->nLocal, tmpShift,
&x[primme->nLocal*blockIndex],1,&r[primme->nLocal*blockIndex],1);
} //for
}
// GD: compute K^{-1}r , or approx.Olsen: K^{-1}(r-ex)
apply_preconditioner_block(r, x, blockSize, primme );
}
}
//------------------------------------------------------------
// JDQMR --- JD inner-outer variants
//------------------------------------------------------------
else { // maxInnerIterations > 0 We perform inner-outer JDQMR.
/* Solve the correction for each block vector. */
for (blockIndex = 0; blockIndex < blockSize; blockIndex++) {
r = &W[primme->nLocal*(basisSize+blockIndex)];
x = &V[primme->nLocal*(basisSize+blockIndex)];
/* Set up the left/right/skew projectors for JDQMR. */
/* The pointers Lprojector, Rprojector(Q/X) point to the */
/* appropriate arrays for use in the projection step */
setup_JD_projectors(x, r, evecs, evecsHat, Kinvx, &xKinvx,
&Lprojector, &RprojectorQ, &RprojectorX,
&sizeLprojector, &sizeRprojectorQ, &sizeRprojectorX,
numLocked, numConvergedStored, primme);
/* Map the index of the block vector to its corresponding eigenvalue */
/* index, and the shift for the correction equation. Also make the */
/* shift available to primme, in case (K-shift I)^-1 is needed */
ritzIndex = iev[blockIndex];
shift = blockOfShifts[blockIndex];
primme->ShiftsForPreconditioner = &blockOfShifts[blockIndex];
ret = inner_solve_zprimme(x, r, &blockNorms[blockIndex], evecs,
evecsHat, UDU, ipivot, &xKinvx, Lprojector, RprojectorQ,
RprojectorX, sizeLprojector, sizeRprojectorQ, sizeRprojectorX,
sol, ritzVals[ritzIndex], shift, eresTol, aNormEstimate,
machEps, linSolverRWork, linSolverRWorkSize, primme);
if (ret != 0) {
primme_PushErrorMessage(Primme_solve_correction, Primme_inner_solve,
ret, __FILE__, __LINE__, primme);
return (INNER_SOLVE_FAILURE);
}
Num_zcopy_zprimme(primme->nLocal, sol, 1,
&V[primme->nLocal*(basisSize+blockIndex)], 1);
} // end for each block vector
} // JDqmr variants
return 0;
}
static int dtr(int numLocked, Complex_Z *hVecs, double *hVals, int *flags,
int basisSize, int numFree, int *iev, Complex_Z *rwork, primme_params *primme)
{
int i; /* Loop variable */
int l, lOpt, lMin; /* Determine how many left side vectors to retain */
int r, rOpt; /* Determine how many right side vectors to retain */
int maxIndex; /* basisSize - 1 */
int restartSize; /* The new restart size */
double currentRitzVal; /* The current Ritz value the solver is computing */
double newVal, optVal; /* Used to find the optimum gap ratio */
/* ---------------------------------------------------------------- */
/* Compute lOpt and rOpt with respect to the first Ritz value being */
/* targeted by the block. */
/* ---------------------------------------------------------------- */
currentRitzVal = hVals[iev[0]];
maxIndex = basisSize-1;
/* If locking is engaged, then lMin must be large enough to retain */
/* the coefficient vector associated with a converged target. */
/* lMin should be no smaller than primme->minRestartSize. */
if (primme->locking) {
lMin = 0;
/* Determine the largest index of any converged but unlocked target */
/* Ritz vector. */
for (l = 0; l < basisSize; l++) {
if ( (flags[l] == CONVERGED || flags[l] == PRACTICALLY_CONVERGED)
&& (numLocked + l < primme->numEvals)) {
lMin = l;
}
}
lMin = max(lMin, min(basisSize, primme->minRestartSize));
}
else {
lMin = min(basisSize, primme->minRestartSize);
}
lOpt = lMin;
rOpt = 0;
optVal = 0.0L;
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile,"DTR basisSize: %d\n", basisSize);
}
/* ---------------------------------------------------------------------- */
/* Compute lOpt and rOpt that maximize the function. */
/* maximize the function (basisSize-numFree-lMin-rMin)* */
/* sqrt((currentRitzVal - hVals[l+1])/ */
/* (hVals[l+1]-hVals[basisSize-1-r])) */
/* ---------------------------------------------------------------------- */
for (l = lMin; l < basisSize - numFree; l++) {
for (r = 0; r < basisSize - l - numFree; r++) {
if ((basisSize - l - r) % primme->maxBlockSize == 0) {
newVal = (basisSize - l - r)
* sqrt((currentRitzVal - hVals[l+1])/
(hVals[l+1]-hVals[maxIndex-r]));
if (newVal > optVal) {
optVal = newVal;
lOpt = l;
rOpt = r;
}
}
}
}
restartSize = lOpt + rOpt;
/* --------------------------------------------------------------- */
/* Swap the rOpt vectors from the right hand side so that they are */
/* contiguous with the vectors from the left hand side. */
/* --------------------------------------------------------------- */
i = basisSize - restartSize;
Num_zcopy_zprimme(i*basisSize, &hVecs[basisSize*lOpt], 1, rwork, 1);
Num_zcopy_zprimme(rOpt*basisSize, &hVecs[basisSize*(basisSize-rOpt)], 1,
&hVecs[basisSize*lOpt], 1);
Num_zcopy_zprimme(i*basisSize, rwork, 1, &hVecs[basisSize*restartSize], 1);
/* Do the same with the eigenvalues of H */
Num_dcopy_primme(i, &hVals[lOpt], 1, (double *) rwork, 1);
Num_dcopy_primme(rOpt, &hVals[(basisSize-rOpt)], 1, &hVals[lOpt], 1);
Num_dcopy_primme(i, (double *) rwork, 1, &hVals[restartSize], 1);
/* Set only those flags lower than restartSize. The rest will be reset */
for (i = 0; i < rOpt; i++) {
flags[lOpt + i] = flags[basisSize-rOpt + i];
}
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile,"DTR restart size: %d L: %d R: %d\n",
restartSize, lOpt, rOpt);
}
reset_flags_zprimme(flags, restartSize, primme->maxBasisSize);
return restartSize;
}
