static double dist_dot(double *x, int incx,
double *y, int incy, primme_params *primme) {
double temp, product;
int count;
temp = Num_dot_dprimme(primme->nLocal, x, incx, y, incy);
count = 1;
(*primme->globalSumDouble)(&temp, &product, &count, primme);
return product;
}
static void compute_resnorms(double *V, double *W, double *hVecs,
double *hVals, int basisSize, double *blockNorms, int *iev, int left,
int right, void *rwork, primme_params *primme) {
int i; /* Loop variable */
int numResiduals; /* Number of residual vectors to be computed */
double *dwork = (double *) rwork; /* pointer casting rwork to double */
double ztmp; /* temp var holding shift */
double tpone = +1.0e+00, tzero = +0.0e+00; /* constants */
numResiduals = right - left + 1;
/* We want to compute residuals r = Ax-hVal*x for the Ritz vectors x */
/* Eqivalently, r = A*V*hVec - hval*V*hVec = W*hVec - hVal*V*hVec. */
/* Compute the Ritz vectors */
Num_gemm_dprimme("N", "N", primme->nLocal, numResiduals, basisSize,
tpone, V, primme->nLocal, hVecs, basisSize, tzero,
&V[primme->nLocal*(basisSize+left)], primme->nLocal);
/* Compute W*hVecs */
Num_gemm_dprimme("N", "N", primme->nLocal, numResiduals, basisSize,
tpone, W, primme->nLocal, hVecs, basisSize, tzero,
&W[primme->nLocal*(basisSize+left)], primme->nLocal);
/* Compute the residuals */
for (i=left; i <= right; i++) {
ztmp = -hVals[iev[i]];
Num_axpy_dprimme(primme->nLocal, ztmp, &V[primme->nLocal*(basisSize+i)],
1, &W[primme->nLocal*(basisSize+i)], 1);
}
/* Compute the residual norms */
for (i=left; i <= right; i++) {
dwork[i] = Num_dot_dprimme(primme->nLocal,
&W[primme->nLocal*(basisSize+i)], 1, &W[primme->nLocal*(basisSize+i)], 1);
}
(*primme->globalSumDouble)(&dwork[left], &blockNorms[left], &numResiduals,
primme);
for (i=left; i <= right; i++) {
blockNorms[i] = sqrt(blockNorms[i]);
}
}
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);
}
/*******************************************************************************
* Subroutine check_practical_convergence()
*
* This function is called after swaping has pushed converged (C)
* and to be projected (P) evecs at the end of blockSize.
* Makes C, P contiguous, projects P, checks and finds practically
* converged evecs (p), and makes p contiguous to C, updating
* flags[], blockNorms[], and numVacancies. Eg:
*
* blockSize
* |------CPCCPPCP| -> |------PPPPCCCC| -> |------PpPpCCCC| ->
* |------PPppCCCC|, numVacancies = 6
*
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*
* INPUT ARRAYS AND PARAMETERS
* ---------------------------
* evecs The locked eigenvectors
* numLocked The number of locked eigenvectors
* basisSize Number of vectors in the basis
* blockSize The number of block vectors
* start Starting index in V,W of vectors converged or to be projected
* numToProject The number of vectors to project.
* tol The required convergence tolerance
* rwork real work array of size: 2*maxEvecsSize*primme->maxBlockSize
* primme Structure containing various solver parameters
*
*
* OUTPUT ARRAYS AND PARAMETERS
* ----------------------------
* V The basis vectors
* W A*V
* iev Indicates which Ritz value each block vector corresponds to
* flags Indicates which Ritz pairs have converged
* blockNorms The norms of the block vectors to be targeted
* recentlyConverged Number of converged vectors in the whole basis V
* = converged+practicallyConverged
* numVacancies Number of Ritz values between left and right that were
* declared converged or practicallyConverged. [left, right]
* can be smaller than the whole V. See while-loop in
* check_convergence.
* left, right Indices indicating which vectors are to be replaced
* ievMax Index of the next Ritz value to be targeted by the block
******************************************************************************/
static void check_practical_convergence(double *V, double *W,
double *evecs, int numLocked, int basisSize, int blockSize, int start,
int numToProject, int *iev, int *flags, double *blockNorms, double tol,
int *recentlyConverged, int *numVacancies, double *rwork,
primme_params *primme) {
int i, n, dimEvecs;
int count;
double normPr;
double normDiff;
double *overlaps; /* Pointer in rwork to keep Q'*r */
double tpone = +1.0e+00, tzero = +0.0e+00, tmone = -1.0e+00; /* constants */
/* convenience variables */
n = primme->nLocal;
dimEvecs = primme->numOrthoConst + numLocked;
/* Subdivide rwork */
overlaps = rwork + dimEvecs*primme->maxBlockSize;
/* --------------------------------------------------------------- */
/* Reset any TO_BE_PROJECTED flags back to UNCONVERGED, and swap */
/* again CONVERGED flags toward the end of the block. Now swapping */
/* occurs in the block basisSize+[start:blockSize]: */
/* [ . . . . . . . P P P P C C C C ] blockSize */
/* start^ ^start+numToProject */
/* --------------------------------------------------------------- */
for (i=start; i < blockSize; i++)
if (flags[iev[i]] == TO_BE_PROJECTED)
flags[iev[i]] = UNCONVERGED;
if (*numVacancies > 0)
swap_UnconvVecs(V, W, primme->nLocal, basisSize, iev, flags,
blockNorms, dimEvecs, blockSize, start);
/* ------------------------------------------------------------------ */
/* Project the numToProject residuals agaist (I-evecs*evecs') */
/* ------------------------------------------------------------------ */
/* overlaps = evecs'*residuals */
Num_gemm_dprimme("C", "N", dimEvecs, numToProject, n, tpone, evecs, n,
&W[(basisSize+start)*n], n, tzero, rwork, dimEvecs);
count = dimEvecs*numToProject;
(*primme->globalSumDouble)(rwork, overlaps, &count, primme);
/* residuals = residuals - evecs*overlaps */
Num_gemm_dprimme("N", "N", n, numToProject, dimEvecs, tmone, evecs, n,
overlaps, dimEvecs, tpone, &W[(basisSize+start)*n], n);
/* ------------------------------------------------------------------ */
/* Compute norms^2 of the projected res and the differences from res */
/* note: ||residual - (I-QQ')residual||=||Q'*r||=||overlaps|| */
/* ------------------------------------------------------------------ */
for (i=0; i < numToProject; i++) {
/* || res - (I-QQ')res || */
rwork[i] = Num_dot_dprimme(dimEvecs, &overlaps[dimEvecs*i], 1,
&overlaps[dimEvecs*i], 1);
/* || (I-QQ')res || */
rwork[i+numToProject] = Num_dot_dprimme(n, &W[(basisSize+start+i)*n], 1,
&W[(basisSize+start+i)*n], 1);
}
/* global sum ||overlaps|| and ||(I-QQ')r|| */
count = 2*numToProject;
(*primme->globalSumDouble)(rwork, &rwork[count], &count, primme);
/* ------------------------------------------------------------------ */
/* For each projected residual check whether there is an accuracy */
/* problem and, if so, declare it PRACTICALLY_CONVERGED to lock later.*/
/* normDiff is a lower bound to the attainable accuracy for this pair */
/* so problems exist only if normDiff > tol. Then, we stop if Tol is */
/* the geometric mean of normPr and r. */
/* ------------------------------------------------------------------ */
for (i=start; i < start+numToProject; i++) {
normDiff = sqrt(rwork[i-start]);
normPr = sqrt(rwork[i-start+numToProject]);
/* printf(" R Pr |R-Pr| %e %e %e \n", blockNorms[i],normPr,normDiff); */
if (normDiff >= tol && normPr < tol*tol/blockNorms[i]/2) {
if (primme->printLevel >= 5 && primme->procID == 0) {
fprintf(primme->outputFile,
" PRACTICALLY_CONVERGED %d norm(I-QQt)r %e bound %e\n",
iev[i],normPr,tol*tol/normDiff);
fflush(primme->outputFile);
}
flags[iev[i]] = PRACTICALLY_CONVERGED;
(*numVacancies)++;
if (numLocked + iev[i] < primme->numEvals){
recentlyConverged++;
}
} /* if practically converged */
} /* for each projected residual */
/* ------------------------------------------------------------------ */
/* Finally swap all practically converged toward the end of the block */
/* to be contiguous with the converged ones. Swap all relevant arrays */
/* ------------------------------------------------------------------ */
start = blockSize - *numVacancies;
swap_UnconvVecs(V, W, primme->nLocal, basisSize, iev, flags, blockNorms,
dimEvecs, blockSize, start);
}
