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main_iter.c
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main_iter.c
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/*******************************************************************************
* Copyright (c) 2018, College of William & Mary
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of the College of William & Mary nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COLLEGE OF WILLIAM & MARY BE LIABLE FOR ANY
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* PRIMME: https://github.com/primme/primme
* Contact: Andreas Stathopoulos, a n d r e a s _at_ c s . w m . e d u
*******************************************************************************
* File: main_iter.c
*
* Purpose - This is the main Davidson-type iteration
*
******************************************************************************/
#ifndef THIS_FILE
#define THIS_FILE "../eigs/main_iter.c"
#endif
#include "numerical.h"
#include "template_normal.h"
#include "common_eigs.h"
/* Keep automatically generated headers under this section */
#ifndef CHECK_TEMPLATE
#include "main_iter.h"
#include "convergence.h"
#include "correction.h"
#include "init.h"
#include "ortho.h"
#include "restart.h"
#include "solve_projection.h"
#include "update_projection.h"
#include "update_W.h"
#include "auxiliary_eigs.h"
#include "auxiliary_eigs_normal.h"
#endif
#ifdef SUPPORTED_TYPE
/*----------------------------------------------------------------------------*
* The following are needed for the Dynamic Method Switching
*----------------------------------------------------------------------------*/
#ifndef MAIN_ITER_PRIVATE_H
#define MAIN_ITER_PRIVATE_H
typedef struct {
/* Time measurements for various components of the solver */
double MV_PR; /* OPp operator MV+PR time */
double MV; /* MV time only */
double PR; /* PRecond only */
double qmr_only; /* c_q only the QMR iteration */
double qmr_plus_MV_PR; /* a QMR plus operators */
double gdk_plus_MV_PR; /* b GD plus operators */
double gdk_plus_MV; /* b_m GD plus MV (i.e., GD without correction) */
/* The following two are not currently updated: */
double project_locked; /* c_p projection time per locked eigenvector in QMR*/
double reortho_locked; /* c_g (usu 2*c_p) ortho per locked vector in outer */
/* Average convergence estimates. Updated at restart/switch/convergence */
double gdk_conv_rate; /* convergence rate of all (|r|/|r0|) seen for GD+k */
double jdq_conv_rate; /* convergence rate of all (|r|/|r0|) seen for JDQMR*/
double JDQMR_slowdown; /* log(gdRate)/log(jdRate) restricted in [1.1, 2.5] */
double ratio_MV_outer; /* TotalMV/outerIts (average of last two updates) */
/* To maintain a convergence rate of all residual reductions seen we need: */
int nextReset; /* When to reset the following averaging sums */
double gdk_sum_logResReductions;/* Sumof all log(residual reductions) in GD*/
double jdq_sum_logResReductions;/* Sumof all log(residual reductions) in JD*/
double gdk_sum_MV; /* Total num of MV resulting in these GD reductions */
double jdq_sum_MV; /* Total num of MV resulting in these JD reductions */
int nevals_by_gdk; /* Number of evals found by GD+k since last reset */
int nevals_by_jdq; /* Number of evals found by JDQMR since last reset */
/* Variables to remember MV/its/time/resNorm/etc since last update/switch */
int numIt_0; /*Remembers starting outer its/MVs since switched */
int numMV_0; /* to current method, or since an epair converged */
double timer_0; /*Remembers starting time since switched to a method*/
/* or since an epair converged with that method */
double time_in_inner; /*Accumulative time spent in inner iterations */
/* since last switch or since an epair converged */
double resid_0; /*First residual norm of the convergence of a method*/
/* since last switch or since an epair converged */
/* Weighted ratio of expected times, for final method recommendation */
double accum_jdq_gdk; /*Expected ratio of accumulative times of JDQMR/GD+k*/
double accum_jdq; /* Accumulates jdq_times += ratio*(gdk+MV+PR) */
double accum_gdk; /* Accumulates gdk_times += gdk+MV+PR */
} primme_CostModel;
#endif /* MAIN_ITER_PRIVATE_H */
#if 0
STATIC void displayModel(primme_CostModel *model);
#endif
/******************************************************************************
* Subroutine main_iter - This routine implements a more general, parallel,
* block (Jacobi)-Davidson outer iteration with a variety of options.
*
* A coarse outline of the algorithm performed is as follows:
*
* 1. Initialize basis V
* 2. while (converged Ritz vectors have become unconverged) do
* 3. Update W=A*V, and H=V'*A*V, and solve the H eigenproblem
* 4. while (not all Ritz pairs have converged) do
* 5. while (maxBasisSize has not been reached)
* 6. Adjust the block size if necessary
* 7. Compute the residual norms of each block vector and
* check for convergence. If a Ritz vector has converged,
* target an unconverged Ritz vector to replace it.
* 8. Solve the correction equation for each residual vector
* 9. Insert corrections in V, orthogonalize, update W and H
* 10. Solve the new H eigenproblem to obtain the next Ritz pairs
* 11. endwhile
* 12. Restart V with appropriate vectors
* 13. If (locking) Lock out Ritz pairs that converged since last restart
* 14. endwhile
* 15. if Ritz vectors have become unconverged, reset convergence flags
* 16. endwhile
*
*
* OUTPUT arrays and parameters
* ----------------------------
* evals The converged Ritz values. It is maintained in sorted order.
* If locking is not engaged, values are copied to this array only
* upon return. If locking is engaged, then values are copied to this
* array as they converge.
*
* resNorms The residual norms corresponding to the converged Ritz vectors
*
* INPUT/OUTPUT arrays and parameters
* ----------------------------------
* evecs Stores initial guesses. Upon return, it contains the converged Ritz
* vectors. If locking is not engaged, then converged Ritz vectors
* are copied to this array just before return.
*
* primme.initSize: On output, it stores the number of converged eigenvectors.
* If smaller than numEvals and locking is used, there are
* only primme.initSize vectors in evecs.
* Without locking all numEvals approximations are in evecs
* but only the initSize ones are converged.
* During the execution, access to primme.initSize gives
* the number of converged pairs up to that point. The pairs
* are available in evals and evecs, but only when locking is used
* ret successful state
* numRet number of returned pairs in evals, evecs, and resNorms
*
* Return Value
* ------------
* error code
******************************************************************************/
TEMPLATE_PLEASE
int main_iter_Sprimme(HEVAL *evals, SCALAR *evecs, PRIMME_INT ldevecs,
HREAL *resNorms, double startTime, int *ret, int *numRet,
primme_context ctx) {
/* Default error is something is wrong in this function */
*ret = PRIMME_MAIN_ITER_FAILURE;
primme_params *primme = ctx.primme;
/* primme parameters */
int i; /* Loop variable */
int blockSize; /* Current block size */
int availableBlockSize; /* There is enough space in basis for this block */
int basisSize; /* Current size of the basis V */
int numLocked; /* Number of locked Ritz vectors */
int numGuesses; /* Current number of initial guesses in evecs */
int nextGuess; /* Index of the next initial guess in evecs */
int numConverged; /* Number of converged Ritz pairs */
int targetShiftIndex; /* Target shift used in the QR factorization */
int recentlyConverged; /* Number of target Ritz pairs that have */
/* converged during the current iteration. */
int maxRecentlyConverged;/* Maximum value allowed for recentlyConverged */
int numConvergedStored; /* Numb of Ritzvecs temporarily stored in evecs */
/* to allow for skew projectors w/o locking */
int LockingProblem; /* Flag==1 if practically converged pairs locked */
int restartLimitReached; /* True when maximum restarts performed */
int nprevhVecs; /* Number of vectors stored in prevhVecs */
int numArbitraryVecs; /* Columns in hVecs computed with RR instead of */
/* the current extraction method. */
int maxEvecsSize; /* Maximum capacity of evecs array */
int numPrevRitzVals = 0; /* Size of the prevRitzVals updated in correction*/
int touch=0; /* param used in inner solver stopping criteria */
int *perm=NULL; /* Permutation on the locked pairs */
int *flags; /* Indicates which Ritz values have converged */
int *map; /* Indices of the closest vector from prevhVecs */
int *lockedFlags=NULL; /* Flags for the locked pairs */
int *ipivot; /* The pivot for the Mfact factorization of M */
int *iev; /* Evalue index each block vector corresponds to */
SCALAR *V; /* Basis vectors */
PRIMME_INT ldV; /* The leading dimension of V */
SCALAR *W; /* Work space storing A*V */
PRIMME_INT ldW; /* The leading dimension of W */
SCALAR *BV=NULL; /* Work space storing B*V */
PRIMME_INT ldBV; /* The leading dimension of BV */
HSCALAR *H; /* Upper triangular portion of V'*A*V */
HSCALAR *VtBV = NULL; /* Upper triangular portion of V'*B*V */
HSCALAR *fVtBV = NULL; /* Cholesky factor of VtBV */
HSCALAR *QtQ = NULL; /* Upper triangular portion of Q'*Q */
HSCALAR *fQtQ = NULL; /* Cholesky factor of QtQ */
HSCALAR *M = NULL; /* The projection Q'*K*B*Q, where Q = [evecs, x] */
/* x is the current Ritz vector and K is a */
/* hermitian preconditioner. */
HSCALAR *Mfact = NULL; /* The factorization of M=Q'KBQ */
SCALAR *Bevecs = NULL; /* B*evecs */
PRIMME_INT ldBevecs; /* Leading dimension of Bevecs */
SCALAR *evecsHat = NULL; /* K^{-1}*B*evecs */
PRIMME_INT ldevecsHat=0; /* The leading dimension of evecsHat */
HSCALAR *hVecs; /* Eigenvectors of H */
HSCALAR *hU = NULL; /* Left singular vectors of R */
HSCALAR *prevhVecs=NULL; /* hVecs from previous iteration */
int numQR; /* Maximum number of QR factorizations */
SCALAR *Q = NULL; /* QR decompositions for harmonic or refined */
PRIMME_INT ldQ; /* The leading dimension of Q */
HSCALAR *R = NULL; /* projection: (A-target[i])*V = QR */
HSCALAR *QtV = NULL; /* Q'*V */
HSCALAR *hVecsRot = NULL; /* transformation of hVecs in arbitrary vectors */
HEVAL *hVals; /* Eigenvalues of H */
HREAL *hSVals = NULL; /* Singular values of R */
HEVAL *prevRitzVals; /* Eigenvalues of H at previous outer iteration */
/* by robust shifting algorithm in correction.c */
HREAL *basisNorms; /* Residual norms of basis at pairs */
HREAL *blockNorms; /* Residual norms corresponding to current block */
/* vectors. */
double smallestResNorm; /* the smallest residual norm in the block */
int reset=0; /* Flag to reset V and W */
int restartsSinceReset=0;/* Restart since last reset of V and W */
int wholeSpace=0; /* search subspace reach max size */
/* Runtime measurement variables for dynamic method switching */
primme_CostModel CostModel; /* Structure holding the runtime estimates of */
/* the parameters of the model.Only visible here */
double tstart=0.0; /* Timing variable for accumulative time spent */
int maxNumRandoms = 10; /* We do not allow more than 10 randomizations */
/* -------------------------------------------------------------- */
/* Allocate objects */
/* -------------------------------------------------------------- */
maxEvecsSize = primme->numOrthoConst + primme->numEvals;
if (primme->projectionParams.projection != primme_proj_RR) {
numQR = 1;
}
else {
numQR = 0;
}
/* Use leading dimension ldOPs for the large dimension mats: V, W and Q */
ldV = ldW = ldBV = ldQ = primme->ldOPs;
ldBevecs = primme->massMatrixMatvec ? primme->ldOPs : ldevecs;
if (primme->massMatrixMatvec) {
CHKERR(Num_malloc_Sprimme(ldBV*primme->maxBasisSize, &BV, ctx));
}
CHKERR(Num_malloc_Sprimme(primme->ldOPs*primme->maxBasisSize, &V, ctx));
CHKERR(Num_malloc_Sprimme(primme->ldOPs*primme->maxBasisSize, &W, ctx));
if (numQR > 0) {
CHKERR(Num_malloc_Sprimme(primme->ldOPs*primme->maxBasisSize*numQR, &Q, ctx));
CHKERR(Num_malloc_SHprimme(
primme->maxBasisSize * primme->maxBasisSize * numQR, &R, ctx));
CHKERR(Num_malloc_SHprimme(
primme->maxBasisSize * primme->maxBasisSize * numQR, &hU, ctx));
}
if (primme->projectionParams.projection == primme_proj_harmonic) {
CHKERR(Num_malloc_SHprimme(
primme->maxBasisSize * primme->maxBasisSize * numQR, &QtV, ctx));
}
CHKERR(Num_malloc_SHprimme(primme->maxBasisSize * primme->maxBasisSize, &H,
ctx));
CHKERR(Num_malloc_SHprimme(primme->maxBasisSize * primme->maxBasisSize,
&hVecs, ctx));
int maxRank; /* maximum size of the main space being orthonormalize */
if (primme->locking) {
maxRank = primme->numOrthoConst + primme->numEvals + primme->maxBasisSize;
} else {
maxRank = primme->numOrthoConst + primme->maxBasisSize;
}
if (primme->orth == primme_orth_explicit_I) {
CHKERR(Num_malloc_SHprimme(maxRank * maxRank, &VtBV, ctx));
CHKERR(Num_malloc_SHprimme(maxRank * maxRank, &fVtBV, ctx));
}
int ldVtBV = maxRank;
int ldfVtBV = maxRank;
if (primme->orth == primme_orth_explicit_I && numQR) {
CHKERR(Num_malloc_SHprimme(
primme->maxBasisSize * primme->maxBasisSize * numQR, &QtQ, ctx));
CHKERR(Num_malloc_SHprimme(
primme->maxBasisSize * primme->maxBasisSize * numQR, &fQtQ, ctx));
}
int ldQtQ = primme->maxBasisSize;
int ldfQtQ = primme->maxBasisSize;
if (primme->projectionParams.projection == primme_proj_refined
|| primme->projectionParams.projection == primme_proj_harmonic) {
CHKERR(Num_malloc_SHprimme(
primme->maxBasisSize * primme->maxBasisSize * numQR, &hVecsRot, ctx));
}
if (primme->correctionParams.precondition &&
primme->correctionParams.maxInnerIterations != 0 &&
primme->correctionParams.projectors.RightQ &&
primme->correctionParams.projectors.SkewQ ) {
ldevecsHat = primme->nLocal;
CHKERR(Num_malloc_Sprimme(ldevecsHat * maxEvecsSize, &evecsHat, ctx));
CHKERR(Num_malloc_SHprimme(maxEvecsSize * maxEvecsSize, &M, ctx));
CHKERR(Num_malloc_SHprimme(maxEvecsSize * maxEvecsSize, &Mfact, ctx));
}
if (primme->massMatrixMatvec && primme->locking) {
CHKERR(Num_malloc_Sprimme(ldBevecs * maxEvecsSize, &Bevecs, ctx));
}
CHKERR(Num_malloc_SHprimme(
primme->maxBasisSize * primme->maxBasisSize, &prevhVecs, ctx));
CHKERR(KIND(Num_malloc_RHprimme, Num_malloc_SHprimme)(primme->maxBasisSize,
&hVals, ctx));
if (numQR > 0) {
CHKERR(Num_malloc_RHprimme(primme->maxBasisSize, &hSVals, ctx));
}
CHKERR(KIND(Num_malloc_RHprimme, Num_malloc_SHprimme)(
primme->maxBasisSize + primme->numEvals, &prevRitzVals, ctx));
CHKERR(Num_malloc_RHprimme(primme->maxBlockSize, &blockNorms, ctx));
CHKERR(Num_malloc_RHprimme(primme->maxBasisSize, &basisNorms, ctx));
CHKERR(
Num_zero_matrix_RHprimme(basisNorms, 1, primme->maxBasisSize, 1, ctx));
/* Integer objects */
CHKERR(Num_malloc_iprimme(primme->numEvals, &perm, ctx));
if (primme->locking) {
CHKERR(Num_malloc_iprimme(primme->numEvals, &lockedFlags, ctx));
}
CHKERR(Num_malloc_iprimme(primme->maxBasisSize, &flags, ctx));
CHKERR(Num_malloc_iprimme(primme->maxBasisSize, &map, ctx));
CHKERR(Num_malloc_iprimme(primme->maxBlockSize, &iev, ctx));
CHKERR(Num_malloc_iprimme(maxEvecsSize, &ipivot, ctx));
/* -------------------------------------------------------------- */
/* Initialize counters and flags */
/* -------------------------------------------------------------- */
primme->stats.numOuterIterations = 0;
primme->stats.numRestarts = 0;
primme->stats.numMatvecs = 0;
primme->stats.numPreconds = 0;
primme->stats.numGlobalSum = 0;
primme->stats.numBroadcast = 0;
primme->stats.volumeGlobalSum = 0;
primme->stats.volumeBroadcast = 0;
primme->stats.flopsDense = 0;
primme->stats.numOrthoInnerProds = 0.0;
primme->stats.elapsedTime = 0.0;
primme->stats.timeMatvec = 0.0;
primme->stats.timePrecond = 0.0;
primme->stats.timeOrtho = 0.0;
primme->stats.timeGlobalSum = 0.0;
primme->stats.timeBroadcast = 0.0;
primme->stats.timeDense = 0.0;
primme->stats.estimateMinEVal = HUGE_VAL;
primme->stats.estimateMaxEVal = -HUGE_VAL;
primme->stats.estimateLargestSVal = -HUGE_VAL;
primme->stats.estimateBNorm = primme->massMatrixMatvec ? -HUGE_VAL : 1.0;
primme->stats.estimateInvBNorm = primme->massMatrixMatvec ? -HUGE_VAL : 1.0;
primme->stats.maxConvTol = 0.0;
primme->stats.estimateResidualError = 0.0;
primme->stats.lockingIssue = 0;
numLocked = 0;
LockingProblem = 0;
blockSize = 0;
*numRet = 0;
for (i=0; i<primme->numEvals; i++) perm[i] = i;
/* -------------------------------------- */
/* Quick return for matrix of dimension 1 */
/* -------------------------------------- */
if (primme->numEvals == 0) {
primme->initSize = 0;
*ret = 0;
goto clean;
}
/* -------------------- */
/* Initialize the basis */
/* -------------------- */
CHKERR(init_basis_Sprimme(V, primme->nLocal, ldV, W, ldW, BV, ldBV, evecs,
ldevecs, Bevecs, ldBevecs, evecsHat, primme->nLocal, M, maxEvecsSize,
Mfact, 0, ipivot, VtBV, ldVtBV, fVtBV, ldfVtBV, maxRank, &basisSize,
&nextGuess, &numGuesses, ctx));
/* Now initSize will store the number of converged pairs */
primme->initSize = 0;
/* ----------------------------------------------------------- */
/* Dynamic method switch means we need to decide whether to */
/* allow inner iterations based on runtime timing measurements */
/* ----------------------------------------------------------- */
if (primme->dynamicMethodSwitch > 0) {
initializeModel(&CostModel, primme);
CostModel.MV = primme->stats.timeMatvec/primme->stats.numMatvecs;
if (primme->numEvals < 5 ||
primme->maxBasisSize + (primme->locking ? primme->numEvals : 0) >=
primme->n)
primme->dynamicMethodSwitch = 1; /* Start tentatively GD+k */
else
primme->dynamicMethodSwitch = 3; /* Start GD+k for 1st pair */
primme->correctionParams.maxInnerIterations = 0;
}
/* ---------------------------------------------------------------------- */
/* Outer most loop */
/* Without locking, restarting can cause converged Ritz values to become */
/* unconverged. Keep performing JD iterations until they remain converged */
/* ---------------------------------------------------------------------- */
while (
primme->stats.numMatvecs < primme->maxMatvecs &&
(primme->maxOuterIterations == 0 ||
primme->stats.numOuterIterations < primme->maxOuterIterations)) {
if (reset > 0) PRINTF(5, "Resetting V, W and QR");
/* Reset convergence flags. This may only reoccur without locking */
primme->initSize = numConverged = numConvergedStored = numLocked;
reset = 0;
for (i=0; i<primme->maxBasisSize; i++)
flags[i] = UNCONVERGED;
/* Compute the initial H and solve for its eigenpairs */
targetShiftIndex = 0;
if (numQR) {
int nQ = 0;
CHKERR(update_Q_Sprimme(BV ? BV : V, primme->nLocal, ldBV, W, ldW, Q,
ldQ, R, primme->maxBasisSize, QtQ, ldQtQ, fQtQ, ldfQtQ,
primme->targetShifts[targetShiftIndex], 0, basisSize, &nQ, ctx));
CHKERRM(numQR && basisSize != nQ, -1, "Not supported deficient QR");
}
if (H)
CHKERR(update_projection_Sprimme(V, ldV, W, ldW, H,
primme->maxBasisSize, primme->nLocal, 0, basisSize,
KIND(1 /*symmetric*/, 0 /* unsymmetric */), ctx));
if (QtV) {
CHKERR(update_projection_Sprimme(
Q, ldQ, V, ldV, QtV, primme->maxBasisSize, primme->nLocal, 0,
basisSize, 0 /*unsymmetric*/, ctx));
}
CHKERR(solve_H_SHprimme(H, basisSize, primme->maxBasisSize,
VtBV
? &VtBV[(primme->numOrthoConst + numLocked) * ldVtBV +
primme->numOrthoConst + numLocked]
: NULL,
ldVtBV, R, primme->maxBasisSize, QtV, primme->maxBasisSize, QtQ,
ldQtQ, hU, basisSize, hVecs, basisSize, hVals, hSVals,
numConverged, ctx));
numArbitraryVecs = 0;
maxRecentlyConverged = availableBlockSize = blockSize = 0;
smallestResNorm = HUGE_VAL;
primme->stats.estimateResidualError = 0.0;
if (!primme->locking) primme->stats.maxConvTol = 0.0;
blockSize = 0;
restartsSinceReset = 0;
/* -------------------------------------------------------------- */
/* Begin the iterative process. Keep restarting until all of the */
/* required eigenpairs have been found (no verification) */
/* -------------------------------------------------------------- */
while (numConverged < primme->numEvals &&
primme->stats.numMatvecs < primme->maxMatvecs &&
(primme->maxOuterIterations == 0 ||
primme->stats.numOuterIterations <
primme->maxOuterIterations) &&
!wholeSpace) {
nprevhVecs = 0;
int candidates_prepared = 0; /* Has prepare_candidates been called? */
/* ----------------------------------------------------------------- */
/* Main block Davidson loop. */
/* Keep adding vectors to the basis V until the basis has reached */
/* maximum size or the basis plus the locked vectors span the entire */
/* space. Once this happens, restart with a smaller basis. */
/* ----------------------------------------------------------------- */
while (basisSize < primme->maxBasisSize &&
primme->stats.numMatvecs < primme->maxMatvecs &&
( primme->maxOuterIterations == 0 ||
primme->stats.numOuterIterations < primme->maxOuterIterations) ) {
primme->stats.numOuterIterations++;
/* When QR are computed and there are more than one target shift, */
/* limit blockSize and the converged values to one. */
if (primme->numTargetShifts > numConverged+1 && numQR) {
availableBlockSize = 1;
maxRecentlyConverged = numConverged-numLocked+1;
}
else {
availableBlockSize = primme->maxBlockSize;
maxRecentlyConverged = max(0, primme->numEvals-numConverged);
}
/* Limit blockSize to vacant vectors in the basis */
availableBlockSize = min(availableBlockSize, primme->maxBasisSize-basisSize);
/* Limit blockSize to remaining values to converge plus one */
availableBlockSize = min(availableBlockSize, maxRecentlyConverged+1);
/* Set the block with the first unconverged pairs */
if (availableBlockSize > 0) {
/* If locking with GD and no preconditioning is running, don't */
/* check practically convergence now, unless whole space. */
int practConvCheck = 0;
if (primme->n <= basisSize + numLocked + primme->numOrthoConst) {
practConvCheck = 1;
} else if (primme->locking && !primme->massMatrixMatvec &&
!primme->correctionParams.precondition &&
primme->correctionParams.maxInnerIterations == 0) {
practConvCheck = -1;
}
CHKERR(prepare_candidates(V, ldV, W, ldW, BV, ldBV,
primme->nLocal, H, primme->maxBasisSize, basisSize,
&V[basisSize * ldV], &W[basisSize * ldW],
BV ? &BV[basisSize * ldBV] : NULL,
1 /* compute approx vectors and residuals */, hVecs,
basisSize, hVals, hSVals, flags, maxRecentlyConverged,
blockNorms, blockSize, availableBlockSize, evecs,
numLocked, ldevecs, Bevecs, ldBevecs, evals, resNorms,
targetShiftIndex, iev, &blockSize, &recentlyConverged,
&numArbitraryVecs, &smallestResNorm, hVecsRot,
primme->maxBasisSize, numConverged, basisNorms, &reset,
VtBV, ldVtBV, prevhVecs, nprevhVecs, primme->maxBasisSize,
practConvCheck, map, startTime, ctx));
assert(recentlyConverged >= 0);
candidates_prepared = 1;
}
else {
blockSize = recentlyConverged = 0;
}
/* If the total number of converged pairs, including the */
/* recentlyConverged ones, are greater than or equal to the */
/* target number of eigenvalues, attempt to restart, verify */
/* their convergence, lock them if necessary, and return. */
/* For locking interior, restart and lock now any converged. */
/* If Q, restart after an eigenpair converged to recompute */
/* QR with a different shift. */
/* Also if it has been converged as many pairs as initial */
/* guesses has introduced in V, then restart and introduce */
/* new guesses. */
numConverged += recentlyConverged;
/* Report iteration */
CHKERR(monitorFun_Sprimme(hVals, basisSize, flags, iev, blockSize,
basisNorms, numConverged, evals, numLocked, lockedFlags,
resNorms, -1, -1.0, NULL, 0.0, primme_event_outer_iteration,
startTime, ctx));
/* Reset touch every time an eigenpair converges */
if (recentlyConverged > 0) touch = 0;
if (primme->dynamicMethodSwitch > 0) {
if (CostModel.resid_0 == -1.0L) /* remember the very */
CostModel.resid_0 = blockNorms[0]; /* first residual */
/* If some pairs converged OR we evaluate JDQMR at every step, */
/* update convergence statistics and consider switching */
if (recentlyConverged > 0 || primme->dynamicMethodSwitch == 2)
{
CostModel.MV =
primme->stats.timeMatvec/primme->stats.numMatvecs;
int ret0 = update_statistics(&CostModel, primme, tstart,
recentlyConverged, 0, numConverged, blockNorms[0]);
if (ret0) switch (primme->dynamicMethodSwitch) {
/* for few evals (dyn=1) evaluate GD+k only at restart*/
case 3:
CHKERR(switch_from_GDpk(&CostModel,ctx));
break;
case 2: case 4:
CHKERR(switch_from_JDQMR(&CostModel,ctx));
}
}
}
if (numConverged >= primme->numEvals ||
(primme->locking && numConverged > numLocked &&
primme->target != primme_smallest &&
primme->target != primme_largest &&
(primme->projectionParams.projection ==
primme_proj_RR ||
primme->target == primme_closest_geq ||
primme->target == primme_closest_leq)) ||
targetShiftIndex < 0 ||
(blockSize == 0 && recentlyConverged > 0) ||
/* NOTE: use the same condition as in restart_refined */
(numQR && fabs(primme->targetShifts[targetShiftIndex] -
primme->targetShifts[min(
primme->numTargetShifts - 1,
numConverged)]) >=
max(primme->aNorm,
primme->stats.estimateLargestSVal)) ||
(numConverged >= nextGuess - primme->numOrthoConst &&
numGuesses > 0)) {
break;
}
if (blockSize > 0) {
/* Solve the correction equations with the new blockSize Ritz */
/* vectors and residuals. */
/* If dynamic method switching, time the inner method */
if (primme->dynamicMethodSwitch > 0) {
tstart = primme_wTimer(); /* accumulate correction time */
}
CHKERR(solve_correction_Sprimme(V, ldV, W, ldW, BV ? BV : V,
ldBV, evecs, ldevecs, Bevecs ? Bevecs : evecs,
Bevecs ? ldBevecs : ldevecs, evecsHat, ldevecsHat, Mfact,
ipivot, evals, numLocked, numConvergedStored, hVals,
prevRitzVals, &numPrevRitzVals, flags, basisSize,
blockNorms, iev, blockSize, &touch, startTime, ctx));
/* ------------------------------------------------------ */
/* If dynamic method switch, accumulate inner method time */
/* ------------------------------------------------------ */
if (primme->dynamicMethodSwitch > 0)
CostModel.time_in_inner += primme_wTimer() - tstart;
} /* end of else blocksize=0 */
/* If locking with GD and no preconditioning is running, check */
/* practically convergence here. The heuristic needs Vlocked' */
/* times r, which is going to be store in Rlocked. */
HSCALAR *Rlocked = NULL;
int ldRlocked = primme->numOrthoConst + numLocked;
int blockSize0 = blockSize;
if (primme->locking && !primme->massMatrixMatvec &&
!primme->correctionParams.precondition &&
primme->correctionParams.maxInnerIterations == 0) {
CHKERR(
Num_malloc_SHprimme(ldRlocked * blockSize, &Rlocked, ctx));
}
/* Orthogonalize the corrections with respect to each other and */
/* the current basis. If basis hasn't expanded with any new */
/* vector, try a random vector */
for (i=0; i < maxNumRandoms; i++) {
int basisSizeOut;
CHKERR(Bortho_block_Sprimme(V, ldV, VtBV, ldVtBV, fVtBV, ldfVtBV,
NULL, 0, basisSize, basisSize + blockSize - 1, evecs,
ldevecs, primme->numOrthoConst + numLocked, BV, ldBV,
i == 0 ? Rlocked : NULL, ldRlocked, primme->nLocal,
maxRank, &basisSizeOut, ctx));
blockSize = basisSizeOut - basisSize;
if (blockSize > 0 || availableBlockSize <= 0) break;
PRINTF(5, "Warning: adding random vector "
"to the search subspace");
CHKERR(Num_larnv_Sprimme(2, primme->iseed, primme->nLocal,
&V[ldV * basisSize], ctx));
blockSize = 1;
}
/* The method failing in expanding the search subspace may be an */
/* indication that a) the orthogonalization error is to large for */
/* distinguishing the new components on the computed correction, */
/* or b) there is no more pairs that satisfy the convergence */
/* criterion. If prepare_candidates gave a candidate, we guess */
/* we are in case a), and otherwise we are in case b). */
if (i >= maxNumRandoms) {
if (availableBlockSize > 0 && blockSize0 <= 0 && reset == 0) {
wholeSpace = 1;
} else {
reset = 2;
}
blockSize = 0;
if (primme->locking && !primme->massMatrixMatvec &&
!primme->correctionParams.precondition &&
primme->correctionParams.maxInnerIterations == 0) {
CHKERR(Num_free_SHprimme(Rlocked, ctx));
}
break;
}
// If locking with GD and no preconditioning is running, check
// practically convergence here. A pair in the block is marked as
// practically converged if the next expression is small enough to
// pass the convergence criterion:
// sqrt(|r|^2 - |Rlocked|^2*(1 + |Xx|^2)),
// where Rlocked is V_locked'*r and Xx is V_locked'*x.
// The term Xx is not totally clear. It appears in the perturbation
// analysis of the eigenproblem with V_locked and x. And it is
// necessary to pass the next test for complex:
// tests/testi-100-LOBPCG_OrthoBasis_Window-100-primme_closest_abs-primme_proj_refined.F
if (primme->locking && !primme->massMatrixMatvec &&
!primme->correctionParams.precondition &&
primme->correctionParams.maxInnerIterations == 0) {
if (numLocked > 0) {
for (i = 0; i < blockSize0 && numConverged < primme->numEvals;
i++) {
HREAL normXx = 0.0;
if (primme->orth == primme_orth_explicit_I) {
HSCALAR *Xx = NULL;
CHKERR(Num_malloc_SHprimme(numLocked, &Xx, ctx));
CHKERR(Num_zero_matrix_SHprimme(
Xx, numLocked, 1, numLocked, ctx));
CHKERR(Num_gemv_SHprimme("N", numLocked, basisSize, 1.0,
&VtBV[ldVtBV * numLocked], ldVtBV,
&hVecs[iev[i] * basisSize], 1, 0.0, Xx, 1, ctx));
normXx = ABS(
Num_dot_SHprimme(numLocked, Xx, 1, Xx, 1, ctx));
CHKERR(Num_free_SHprimme(Xx, ctx));
}
HREAL normRlockedi = ABS(
Num_dot_SHprimme(ldRlocked, &Rlocked[ldRlocked * i],
1, &Rlocked[ldRlocked * i], 1, ctx));
HREAL newBlockNorm =
sqrt(max(blockNorms[i] * blockNorms[i] -
normRlockedi * (1. + normXx),
0.0));
CHKERR(check_convergence_Sprimme(&V[(basisSize + i) * ldV],
ldV, 1 /* given X */, NULL, 0, 0 /* not given R */,
evecs, numLocked, ldevecs, Bevecs, ldBevecs, VtBV,
ldVtBV, 0, 1, &flags[iev[i]], &newBlockNorm,
&hVals[iev[i]], &reset,
-1 /* don't check practically convergence */, ctx));
basisNorms[iev[i]] = newBlockNorm;
if (flags[iev[i]] == CONVERGED) {
flags[iev[i]] = PRACTICALLY_CONVERGED;
numConverged++;
/* Report a pair was soft converged */
CHKERR(monitorFun_Sprimme(hVals, basisSize, flags,
&iev[i], 1, basisNorms, numConverged, NULL, 0,
NULL, NULL, -1, -1.0, NULL, 0.0,
primme_event_converged, startTime, ctx));
}
}
}
CHKERR(Num_free_SHprimme(Rlocked, ctx));
if (numConverged > numLocked &&
primme->target != primme_smallest &&
primme->target != primme_largest &&
(primme->projectionParams.projection == primme_proj_RR ||
primme->target == primme_closest_geq ||
primme->target == primme_closest_leq)) {
break;
}
}
/* Compute W = A*V for the orthogonalized corrections */
CHKERR(matrixMatvec_Sprimme(V, primme->nLocal, ldV, W, ldW,
basisSize, blockSize, ctx));
if (numQR) {
int nQ = basisSize;
CHKERR(update_Q_Sprimme(BV ? BV : V, primme->nLocal, ldBV, W,
ldW, Q, ldQ, R, primme->maxBasisSize, QtQ, ldQtQ, fQtQ,
ldfQtQ, primme->targetShifts[targetShiftIndex], basisSize,
blockSize, &nQ, ctx));
if (basisSize + blockSize != nQ) {
blockSize = 0;
reset = 1;
break;
}
}
/* Extend H by blockSize columns and rows and solve the */
/* eigenproblem for the new H. */
if (H)
CHKERR(update_projection_Sprimme(V, ldV, W, ldW, H,
primme->maxBasisSize, primme->nLocal, basisSize, blockSize,
KIND(1 /*symmetric*/, 0 /* unsymmetric */), ctx));
if (QtV)
CHKERR(update_projection_Sprimme(
Q, ldQ, V, ldV, QtV, primme->maxBasisSize, primme->nLocal,
basisSize, blockSize, 0 /*unsymmetric*/, ctx));
/* Copy hVecs into prevhVecs */
CHKERR(Num_copy_matrix_SHprimme(hVecs, basisSize, basisSize,
basisSize, prevhVecs, primme->maxBasisSize, ctx));
CHKERR(Num_zero_matrix_SHprimme(&prevhVecs[basisSize],
primme->maxBasisSize - basisSize, basisSize,
primme->maxBasisSize, ctx));
nprevhVecs = basisSize;
basisSize += blockSize;
blockSize = 0;
CHKERR(solve_H_SHprimme(H, basisSize, primme->maxBasisSize,
VtBV
? &VtBV[(primme->numOrthoConst + numLocked) * ldVtBV +
primme->numOrthoConst + numLocked]
: NULL,
ldVtBV, R, primme->maxBasisSize, QtV, primme->maxBasisSize,
QtQ, ldQtQ, hU, basisSize, hVecs, basisSize, hVals, hSVals,
numConverged, ctx));
numArbitraryVecs = 0;
candidates_prepared = 0;
/* If QR decomposition accumulates so much error, force it to */
/* reset by setting targetShiftIndex to -1. We use the next */
/* heuristic. Note that if (s_0, u_0, y_0) is the smallest triplet*/
/* of R, (A-tau*I)*V = Q*R, and l_0 is the Rayleigh quotient of */
/* V*y_0, then */
/* |l_0-tau| = |y_0'*V'*(A-tau*I)*V*y_0| = |y_0'*V'*Q*R*y_0| = */
/* = |y_0'*V'*Q*u_0*s_0| <= s_0. */
/* So when |l_0-tau|-machEps*|A| > s_0, we consider to reset the */
/* QR factorization. machEps*|A| is the error computing l_0. */
/* NOTE: rarely observed |l_0-tau|-machEps*|A| slightly greater */
/* than s_0 after resetting. The condition restartsSinceReset > 0 */
/* avoids infinite loop in those cases. */
double eps_orth;
CHKERR(machineEpsOrth_Sprimme(&eps_orth, ctx));
if (primme->projectionParams.projection == primme_proj_refined &&
basisSize > 0 && restartsSinceReset > 1 &&
targetShiftIndex >= 0 &&
ABS((HSCALAR)primme->targetShifts[targetShiftIndex] -
hVals[0]) -
max(primme->aNorm,
primme->stats.estimateLargestSVal) *
eps_orth >
hSVals[0]) {
reset = 2;
PRINTF(5, "Detected some errors in QR");
break;
}
/* --------------------------------------------------------------- */
} /* while (basisSize<maxBasisSize && basisSize<n-orthoConst-numLocked)
* --------------------------------------------------------------- */
/* If wholeSpace, reset if the accumulated errors on the residual */
/* vectors are too large */
if (basisSize >= primme->n - primme->numOrthoConst - numLocked) {
if (primme->stats.maxConvTol < primme->stats.estimateResidualError)
reset = 1;
}
if (reset > 0) break;
/* ----------------------------------------------------------------- */
/* Restart basis will need the final coefficient vectors in hVecs */
/* to lock out converged vectors and to compute X and R for the next */
/* iteration. The function prepare_vecs will make sure that hVecs */
/* has proper coefficient vectors. */
/* ----------------------------------------------------------------- */
if (!candidates_prepared) {
/* -------------------------------------------------------------- */
/* TODO: merge all this logic in the regular main loop. After all */
/* restarting is a regular step that also shrinks the basis. */
/* -------------------------------------------------------------- */
int j,k,l,m;
double *dummySmallestResNorm, dummyZero = 0.0;
if (blockSize > 0) {
availableBlockSize = blockSize;
maxRecentlyConverged = 0;
}
/* When there are more than one target shift, */
/* limit blockSize and the converged values to one. */
else if (primme->numTargetShifts > numConverged+1) {
if (primme->locking) {
maxRecentlyConverged =
max(min(primme->numEvals, numLocked+1) - numConverged, 0);
}
else {
maxRecentlyConverged =
max(min(primme->numEvals, numConverged+1) - numConverged, 0);
}
availableBlockSize = maxRecentlyConverged;
}
else {
maxRecentlyConverged = max(0, primme->numEvals-numConverged);
/* Limit blockSize to vacant vectors in the basis */
availableBlockSize = max(0, min(primme->maxBlockSize, primme->maxBasisSize-(numConverged-numLocked)));
/* Limit blockSize to remaining values to converge plus one */
availableBlockSize = min(availableBlockSize, maxRecentlyConverged+1);
}
/* Limit basisSize to the matrix dimension */
availableBlockSize =
max(0, min(availableBlockSize,
primme->n - numLocked - primme->numOrthoConst));
// Calling prepare_candidates before restarting is compulsory when:
// - the order of the Ritz pairs depends on the residual vector
// norms (e.g. when using refine extraction, or target being
// closest to a point but on the left/right); or
// - the search subspace is exhausted.
// Otherwise we avoid calling prepare_candidates when the method
// restarts all the time, like in LOBPCG.
if (availableBlockSize <= 0 ||
primme->minRestartSize +
primme->restartingParams.maxPrevRetain +
availableBlockSize <
primme->maxBasisSize ||
primme->numOrthoConst + numLocked + basisSize >= primme->n ||
primme->projectionParams.projection != primme_proj_RR) {
// NOTE: setting smallestResNorm to zero may overpass the inner
// product condition (ip) and result in a smaller
// numArbitraryVecs before restarting. This helps or is needed to
// pass testi-100-LOBPCG_OrthoBasis_Window-100-primme_closest_abs
// -primme_proj_refined.F
if (primme->target == primme_closest_abs ||
primme->target == primme_largest_abs) {
dummySmallestResNorm = &dummyZero;
} else {
dummySmallestResNorm = &smallestResNorm;
}
CHKERR(prepare_candidates(V, ldV, W, ldW, BV, ldBV,
primme->nLocal, H, primme->maxBasisSize, basisSize, NULL,
NULL, NULL,
0 /* Not compute approx vectors and residuals */, hVecs,
basisSize, hVals, hSVals, flags, maxRecentlyConverged,
blockNorms, blockSize, availableBlockSize, evecs,
numLocked, ldevecs, Bevecs, ldBevecs, evals, resNorms,
targetShiftIndex, iev, &blockSize, &recentlyConverged,
&numArbitraryVecs, dummySmallestResNorm, hVecsRot,
primme->maxBasisSize, numConverged, basisNorms, &reset,
VtBV, ldVtBV, prevhVecs, nprevhVecs, primme->maxBasisSize,
0, map, startTime, ctx));
assert(recentlyConverged >= 0);
// When QR is computed and there are more than one target shift
// and some eigenpair has converged values to one, don't provide
// candidate for the next iteration, because it may be the
// closest to a different target.