Actual source code: pipefcg.c

  1: #include <../src/ksp/ksp/impls/fcg/pipefcg/pipefcgimpl.h>

  3: static PetscBool  cited      = PETSC_FALSE;
  4: static const char citation[] = "@article{SSM2016,\n"
  5:                                "  author = {P. Sanan and S.M. Schnepp and D.A. May},\n"
  6:                                "  title = {Pipelined, Flexible Krylov Subspace Methods},\n"
  7:                                "  journal = {SIAM Journal on Scientific Computing},\n"
  8:                                "  volume = {38},\n"
  9:                                "  number = {5},\n"
 10:                                "  pages = {C441-C470},\n"
 11:                                "  year = {2016},\n"
 12:                                "  doi = {10.1137/15M1049130},\n"
 13:                                "  URL = {http://dx.doi.org/10.1137/15M1049130},\n"
 14:                                "  eprint = {http://dx.doi.org/10.1137/15M1049130}\n"
 15:                                "}\n";

 17: #define KSPPIPEFCG_DEFAULT_MMAX       15
 18: #define KSPPIPEFCG_DEFAULT_NPREALLOC  5
 19: #define KSPPIPEFCG_DEFAULT_VECB       5
 20: #define KSPPIPEFCG_DEFAULT_TRUNCSTRAT KSP_FCD_TRUNC_TYPE_NOTAY

 22: static PetscErrorCode KSPAllocateVectors_PIPEFCG(KSP ksp, PetscInt nvecsneeded, PetscInt chunksize)
 23: {
 24:   KSP_PIPEFCG *pipefcg;
 25:   PetscInt     nnewvecs, nvecsprev;

 27:   PetscFunctionBegin;
 28:   pipefcg = (KSP_PIPEFCG *)ksp->data;

 30:   /* Allocate enough new vectors to add chunksize new vectors, reach nvecsneedtotal, or to reach mmax+1, whichever is smallest */
 31:   if (pipefcg->nvecs < PetscMin(pipefcg->mmax + 1, nvecsneeded)) {
 32:     nvecsprev = pipefcg->nvecs;
 33:     nnewvecs  = PetscMin(PetscMax(nvecsneeded - pipefcg->nvecs, chunksize), pipefcg->mmax + 1 - pipefcg->nvecs);
 34:     PetscCall(KSPCreateVecs(ksp, nnewvecs, &pipefcg->pQvecs[pipefcg->nchunks], 0, NULL));
 35:     PetscCall(KSPCreateVecs(ksp, nnewvecs, &pipefcg->pZETAvecs[pipefcg->nchunks], 0, NULL));
 36:     PetscCall(KSPCreateVecs(ksp, nnewvecs, &pipefcg->pPvecs[pipefcg->nchunks], 0, NULL));
 37:     PetscCall(KSPCreateVecs(ksp, nnewvecs, &pipefcg->pSvecs[pipefcg->nchunks], 0, NULL));
 38:     pipefcg->nvecs += nnewvecs;
 39:     for (PetscInt i = 0; i < nnewvecs; ++i) {
 40:       pipefcg->Qvecs[nvecsprev + i]    = pipefcg->pQvecs[pipefcg->nchunks][i];
 41:       pipefcg->ZETAvecs[nvecsprev + i] = pipefcg->pZETAvecs[pipefcg->nchunks][i];
 42:       pipefcg->Pvecs[nvecsprev + i]    = pipefcg->pPvecs[pipefcg->nchunks][i];
 43:       pipefcg->Svecs[nvecsprev + i]    = pipefcg->pSvecs[pipefcg->nchunks][i];
 44:     }
 45:     pipefcg->chunksizes[pipefcg->nchunks] = nnewvecs;
 46:     ++pipefcg->nchunks;
 47:   }
 48:   PetscFunctionReturn(PETSC_SUCCESS);
 49: }

 51: static PetscErrorCode KSPSetUp_PIPEFCG(KSP ksp)
 52: {
 53:   KSP_PIPEFCG   *pipefcg;
 54:   const PetscInt nworkstd = 5;

 56:   PetscFunctionBegin;
 57:   pipefcg = (KSP_PIPEFCG *)ksp->data;

 59:   /* Allocate "standard" work vectors (not including the basis and transformed basis vectors) */
 60:   PetscCall(KSPSetWorkVecs(ksp, nworkstd));

 62:   /* Allocated space for pointers to additional work vectors
 63:    note that mmax is the number of previous directions, so we add 1 for the current direction,
 64:    and an extra 1 for the prealloc (which might be empty) */
 65:   PetscCall(PetscMalloc4(pipefcg->mmax + 1, &pipefcg->Pvecs, pipefcg->mmax + 1, &pipefcg->pPvecs, pipefcg->mmax + 1, &pipefcg->Svecs, pipefcg->mmax + 1, &pipefcg->pSvecs));
 66:   PetscCall(PetscMalloc4(pipefcg->mmax + 1, &pipefcg->Qvecs, pipefcg->mmax + 1, &pipefcg->pQvecs, pipefcg->mmax + 1, &pipefcg->ZETAvecs, pipefcg->mmax + 1, &pipefcg->pZETAvecs));
 67:   PetscCall(PetscMalloc4(pipefcg->mmax + 1, &pipefcg->Pold, pipefcg->mmax + 1, &pipefcg->Sold, pipefcg->mmax + 1, &pipefcg->Qold, pipefcg->mmax + 1, &pipefcg->ZETAold));
 68:   PetscCall(PetscMalloc1(pipefcg->mmax + 1, &pipefcg->chunksizes));
 69:   PetscCall(PetscMalloc3(pipefcg->mmax + 2, &pipefcg->dots, pipefcg->mmax + 1, &pipefcg->etas, pipefcg->mmax + 2, &pipefcg->redux));

 71:   /* If the requested number of preallocated vectors is greater than mmax reduce nprealloc */
 72:   if (pipefcg->nprealloc > pipefcg->mmax + 1) PetscCall(PetscInfo(NULL, "Requested nprealloc=%" PetscInt_FMT " is greater than m_max+1=%" PetscInt_FMT ". Resetting nprealloc = m_max+1.\n", pipefcg->nprealloc, pipefcg->mmax + 1));

 74:   /* Preallocate additional work vectors */
 75:   PetscCall(KSPAllocateVectors_PIPEFCG(ksp, pipefcg->nprealloc, pipefcg->nprealloc));
 76:   PetscFunctionReturn(PETSC_SUCCESS);
 77: }

 79: static PetscErrorCode KSPSolve_PIPEFCG_cycle(KSP ksp)
 80: {
 81:   PetscInt     i, j, k, idx, kdx, mi;
 82:   KSP_PIPEFCG *pipefcg;
 83:   PetscScalar  alpha = 0.0, gamma, *betas, *dots;
 84:   PetscReal    dp    = 0.0, delta, *eta, *etas;
 85:   Vec          B, R, Z, X, Qcurr, W, ZETAcurr, M, N, Pcurr, Scurr, *redux;
 86:   Mat          Amat, Pmat;

 88:   PetscFunctionBegin;
 89:   /* We have not checked these routines for use with complex numbers. The inner products
 90:      are likely not defined correctly for that case */
 91:   PetscCheck(!PetscDefined(USE_COMPLEX) || PetscDefined(SKIP_COMPLEX), PETSC_COMM_WORLD, PETSC_ERR_SUP, "PIPEFGMRES has not been implemented for use with complex scalars");

 93: #define VecXDot(x, y, a)          (pipefcg->type == KSP_CG_HERMITIAN ? VecDot(x, y, a) : VecTDot(x, y, a))
 94: #define VecXDotBegin(x, y, a)     (pipefcg->type == KSP_CG_HERMITIAN ? VecDotBegin(x, y, a) : VecTDotBegin(x, y, a))
 95: #define VecXDotEnd(x, y, a)       (pipefcg->type == KSP_CG_HERMITIAN ? VecDotEnd(x, y, a) : VecTDotEnd(x, y, a))
 96: #define VecMXDot(x, n, y, a)      (pipefcg->type == KSP_CG_HERMITIAN ? VecMDot(x, n, y, a) : VecMTDot(x, n, y, a))
 97: #define VecMXDotBegin(x, n, y, a) (pipefcg->type == KSP_CG_HERMITIAN ? VecMDotBegin(x, n, y, a) : VecMTDotBegin(x, n, y, a))
 98: #define VecMXDotEnd(x, n, y, a)   (pipefcg->type == KSP_CG_HERMITIAN ? VecMDotEnd(x, n, y, a) : VecMTDotEnd(x, n, y, a))

100:   pipefcg = (KSP_PIPEFCG *)ksp->data;
101:   X       = ksp->vec_sol;
102:   B       = ksp->vec_rhs;
103:   R       = ksp->work[0];
104:   Z       = ksp->work[1];
105:   W       = ksp->work[2];
106:   M       = ksp->work[3];
107:   N       = ksp->work[4];

109:   redux = pipefcg->redux;
110:   dots  = pipefcg->dots;
111:   etas  = pipefcg->etas;
112:   betas = dots; /* dots takes the result of all dot products of which the betas are a subset */

114:   PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));

116:   /* Compute cycle initial residual */
117:   PetscCall(KSP_MatMult(ksp, Amat, X, R));
118:   PetscCall(VecAYPX(R, -1.0, B));    /* r <- b - Ax */
119:   PetscCall(KSP_PCApply(ksp, R, Z)); /* z <- Br     */

121:   Pcurr    = pipefcg->Pvecs[0];
122:   Scurr    = pipefcg->Svecs[0];
123:   Qcurr    = pipefcg->Qvecs[0];
124:   ZETAcurr = pipefcg->ZETAvecs[0];
125:   PetscCall(VecCopy(Z, Pcurr));
126:   PetscCall(KSP_MatMult(ksp, Amat, Pcurr, Scurr)); /* S = Ap     */
127:   PetscCall(VecCopy(Scurr, W));                    /* w = s = Az */

129:   /* Initial state of pipelining intermediates */
130:   redux[0] = R;
131:   redux[1] = W;
132:   PetscCall(VecMXDotBegin(Z, 2, redux, dots));
133:   PetscCall(PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)Z))); /* perform asynchronous reduction */
134:   PetscCall(KSP_PCApply(ksp, W, M));                                        /* m = B(w) */
135:   PetscCall(KSP_MatMult(ksp, Amat, M, N));                                  /* n = Am   */
136:   PetscCall(VecCopy(M, Qcurr));                                             /* q = m    */
137:   PetscCall(VecCopy(N, ZETAcurr));                                          /* zeta = n */
138:   PetscCall(VecMXDotEnd(Z, 2, redux, dots));
139:   gamma   = dots[0];
140:   delta   = PetscRealPart(dots[1]);
141:   etas[0] = delta;
142:   alpha   = gamma / delta;

144:   i = 0;
145:   do {
146:     ksp->its++;

148:     /* Update X, R, Z, W */
149:     PetscCall(VecAXPY(X, +alpha, Pcurr));    /* x <- x + alpha * pi    */
150:     PetscCall(VecAXPY(R, -alpha, Scurr));    /* r <- r - alpha * si    */
151:     PetscCall(VecAXPY(Z, -alpha, Qcurr));    /* z <- z - alpha * qi    */
152:     PetscCall(VecAXPY(W, -alpha, ZETAcurr)); /* w <- w - alpha * zetai */

154:     /* Compute norm for convergence check */
155:     switch (ksp->normtype) {
156:     case KSP_NORM_PRECONDITIONED:
157:       PetscCall(VecNorm(Z, NORM_2, &dp)); /* dp <- sqrt(z'*z) = sqrt(e'*A'*B'*B*A*e) */
158:       break;
159:     case KSP_NORM_UNPRECONDITIONED:
160:       PetscCall(VecNorm(R, NORM_2, &dp)); /* dp <- sqrt(r'*r) = sqrt(e'*A'*A*e)      */
161:       break;
162:     case KSP_NORM_NATURAL:
163:       dp = PetscSqrtReal(PetscAbsScalar(gamma)); /* dp <- sqrt(r'*z) = sqrt(e'*A'*B*A*e)    */
164:       break;
165:     case KSP_NORM_NONE:
166:       dp = 0.0;
167:       break;
168:     default:
169:       SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "%s", KSPNormTypes[ksp->normtype]);
170:     }

172:     /* Check for convergence */
173:     ksp->rnorm = dp;
174:     PetscCall(KSPLogResidualHistory(ksp, dp));
175:     PetscCall(KSPMonitor(ksp, ksp->its, dp));
176:     PetscCall((*ksp->converged)(ksp, ksp->its, dp, &ksp->reason, ksp->cnvP));
177:     if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);

179:     /* Computations of current iteration done */
180:     ++i;

182:     /* If needbe, allocate a new chunk of vectors in P and C */
183:     PetscCall(KSPAllocateVectors_PIPEFCG(ksp, i + 1, pipefcg->vecb));

185:     /* Note that we wrap around and start clobbering old vectors */
186:     idx      = i % (pipefcg->mmax + 1);
187:     Pcurr    = pipefcg->Pvecs[idx];
188:     Scurr    = pipefcg->Svecs[idx];
189:     Qcurr    = pipefcg->Qvecs[idx];
190:     ZETAcurr = pipefcg->ZETAvecs[idx];
191:     eta      = pipefcg->etas + idx;

193:     /* number of old directions to orthogonalize against */
194:     switch (pipefcg->truncstrat) {
195:     case KSP_FCD_TRUNC_TYPE_STANDARD:
196:       mi = pipefcg->mmax;
197:       break;
198:     case KSP_FCD_TRUNC_TYPE_NOTAY:
199:       mi = ((i - 1) % pipefcg->mmax) + 1;
200:       break;
201:     default:
202:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unrecognized Truncation Strategy");
203:     }

205:     /* Pick old p,s,q,zeta in a way suitable for VecMDot */
206:     PetscCall(VecCopy(Z, Pcurr));
207:     for (k = PetscMax(0, i - mi), j = 0; k < i; ++j, ++k) {
208:       kdx                 = k % (pipefcg->mmax + 1);
209:       pipefcg->Pold[j]    = pipefcg->Pvecs[kdx];
210:       pipefcg->Sold[j]    = pipefcg->Svecs[kdx];
211:       pipefcg->Qold[j]    = pipefcg->Qvecs[kdx];
212:       pipefcg->ZETAold[j] = pipefcg->ZETAvecs[kdx];
213:       redux[j]            = pipefcg->Svecs[kdx];
214:     }
215:     redux[j]     = R; /* If the above loop is not executed redux contains only R => all beta_k = 0, only gamma, delta != 0 */
216:     redux[j + 1] = W;

218:     PetscCall(VecMXDotBegin(Z, j + 2, redux, betas));                         /* Start split reductions for beta_k = (z,s_k), gamma = (z,r), delta = (z,w) */
219:     PetscCall(PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)Z))); /* perform asynchronous reduction */
220:     PetscCall(VecWAXPY(N, -1.0, R, W));                                       /* m = u + B(w-r): (a) ntmp = w-r              */
221:     PetscCall(KSP_PCApply(ksp, N, M));                                        /* m = u + B(w-r): (b) mtmp = B(ntmp) = B(w-r) */
222:     PetscCall(VecAXPY(M, 1.0, Z));                                            /* m = u + B(w-r): (c) m = z + mtmp            */
223:     PetscCall(KSP_MatMult(ksp, Amat, M, N));                                  /* n = Am                                      */
224:     PetscCall(VecMXDotEnd(Z, j + 2, redux, betas));                           /* Finish split reductions */
225:     gamma = betas[j];
226:     delta = PetscRealPart(betas[j + 1]);

228:     *eta = 0.;
229:     for (k = PetscMax(0, i - mi), j = 0; k < i; ++j, ++k) {
230:       kdx = k % (pipefcg->mmax + 1);
231:       betas[j] /= -etas[kdx]; /* betak  /= etak */
232:       *eta -= PetscAbsScalar(betas[j]) * PetscAbsScalar(betas[j]) * etas[kdx];
233:       /* etaitmp = -betaik^2 * etak */
234:     }
235:     *eta += delta; /* etai    = delta -betaik^2 * etak */
236:     if (*eta < 0.) {
237:       pipefcg->norm_breakdown = PETSC_TRUE;
238:       PetscCall(PetscInfo(ksp, "Restart due to square root breakdown at it = %" PetscInt_FMT "\n", ksp->its));
239:       break;
240:     } else {
241:       alpha = gamma / (*eta); /* alpha = gamma/etai */
242:     }

244:     /* project out stored search directions using classical G-S */
245:     PetscCall(VecCopy(Z, Pcurr));
246:     PetscCall(VecCopy(W, Scurr));
247:     PetscCall(VecCopy(M, Qcurr));
248:     PetscCall(VecCopy(N, ZETAcurr));
249:     PetscCall(VecMAXPY(Pcurr, j, betas, pipefcg->Pold));       /* pi    <- ui - sum_k beta_k p_k    */
250:     PetscCall(VecMAXPY(Scurr, j, betas, pipefcg->Sold));       /* si    <- wi - sum_k beta_k s_k    */
251:     PetscCall(VecMAXPY(Qcurr, j, betas, pipefcg->Qold));       /* qi    <- m  - sum_k beta_k q_k    */
252:     PetscCall(VecMAXPY(ZETAcurr, j, betas, pipefcg->ZETAold)); /* zetai <- n  - sum_k beta_k zeta_k */

254:   } while (ksp->its < ksp->max_it);
255:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
256:   PetscFunctionReturn(PETSC_SUCCESS);
257: }

259: static PetscErrorCode KSPSolve_PIPEFCG(KSP ksp)
260: {
261:   KSP_PIPEFCG *pipefcg;
262:   PetscScalar  gamma;
263:   PetscReal    dp = 0.0;
264:   Vec          B, R, Z, X;
265:   Mat          Amat, Pmat;

267: #define VecXDot(x, y, a) (pipefcg->type == KSP_CG_HERMITIAN ? VecDot(x, y, a) : VecTDot(x, y, a))

269:   PetscFunctionBegin;
270:   PetscCall(PetscCitationsRegister(citation, &cited));

272:   pipefcg = (KSP_PIPEFCG *)ksp->data;
273:   X       = ksp->vec_sol;
274:   B       = ksp->vec_rhs;
275:   R       = ksp->work[0];
276:   Z       = ksp->work[1];

278:   PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));

280:   /* Compute initial residual needed for convergence check*/
281:   ksp->its = 0;
282:   if (!ksp->guess_zero) {
283:     PetscCall(KSP_MatMult(ksp, Amat, X, R));
284:     PetscCall(VecAYPX(R, -1.0, B)); /* r <- b - Ax                             */
285:   } else {
286:     PetscCall(VecCopy(B, R)); /* r <- b (x is 0)                         */
287:   }
288:   switch (ksp->normtype) {
289:   case KSP_NORM_PRECONDITIONED:
290:     PetscCall(KSP_PCApply(ksp, R, Z));  /* z <- Br                                 */
291:     PetscCall(VecNorm(Z, NORM_2, &dp)); /* dp <- dqrt(z'*z) = sqrt(e'*A'*B'*B*A*e) */
292:     break;
293:   case KSP_NORM_UNPRECONDITIONED:
294:     PetscCall(VecNorm(R, NORM_2, &dp)); /* dp <- sqrt(r'*r) = sqrt(e'*A'*A*e)      */
295:     break;
296:   case KSP_NORM_NATURAL:
297:     PetscCall(KSP_PCApply(ksp, R, Z)); /* z <- Br                                 */
298:     PetscCall(VecXDot(Z, R, &gamma));
299:     dp = PetscSqrtReal(PetscAbsScalar(gamma)); /* dp <- sqrt(r'*z) = sqrt(e'*A'*B*A*e)    */
300:     break;
301:   case KSP_NORM_NONE:
302:     dp = 0.0;
303:     break;
304:   default:
305:     SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "%s", KSPNormTypes[ksp->normtype]);
306:   }

308:   /* Initial Convergence Check */
309:   PetscCall(KSPLogResidualHistory(ksp, dp));
310:   PetscCall(KSPMonitor(ksp, 0, dp));
311:   ksp->rnorm = dp;
312:   PetscCall((*ksp->converged)(ksp, 0, dp, &ksp->reason, ksp->cnvP));
313:   if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);

315:   do {
316:     /* A cycle is broken only if a norm breakdown occurs. If not the entire solve happens in a single cycle.
317:        This is coded this way to allow both truncation and truncation-restart strategy
318:        (see KSPFCDGetNumOldDirections()) */
319:     PetscCall(KSPSolve_PIPEFCG_cycle(ksp));
320:     if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);
321:     if (pipefcg->norm_breakdown) {
322:       pipefcg->n_restarts++;
323:       pipefcg->norm_breakdown = PETSC_FALSE;
324:     }
325:   } while (ksp->its < ksp->max_it);

327:   if (ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
328:   PetscFunctionReturn(PETSC_SUCCESS);
329: }

331: static PetscErrorCode KSPDestroy_PIPEFCG(KSP ksp)
332: {
333:   KSP_PIPEFCG *pipefcg;

335:   PetscFunctionBegin;
336:   pipefcg = (KSP_PIPEFCG *)ksp->data;

338:   /* Destroy "standard" work vecs */
339:   PetscCall(VecDestroyVecs(ksp->nwork, &ksp->work));

341:   /* Destroy vectors of old directions and the arrays that manage pointers to them */
342:   if (pipefcg->nvecs) {
343:     for (PetscInt i = 0; i < pipefcg->nchunks; ++i) {
344:       PetscCall(VecDestroyVecs(pipefcg->chunksizes[i], &pipefcg->pPvecs[i]));
345:       PetscCall(VecDestroyVecs(pipefcg->chunksizes[i], &pipefcg->pSvecs[i]));
346:       PetscCall(VecDestroyVecs(pipefcg->chunksizes[i], &pipefcg->pQvecs[i]));
347:       PetscCall(VecDestroyVecs(pipefcg->chunksizes[i], &pipefcg->pZETAvecs[i]));
348:     }
349:   }
350:   PetscCall(PetscFree4(pipefcg->Pvecs, pipefcg->Svecs, pipefcg->pPvecs, pipefcg->pSvecs));
351:   PetscCall(PetscFree4(pipefcg->Qvecs, pipefcg->ZETAvecs, pipefcg->pQvecs, pipefcg->pZETAvecs));
352:   PetscCall(PetscFree4(pipefcg->Pold, pipefcg->Sold, pipefcg->Qold, pipefcg->ZETAold));
353:   PetscCall(PetscFree(pipefcg->chunksizes));
354:   PetscCall(PetscFree3(pipefcg->dots, pipefcg->etas, pipefcg->redux));
355:   PetscCall(KSPDestroyDefault(ksp));
356:   PetscFunctionReturn(PETSC_SUCCESS);
357: }

359: static PetscErrorCode KSPView_PIPEFCG(KSP ksp, PetscViewer viewer)
360: {
361:   KSP_PIPEFCG *pipefcg = (KSP_PIPEFCG *)ksp->data;
362:   PetscBool    isascii, isstring;
363:   const char  *truncstr;

365:   PetscFunctionBegin;
366:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
367:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSTRING, &isstring));

369:   if (pipefcg->truncstrat == KSP_FCD_TRUNC_TYPE_STANDARD) {
370:     truncstr = "Using standard truncation strategy";
371:   } else if (pipefcg->truncstrat == KSP_FCD_TRUNC_TYPE_NOTAY) {
372:     truncstr = "Using Notay's truncation strategy";
373:   } else {
374:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Undefined FCD truncation strategy");
375:   }

377:   if (isascii) {
378:     PetscCall(PetscViewerASCIIPrintf(viewer, "  max previous directions = %" PetscInt_FMT "\n", pipefcg->mmax));
379:     PetscCall(PetscViewerASCIIPrintf(viewer, "  preallocated %" PetscInt_FMT " directions\n", PetscMin(pipefcg->nprealloc, pipefcg->mmax + 1)));
380:     PetscCall(PetscViewerASCIIPrintf(viewer, "  %s\n", truncstr));
381:     PetscCall(PetscViewerASCIIPrintf(viewer, "  restarts performed = %" PetscInt_FMT " \n", pipefcg->n_restarts));
382:   } else if (isstring) {
383:     PetscCall(PetscViewerStringSPrintf(viewer, "max previous directions = %" PetscInt_FMT ", preallocated %" PetscInt_FMT " directions, %s truncation strategy", pipefcg->mmax, pipefcg->nprealloc, truncstr));
384:   }
385:   PetscFunctionReturn(PETSC_SUCCESS);
386: }

388: /*@
389:   KSPPIPEFCGSetMmax - set the maximum number of previous directions `KSPPIPEFCG` will store for orthogonalization

391:   Logically Collective

393:   Input Parameters:
394: + ksp  - the Krylov space context
395: - mmax - the maximum number of previous directions to orthogonalize against

397:   Options Database Key:
398: . -ksp_pipefcg_mmax N - maximum number of previous directions

400:   Level: intermediate

402:   Note:
403:   `mmax` + 1 directions are stored (`mmax` previous ones along with the current one)
404:   and whether all are used in each iteration also depends on the truncation strategy, see `KSPPIPEFCGSetTruncationType()`

406: .seealso: [](ch_ksp), `KSPPIPEFCG`, `KSPPIPEFCGSetTruncationType()`, `KSPPIPEFCGSetNprealloc()`, `KSPFCGSetMmax()`, `KSPFCGGetMmax()`
407: @*/
408: PetscErrorCode KSPPIPEFCGSetMmax(KSP ksp, PetscInt mmax)
409: {
410:   KSP_PIPEFCG *pipefcg = (KSP_PIPEFCG *)ksp->data;

412:   PetscFunctionBegin;
415:   pipefcg->mmax = mmax;
416:   PetscFunctionReturn(PETSC_SUCCESS);
417: }

419: /*@
420:   KSPPIPEFCGGetMmax - get the maximum number of previous directions `KSPPIPEFCG` will store

422:   Not Collective

424:   Input Parameter:
425: . ksp - the Krylov space context

427:   Output Parameter:
428: . mmax - the maximum number of previous directions allowed for orthogonalization

430:   Level: intermediate

432: .seealso: [](ch_ksp), `KSPPIPEFCG`, `KSPPIPEFCGGetTruncationType()`, `KSPPIPEFCGGetNprealloc()`, `KSPPIPEFCGSetMmax()`, `KSPFCGGetMmax()`, `KSPFCGSetMmax()`
433: @*/
434: PetscErrorCode KSPPIPEFCGGetMmax(KSP ksp, PetscInt *mmax)
435: {
436:   KSP_PIPEFCG *pipefcg = (KSP_PIPEFCG *)ksp->data;

438:   PetscFunctionBegin;
440:   *mmax = pipefcg->mmax;
441:   PetscFunctionReturn(PETSC_SUCCESS);
442: }

444: /*@
445:   KSPPIPEFCGSetNprealloc - set the number of directions to preallocate with `KSPPIPEFCG`

447:   Logically Collective

449:   Input Parameters:
450: + ksp       - the Krylov space context
451: - nprealloc - the number of vectors to preallocate

453:   Options Database Key:
454: . -ksp_pipefcg_nprealloc N - the number of vectors to preallocate

456:   Level: advanced

458: .seealso: [](ch_ksp), `KSPPIPEFCG`, `KSPPIPEFCGSetTruncationType()`, `KSPPIPEFCGGetNprealloc()`, `KSPPIPEFCGSetMmax()`, `KSPPIPEFCGGetMmax()`
459: @*/
460: PetscErrorCode KSPPIPEFCGSetNprealloc(KSP ksp, PetscInt nprealloc)
461: {
462:   KSP_PIPEFCG *pipefcg = (KSP_PIPEFCG *)ksp->data;

464:   PetscFunctionBegin;
467:   pipefcg->nprealloc = nprealloc;
468:   PetscFunctionReturn(PETSC_SUCCESS);
469: }

471: /*@
472:   KSPPIPEFCGGetNprealloc - get the number of directions to preallocate by `KSPPIPEFCG`

474:   Not Collective

476:   Input Parameter:
477: . ksp - the Krylov space context

479:   Output Parameter:
480: . nprealloc - the number of directions preallocated

482:   Level: advanced

484: .seealso: [](ch_ksp), `KSPPIPEFCG`, `KSPPIPEFCGGetTruncationType()`, `KSPPIPEFCGSetNprealloc()`, `KSPPIPEFCGSetMmax()`, `KSPPIPEFCGGetMmax()`
485: @*/
486: PetscErrorCode KSPPIPEFCGGetNprealloc(KSP ksp, PetscInt *nprealloc)
487: {
488:   KSP_PIPEFCG *pipefcg = (KSP_PIPEFCG *)ksp->data;

490:   PetscFunctionBegin;
492:   *nprealloc = pipefcg->nprealloc;
493:   PetscFunctionReturn(PETSC_SUCCESS);
494: }

496: /*@
497:   KSPPIPEFCGSetTruncationType - specify how many of its stored previous directions `KSPPIPEFCG` uses during orthogonalization

499:   Logically Collective

501:   Input Parameters:
502: + ksp        - the Krylov space context
503: - truncstrat - the choice of strategy
504: .vb
505:   KSP_FCD_TRUNC_TYPE_STANDARD uses all (up to `mmax`) stored directions
506:   KSP_FCD_TRUNC_TYPE_NOTAY uses `max(1,mod(i,mmax))` stored directions at iteration i = 0, 1, ...
507: .ve

509:   Options Database Key:
510: . -ksp_pipefcg_truncation_type (standard|notay) - which stored search directions to orthogonalize against

512:   Level: intermediate

514: .seealso: [](ch_ksp), `KSPPIPEFCG`, `KSPPIPEFCGGetTruncationType`, `KSPFCDTruncationType`, `KSP_FCD_TRUNC_TYPE_STANDARD`, `KSP_FCD_TRUNC_TYPE_NOTAY`
515: @*/
516: PetscErrorCode KSPPIPEFCGSetTruncationType(KSP ksp, KSPFCDTruncationType truncstrat)
517: {
518:   KSP_PIPEFCG *pipefcg = (KSP_PIPEFCG *)ksp->data;

520:   PetscFunctionBegin;
523:   pipefcg->truncstrat = truncstrat;
524:   PetscFunctionReturn(PETSC_SUCCESS);
525: }

527: /*@
528:   KSPPIPEFCGGetTruncationType - get the truncation strategy employed by `KSPPIPEFCG`

530:   Not Collective

532:   Input Parameter:
533: . ksp - the Krylov space context

535:   Output Parameter:
536: . truncstrat - the strategy type

538:   Level: intermediate

540: .seealso: [](ch_ksp), `KSPPIPEFCG`, `KSPPIPEFCGSetTruncationType()`, `KSPFCDTruncationType`, `KSP_FCD_TRUNC_TYPE_STANDARD`, `KSP_FCD_TRUNC_TYPE_NOTAY`
541: @*/
542: PetscErrorCode KSPPIPEFCGGetTruncationType(KSP ksp, KSPFCDTruncationType *truncstrat)
543: {
544:   KSP_PIPEFCG *pipefcg = (KSP_PIPEFCG *)ksp->data;

546:   PetscFunctionBegin;
548:   *truncstrat = pipefcg->truncstrat;
549:   PetscFunctionReturn(PETSC_SUCCESS);
550: }

552: static PetscErrorCode KSPSetFromOptions_PIPEFCG(KSP ksp, PetscOptionItems PetscOptionsObject)
553: {
554:   KSP_PIPEFCG *pipefcg = (KSP_PIPEFCG *)ksp->data;
555:   PetscInt     mmax, nprealloc;
556:   PetscBool    flg;

558:   PetscFunctionBegin;
559:   PetscOptionsHeadBegin(PetscOptionsObject, "KSP PIPEFCG options");
560:   PetscCall(PetscOptionsInt("-ksp_pipefcg_mmax", "Number of search directions to storue", "KSPPIPEFCGSetMmax", pipefcg->mmax, &mmax, &flg));
561:   if (flg) PetscCall(KSPPIPEFCGSetMmax(ksp, mmax));
562:   PetscCall(PetscOptionsInt("-ksp_pipefcg_nprealloc", "Number of directions to preallocate", "KSPPIPEFCGSetNprealloc", pipefcg->nprealloc, &nprealloc, &flg));
563:   if (flg) PetscCall(KSPPIPEFCGSetNprealloc(ksp, nprealloc));
564:   PetscCall(PetscOptionsEnum("-ksp_pipefcg_truncation_type", "Truncation approach for directions", "KSPFCGSetTruncationType", KSPFCDTruncationTypes, (PetscEnum)pipefcg->truncstrat, (PetscEnum *)&pipefcg->truncstrat, NULL));
565:   PetscOptionsHeadEnd();
566:   PetscFunctionReturn(PETSC_SUCCESS);
567: }

569: /*MC
570:   KSPPIPEFCG - Implements a Pipelined, Flexible Conjugate Gradient method {cite}`sananschneppmay2016`. [](sec_pipelineksp). [](sec_flexibleksp)

572:   Options Database Keys:
573: +   -ksp_pipefcg_mmax N                           - The number of previous search directions to store
574: .   -ksp_pipefcg_nprealloc N                      - The number of previous search directions to preallocate
575: -   -ksp_pipefcg_truncation_type (standard|notay) - which stored search directions to orthogonalize against

577:   Level: intermediate

579:   Notes:
580:   Pipelined version of `KSPFCG` that overlaps communication (global reductions) with computation (preconditioner application and matrix-vector products) to reduce the impact of communication latency on parallel performance.

582:   Supports left preconditioning only.

584:   The natural "norm" for this method is $(u,Au)$, where $u$ is the preconditioned residual. As with standard `KSPCG`, this norm is available at no additional computational cost.
585:   Choosing preconditioned or unpreconditioned norms involve an extra blocking global reduction, thus removing any benefit from pipelining.

587:   MPI configuration may be necessary for reductions to make asynchronous progress, which is important for performance of pipelined methods.
588:   See [](doc_faq_pipelined)

590:   Contributed by:
591:   Patrick Sanan and Sascha M. Schnepp

593: .seealso: [](ch_ksp), [](doc_faq_pipelined), [](sec_pipelineksp), [](sec_flexibleksp), `KSPFCG`, `KSPPIPECG`, `KSPPIPECR`, `KSPGCR`, `KSPPIPEGCR`, `KSPFGMRES`,
594:           `KSPCG`, `KSPPIPEFCGSetMmax()`, `KSPPIPEFCGGetMmax()`, `KSPPIPEFCGSetNprealloc()`,
595:           `KSPPIPEFCGGetNprealloc()`, `KSPPIPEFCGSetTruncationType()`, `KSPPIPEFCGGetTruncationType()`
596: M*/
597: PETSC_EXTERN PetscErrorCode KSPCreate_PIPEFCG(KSP ksp)
598: {
599:   KSP_PIPEFCG *pipefcg;

601:   PetscFunctionBegin;
602:   PetscCall(PetscNew(&pipefcg));
603:   pipefcg->type       = !PetscDefined(USE_COMPLEX) ? KSP_CG_SYMMETRIC : KSP_CG_HERMITIAN;
604:   pipefcg->mmax       = KSPPIPEFCG_DEFAULT_MMAX;
605:   pipefcg->nprealloc  = KSPPIPEFCG_DEFAULT_NPREALLOC;
606:   pipefcg->nvecs      = 0;
607:   pipefcg->vecb       = KSPPIPEFCG_DEFAULT_VECB;
608:   pipefcg->nchunks    = 0;
609:   pipefcg->truncstrat = KSPPIPEFCG_DEFAULT_TRUNCSTRAT;
610:   pipefcg->n_restarts = 0;

612:   ksp->data = (void *)pipefcg;

614:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 2));
615:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NATURAL, PC_LEFT, 1));
616:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_LEFT, 1));
617:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));

619:   ksp->ops->setup          = KSPSetUp_PIPEFCG;
620:   ksp->ops->solve          = KSPSolve_PIPEFCG;
621:   ksp->ops->destroy        = KSPDestroy_PIPEFCG;
622:   ksp->ops->view           = KSPView_PIPEFCG;
623:   ksp->ops->setfromoptions = KSPSetFromOptions_PIPEFCG;
624:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
625:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
626:   PetscFunctionReturn(PETSC_SUCCESS);
627: }