Actual source code: cg.c


  2: /*
  3:     This file implements the conjugate gradient method in PETSc as part of
  4:     KSP. You can use this as a starting point for implementing your own
  5:     Krylov method that is not provided with PETSc.

  7:     The following basic routines are required for each Krylov method.
  8:         KSPCreate_XXX()          - Creates the Krylov context
  9:         KSPSetFromOptions_XXX()  - Sets runtime options
 10:         KSPSolve_XXX()           - Runs the Krylov method
 11:         KSPDestroy_XXX()         - Destroys the Krylov context, freeing all
 12:                                    memory it needed
 13:     Here the "_XXX" denotes a particular implementation, in this case
 14:     we use _CG (e.g. KSPCreate_CG, KSPDestroy_CG). These routines
 15:     are actually called via the common user interface routines
 16:     KSPSetType(), KSPSetFromOptions(), KSPSolve(), and KSPDestroy() so the
 17:     application code interface remains identical for all preconditioners.

 19:     Other basic routines for the KSP objects include
 20:         KSPSetUp_XXX()
 21:         KSPView_XXX()            - Prints details of solver being used.

 23:     Detailed Notes:
 24:     By default, this code implements the CG (Conjugate Gradient) method,
 25:     which is valid for real symmetric (and complex Hermitian) positive
 26:     definite matrices. Note that for the complex Hermitian case, the
 27:     VecDot() arguments within the code MUST remain in the order given
 28:     for correct computation of inner products.

 30:     Reference: Hestenes and Steifel, 1952.

 32:     By switching to the indefinite vector inner product, VecTDot(), the
 33:     same code is used for the complex symmetric case as well.  The user
 34:     must call KSPCGSetType(ksp,KSP_CG_SYMMETRIC) or use the option
 35:     -ksp_cg_type symmetric to invoke this variant for the complex case.
 36:     Note, however, that the complex symmetric code is NOT valid for
 37:     all such matrices ... and thus we don't recommend using this method.
 38: */
 39: /*
 40:     cgimpl.h defines the simple data structured used to store information
 41:     related to the type of matrix (e.g. complex symmetric) being solved and
 42:     data used during the optional Lanczo process used to compute eigenvalues
 43: */
 44: #include <../src/ksp/ksp/impls/cg/cgimpl.h>
 45: extern PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP, PetscReal *, PetscReal *);
 46: extern PetscErrorCode KSPComputeEigenvalues_CG(KSP, PetscInt, PetscReal *, PetscReal *, PetscInt *);

 48: static PetscErrorCode KSPCGSetObjectiveTarget_CG(KSP ksp, PetscReal obj_min)
 49: {
 50:   KSP_CG *cg = (KSP_CG *)ksp->data;

 52:   PetscFunctionBegin;
 53:   cg->obj_min = obj_min;
 54:   PetscFunctionReturn(PETSC_SUCCESS);
 55: }

 57: static PetscErrorCode KSPCGSetRadius_CG(KSP ksp, PetscReal radius)
 58: {
 59:   KSP_CG *cg = (KSP_CG *)ksp->data;

 61:   PetscFunctionBegin;
 62:   cg->radius = radius;
 63:   PetscFunctionReturn(PETSC_SUCCESS);
 64: }

 66: /*
 67:      KSPSetUp_CG - Sets up the workspace needed by the CG method.

 69:       This is called once, usually automatically by KSPSolve() or KSPSetUp()
 70:      but can be called directly by KSPSetUp()
 71: */
 72: static PetscErrorCode KSPSetUp_CG(KSP ksp)
 73: {
 74:   KSP_CG  *cgP   = (KSP_CG *)ksp->data;
 75:   PetscInt maxit = ksp->max_it, nwork = 3;

 77:   PetscFunctionBegin;
 78:   /* get work vectors needed by CG */
 79:   if (cgP->singlereduction) nwork += 2;
 80:   PetscCall(KSPSetWorkVecs(ksp, nwork));

 82:   /*
 83:      If user requested computations of eigenvalues then allocate
 84:      work space needed
 85:   */
 86:   if (ksp->calc_sings) {
 87:     PetscCall(PetscFree4(cgP->e, cgP->d, cgP->ee, cgP->dd));
 88:     PetscCall(PetscMalloc4(maxit, &cgP->e, maxit, &cgP->d, maxit, &cgP->ee, maxit, &cgP->dd));

 90:     ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
 91:     ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_CG;
 92:   }
 93:   PetscFunctionReturn(PETSC_SUCCESS);
 94: }

 96: /*
 97:      A macro used in the following KSPSolve_CG and KSPSolve_CG_SingleReduction routines
 98: */
 99: #define VecXDot(x, y, a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x, y, a) : VecTDot(x, y, a))

101: /*
102:      KSPSolve_CG - This routine actually applies the conjugate gradient method

104:      Note : this routine can be replaced with another one (see below) which implements
105:             another variant of CG.

107:    Input Parameter:
108: .     ksp - the Krylov space object that was set to use conjugate gradient, by, for
109:             example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
110: */
111: static PetscErrorCode KSPSolve_CG(KSP ksp)
112: {
113:   PetscInt    i, stored_max_it, eigs;
114:   PetscScalar dpi = 0.0, a = 1.0, beta, betaold = 1.0, b = 0, *e = NULL, *d = NULL, dpiold;
115:   PetscReal   dp = 0.0;
116:   PetscReal   r2, norm_p, norm_d, dMp;
117:   Vec         X, B, Z, R, P, W;
118:   KSP_CG     *cg;
119:   Mat         Amat, Pmat;
120:   PetscBool   diagonalscale, testobj;

122:   PetscFunctionBegin;
123:   PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale));
124:   PetscCheck(!diagonalscale, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name);

126:   cg            = (KSP_CG *)ksp->data;
127:   eigs          = ksp->calc_sings;
128:   stored_max_it = ksp->max_it;
129:   X             = ksp->vec_sol;
130:   B             = ksp->vec_rhs;
131:   R             = ksp->work[0];
132:   Z             = ksp->work[1];
133:   P             = ksp->work[2];
134:   W             = Z;
135:   r2            = PetscSqr(cg->radius);

137:   if (eigs) {
138:     e    = cg->e;
139:     d    = cg->d;
140:     e[0] = 0.0;
141:   }
142:   PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));

144:   ksp->its = 0;
145:   if (!ksp->guess_zero) {
146:     PetscCall(KSP_MatMult(ksp, Amat, X, R)); /*    r <- b - Ax                       */

148:     PetscCall(VecAYPX(R, -1.0, B));
149:     if (cg->radius) { /* XXX direction? */
150:       PetscCall(VecNorm(X, NORM_2, &norm_d));
151:       norm_d *= norm_d;
152:     }
153:   } else {
154:     PetscCall(VecCopy(B, R)); /*    r <- b (x is 0)                   */
155:     norm_d = 0.0;
156:   }
157:   /* This may be true only on a subset of MPI ranks; setting it here so it will be detected by the first norm computation below */
158:   if (ksp->reason == KSP_DIVERGED_PC_FAILED) PetscCall(VecSetInf(R));

160:   switch (ksp->normtype) {
161:   case KSP_NORM_PRECONDITIONED:
162:     PetscCall(KSP_PCApply(ksp, R, Z));  /*    z <- Br                           */
163:     PetscCall(VecNorm(Z, NORM_2, &dp)); /*    dp <- z'*z = e'*A'*B'*B*A*e       */
164:     KSPCheckNorm(ksp, dp);
165:     break;
166:   case KSP_NORM_UNPRECONDITIONED:
167:     PetscCall(VecNorm(R, NORM_2, &dp)); /*    dp <- r'*r = e'*A'*A*e            */
168:     KSPCheckNorm(ksp, dp);
169:     break;
170:   case KSP_NORM_NATURAL:
171:     PetscCall(KSP_PCApply(ksp, R, Z)); /*    z <- Br                           */
172:     PetscCall(VecXDot(Z, R, &beta));   /*    beta <- z'*r                      */
173:     KSPCheckDot(ksp, beta);
174:     dp = PetscSqrtReal(PetscAbsScalar(beta)); /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
175:     break;
176:   case KSP_NORM_NONE:
177:     dp = 0.0;
178:     break;
179:   default:
180:     SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "%s", KSPNormTypes[ksp->normtype]);
181:   }

183:   /* Initialize objective function
184:      obj = 1/2 x^T A x - x^T b */
185:   testobj = (PetscBool)(cg->obj_min < 0.0);
186:   PetscCall(VecXDot(R, X, &a));
187:   cg->obj = 0.5 * PetscRealPart(a);
188:   PetscCall(VecXDot(B, X, &a));
189:   cg->obj -= 0.5 * PetscRealPart(a);

191:   PetscCall(PetscInfo(ksp, "it %" PetscInt_FMT " obj %g\n", ksp->its, (double)cg->obj));
192:   PetscCall(KSPLogResidualHistory(ksp, dp));
193:   PetscCall(KSPMonitor(ksp, ksp->its, dp));
194:   ksp->rnorm = dp;

196:   PetscCall((*ksp->converged)(ksp, ksp->its, dp, &ksp->reason, ksp->cnvP)); /* test for convergence */

198:   if (!ksp->reason && testobj && cg->obj <= cg->obj_min) {
199:     PetscCall(PetscInfo(ksp, "converged to objective target minimum\n"));
200:     ksp->reason = KSP_CONVERGED_ATOL;
201:   }

203:   if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);

205:   if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) { PetscCall(KSP_PCApply(ksp, R, Z)); /*     z <- Br                           */ }
206:   if (ksp->normtype != KSP_NORM_NATURAL) {
207:     PetscCall(VecXDot(Z, R, &beta)); /*     beta <- z'*r                      */
208:     KSPCheckDot(ksp, beta);
209:   }

211:   i = 0;
212:   do {
213:     ksp->its = i + 1;
214:     if (beta == 0.0) {
215:       ksp->reason = KSP_CONVERGED_ATOL;
216:       PetscCall(PetscInfo(ksp, "converged due to beta = 0\n"));
217:       break;
218: #if !defined(PETSC_USE_COMPLEX)
219:     } else if ((i > 0) && (beta * betaold < 0.0)) {
220:       PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Diverged due to indefinite preconditioner, beta %g, betaold %g", (double)beta, (double)betaold);
221:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
222:       PetscCall(PetscInfo(ksp, "diverging due to indefinite preconditioner\n"));
223:       break;
224: #endif
225:     }
226:     if (!i) {
227:       PetscCall(VecCopy(Z, P)); /*     p <- z                           */
228:       if (cg->radius) {
229:         PetscCall(VecNorm(P, NORM_2, &norm_p));
230:         norm_p *= norm_p;
231:         dMp = 0.0;
232:         if (!ksp->guess_zero) { PetscCall(VecDotRealPart(X, P, &dMp)); }
233:       }
234:       b = 0.0;
235:     } else {
236:       b = beta / betaold;
237:       if (eigs) {
238:         PetscCheck(ksp->max_it == stored_max_it, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Can not change maxit AND calculate eigenvalues");
239:         e[i] = PetscSqrtReal(PetscAbsScalar(b)) / a;
240:       }
241:       PetscCall(VecAYPX(P, b, Z)); /*     p <- z + b* p                    */
242:       if (cg->radius) {
243:         PetscCall(VecDotRealPart(X, P, &dMp));
244:         PetscCall(VecNorm(P, NORM_2, &norm_p));
245:         norm_p *= norm_p;
246:       }
247:     }
248:     dpiold = dpi;
249:     PetscCall(KSP_MatMult(ksp, Amat, P, W)); /*     w <- Ap                          */
250:     PetscCall(VecXDot(P, W, &dpi));          /*     dpi <- p'w                       */
251:     KSPCheckDot(ksp, dpi);
252:     betaold = beta;

254:     if ((dpi == 0.0) || ((i > 0) && ((PetscSign(PetscRealPart(dpi)) * PetscSign(PetscRealPart(dpiold))) < 0.0))) {
255:       if (cg->radius) {
256:         a = 0.0;
257:         if (i == 0) {
258:           if (norm_p > 0.0) {
259:             a = PetscSqrtReal(r2 / norm_p);
260:           } else {
261:             PetscCall(VecNorm(R, NORM_2, &dp));
262:             a = cg->radius > dp ? 1.0 : cg->radius / dp;
263:           }
264:         } else if (norm_p > 0.0) {
265:           a = (PetscSqrtReal(dMp * dMp + norm_p * (r2 - norm_d)) - dMp) / norm_p;
266:         }
267:         PetscCall(VecAXPY(X, a, P)); /*     x <- x + ap                      */
268:         cg->obj += PetscRealPart(a * (0.5 * a * dpi - betaold));
269:       }
270:       PetscCall(PetscInfo(ksp, "it %" PetscInt_FMT " N obj %g\n", i + 1, (double)cg->obj));
271:       if (ksp->converged_neg_curve) {
272:         PetscCall(PetscInfo(ksp, "converged due to negative curvature: %g\n", (double)(PetscRealPart(dpi))));
273:         ksp->reason = KSP_CONVERGED_NEG_CURVE;
274:       } else {
275:         PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Diverged due to indefinite matrix, dpi %g, dpiold %g", (double)PetscRealPart(dpi), (double)PetscRealPart(dpiold));
276:         ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
277:         PetscCall(PetscInfo(ksp, "diverging due to indefinite matrix\n"));
278:       }
279:       break;
280:     }
281:     a = beta / dpi; /*     a = beta/p'w                     */
282:     if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b)) * e[i] + 1.0 / a;
283:     if (cg->radius) { /* Steihaugh-Toint */
284:       PetscReal norm_dp1 = norm_d + PetscRealPart(a) * (2.0 * dMp + PetscRealPart(a) * norm_p);
285:       if (norm_dp1 > r2) {
286:         ksp->reason = KSP_CONVERGED_STEP_LENGTH;
287:         PetscCall(PetscInfo(ksp, "converged to the trust region radius %g\n", (double)cg->radius));
288:         if (norm_p > 0.0) {
289:           dp = (PetscSqrtReal(dMp * dMp + norm_p * (r2 - norm_d)) - dMp) / norm_p;
290:           PetscCall(VecAXPY(X, dp, P)); /*     x <- x + ap                      */
291:           cg->obj += PetscRealPart(dp * (0.5 * dp * dpi - beta));
292:         }
293:         PetscCall(PetscInfo(ksp, "it %" PetscInt_FMT " R obj %g\n", i + 1, (double)cg->obj));
294:         break;
295:       }
296:     }
297:     PetscCall(VecAXPY(X, a, P));  /*     x <- x + ap                      */
298:     PetscCall(VecAXPY(R, -a, W)); /*     r <- r - aw                      */
299:     if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i + 2) {
300:       PetscCall(KSP_PCApply(ksp, R, Z));  /*     z <- Br                          */
301:       PetscCall(VecNorm(Z, NORM_2, &dp)); /*     dp <- z'*z                       */
302:       KSPCheckNorm(ksp, dp);
303:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i + 2) {
304:       PetscCall(VecNorm(R, NORM_2, &dp)); /*     dp <- r'*r                       */
305:       KSPCheckNorm(ksp, dp);
306:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
307:       PetscCall(KSP_PCApply(ksp, R, Z)); /*     z <- Br                          */
308:       PetscCall(VecXDot(Z, R, &beta));   /*     beta <- r'*z                     */
309:       KSPCheckDot(ksp, beta);
310:       dp = PetscSqrtReal(PetscAbsScalar(beta));
311:     } else {
312:       dp = 0.0;
313:     }
314:     cg->obj -= PetscRealPart(0.5 * a * betaold);
315:     PetscCall(PetscInfo(ksp, "it %" PetscInt_FMT " obj %g\n", i + 1, (double)cg->obj));

317:     ksp->rnorm = dp;
318:     PetscCall(KSPLogResidualHistory(ksp, dp));
319:     PetscCall(KSPMonitor(ksp, i + 1, dp));
320:     PetscCall((*ksp->converged)(ksp, i + 1, dp, &ksp->reason, ksp->cnvP));

322:     if (!ksp->reason && testobj && cg->obj <= cg->obj_min) {
323:       PetscCall(PetscInfo(ksp, "converged to objective target minimum\n"));
324:       ksp->reason = KSP_CONVERGED_ATOL;
325:     }

327:     if (ksp->reason) break;

329:     if (cg->radius) {
330:       PetscCall(VecNorm(X, NORM_2, &norm_d));
331:       norm_d *= norm_d;
332:     }

334:     if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i + 2)) { PetscCall(KSP_PCApply(ksp, R, Z)); /*     z <- Br                          */ }
335:     if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i + 2)) {
336:       PetscCall(VecXDot(Z, R, &beta)); /*     beta <- z'*r                     */
337:       KSPCheckDot(ksp, beta);
338:     }

340:     i++;
341:   } while (i < ksp->max_it);
342:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
343:   PetscFunctionReturn(PETSC_SUCCESS);
344: }

346: /*
347:        KSPSolve_CG_SingleReduction

349:        This variant of CG is identical in exact arithmetic to the standard algorithm,
350:        but is rearranged to use only a single reduction stage per iteration, using additional
351:        intermediate vectors.

353:        See KSPCGUseSingleReduction_CG()

355: */
356: static PetscErrorCode KSPSolve_CG_SingleReduction(KSP ksp)
357: {
358:   PetscInt    i, stored_max_it, eigs;
359:   PetscScalar dpi = 0.0, a = 1.0, beta, betaold = 1.0, b = 0, *e = NULL, *d = NULL, delta, dpiold, tmp[2];
360:   PetscReal   dp = 0.0;
361:   Vec         X, B, Z, R, P, S, W, tmpvecs[2];
362:   KSP_CG     *cg;
363:   Mat         Amat, Pmat;
364:   PetscBool   diagonalscale;

366:   PetscFunctionBegin;
367:   PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale));
368:   PetscCheck(!diagonalscale, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name);

370:   cg            = (KSP_CG *)ksp->data;
371:   eigs          = ksp->calc_sings;
372:   stored_max_it = ksp->max_it;
373:   X             = ksp->vec_sol;
374:   B             = ksp->vec_rhs;
375:   R             = ksp->work[0];
376:   Z             = ksp->work[1];
377:   P             = ksp->work[2];
378:   S             = ksp->work[3];
379:   W             = ksp->work[4];

381:   if (eigs) {
382:     e    = cg->e;
383:     d    = cg->d;
384:     e[0] = 0.0;
385:   }
386:   PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));

388:   ksp->its = 0;
389:   if (!ksp->guess_zero) {
390:     PetscCall(KSP_MatMult(ksp, Amat, X, R)); /*    r <- b - Ax                       */
391:     PetscCall(VecAYPX(R, -1.0, B));
392:   } else {
393:     PetscCall(VecCopy(B, R)); /*    r <- b (x is 0)                   */
394:   }

396:   switch (ksp->normtype) {
397:   case KSP_NORM_PRECONDITIONED:
398:     PetscCall(KSP_PCApply(ksp, R, Z));  /*    z <- Br                           */
399:     PetscCall(VecNorm(Z, NORM_2, &dp)); /*    dp <- z'*z = e'*A'*B'*B*A'*e'     */
400:     KSPCheckNorm(ksp, dp);
401:     break;
402:   case KSP_NORM_UNPRECONDITIONED:
403:     PetscCall(VecNorm(R, NORM_2, &dp)); /*    dp <- r'*r = e'*A'*A*e            */
404:     KSPCheckNorm(ksp, dp);
405:     break;
406:   case KSP_NORM_NATURAL:
407:     PetscCall(KSP_PCApply(ksp, R, Z)); /*    z <- Br                           */
408:     PetscCall(KSP_MatMult(ksp, Amat, Z, S));
409:     PetscCall(VecXDot(Z, S, &delta)); /*    delta <- z'*A*z = r'*B*A*B*r      */
410:     PetscCall(VecXDot(Z, R, &beta));  /*    beta <- z'*r                      */
411:     KSPCheckDot(ksp, beta);
412:     dp = PetscSqrtReal(PetscAbsScalar(beta)); /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
413:     break;
414:   case KSP_NORM_NONE:
415:     dp = 0.0;
416:     break;
417:   default:
418:     SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "%s", KSPNormTypes[ksp->normtype]);
419:   }
420:   PetscCall(KSPLogResidualHistory(ksp, dp));
421:   PetscCall(KSPMonitor(ksp, 0, dp));
422:   ksp->rnorm = dp;

424:   PetscCall((*ksp->converged)(ksp, 0, dp, &ksp->reason, ksp->cnvP)); /* test for convergence */
425:   if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);

427:   if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) { PetscCall(KSP_PCApply(ksp, R, Z)); /*    z <- Br                           */ }
428:   if (ksp->normtype != KSP_NORM_NATURAL) {
429:     PetscCall(KSP_MatMult(ksp, Amat, Z, S));
430:     PetscCall(VecXDot(Z, S, &delta)); /*    delta <- z'*A*z = r'*B*A*B*r      */
431:     PetscCall(VecXDot(Z, R, &beta));  /*    beta <- z'*r                      */
432:     KSPCheckDot(ksp, beta);
433:   }

435:   i = 0;
436:   do {
437:     ksp->its = i + 1;
438:     if (beta == 0.0) {
439:       ksp->reason = KSP_CONVERGED_ATOL;
440:       PetscCall(PetscInfo(ksp, "converged due to beta = 0\n"));
441:       break;
442: #if !defined(PETSC_USE_COMPLEX)
443:     } else if ((i > 0) && (beta * betaold < 0.0)) {
444:       PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Diverged due to indefinite preconditioner");
445:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
446:       PetscCall(PetscInfo(ksp, "diverging due to indefinite preconditioner\n"));
447:       break;
448: #endif
449:     }
450:     if (!i) {
451:       PetscCall(VecCopy(Z, P)); /*    p <- z                           */
452:       b = 0.0;
453:     } else {
454:       b = beta / betaold;
455:       if (eigs) {
456:         PetscCheck(ksp->max_it == stored_max_it, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Can not change maxit AND calculate eigenvalues");
457:         e[i] = PetscSqrtReal(PetscAbsScalar(b)) / a;
458:       }
459:       PetscCall(VecAYPX(P, b, Z)); /*    p <- z + b* p                     */
460:     }
461:     dpiold = dpi;
462:     if (!i) {
463:       PetscCall(KSP_MatMult(ksp, Amat, P, W)); /*    w <- Ap                           */
464:       PetscCall(VecXDot(P, W, &dpi));          /*    dpi <- p'w                        */
465:     } else {
466:       PetscCall(VecAYPX(W, beta / betaold, S));                 /*    w <- Ap                           */
467:       dpi = delta - beta * beta * dpiold / (betaold * betaold); /*    dpi <- p'w                        */
468:     }
469:     betaold = beta;
470:     KSPCheckDot(ksp, beta);

472:     if ((dpi == 0.0) || ((i > 0) && (PetscRealPart(dpi * dpiold) <= 0.0))) {
473:       PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Diverged due to indefinite matrix");
474:       ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
475:       PetscCall(PetscInfo(ksp, "diverging due to indefinite or negative definite matrix\n"));
476:       break;
477:     }
478:     a = beta / dpi; /*    a = beta/p'w                      */
479:     if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b)) * e[i] + 1.0 / a;
480:     PetscCall(VecAXPY(X, a, P));  /*    x <- x + ap                       */
481:     PetscCall(VecAXPY(R, -a, W)); /*    r <- r - aw                       */
482:     if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i + 2) {
483:       PetscCall(KSP_PCApply(ksp, R, Z)); /*    z <- Br                           */
484:       PetscCall(KSP_MatMult(ksp, Amat, Z, S));
485:       PetscCall(VecNorm(Z, NORM_2, &dp)); /*    dp <- z'*z                        */
486:       KSPCheckNorm(ksp, dp);
487:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i + 2) {
488:       PetscCall(VecNorm(R, NORM_2, &dp)); /*    dp <- r'*r                        */
489:       KSPCheckNorm(ksp, dp);
490:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
491:       PetscCall(KSP_PCApply(ksp, R, Z)); /*    z <- Br                           */
492:       tmpvecs[0] = S;
493:       tmpvecs[1] = R;
494:       PetscCall(KSP_MatMult(ksp, Amat, Z, S));
495:       PetscCall(VecMDot(Z, 2, tmpvecs, tmp)); /*    delta <- z'*A*z = r'*B*A*B*r      */
496:       delta = tmp[0];
497:       beta  = tmp[1]; /*    beta <- z'*r                      */
498:       KSPCheckDot(ksp, beta);
499:       dp = PetscSqrtReal(PetscAbsScalar(beta)); /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
500:     } else {
501:       dp = 0.0;
502:     }
503:     ksp->rnorm = dp;
504:     PetscCall(KSPLogResidualHistory(ksp, dp));
505:     PetscCall(KSPMonitor(ksp, i + 1, dp));
506:     PetscCall((*ksp->converged)(ksp, i + 1, dp, &ksp->reason, ksp->cnvP));
507:     if (ksp->reason) break;

509:     if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i + 2)) {
510:       PetscCall(KSP_PCApply(ksp, R, Z)); /*    z <- Br                           */
511:       PetscCall(KSP_MatMult(ksp, Amat, Z, S));
512:     }
513:     if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i + 2)) {
514:       tmpvecs[0] = S;
515:       tmpvecs[1] = R;
516:       PetscCall(VecMDot(Z, 2, tmpvecs, tmp));
517:       delta = tmp[0];
518:       beta  = tmp[1];         /*    delta <- z'*A*z = r'*B'*A*B*r     */
519:       KSPCheckDot(ksp, beta); /*    beta <- z'*r                      */
520:     }

522:     i++;
523:   } while (i < ksp->max_it);
524:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
525:   PetscFunctionReturn(PETSC_SUCCESS);
526: }

528: /*
529:      KSPDestroy_CG - Frees resources allocated in KSPSetup_CG and clears function
530:                      compositions from KSPCreate_CG. If adding your own KSP implementation,
531:                      you must be sure to free all allocated resources here to prevent
532:                      leaks.
533: */
534: PetscErrorCode KSPDestroy_CG(KSP ksp)
535: {
536:   KSP_CG *cg = (KSP_CG *)ksp->data;

538:   PetscFunctionBegin;
539:   PetscCall(PetscFree4(cg->e, cg->d, cg->ee, cg->dd));
540:   PetscCall(KSPDestroyDefault(ksp));
541:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPCGSetObjectiveTarget_C", NULL));
542:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPCGSetRadius_C", NULL));
543:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPCGSetType_C", NULL));
544:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPCGUseSingleReduction_C", NULL));
545:   PetscFunctionReturn(PETSC_SUCCESS);
546: }

548: /*
549:      KSPView_CG - Prints information about the current Krylov method being used.
550:                   If your Krylov method has special options or flags that information
551:                   should be printed here.
552: */
553: PetscErrorCode KSPView_CG(KSP ksp, PetscViewer viewer)
554: {
555:   KSP_CG   *cg = (KSP_CG *)ksp->data;
556:   PetscBool iascii;

558:   PetscFunctionBegin;
559:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
560:   if (iascii) {
561: #if defined(PETSC_USE_COMPLEX)
562:     PetscCall(PetscViewerASCIIPrintf(viewer, "  variant %s\n", KSPCGTypes[cg->type]));
563: #endif
564:     if (cg->singlereduction) PetscCall(PetscViewerASCIIPrintf(viewer, "  using single-reduction variant\n"));
565:   }
566:   PetscFunctionReturn(PETSC_SUCCESS);
567: }

569: /*
570:     KSPSetFromOptions_CG - Checks the options database for options related to the
571:                            conjugate gradient method.
572: */
573: PetscErrorCode KSPSetFromOptions_CG(KSP ksp, PetscOptionItems *PetscOptionsObject)
574: {
575:   KSP_CG   *cg = (KSP_CG *)ksp->data;
576:   PetscBool flg;

578:   PetscFunctionBegin;
579:   PetscOptionsHeadBegin(PetscOptionsObject, "KSP CG and CGNE options");
580: #if defined(PETSC_USE_COMPLEX)
581:   PetscCall(PetscOptionsEnum("-ksp_cg_type", "Matrix is Hermitian or complex symmetric", "KSPCGSetType", KSPCGTypes, (PetscEnum)cg->type, (PetscEnum *)&cg->type, NULL));
582: #endif
583:   PetscCall(PetscOptionsBool("-ksp_cg_single_reduction", "Merge inner products into single MPI_Allreduce()", "KSPCGUseSingleReduction", cg->singlereduction, &cg->singlereduction, &flg));
584:   if (flg) PetscCall(KSPCGUseSingleReduction(ksp, cg->singlereduction));
585:   PetscOptionsHeadEnd();
586:   PetscFunctionReturn(PETSC_SUCCESS);
587: }

589: /*
590:     KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
591:                       This routine is registered below in KSPCreate_CG() and called from the
592:                       routine KSPCGSetType() (see the file cgtype.c).
593: */
594: PetscErrorCode KSPCGSetType_CG(KSP ksp, KSPCGType type)
595: {
596:   KSP_CG *cg = (KSP_CG *)ksp->data;

598:   PetscFunctionBegin;
599:   cg->type = type;
600:   PetscFunctionReturn(PETSC_SUCCESS);
601: }

603: /*
604:     KSPCGUseSingleReduction_CG

606:     This routine sets a flag to use a variant of CG. Note that (in somewhat
607:     atypical fashion) it also swaps out the routine called when KSPSolve()
608:     is invoked.
609: */
610: static PetscErrorCode KSPCGUseSingleReduction_CG(KSP ksp, PetscBool flg)
611: {
612:   KSP_CG *cg = (KSP_CG *)ksp->data;

614:   PetscFunctionBegin;
615:   cg->singlereduction = flg;
616:   if (cg->singlereduction) {
617:     ksp->ops->solve = KSPSolve_CG_SingleReduction;
618:   } else {
619:     ksp->ops->solve = KSPSolve_CG;
620:   }
621:   PetscFunctionReturn(PETSC_SUCCESS);
622: }

624: PETSC_INTERN PetscErrorCode KSPBuildResidual_CG(KSP ksp, Vec t, Vec v, Vec *V)
625: {
626:   PetscFunctionBegin;
627:   PetscCall(VecCopy(ksp->work[0], v));
628:   *V = v;
629:   PetscFunctionReturn(PETSC_SUCCESS);
630: }

632: /*MC
633:      KSPCG - The Preconditioned Conjugate Gradient (PCG) iterative method

635:    Options Database Keys:
636: +   -ksp_cg_type Hermitian - (for complex matrices only) indicates the matrix is Hermitian, see `KSPCGSetType()`
637: .   -ksp_cg_type symmetric - (for complex matrices only) indicates the matrix is symmetric
638: -   -ksp_cg_single_reduction - performs both inner products needed in the algorithm with a single `MPI_Allreduce()` call, see `KSPCGUseSingleReduction()`

640:    Level: beginner

642:    Notes:
643:     The PCG method requires both the matrix and preconditioner to be symmetric positive (or negative) (semi) definite.

645:    Only left preconditioning is supported; there are several ways to motivate preconditioned CG, but they all produce the same algorithm.
646:    One can interpret preconditioning A with B to mean any of the following\:
647: .n  (1) Solve a left-preconditioned system BAx = Bb, using inv(B) to define an inner product in the algorithm.
648: .n  (2) Solve a right-preconditioned system ABy = b, x = By, using B to define an inner product in the algorithm.
649: .n  (3) Solve a symmetrically-preconditioned system, E^TAEy = E^Tb, x = Ey, where B = EE^T.
650: .n  (4) Solve Ax=b with CG, but use the inner product defined by B to define the method [2].
651: .n  In all cases, the resulting algorithm only requires application of B to vectors.

653:    For complex numbers there are two different CG methods, one for Hermitian symmetric matrices and one for non-Hermitian symmetric matrices. Use
654:    `KSPCGSetType()` to indicate which type you are using.

656:    One can use `KSPSetComputeEigenvalues()` and `KSPComputeEigenvalues()` to compute the eigenvalues of the (preconditioned) operator

658:    Developer Notes:
659:     KSPSolve_CG() should actually query the matrix to determine if it is Hermitian symmetric or not and NOT require the user to
660:    indicate it to the `KSP` object.

662:    References:
663: +  * - Magnus R. Hestenes and Eduard Stiefel, Methods of Conjugate Gradients for Solving Linear Systems,
664:    Journal of Research of the National Bureau of Standards Vol. 49, No. 6, December 1952 Research Paper 2379
665: -  * - Josef Malek and Zdenek Strakos, Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs,
666:     SIAM, 2014.

668: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPSetComputeEigenvalues()`, `KSPComputeEigenvalues()`
669:           `KSPCGSetType()`, `KSPCGUseSingleReduction()`, `KSPPIPECG`, `KSPGROPPCG`
670: M*/

672: /*
673:     KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the
674:        function pointers for all the routines it needs to call (KSPSolve_CG() etc)

676:     It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
677: */
678: PETSC_EXTERN PetscErrorCode KSPCreate_CG(KSP ksp)
679: {
680:   KSP_CG *cg;

682:   PetscFunctionBegin;
683:   PetscCall(PetscNew(&cg));
684: #if !defined(PETSC_USE_COMPLEX)
685:   cg->type = KSP_CG_SYMMETRIC;
686: #else
687:   cg->type = KSP_CG_HERMITIAN;
688: #endif
689:   cg->obj_min = 0.0;
690:   ksp->data   = (void *)cg;

692:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
693:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_LEFT, 2));
694:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NATURAL, PC_LEFT, 2));
695:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));

697:   /*
698:        Sets the functions that are associated with this data structure
699:        (in C++ this is the same as defining virtual functions)
700:   */
701:   ksp->ops->setup          = KSPSetUp_CG;
702:   ksp->ops->solve          = KSPSolve_CG;
703:   ksp->ops->destroy        = KSPDestroy_CG;
704:   ksp->ops->view           = KSPView_CG;
705:   ksp->ops->setfromoptions = KSPSetFromOptions_CG;
706:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
707:   ksp->ops->buildresidual  = KSPBuildResidual_CG;

709:   /*
710:       Attach the function KSPCGSetType_CG() to this object. The routine
711:       KSPCGSetType() checks for this attached function and calls it if it finds
712:       it. (Sort of like a dynamic member function that can be added at run time
713:   */
714:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPCGSetType_C", KSPCGSetType_CG));
715:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPCGUseSingleReduction_C", KSPCGUseSingleReduction_CG));
716:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPCGSetRadius_C", KSPCGSetRadius_CG));
717:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPCGSetObjectiveTarget_C", KSPCGSetObjectiveTarget_CG));
718:   PetscFunctionReturn(PETSC_SUCCESS);
719: }