Actual source code: cg.c

petsc-3.10.3 2018-12-18
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  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 are
 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: /*
 49:      KSPSetUp_CG - Sets up the workspace needed by the CG method.

 51:       This is called once, usually automatically by KSPSolve() or KSPSetUp()
 52:      but can be called directly by KSPSetUp()
 53: */
 54: static PetscErrorCode KSPSetUp_CG(KSP ksp)
 55: {
 56:   KSP_CG         *cgP = (KSP_CG*)ksp->data;
 58:   PetscInt       maxit = ksp->max_it,nwork = 3;

 61:   /* get work vectors needed by CG */
 62:   if (cgP->singlereduction) nwork += 2;
 63:   KSPSetWorkVecs(ksp,nwork);

 65:   /*
 66:      If user requested computations of eigenvalues then allocate work
 67:      work space needed
 68:   */
 69:   if (ksp->calc_sings) {
 70:     /* get space to store tridiagonal matrix for Lanczos */
 71:     PetscMalloc4(maxit+1,&cgP->e,maxit+1,&cgP->d,maxit+1,&cgP->ee,maxit+1,&cgP->dd);
 72:     PetscLogObjectMemory((PetscObject)ksp,2*(maxit+1)*(sizeof(PetscScalar)+sizeof(PetscReal)));

 74:     ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
 75:     ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_CG;
 76:   }
 77:   return(0);
 78: }

 80: /*
 81:      A macro used in the following KSPSolve_CG and KSPSolve_CG_SingleReduction routines
 82: */
 83: #define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))

 85: /*
 86:      KSPSolve_CG - This routine actually applies the conjugate gradient method

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

 91:    Input Parameter:
 92: .     ksp - the Krylov space object that was set to use conjugate gradient, by, for
 93:             example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
 94: */
 95: static PetscErrorCode KSPSolve_CG(KSP ksp)
 96: {
 98:   PetscInt       i,stored_max_it,eigs;
 99:   PetscScalar    dpi = 0.0,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0,dpiold;
100:   PetscReal      dp  = 0.0;
101:   Vec            X,B,Z,R,P,W;
102:   KSP_CG         *cg;
103:   Mat            Amat,Pmat;
104:   PetscBool      diagonalscale;

107:   PCGetDiagonalScale(ksp->pc,&diagonalscale);
108:   if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);

110:   cg            = (KSP_CG*)ksp->data;
111:   eigs          = ksp->calc_sings;
112:   stored_max_it = ksp->max_it;
113:   X             = ksp->vec_sol;
114:   B             = ksp->vec_rhs;
115:   R             = ksp->work[0];
116:   Z             = ksp->work[1];
117:   P             = ksp->work[2];
118:   W             = Z;

120:   if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
121:   PCGetOperators(ksp->pc,&Amat,&Pmat);

123:   ksp->its = 0;
124:   if (!ksp->guess_zero) {
125:     KSP_MatMult(ksp,Amat,X,R);            /*    r <- b - Ax                       */
126:     VecAYPX(R,-1.0,B);
127:   } else {
128:     VecCopy(B,R);                         /*    r <- b (x is 0)                   */
129:   }

131:   switch (ksp->normtype) {
132:     case KSP_NORM_PRECONDITIONED:
133:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
134:       VecNorm(Z,NORM_2,&dp);              /*    dp <- z'*z = e'*A'*B'*B*A'*e'     */
135:       break;
136:     case KSP_NORM_UNPRECONDITIONED:
137:       VecNorm(R,NORM_2,&dp);              /*    dp <- r'*r = e'*A'*A*e            */
138:       break;
139:     case KSP_NORM_NATURAL:
140:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
141:       VecXDot(Z,R,&beta);                 /*    beta <- z'*r                      */
142:       KSPCheckDot(ksp,beta);
143:       dp = PetscSqrtReal(PetscAbsScalar(beta));                /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
144:       break;
145:     case KSP_NORM_NONE:
146:       dp = 0.0;
147:       break;
148:     default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
149:   }
150:   KSPLogResidualHistory(ksp,dp);
151:   KSPMonitor(ksp,0,dp);
152:   ksp->rnorm = dp;

154:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);     /* test for convergence */
155:   if (ksp->reason) return(0);

157:   if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
158:     KSP_PCApply(ksp,R,Z);                /*     z <- Br                           */
159:   }
160:   if (ksp->normtype != KSP_NORM_NATURAL) {
161:     VecXDot(Z,R,&beta);                  /*     beta <- z'*r                      */
162:     KSPCheckDot(ksp,beta);
163:   }

165:   i = 0;
166:   do {
167:     ksp->its = i+1;
168:     if (beta == 0.0) {
169:       ksp->reason = KSP_CONVERGED_ATOL;
170:       PetscInfo(ksp,"converged due to beta = 0\n");
171:       break;
172: #if !defined(PETSC_USE_COMPLEX)
173:     } else if ((i > 0) && (beta*betaold < 0.0)) {
174:       if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"Diverged due to indefinite preconditioner");
175:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
176:       PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
177:       break;
178: #endif
179:     }
180:     if (!i) {
181:       VecCopy(Z,P);                       /*     p <- z                           */
182:       b    = 0.0;
183:     } else {
184:       b = beta/betaold;
185:       if (eigs) {
186:         if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
187:         e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
188:       }
189:       VecAYPX(P,b,Z);                     /*     p <- z + b* p                    */
190:     }
191:     dpiold = dpi;
192:     KSP_MatMult(ksp,Amat,P,W);            /*     w <- Ap                          */
193:     VecXDot(P,W,&dpi);                    /*     dpi <- p'w                       */
194:     KSPCheckDot(ksp,dpi);
195:     betaold = beta;

197:     if ((dpi == 0.0) || ((i > 0) && (PetscRealPart(dpi*dpiold) <= 0.0))) {
198:       if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"Diverged due to indefinite matrix");
199:       ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
200:       PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
201:       break;
202:     }
203:     a = beta/dpi;                                              /*     a = beta/p'w                     */
204:     if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
205:     VecAXPY(X,a,P);                       /*     x <- x + ap                      */
206:     VecAXPY(R,-a,W);                      /*     r <- r - aw                      */
207:     if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
208:       KSP_PCApply(ksp,R,Z);               /*     z <- Br                          */
209:       VecNorm(Z,NORM_2,&dp);              /*     dp <- z'*z                       */
210:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
211:       VecNorm(R,NORM_2,&dp);              /*     dp <- r'*r                       */
212:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
213:       KSP_PCApply(ksp,R,Z);               /*     z <- Br                          */
214:       VecXDot(Z,R,&beta);                 /*     beta <- r'*z                     */
215:       KSPCheckDot(ksp,beta);
216:       dp = PetscSqrtReal(PetscAbsScalar(beta));
217:     } else {
218:       dp = 0.0;
219:     }
220:     ksp->rnorm = dp;
221:     KSPLogResidualHistory(ksp,dp);
222:     if (eigs) cg->ned = ksp->its;
223:     KSPMonitor(ksp,i+1,dp);
224:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
225:     if (ksp->reason) break;

227:     if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)) {
228:       KSP_PCApply(ksp,R,Z);               /*     z <- Br                          */
229:     }
230:     if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)) {
231:       VecXDot(Z,R,&beta);                 /*     beta <- z'*r                     */
232:       KSPCheckDot(ksp,beta);
233:     }

235:     i++;
236:   } while (i<ksp->max_it);
237:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
238:   return(0);
239: }

241: /*    
242:        KSPSolve_CG_SingleReduction

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

248:        See KSPCGUseSingleReduction_CG()

250: */
251: static PetscErrorCode KSPSolve_CG_SingleReduction(KSP ksp)
252: {
254:   PetscInt       i,stored_max_it,eigs;
255:   PetscScalar    dpi = 0.0,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0,delta,dpiold,tmp[2];
256:   PetscReal      dp  = 0.0;
257:   Vec            X,B,Z,R,P,S,W,tmpvecs[2];
258:   KSP_CG         *cg;
259:   Mat            Amat,Pmat;
260:   PetscBool      diagonalscale;

263:   PCGetDiagonalScale(ksp->pc,&diagonalscale);
264:   if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);

266:   cg            = (KSP_CG*)ksp->data;
267:   eigs          = ksp->calc_sings;
268:   stored_max_it = ksp->max_it;
269:   X             = ksp->vec_sol;
270:   B             = ksp->vec_rhs;
271:   R             = ksp->work[0];
272:   Z             = ksp->work[1];
273:   P             = ksp->work[2];
274:   S             = ksp->work[3];
275:   W             = ksp->work[4];

277:   if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
278:   PCGetOperators(ksp->pc,&Amat,&Pmat);

280:   ksp->its = 0;
281:   if (!ksp->guess_zero) {
282:     KSP_MatMult(ksp,Amat,X,R);            /*    r <- b - Ax                       */
283:     VecAYPX(R,-1.0,B);
284:   } else {
285:     VecCopy(B,R);                         /*    r <- b (x is 0)                   */
286:   }

288:   switch (ksp->normtype) {
289:     case KSP_NORM_PRECONDITIONED:
290:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
291:       VecNorm(Z,NORM_2,&dp);              /*    dp <- z'*z = e'*A'*B'*B*A'*e'     */
292:       break;
293:     case KSP_NORM_UNPRECONDITIONED:
294:       VecNorm(R,NORM_2,&dp);              /*    dp <- r'*r = e'*A'*A*e            */
295:       break;
296:     case KSP_NORM_NATURAL:
297:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
298:       KSP_MatMult(ksp,Amat,Z,S);
299:       VecXDot(Z,S,&delta);                /*    delta <- z'*A*z = r'*B*A*B*r      */
300:       VecXDot(Z,R,&beta);                 /*    beta <- z'*r                      */
301:       KSPCheckDot(ksp,beta);
302:       dp = PetscSqrtReal(PetscAbsScalar(beta));                /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
303:       break;
304:     case KSP_NORM_NONE:
305:       dp = 0.0;
306:       break;
307:     default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
308:   }
309:   KSPLogResidualHistory(ksp,dp);
310:   KSPMonitor(ksp,0,dp);
311:   ksp->rnorm = dp;

313:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);     /* test for convergence */
314:   if (ksp->reason) return(0);

316:   if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
317:     KSP_PCApply(ksp,R,Z);                 /*    z <- Br                           */
318:   }
319:   if (ksp->normtype != KSP_NORM_NATURAL) {
320:     KSP_MatMult(ksp,Amat,Z,S);
321:     VecXDot(Z,S,&delta);                  /*    delta <- z'*A*z = r'*B*A*B*r      */
322:     VecXDot(Z,R,&beta);                   /*    beta <- z'*r                      */
323:     KSPCheckDot(ksp,beta);
324:   }

326:   i = 0;
327:   do {
328:     ksp->its = i+1;
329:     if (beta == 0.0) {
330:       ksp->reason = KSP_CONVERGED_ATOL;
331:       PetscInfo(ksp,"converged due to beta = 0\n");
332:       break;
333: #if !defined(PETSC_USE_COMPLEX)
334:     } else if ((i > 0) && (beta*betaold < 0.0)) {
335:       if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"Diverged due to indefinite preconditioner");
336:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
337:       PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
338:       break;
339: #endif
340:     }
341:     if (!i) {
342:       VecCopy(Z,P);                       /*    p <- z                           */
343:       b    = 0.0;
344:     } else {
345:       b = beta/betaold;
346:       if (eigs) {
347:         if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
348:         e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
349:       }
350:       VecAYPX(P,b,Z);                     /*    p <- z + b* p                     */
351:     }
352:     dpiold = dpi;
353:     if (!i) {
354:       KSP_MatMult(ksp,Amat,P,W);          /*    w <- Ap                           */
355:       VecXDot(P,W,&dpi);                  /*    dpi <- p'w                        */
356:     } else {
357:       VecAYPX(W,beta/betaold,S);          /*    w <- Ap                           */
358:       dpi  = delta - beta*beta*dpiold/(betaold*betaold);       /*    dpi <- p'w                        */
359:     }
360:     betaold = beta;
361:     KSPCheckDot(ksp,beta);

363:     if ((dpi == 0.0) || ((i > 0) && (PetscRealPart(dpi*dpiold) <= 0.0))) {
364:       if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"Diverged due to indefinite matrix");
365:       ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
366:       PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
367:       break;
368:     }
369:     a = beta/dpi;                                              /*    a = beta/p'w                      */
370:     if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
371:     VecAXPY(X,a,P);                       /*    x <- x + ap                       */
372:     VecAXPY(R,-a,W);                      /*    r <- r - aw                       */
373:     if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
374:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
375:       KSP_MatMult(ksp,Amat,Z,S);
376:       VecNorm(Z,NORM_2,&dp);              /*    dp <- z'*z                        */
377:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
378:       VecNorm(R,NORM_2,&dp);              /*    dp <- r'*r                        */
379:     } else if (ksp->normtype == KSP_NORM_NATURAL) {
380:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
381:       tmpvecs[0] = S; tmpvecs[1] = R;
382:       KSP_MatMult(ksp,Amat,Z,S);
383:       VecMDot(Z,2,tmpvecs,tmp);          /*    delta <- z'*A*z = r'*B*A*B*r      */
384:       delta = tmp[0]; beta = tmp[1];                           /*    beta <- z'*r                      */
385:       KSPCheckDot(ksp,beta);
386:       dp = PetscSqrtReal(PetscAbsScalar(beta));                /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
387:     } else {
388:       dp = 0.0;
389:     }
390:     ksp->rnorm = dp;
391:     KSPLogResidualHistory(ksp,dp);
392:     if (eigs) cg->ned = ksp->its;
393:     KSPMonitor(ksp,i+1,dp);
394:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
395:     if (ksp->reason) break;

397:     if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)) {
398:       KSP_PCApply(ksp,R,Z);               /*    z <- Br                           */
399:       KSP_MatMult(ksp,Amat,Z,S);
400:     }
401:     if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)) {
402:       tmpvecs[0] = S; tmpvecs[1] = R;
403:       VecMDot(Z,2,tmpvecs,tmp);
404:       delta = tmp[0]; beta = tmp[1];                           /*    delta <- z'*A*z = r'*B'*A*B*r     */
405:       KSPCheckDot(ksp,beta);                                   /*    beta <- z'*r                      */
406:     }

408:     i++;
409:   } while (i<ksp->max_it);
410:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
411:   return(0);
412: }

414: /*
415:      KSPDestroy_CG - Frees resources allocated in KSPSetup_CG and clears function
416:                      compositions from KSPCreate_CG. If adding your own KSP implementation,
417:                      you must be sure to free all allocated resources here to prevent
418:                      leaks.
419: */
420: PetscErrorCode KSPDestroy_CG(KSP ksp)
421: {
422:   KSP_CG         *cg = (KSP_CG*)ksp->data;

426:   /* free space used for singular value calculations */
427:   if (ksp->calc_sings) {
428:     PetscFree4(cg->e,cg->d,cg->ee,cg->dd);
429:   }
430:   KSPDestroyDefault(ksp);
431:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",NULL);
432:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",NULL);
433:   return(0);
434: }

436: /*
437:      KSPView_CG - Prints information about the current Krylov method being used.
438:                   If your Krylov method has special options or flags that information 
439:                   should be printed here.
440: */
441: PetscErrorCode KSPView_CG(KSP ksp,PetscViewer viewer)
442: {
443:   KSP_CG         *cg = (KSP_CG*)ksp->data;
445:   PetscBool      iascii;

448:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
449:   if (iascii) {
450: #if defined(PETSC_USE_COMPLEX)
451:     PetscViewerASCIIPrintf(viewer,"  variant %s\n",KSPCGTypes[cg->type]);
452: #endif
453:     if (cg->singlereduction) {
454:       PetscViewerASCIIPrintf(viewer,"  using single-reduction variant\n");
455:     }
456:   }
457:   return(0);
458: }

460: /*
461:     KSPSetFromOptions_CG - Checks the options database for options related to the
462:                            conjugate gradient method.
463: */
464: PetscErrorCode KSPSetFromOptions_CG(PetscOptionItems *PetscOptionsObject,KSP ksp)
465: {
467:   KSP_CG         *cg = (KSP_CG*)ksp->data;

470:   PetscOptionsHead(PetscOptionsObject,"KSP CG and CGNE options");
471: #if defined(PETSC_USE_COMPLEX)
472:   PetscOptionsEnum("-ksp_cg_type","Matrix is Hermitian or complex symmetric","KSPCGSetType",KSPCGTypes,(PetscEnum)cg->type,
473:                           (PetscEnum*)&cg->type,NULL);
474: #endif
475:   PetscOptionsBool("-ksp_cg_single_reduction","Merge inner products into single MPIU_Allreduce()","KSPCGUseSingleReduction",cg->singlereduction,&cg->singlereduction,NULL);
476:   PetscOptionsTail();
477:   return(0);
478: }

480: /*
481:     KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
482:                       This routine is registered below in KSPCreate_CG() and called from the
483:                       routine KSPCGSetType() (see the file cgtype.c).
484: */
485: PetscErrorCode  KSPCGSetType_CG(KSP ksp,KSPCGType type)
486: {
487:   KSP_CG *cg = (KSP_CG*)ksp->data;

490:   cg->type = type;
491:   return(0);
492: }

494: /*
495:     KSPCGUseSingleReduction_CG

497:     This routine sets a flag to use a variant of CG. Note that (in somewhat
498:     atypical fashion) it also swaps out the routine called when KSPSolve()
499:     is invoked.
500: */
501: static PetscErrorCode  KSPCGUseSingleReduction_CG(KSP ksp,PetscBool flg)
502: {
503:   KSP_CG *cg = (KSP_CG*)ksp->data;

506:   cg->singlereduction = flg;
507:   if (cg->singlereduction) {
508:     ksp->ops->solve = KSPSolve_CG_SingleReduction;
509:   } else {
510:     ksp->ops->solve = KSPSolve_CG;
511:   }
512:   return(0);
513: }

515: /*
516:     KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the
517:        function pointers for all the routines it needs to call (KSPSolve_CG() etc)

519:     It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
520: */
521: /*MC
522:      KSPCG - The Preconditioned Conjugate Gradient (PCG) iterative method

524:    Options Database Keys:
525: +   -ksp_cg_type Hermitian - (for complex matrices only) indicates the matrix is Hermitian, see KSPCGSetType()
526: .   -ksp_cg_type symmetric - (for complex matrices only) indicates the matrix is symmetric
527: -   -ksp_cg_single_reduction - performs both inner products needed in the algorithm with a single MPIU_Allreduce() call, see KSPCGUseSingleReduction()

529:    Level: beginner

531:    Notes:
532:     The PCG method requires both the matrix and preconditioner to be symmetric positive (or negative) (semi) definite.  
533:    
534:    Only left preconditioning is supported; there are several ways to motivate preconditioned CG, but they all produce the same algorithm. 
535:    One can interpret preconditioning A with B to mean any of the following\:
536: .n  (1) Solve a left-preconditioned system BAx = Bb, using inv(B) to define an inner product in the algorithm.
537: .n  (2) Solve a right-preconditioned system ABy = b, x = By, using B to define an inner product in the algorithm.
538: .n  (3) Solve a symmetrically-preconditioned system, E^TAEy = E^Tb, x = Ey, where B = EE^T.
539: .n  (4) Solve Ax=b with CG, but use the inner product defined by B to define the method [2].
540: .n  In all cases, the resulting algorithm only requires application of B to vectors.

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

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

549:    References:
550: .   1. - Magnus R. Hestenes and Eduard Stiefel, Methods of Conjugate Gradients for Solving Linear Systems,
551:    Journal of Research of the National Bureau of Standards Vol. 49, No. 6, December 1952 Research Paper 2379
552: .   2. - Josef Malek and Zdenek Strakos, Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs, 
553:     SIAM, 2014.

555: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
556:            KSPCGSetType(), KSPCGUseSingleReduction(), KSPPIPECG, KSPGROPPCG

558: M*/
559: PETSC_EXTERN PetscErrorCode KSPCreate_CG(KSP ksp)
560: {
562:   KSP_CG         *cg;

565:   PetscNewLog(ksp,&cg);
566: #if !defined(PETSC_USE_COMPLEX)
567:   cg->type = KSP_CG_SYMMETRIC;
568: #else
569:   cg->type = KSP_CG_HERMITIAN;
570: #endif
571:   ksp->data = (void*)cg;

573:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
574:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
575:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
576:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

578:   /*
579:        Sets the functions that are associated with this data structure
580:        (in C++ this is the same as defining virtual functions)
581:   */
582:   ksp->ops->setup          = KSPSetUp_CG;
583:   ksp->ops->solve          = KSPSolve_CG;
584:   ksp->ops->destroy        = KSPDestroy_CG;
585:   ksp->ops->view           = KSPView_CG;
586:   ksp->ops->setfromoptions = KSPSetFromOptions_CG;
587:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
588:   ksp->ops->buildresidual  = KSPBuildResidualDefault;

590:   /*
591:       Attach the function KSPCGSetType_CG() to this object. The routine
592:       KSPCGSetType() checks for this attached function and calls it if it finds
593:       it. (Sort of like a dynamic member function that can be added at run time
594:   */
595:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CG);
596:   PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",KSPCGUseSingleReduction_CG);
597:   return(0);
598: }