Actual source code: cg.c

  1: #define PETSCKSP_DLL

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

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

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

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

 31:     Reference: Hestenes and Steifel, 1952.

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

 49: /*
 50:      KSPSetUp_CG - Sets up the workspace needed by the CG method. 

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

 64:   /* 
 65:        This implementation of CG only handles left preconditioning
 66:      so generate an error otherwise.
 67:   */
 68:   if (ksp->pc_side == PC_RIGHT) {
 69:     SETERRQ(PETSC_ERR_SUP,"No right preconditioning for KSPCG");
 70:   } else if (ksp->pc_side == PC_SYMMETRIC) {
 71:     SETERRQ(PETSC_ERR_SUP,"No symmetric preconditioning for KSPCG");
 72:   }

 74:   /* get work vectors needed by CG */
 75:   if (cgP->singlereduction) nwork += 2;
 76:   KSPDefaultGetWork(ksp,nwork);

 78:   /*
 79:      If user requested computations of eigenvalues then allocate work
 80:      work space needed
 81:   */
 82:   if (ksp->calc_sings) {
 83:     /* get space to store tridiagonal matrix for Lanczos */
 84:     PetscMalloc4(maxit+1,PetscScalar,&cgP->e,maxit+1,PetscScalar,&cgP->d,maxit+1,PetscReal,&cgP->ee,maxit+1,PetscReal,&cgP->dd);
 85:     PetscLogObjectMemory(ksp,2*(maxit+1)*(sizeof(PetscScalar)+sizeof(PetscReal)));
 86:     ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
 87:     ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_CG;
 88:   }
 89:   return(0);
 90: }

 92: /*
 93:        KSPSolve_CG - This routine actually applies the conjugate gradient  method

 95:    This routine is MUCH too messy. I has too many options (norm type and single reduction) embedded making the code confusing and likely to be buggy.

 97:    Input Parameter:
 98: .     ksp - the Krylov space object that was set to use conjugate gradient, by, for 
 99:             example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
100: */
103: PetscErrorCode  KSPSolve_CG(KSP ksp)
104: {
106:   PetscInt       i,stored_max_it,eigs;
107:   PetscScalar    dpi = 0.0,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0,delta,dpiold;
108:   PetscReal      dp = 0.0;
109:   Vec            X,B,Z,R,P,S,W;
110:   KSP_CG         *cg;
111:   Mat            Amat,Pmat;
112:   MatStructure   pflag;
113:   PetscTruth     diagonalscale;

116:   PCDiagonalScale(ksp->pc,&diagonalscale);
117:   if (diagonalscale) SETERRQ1(PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);

119:   cg            = (KSP_CG*)ksp->data;
120:   eigs          = ksp->calc_sings;
121:   stored_max_it = ksp->max_it;
122:   X             = ksp->vec_sol;
123:   B             = ksp->vec_rhs;
124:   R             = ksp->work[0];
125:   Z             = ksp->work[1];
126:   P             = ksp->work[2];
127:   if (cg->singlereduction) {
128:     S           = ksp->work[3];
129:     W           = ksp->work[4];
130:   } else {
131:     S           = 0;            /* unused */
132:     W           = Z;
133:   }

135: #if !defined(PETSC_USE_COMPLEX)
136: #define VecXDot(x,y,a) VecDot(x,y,a)
137: #else
138: #define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
139: #endif

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

144:   ksp->its = 0;
145:   if (!ksp->guess_zero) {
146:     KSP_MatMult(ksp,Amat,X,R);            /*     r <- b - Ax     */
147:     VecAYPX(R,-1.0,B);
148:   } else {
149:     VecCopy(B,R);                         /*     r <- b (x is 0) */
150:   }

152:   if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
153:     KSP_PCApply(ksp,R,Z);                   /*     z <- Br         */
154:     VecNorm(Z,NORM_2,&dp);                /*    dp <- z'*z = e'*A'*B'*B*A'*e'     */
155:   } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
156:     VecNorm(R,NORM_2,&dp);                /*    dp <- r'*r = e'*A'*A*e            */
157:   } else if (ksp->normtype == KSP_NORM_NATURAL) {
158:     KSP_PCApply(ksp,R,Z);                   /*     z <- Br         */
159:     if (cg->singlereduction) {
160:       KSP_MatMult(ksp,Amat,Z,S);
161:       VecXDot(Z,S,&delta);
162:     }
163:     VecXDot(Z,R,&beta);                     /*  beta <- z'*r       */
164:     if PetscIsInfOrNanScalar(beta) SETERRQ(PETSC_ERR_FP,"Infinite or not-a-number generated in dot product");
165:     dp = sqrt(PetscAbsScalar(beta));                           /*    dp <- r'*z = r'*B*r = e'*A'*B*A*e */
166:   } else dp = 0.0;
167:   KSPLogResidualHistory(ksp,dp);
168:   KSPMonitor(ksp,0,dp);                              /* call any registered monitor routines */
169:   ksp->rnorm = dp;

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

174:   if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)){
175:     KSP_PCApply(ksp,R,Z);                   /*     z <- Br         */
176:   }
177:   if (ksp->normtype != KSP_NORM_NATURAL){
178:     if (cg->singlereduction) {
179:       KSP_MatMult(ksp,Amat,Z,S);
180:       VecXDot(Z,S,&delta);
181:     }
182:     VecXDot(Z,R,&beta);         /*  beta <- z'*r       */
183:     if PetscIsInfOrNanScalar(beta) SETERRQ(PETSC_ERR_FP,"Infinite or not-a-number generated in dot product");
184:   }
185: 
186:   i = 0;
187:   do {
188:      ksp->its = i+1;
189:      if (beta == 0.0) {
190:        ksp->reason = KSP_CONVERGED_ATOL;
191:        PetscInfo(ksp,"converged due to beta = 0\n");
192:        break;
193: #if !defined(PETSC_USE_COMPLEX)
194:      } else if (beta < 0.0) {
195:        ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
196:        PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
197:        break;
198: #endif
199:      }
200:      if (!i) {
201:        VecCopy(Z,P);         /*     p <- z          */
202:        b = 0.0;
203:      } else {
204:        b = beta/betaold;
205:        if (eigs) {
206:          if (ksp->max_it != stored_max_it) {
207:            SETERRQ(PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
208:          }
209:          e[i] = sqrt(PetscAbsScalar(b))/a;
210:        }
211:        VecAYPX(P,b,Z);    /*     p <- z + b* p   */
212:      }
213:      dpiold = dpi;
214:      if (!cg->singlereduction || !i) {
215:        KSP_MatMult(ksp,Amat,P,W);          /*     w <- Kp         */
216:        VecXDot(P,W,&dpi);                  /*     dpi <- p'w     */
217:      } else {
218:         VecAYPX(W,beta/betaold,S);                  /*     w <- Kp         */
219:         dpi = delta - beta*beta*dpiold/(betaold*betaold);              /*     dpi <- p'w     */
220:      }
221:      betaold = beta;
222:      if PetscIsInfOrNanScalar(dpi) SETERRQ(PETSC_ERR_FP,"Infinite or not-a-number generated in dot product");

224:      if (PetscRealPart(dpi) <= 0.0) {
225:        ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
226:        PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
227:        break;
228:      }
229:      a = beta/dpi;                                 /*     a = beta/p'w   */
230:      if (eigs) {
231:        d[i] = sqrt(PetscAbsScalar(b))*e[i] + 1.0/a;
232:      }
233:      VecAXPY(X,a,P);          /*     x <- x + ap     */
234:      VecAXPY(R,-a,W);                      /*     r <- r - aw    */
235:      if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
236:        KSP_PCApply(ksp,R,Z);               /*     z <- Br         */
237:        if (cg->singlereduction) {
238:          KSP_MatMult(ksp,Amat,Z,S);
239:        }
240:        VecNorm(Z,NORM_2,&dp);              /*    dp <- z'*z       */
241:      } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
242:        VecNorm(R,NORM_2,&dp);              /*    dp <- r'*r       */
243:      } else if (ksp->normtype == KSP_NORM_NATURAL) {
244:        KSP_PCApply(ksp,R,Z);               /*     z <- Br         */
245:        if (cg->singlereduction) {
246:          PetscScalar tmp[2];
247:          Vec         vecs[2];
248:          vecs[0] = S; vecs[1] = R;
249:          KSP_MatMult(ksp,Amat,Z,S);
250:          /*VecXDot(Z,S,&delta);
251:            VecXDot(Z,R,&beta); */    /*  beta <- r'*z       */
252:          VecMDot(Z,2,vecs,tmp);
253:          delta = tmp[0]; beta = tmp[1];
254:        } else {
255:          VecXDot(Z,R,&beta);     /*  beta <- r'*z       */
256:        }
257:        if PetscIsInfOrNanScalar(beta) SETERRQ(PETSC_ERR_FP,"Infinite or not-a-number generated in dot product");
258:        dp = sqrt(PetscAbsScalar(beta));
259:      } else {
260:        dp = 0.0;
261:      }
262:      ksp->rnorm = dp;
263:      KSPLogResidualHistory(ksp,dp);
264:      KSPMonitor(ksp,i+1,dp);
265:      (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
266:      if (ksp->reason) break;

268:      if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)){
269:        KSP_PCApply(ksp,R,Z);                   /*     z <- Br         */
270:        if (cg->singlereduction) {
271:          KSP_MatMult(ksp,Amat,Z,S);
272:        }
273:      }
274:      if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)){
275:        if (cg->singlereduction) {
276:          PetscScalar tmp[2];
277:          Vec         vecs[2];
278:          vecs[0] = S; vecs[1] = R;
279:          /* VecXDot(Z,R,&beta);   */     /*  beta <- z'*r       */
280:          /* VecXDot(Z,S,&delta);*/
281:          VecMDot(Z,2,vecs,tmp);
282:          delta = tmp[0]; beta = tmp[1];
283:        } else {
284:          VecXDot(Z,R,&beta);        /*  beta <- z'*r       */
285:        }
286:        if PetscIsInfOrNanScalar(beta) SETERRQ(PETSC_ERR_FP,"Infinite or not-a-number generated in dot product");
287:      }

289:      i++;
290:   } while (i<ksp->max_it);
291:   if (i >= ksp->max_it) {
292:     ksp->reason = KSP_DIVERGED_ITS;
293:   }
294:   return(0);
295: }
296: /*
297:        KSPDestroy_CG - Frees all memory space used by the Krylov method

299: */
302: PetscErrorCode KSPDestroy_CG(KSP ksp)
303: {
304:   KSP_CG         *cg = (KSP_CG*)ksp->data;

308:   /* free space used for singular value calculations */
309:   if (ksp->calc_sings) {
310:     PetscFree4(cg->e,cg->dd,cg->ee,cg->dd);
311:   }
312:   KSPDefaultDestroy(ksp);
313:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPCGSetType_C","",PETSC_NULL);
314:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPCGUseSingleReduction_C","",PETSC_NULL);
315:   return(0);
316: }

318: /*
319:      KSPView_CG - Prints information about the current Krylov method being used

321:       Currently this only prints information to a file (or stdout) about the 
322:       symmetry of the problem. If your Krylov method has special options or 
323:       flags that information should be printed here.

325: */
328: PetscErrorCode KSPView_CG(KSP ksp,PetscViewer viewer)
329: {
330: #if defined(PETSC_USE_COMPLEX)
331:   KSP_CG         *cg = (KSP_CG *)ksp->data;
333:   PetscTruth     iascii;

336:   PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);
337:   if (iascii) {
338:     PetscViewerASCIIPrintf(viewer,"  CG or CGNE: variant %s\n",KSPCGTypes[cg->type]);
339:   } else {
340:     SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported for KSP cg",((PetscObject)viewer)->type_name);
341:   }
342: #endif
343:   return(0);
344: }

346: /*
347:     KSPSetFromOptions_CG - Checks the options database for options related to the 
348:                            conjugate gradient method.
349: */
352: PetscErrorCode KSPSetFromOptions_CG(KSP ksp)
353: {
355:   KSP_CG         *cg = (KSP_CG *)ksp->data;

358:   PetscOptionsHead("KSP CG and CGNE options");
359: #if defined(PETSC_USE_COMPLEX)
360:   PetscOptionsEnum("-ksp_cg_type","Matrix is Hermitian or complex symmetric","KSPCGSetType",KSPCGTypes,(PetscEnum)cg->type,
361:                           (PetscEnum*)&cg->type,PETSC_NULL);
362: #endif
363:   PetscOptionsTruth("-ksp_cg_single_reduction","Merge inner products into single MPI_Allreduce()",
364:                            "KSPCGUseSingleReduction",cg->singlereduction,&cg->singlereduction,PETSC_NULL);
365:   PetscOptionsTail();
366:   return(0);
367: }

369: /*
370:     KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
371:                       This routine is registered below in KSPCreate_CG() and called from the 
372:                       routine KSPCGSetType() (see the file cgtype.c).

375: */
379: PetscErrorCode  KSPCGSetType_CG(KSP ksp,KSPCGType type)
380: {
381:   KSP_CG *cg = (KSP_CG *)ksp->data;

384:   cg->type = type;
385:   return(0);
386: }

392: PetscErrorCode  KSPCGUseSingleReduction_CG(KSP ksp,PetscTruth flg)
393: {
394:   KSP_CG *cg  = (KSP_CG *)ksp->data;

397:   cg->singlereduction = flg;
398:   return(0);
399: }

402: /*
403:     KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the 
404:        function pointers for all the routines it needs to call (KSPSolve_CG() etc)

407: */
408: /*MC
409:      KSPCG - The preconditioned conjugate gradient (PCG) iterative method

411:    Options Database Keys:
412: +   -ksp_cg_type Hermitian - (for complex matrices only) indicates the matrix is Hermitian
413: .   -ksp_cg_type symmetric - (for complex matrices only) indicates the matrix is symmetric
414: -   -ksp_cg_single_reduction - performs both inner products needed in the algorithm with a single MPI_Allreduce() call, see KSPCGUseSingleReduction()

416:    Level: beginner

418:    Notes: The PCG method requires both the matrix and preconditioner to 
419:           be symmetric positive (semi) definite

421:    References:
422:    Methods of Conjugate Gradients for Solving Linear Systems, Magnus R. Hestenes and Eduard Stiefel,
423:    Journal of Research of the National Bureau of Standards Vol. 49, No. 6, December 1952 Research Paper 2379
424:    pp. 409--436.

426: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
427:            KSPCGSetType(), KSPCGUseSingleReduction()

429: M*/
433: PetscErrorCode  KSPCreate_CG(KSP ksp)
434: {
436:   KSP_CG         *cg;

439:   PetscNewLog(ksp,KSP_CG,&cg);
440: #if !defined(PETSC_USE_COMPLEX)
441:   cg->type                       = KSP_CG_SYMMETRIC;
442: #else
443:   cg->type                       = KSP_CG_HERMITIAN;
444: #endif
445:   ksp->data                      = (void*)cg;
446:   ksp->pc_side                   = PC_LEFT;

448:   /*
449:        Sets the functions that are associated with this data structure 
450:        (in C++ this is the same as defining virtual functions)
451:   */
452:   ksp->ops->setup                = KSPSetUp_CG;
453:   ksp->ops->solve                = KSPSolve_CG;
454:   ksp->ops->destroy              = KSPDestroy_CG;
455:   ksp->ops->view                 = KSPView_CG;
456:   ksp->ops->setfromoptions       = KSPSetFromOptions_CG;
457:   ksp->ops->buildsolution        = KSPDefaultBuildSolution;
458:   ksp->ops->buildresidual        = KSPDefaultBuildResidual;

460:   /*
461:       Attach the function KSPCGSetType_CG() to this object. The routine 
462:       KSPCGSetType() checks for this attached function and calls it if it finds
463:       it. (Sort of like a dynamic member function that can be added at run time
464:   */
465:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPCGSetType_C","KSPCGSetType_CG", KSPCGSetType_CG);
466:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPCGUseSingleReduction_C","KSPCGUseSingleReduction_CG", KSPCGUseSingleReduction_CG);
467:   return(0);
468: }