Actual source code: qcg.c

petsc-master 2020-09-19
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  2: #include <../src/ksp/ksp/impls/qcg/qcgimpl.h>

  4: static PetscErrorCode KSPQCGQuadraticRoots(Vec,Vec,PetscReal,PetscReal*,PetscReal*);

  6: /*@
  7:     KSPQCGSetTrustRegionRadius - Sets the radius of the trust region.

  9:     Logically Collective on ksp

 11:     Input Parameters:
 12: +   ksp   - the iterative context
 13: -   delta - the trust region radius (Infinity is the default)

 15:     Options Database Key:
 16: .   -ksp_qcg_trustregionradius <delta>

 18:     Level: advanced

 20: @*/
 21: PetscErrorCode  KSPQCGSetTrustRegionRadius(KSP ksp,PetscReal delta)
 22: {

 27:   if (delta < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
 28:   PetscTryMethod(ksp,"KSPQCGSetTrustRegionRadius_C",(KSP,PetscReal),(ksp,delta));
 29:   return(0);
 30: }

 32: /*@
 33:     KSPQCGGetTrialStepNorm - Gets the norm of a trial step vector.  The WCG step may be
 34:     constrained, so this is not necessarily the length of the ultimate step taken in QCG.

 36:     Not Collective

 38:     Input Parameter:
 39: .   ksp - the iterative context

 41:     Output Parameter:
 42: .   tsnorm - the norm

 44:     Level: advanced
 45: @*/
 46: PetscErrorCode  KSPQCGGetTrialStepNorm(KSP ksp,PetscReal *tsnorm)
 47: {

 52:   PetscUseMethod(ksp,"KSPQCGGetTrialStepNorm_C",(KSP,PetscReal*),(ksp,tsnorm));
 53:   return(0);
 54: }

 56: /*@
 57:     KSPQCGGetQuadratic - Gets the value of the quadratic function, evaluated at the new iterate:

 59:        q(s) = g^T * s + 0.5 * s^T * H * s

 61:     which satisfies the Euclidian Norm trust region constraint

 63:        || D * s || <= delta,

 65:     where

 67:      delta is the trust region radius,
 68:      g is the gradient vector, and
 69:      H is Hessian matrix,
 70:      D is a scaling matrix.

 72:     Collective on ksp

 74:     Input Parameter:
 75: .   ksp - the iterative context

 77:     Output Parameter:
 78: .   quadratic - the quadratic function evaluated at the new iterate

 80:     Level: advanced
 81: @*/
 82: PetscErrorCode  KSPQCGGetQuadratic(KSP ksp,PetscReal *quadratic)
 83: {

 88:   PetscUseMethod(ksp,"KSPQCGGetQuadratic_C",(KSP,PetscReal*),(ksp,quadratic));
 89:   return(0);
 90: }


 93: PetscErrorCode KSPSolve_QCG(KSP ksp)
 94: {
 95: /*
 96:    Correpondence with documentation above:
 97:       B = g = gradient,
 98:       X = s = step
 99:    Note:  This is not coded correctly for complex arithmetic!
100:  */

102:   KSP_QCG        *pcgP = (KSP_QCG*)ksp->data;
103:   Mat            Amat,Pmat;
104:   Vec            W,WA,WA2,R,P,ASP,BS,X,B;
105:   PetscScalar    scal,beta,rntrn,step;
106:   PetscReal      q1,q2,xnorm,step1,step2,rnrm = 0.0,btx,xtax;
107:   PetscReal      ptasp,rtr,wtasp,bstp;
108:   PetscReal      dzero = 0.0,bsnrm = 0.0;
110:   PetscInt       i,maxit;
111:   PC             pc = ksp->pc;
112:   PCSide         side;
113:   PetscBool      diagonalscale;

116:   PCGetDiagonalScale(ksp->pc,&diagonalscale);
117:   if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
118:   if (ksp->transpose_solve) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Currently does not support transpose solve");

120:   ksp->its = 0;
121:   maxit    = ksp->max_it;
122:   WA       = ksp->work[0];
123:   R        = ksp->work[1];
124:   P        = ksp->work[2];
125:   ASP      = ksp->work[3];
126:   BS       = ksp->work[4];
127:   W        = ksp->work[5];
128:   WA2      = ksp->work[6];
129:   X        = ksp->vec_sol;
130:   B        = ksp->vec_rhs;

132:   if (pcgP->delta <= dzero) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Input error: delta <= 0");
133:   KSPGetPCSide(ksp,&side);
134:   if (side != PC_SYMMETRIC) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Requires symmetric preconditioner!");

136:   /* Initialize variables */
137:   VecSet(W,0.0);  /* W = 0 */
138:   VecSet(X,0.0);  /* X = 0 */
139:   PCGetOperators(pc,&Amat,&Pmat);

141:   /* Compute:  BS = D^{-1} B */
142:   PCApplySymmetricLeft(pc,B,BS);

144:   if (ksp->normtype != KSP_NORM_NONE) {
145:     VecNorm(BS,NORM_2,&bsnrm);
146:     KSPCheckNorm(ksp,bsnrm);
147:   }
148:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
149:   ksp->its   = 0;
150:   ksp->rnorm = bsnrm;
151:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
152:   KSPLogResidualHistory(ksp,bsnrm);
153:   KSPMonitor(ksp,0,bsnrm);
154:   (*ksp->converged)(ksp,0,bsnrm,&ksp->reason,ksp->cnvP);
155:   if (ksp->reason) return(0);

157:   /* Compute the initial scaled direction and scaled residual */
158:   VecCopy(BS,R);
159:   VecScale(R,-1.0);
160:   VecCopy(R,P);
161:   VecDotRealPart(R,R,&rtr);

163:   for (i=0; i<=maxit; i++) {
164:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
165:     ksp->its++;
166:     PetscObjectSAWsGrantAccess((PetscObject)ksp);

168:     /* Compute:  asp = D^{-T}*A*D^{-1}*p  */
169:     PCApplySymmetricRight(pc,P,WA);
170:     KSP_MatMult(ksp,Amat,WA,WA2);
171:     PCApplySymmetricLeft(pc,WA2,ASP);

173:     /* Check for negative curvature */
174:     VecDotRealPart(P,ASP,&ptasp);
175:     if (ptasp <= dzero) {

177:       /* Scaled negative curvature direction:  Compute a step so that
178:         ||w + step*p|| = delta and QS(w + step*p) is least */

180:       if (!i) {
181:         VecCopy(P,X);
182:         VecNorm(X,NORM_2,&xnorm);
183:         KSPCheckNorm(ksp,xnorm);
184:         scal = pcgP->delta / xnorm;
185:         VecScale(X,scal);
186:       } else {
187:         /* Compute roots of quadratic */
188:         KSPQCGQuadraticRoots(W,P,pcgP->delta,&step1,&step2);
189:         VecDotRealPart(W,ASP,&wtasp);
190:         VecDotRealPart(BS,P,&bstp);
191:         VecCopy(W,X);
192:         q1   = step1*(bstp + wtasp + .5*step1*ptasp);
193:         q2   = step2*(bstp + wtasp + .5*step2*ptasp);
194:         if (q1 <= q2) {
195:           VecAXPY(X,step1,P);
196:         } else {
197:           VecAXPY(X,step2,P);
198:         }
199:       }
200:       pcgP->ltsnrm = pcgP->delta;                       /* convergence in direction of */
201:       ksp->reason  = KSP_CONVERGED_CG_NEG_CURVE;  /* negative curvature */
202:       if (!i) {
203:         PetscInfo1(ksp,"negative curvature: delta=%g\n",(double)pcgP->delta);
204:       } else {
205:         PetscInfo3(ksp,"negative curvature: step1=%g, step2=%g, delta=%g\n",(double)step1,(double)step2,(double)pcgP->delta);
206:       }

208:     } else {
209:       /* Compute step along p */
210:       step = rtr/ptasp;
211:       VecCopy(W,X);        /*  x = w  */
212:       VecAXPY(X,step,P);   /*  x <- step*p + x  */
213:       VecNorm(X,NORM_2,&pcgP->ltsnrm);
214:       KSPCheckNorm(ksp,pcgP->ltsnrm);

216:       if (pcgP->ltsnrm > pcgP->delta) {
217:         /* Since the trial iterate is outside the trust region,
218:             evaluate a constrained step along p so that
219:                     ||w + step*p|| = delta
220:           The positive step is always better in this case. */
221:         if (!i) {
222:           scal = pcgP->delta / pcgP->ltsnrm;
223:           VecScale(X,scal);
224:         } else {
225:           /* Compute roots of quadratic */
226:           KSPQCGQuadraticRoots(W,P,pcgP->delta,&step1,&step2);
227:           VecCopy(W,X);
228:           VecAXPY(X,step1,P);  /*  x <- step1*p + x  */
229:         }
230:         pcgP->ltsnrm = pcgP->delta;
231:         ksp->reason  = KSP_CONVERGED_CG_CONSTRAINED; /* convergence along constrained step */
232:         if (!i) {
233:           PetscInfo1(ksp,"constrained step: delta=%g\n",(double)pcgP->delta);
234:         } else {
235:           PetscInfo3(ksp,"constrained step: step1=%g, step2=%g, delta=%g\n",(double)step1,(double)step2,(double)pcgP->delta);
236:         }

238:       } else {
239:         /* Evaluate the current step */
240:         VecCopy(X,W);  /* update interior iterate */
241:         VecAXPY(R,-step,ASP); /* r <- -step*asp + r */
242:         if (ksp->normtype != KSP_NORM_NONE) {
243:           VecNorm(R,NORM_2,&rnrm);
244:           KSPCheckNorm(ksp,rnrm);
245:         }
246:         PetscObjectSAWsTakeAccess((PetscObject)ksp);
247:         ksp->rnorm = rnrm;
248:         PetscObjectSAWsGrantAccess((PetscObject)ksp);
249:         KSPLogResidualHistory(ksp,rnrm);
250:         KSPMonitor(ksp,i+1,rnrm);
251:         (*ksp->converged)(ksp,i+1,rnrm,&ksp->reason,ksp->cnvP);
252:         if (ksp->reason) {                 /* convergence for */
253:           PetscInfo3(ksp,"truncated step: step=%g, rnrm=%g, delta=%g\n",(double)PetscRealPart(step),(double)rnrm,(double)pcgP->delta);
254:         }
255:       }
256:     }
257:     if (ksp->reason) break;  /* Convergence has been attained */
258:     else {                   /* Compute a new AS-orthogonal direction */
259:       VecDot(R,R,&rntrn);
260:       beta = rntrn/rtr;
261:       VecAYPX(P,beta,R);  /*  p <- r + beta*p  */
262:       rtr  = PetscRealPart(rntrn);
263:     }
264:   }
265:   if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;

267:   /* Unscale x */
268:   VecCopy(X,WA2);
269:   PCApplySymmetricRight(pc,WA2,X);

271:   KSP_MatMult(ksp,Amat,X,WA);
272:   VecDotRealPart(B,X,&btx);
273:   VecDotRealPart(X,WA,&xtax);

275:   pcgP->quadratic = btx + .5*xtax;
276:   return(0);
277: }

279: PetscErrorCode KSPSetUp_QCG(KSP ksp)
280: {

284:   /* Get work vectors from user code */
285:   KSPSetWorkVecs(ksp,7);
286:   return(0);
287: }

289: PetscErrorCode KSPDestroy_QCG(KSP ksp)
290: {

294:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGGetQuadratic_C",NULL);
295:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGGetTrialStepNorm_C",NULL);
296:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGSetTrustRegionRadius_C",NULL);
297:   KSPDestroyDefault(ksp);
298:   return(0);
299: }

301: static PetscErrorCode  KSPQCGSetTrustRegionRadius_QCG(KSP ksp,PetscReal delta)
302: {
303:   KSP_QCG *cgP = (KSP_QCG*)ksp->data;

306:   cgP->delta = delta;
307:   return(0);
308: }

310: static PetscErrorCode  KSPQCGGetTrialStepNorm_QCG(KSP ksp,PetscReal *ltsnrm)
311: {
312:   KSP_QCG *cgP = (KSP_QCG*)ksp->data;

315:   *ltsnrm = cgP->ltsnrm;
316:   return(0);
317: }

319: static PetscErrorCode  KSPQCGGetQuadratic_QCG(KSP ksp,PetscReal *quadratic)
320: {
321:   KSP_QCG *cgP = (KSP_QCG*)ksp->data;

324:   *quadratic = cgP->quadratic;
325:   return(0);
326: }

328: PetscErrorCode KSPSetFromOptions_QCG(PetscOptionItems *PetscOptionsObject,KSP ksp)
329: {
331:   PetscReal      delta;
332:   KSP_QCG        *cgP = (KSP_QCG*)ksp->data;
333:   PetscBool      flg;

336:   PetscOptionsHead(PetscOptionsObject,"KSP QCG Options");
337:   PetscOptionsReal("-ksp_qcg_trustregionradius","Trust Region Radius","KSPQCGSetTrustRegionRadius",cgP->delta,&delta,&flg);
338:   if (flg) { KSPQCGSetTrustRegionRadius(ksp,delta); }
339:   PetscOptionsTail();
340:   return(0);
341: }

343: /*MC
344:      KSPQCG -   Code to run conjugate gradient method subject to a constraint
345:          on the solution norm. This is used in Trust Region methods for nonlinear equations, SNESNEWTONTR

347:    Options Database Keys:
348: .      -ksp_qcg_trustregionradius <r> - Trust Region Radius

350:    Notes:
351:     This is rarely used directly

353:    Level: developer

355:   Notes:
356:     Use preconditioned conjugate gradient to compute
357:       an approximate minimizer of the quadratic function

359:             q(s) = g^T * s + .5 * s^T * H * s

361:    subject to the Euclidean norm trust region constraint

363:             || D * s || <= delta,

365:    where

367:      delta is the trust region radius,
368:      g is the gradient vector, and
369:      H is Hessian matrix,
370:      D is a scaling matrix.

372:    KSPConvergedReason may be
373: $  KSP_CONVERGED_CG_NEG_CURVE if convergence is reached along a negative curvature direction,
374: $  KSP_CONVERGED_CG_CONSTRAINED if convergence is reached along a constrained step,
375: $  other KSP converged/diverged reasons


378:   Notes:
379:   Currently we allow symmetric preconditioning with the following scaling matrices:
380:       PCNONE:   D = Identity matrix
381:       PCJACOBI: D = diag [d_1, d_2, ...., d_n], where d_i = sqrt(H[i,i])
382:       PCICC:    D = L^T, implemented with forward and backward solves.
383:                 Here L is an incomplete Cholesky factor of H.

385:   References:
386: .  1. - Trond Steihaug, The Conjugate Gradient Method and Trust Regions in Large Scale Optimization,
387:    SIAM Journal on Numerical Analysis, Vol. 20, No. 3 (Jun., 1983).

389: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPQCGSetTrustRegionRadius()
390:            KSPQCGGetTrialStepNorm(), KSPQCGGetQuadratic()
391: M*/

393: PETSC_EXTERN PetscErrorCode KSPCreate_QCG(KSP ksp)
394: {
396:   KSP_QCG        *cgP;

399:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_SYMMETRIC,3);
400:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_SYMMETRIC,1);
401:   PetscNewLog(ksp,&cgP);

403:   ksp->data                = (void*)cgP;
404:   ksp->ops->setup          = KSPSetUp_QCG;
405:   ksp->ops->setfromoptions = KSPSetFromOptions_QCG;
406:   ksp->ops->solve          = KSPSolve_QCG;
407:   ksp->ops->destroy        = KSPDestroy_QCG;
408:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
409:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
410:   ksp->ops->view           = NULL;

412:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGGetQuadratic_C",KSPQCGGetQuadratic_QCG);
413:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGGetTrialStepNorm_C",KSPQCGGetTrialStepNorm_QCG);
414:   PetscObjectComposeFunction((PetscObject)ksp,"KSPQCGSetTrustRegionRadius_C",KSPQCGSetTrustRegionRadius_QCG);
415:   cgP->delta = PETSC_MAX_REAL; /* default trust region radius is infinite */
416:   return(0);
417: }

419: /* ---------------------------------------------------------- */
420: /*
421:   KSPQCGQuadraticRoots - Computes the roots of the quadratic,
422:          ||s + step*p|| - delta = 0
423:    such that step1 >= 0 >= step2.
424:    where
425:       delta:
426:         On entry delta must contain scalar delta.
427:         On exit delta is unchanged.
428:       step1:
429:         On entry step1 need not be specified.
430:         On exit step1 contains the non-negative root.
431:       step2:
432:         On entry step2 need not be specified.
433:         On exit step2 contains the non-positive root.
434:    C code is translated from the Fortran version of the MINPACK-2 Project,
435:    Argonne National Laboratory, Brett M. Averick and Richard G. Carter.
436: */
437: static PetscErrorCode KSPQCGQuadraticRoots(Vec s,Vec p,PetscReal delta,PetscReal *step1,PetscReal *step2)
438: {
439:   PetscReal      dsq,ptp,pts,rad,sts;

443:   VecDotRealPart(p,s,&pts);
444:   VecDotRealPart(p,p,&ptp);
445:   VecDotRealPart(s,s,&sts);
446:   dsq  = delta*delta;
447:   rad  = PetscSqrtReal((pts*pts) - ptp*(sts - dsq));
448:   if (pts > 0.0) {
449:     *step2 = -(pts + rad)/ptp;
450:     *step1 = (sts - dsq)/(ptp * *step2);
451:   } else {
452:     *step1 = -(pts - rad)/ptp;
453:     *step2 = (sts - dsq)/(ptp * *step1);
454:   }
455:   return(0);
456: }