Actual source code: lmvm.c

petsc-3.7.7 2017-09-25
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  1: #include <petsctaolinesearch.h>
  2: #include <../src/tao/matrix/lmvmmat.h>
  3: #include <../src/tao/unconstrained/impls/lmvm/lmvm.h>

  5: #define LMVM_BFGS                0
  6: #define LMVM_SCALED_GRADIENT     1
  7: #define LMVM_GRADIENT            2

 11: static PetscErrorCode TaoSolve_LMVM(Tao tao)
 12: {
 13:   TAO_LMVM                     *lmP = (TAO_LMVM *)tao->data;
 14:   PetscReal                    f, fold, gdx, gnorm;
 15:   PetscReal                    step = 1.0;
 16:   PetscReal                    delta;
 17:   PetscErrorCode               ierr;
 18:   PetscInt                     stepType;
 19:   TaoConvergedReason           reason = TAO_CONTINUE_ITERATING;
 20:   TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;


 24:   if (tao->XL || tao->XU || tao->ops->computebounds) {
 25:     PetscPrintf(((PetscObject)tao)->comm,"WARNING: Variable bounds have been set but will be ignored by lmvm algorithm\n");
 26:   }

 28:   /*  Check convergence criteria */
 29:   TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);
 30:   TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);

 32:   if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");

 34:   TaoMonitor(tao, tao->niter, f, gnorm, 0.0, step, &reason);
 35:   if (reason != TAO_CONTINUE_ITERATING) return(0);

 37:   /*  Set initial scaling for the function */
 38:   if (f != 0.0) {
 39:     delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
 40:   } else {
 41:     delta = 2.0 / (gnorm*gnorm);
 42:   }
 43:   MatLMVMSetDelta(lmP->M,delta);

 45:   /*  Set counter for gradient/reset steps */
 46:   lmP->bfgs = 0;
 47:   lmP->sgrad = 0;
 48:   lmP->grad = 0;

 50:   /*  Have not converged; continue with Newton method */
 51:   while (reason == TAO_CONTINUE_ITERATING) {
 52:     /*  Compute direction */
 53:     MatLMVMUpdate(lmP->M,tao->solution,tao->gradient);
 54:     MatLMVMSolve(lmP->M, tao->gradient, lmP->D);
 55:     ++lmP->bfgs;

 57:     /*  Check for success (descent direction) */
 58:     VecDot(lmP->D, tao->gradient, &gdx);
 59:     if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
 60:       /* Step is not descent or direction produced not a number
 61:          We can assert bfgsUpdates > 1 in this case because
 62:          the first solve produces the scaled gradient direction,
 63:          which is guaranteed to be descent

 65:          Use steepest descent direction (scaled)
 66:       */

 68:       ++lmP->grad;

 70:       if (f != 0.0) {
 71:         delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
 72:       } else {
 73:         delta = 2.0 / (gnorm*gnorm);
 74:       }
 75:       MatLMVMSetDelta(lmP->M, delta);
 76:       MatLMVMReset(lmP->M);
 77:       MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);
 78:       MatLMVMSolve(lmP->M,tao->gradient, lmP->D);

 80:       /* On a reset, the direction cannot be not a number; it is a
 81:          scaled gradient step.  No need to check for this condition. */

 83:       lmP->bfgs = 1;
 84:       ++lmP->sgrad;
 85:       stepType = LMVM_SCALED_GRADIENT;
 86:     } else {
 87:       if (1 == lmP->bfgs) {
 88:         /*  The first BFGS direction is always the scaled gradient */
 89:         ++lmP->sgrad;
 90:         stepType = LMVM_SCALED_GRADIENT;
 91:       } else {
 92:         ++lmP->bfgs;
 93:         stepType = LMVM_BFGS;
 94:       }
 95:     }
 96:     VecScale(lmP->D, -1.0);

 98:     /*  Perform the linesearch */
 99:     fold = f;
100:     VecCopy(tao->solution, lmP->Xold);
101:     VecCopy(tao->gradient, lmP->Gold);

103:     TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step,&ls_status);
104:     TaoAddLineSearchCounts(tao);

106:     while (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER && (stepType != LMVM_GRADIENT)) {
107:       /*  Linesearch failed */
108:       /*  Reset factors and use scaled gradient step */
109:       f = fold;
110:       VecCopy(lmP->Xold, tao->solution);
111:       VecCopy(lmP->Gold, tao->gradient);

113:       switch(stepType) {
114:       case LMVM_BFGS:
115:         /*  Failed to obtain acceptable iterate with BFGS step */
116:         /*  Attempt to use the scaled gradient direction */

118:         if (f != 0.0) {
119:           delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
120:         } else {
121:           delta = 2.0 / (gnorm*gnorm);
122:         }
123:         MatLMVMSetDelta(lmP->M, delta);
124:         MatLMVMReset(lmP->M);
125:         MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);
126:         MatLMVMSolve(lmP->M, tao->gradient, lmP->D);

128:         /* On a reset, the direction cannot be not a number; it is a
129:            scaled gradient step.  No need to check for this condition. */

131:         lmP->bfgs = 1;
132:         ++lmP->sgrad;
133:         stepType = LMVM_SCALED_GRADIENT;
134:         break;

136:       case LMVM_SCALED_GRADIENT:
137:         /* The scaled gradient step did not produce a new iterate;
138:            attempt to use the gradient direction.
139:            Need to make sure we are not using a different diagonal scaling */
140:         MatLMVMSetDelta(lmP->M, 1.0);
141:         MatLMVMReset(lmP->M);
142:         MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);
143:         MatLMVMSolve(lmP->M, tao->gradient, lmP->D);

145:         lmP->bfgs = 1;
146:         ++lmP->grad;
147:         stepType = LMVM_GRADIENT;
148:         break;
149:       }
150:       VecScale(lmP->D, -1.0);

152:       /*  Perform the linesearch */
153:       TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step, &ls_status);
154:       TaoAddLineSearchCounts(tao);
155:     }

157:     if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) {
158:       /*  Failed to find an improving point */
159:       f = fold;
160:       VecCopy(lmP->Xold, tao->solution);
161:       VecCopy(lmP->Gold, tao->gradient);
162:       step = 0.0;
163:       reason = TAO_DIVERGED_LS_FAILURE;
164:       tao->reason = TAO_DIVERGED_LS_FAILURE;
165:     }

167:     /*  Check for termination */
168:     TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);

170:     tao->niter++;
171:     TaoMonitor(tao,tao->niter,f,gnorm,0.0,step,&reason);
172:   }
173:   return(0);
174: }

178: static PetscErrorCode TaoSetUp_LMVM(Tao tao)
179: {
180:   TAO_LMVM       *lmP = (TAO_LMVM *)tao->data;
181:   PetscInt       n,N;
183:   KSP            H0ksp;

186:   /* Existence of tao->solution checked in TaoSetUp() */
187:   if (!tao->gradient) {VecDuplicate(tao->solution,&tao->gradient);  }
188:   if (!tao->stepdirection) {VecDuplicate(tao->solution,&tao->stepdirection);  }
189:   if (!lmP->D) {VecDuplicate(tao->solution,&lmP->D);  }
190:   if (!lmP->Xold) {VecDuplicate(tao->solution,&lmP->Xold);  }
191:   if (!lmP->Gold) {VecDuplicate(tao->solution,&lmP->Gold);  }

193:   /*  Create matrix for the limited memory approximation */
194:   VecGetLocalSize(tao->solution,&n);
195:   VecGetSize(tao->solution,&N);
196:   MatCreateLMVM(((PetscObject)tao)->comm,n,N,&lmP->M);
197:   MatLMVMAllocateVectors(lmP->M,tao->solution);

199:   /* If the user has set a matrix to solve as the initial H0, set the options prefix here, and set up the KSP */
200:   if (lmP->H0) {
201:     const char *prefix;
202:     PC H0pc;

204:     MatLMVMSetH0(lmP->M, lmP->H0);
205:     MatLMVMGetH0KSP(lmP->M, &H0ksp);

207:     TaoGetOptionsPrefix(tao, &prefix);
208:     KSPSetOptionsPrefix(H0ksp, prefix);
209:     PetscObjectAppendOptionsPrefix((PetscObject)H0ksp, "tao_h0_");
210:     KSPGetPC(H0ksp, &H0pc);
211:     PetscObjectAppendOptionsPrefix((PetscObject)H0pc,  "tao_h0_");

213:     KSPSetFromOptions(H0ksp);
214:     KSPSetUp(H0ksp);
215:   }

217:   return(0);
218: }

220: /* ---------------------------------------------------------- */
223: static PetscErrorCode TaoDestroy_LMVM(Tao tao)
224: {
225:   TAO_LMVM       *lmP = (TAO_LMVM *)tao->data;

229:   if (tao->setupcalled) {
230:     VecDestroy(&lmP->Xold);
231:     VecDestroy(&lmP->Gold);
232:     VecDestroy(&lmP->D);
233:     MatDestroy(&lmP->M);
234:   }

236:   if (lmP->H0) {
237:     PetscObjectDereference((PetscObject)lmP->H0);
238:   }

240:   PetscFree(tao->data);

242:   return(0);
243: }

245: /*------------------------------------------------------------*/
248: static PetscErrorCode TaoSetFromOptions_LMVM(PetscOptionItems *PetscOptionsObject,Tao tao)
249: {

253:   PetscOptionsHead(PetscOptionsObject,"Limited-memory variable-metric method for unconstrained optimization");
254:   TaoLineSearchSetFromOptions(tao->linesearch);
255:   PetscOptionsTail();
256:   return(0);
257: }

259: /*------------------------------------------------------------*/
262: static PetscErrorCode TaoView_LMVM(Tao tao, PetscViewer viewer)
263: {
264:   TAO_LMVM       *lm = (TAO_LMVM *)tao->data;
265:   PetscBool      isascii;

269:   PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii);
270:   if (isascii) {
271:     PetscViewerASCIIPushTab(viewer);
272:     PetscViewerASCIIPrintf(viewer, "BFGS steps: %D\n", lm->bfgs);
273:     PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %D\n", lm->sgrad);
274:     PetscViewerASCIIPrintf(viewer, "Gradient steps: %D\n", lm->grad);
275:     PetscViewerASCIIPopTab(viewer);
276:   }
277:   return(0);
278: }

280: /* ---------------------------------------------------------- */

282: /*MC
283:      TAOLMVM - Limited Memory Variable Metric method is a quasi-Newton
284:      optimization solver for unconstrained minimization. It solves
285:      the Newton step
286:               Hkdk = - gk

288:      using an approximation Bk in place of Hk, where Bk is composed using
289:      the BFGS update formula. A More-Thuente line search is then used
290:      to computed the steplength in the dk direction
291:   Options Database Keys:
292: +     -tao_lmm_vectors - number of vectors to use for approximation
293: .     -tao_lmm_scale_type - "none","scalar","broyden"
294: .     -tao_lmm_limit_type - "none","average","relative","absolute"
295: .     -tao_lmm_rescale_type - "none","scalar","gl"
296: .     -tao_lmm_limit_mu - mu limiting factor
297: .     -tao_lmm_limit_nu - nu limiting factor
298: .     -tao_lmm_delta_min - minimum delta value
299: .     -tao_lmm_delta_max - maximum delta value
300: .     -tao_lmm_broyden_phi - phi factor for Broyden scaling
301: .     -tao_lmm_scalar_alpha - alpha factor for scalar scaling
302: .     -tao_lmm_rescale_alpha - alpha factor for rescaling diagonal
303: .     -tao_lmm_rescale_beta - beta factor for rescaling diagonal
304: .     -tao_lmm_scalar_history - amount of history for scalar scaling
305: .     -tao_lmm_rescale_history - amount of history for rescaling diagonal
306: -     -tao_lmm_eps - rejection tolerance

308:   Level: beginner
309: M*/

313: PETSC_EXTERN PetscErrorCode TaoCreate_LMVM(Tao tao)
314: {
315:   TAO_LMVM       *lmP;
316:   const char     *morethuente_type = TAOLINESEARCHMT;

320:   tao->ops->setup = TaoSetUp_LMVM;
321:   tao->ops->solve = TaoSolve_LMVM;
322:   tao->ops->view = TaoView_LMVM;
323:   tao->ops->setfromoptions = TaoSetFromOptions_LMVM;
324:   tao->ops->destroy = TaoDestroy_LMVM;

326:   PetscNewLog(tao,&lmP);
327:   lmP->D = 0;
328:   lmP->M = 0;
329:   lmP->Xold = 0;
330:   lmP->Gold = 0;
331:   lmP->H0   = NULL;

333:   tao->data = (void*)lmP;
334:   /* Override default settings (unless already changed) */
335:   if (!tao->max_it_changed) tao->max_it = 2000;
336:   if (!tao->max_funcs_changed) tao->max_funcs = 4000;

338:   TaoLineSearchCreate(((PetscObject)tao)->comm,&tao->linesearch);
339:   TaoLineSearchSetType(tao->linesearch,morethuente_type);
340:   TaoLineSearchUseTaoRoutines(tao->linesearch,tao);
341:   TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);
342:   return(0);
343: }