Actual source code: owlqn.c

      1: #include <petsctaolinesearch.h>
      2: #include <../src/tao/unconstrained/impls/owlqn/owlqn.h>

      4: #define OWLQN_BFGS            0
      5: #define OWLQN_SCALED_GRADIENT 1
      6: #define OWLQN_GRADIENT        2

      8: static PetscErrorCode ProjDirect_OWLQN(Vec d, Vec g)
      9: {
     10:   const PetscReal *gptr;
     11:   PetscReal       *dptr;
     12:   PetscInt         low, high, low1, high1, i;

     14:   PetscFunctionBegin;
     15:   PetscCall(VecGetOwnershipRange(d, &low, &high));
     16:   PetscCall(VecGetOwnershipRange(g, &low1, &high1));

     18:   PetscCall(VecGetArrayRead(g, &gptr));
     19:   PetscCall(VecGetArray(d, &dptr));
     20:   for (i = 0; i < high - low; i++) {
     21:     if (dptr[i] * gptr[i] <= 0.0) dptr[i] = 0.0;
     22:   }
     23:   PetscCall(VecRestoreArray(d, &dptr));
     24:   PetscCall(VecRestoreArrayRead(g, &gptr));
     25:   PetscFunctionReturn(PETSC_SUCCESS);
     26: }

     28: static PetscErrorCode ComputePseudoGrad_OWLQN(Vec x, Vec gv, PetscReal lambda)
     29: {
     30:   const PetscReal *xptr;
     31:   PetscReal       *gptr;
     32:   PetscInt         low, high, low1, high1, i;

     34:   PetscFunctionBegin;
     35:   PetscCall(VecGetOwnershipRange(x, &low, &high));
     36:   PetscCall(VecGetOwnershipRange(gv, &low1, &high1));

     38:   PetscCall(VecGetArrayRead(x, &xptr));
     39:   PetscCall(VecGetArray(gv, &gptr));
     40:   for (i = 0; i < high - low; i++) {
     41:     if (xptr[i] < 0.0) gptr[i] = gptr[i] - lambda;
     42:     else if (xptr[i] > 0.0) gptr[i] = gptr[i] + lambda;
     43:     else if (gptr[i] + lambda < 0.0) gptr[i] = gptr[i] + lambda;
     44:     else if (gptr[i] - lambda > 0.0) gptr[i] = gptr[i] - lambda;
     45:     else gptr[i] = 0.0;
     46:   }
     47:   PetscCall(VecRestoreArray(gv, &gptr));
     48:   PetscCall(VecRestoreArrayRead(x, &xptr));
     49:   PetscFunctionReturn(PETSC_SUCCESS);
     50: }

     52: static PetscErrorCode TaoSolve_OWLQN(Tao tao)
     53: {
     54:   TAO_OWLQN                   *lmP = (TAO_OWLQN *)tao->data;
     55:   PetscReal                    f, fold, gdx, gnorm;
     56:   PetscReal                    step = 1.0;
     57:   PetscReal                    delta;
     58:   PetscInt                     stepType;
     59:   PetscInt                     iter      = 0;
     60:   TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;

     62:   PetscFunctionBegin;
     63:   if (tao->XL || tao->XU || tao->ops->computebounds) PetscCall(PetscInfo(tao, "WARNING: Variable bounds have been set but will be ignored by owlqn algorithm\n"));

     65:   /* Check convergence criteria */
     66:   PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient));
     67:   PetscCall(VecCopy(tao->gradient, lmP->GV));
     68:   PetscCall(ComputePseudoGrad_OWLQN(tao->solution, lmP->GV, lmP->lambda));
     69:   PetscCall(VecNorm(lmP->GV, NORM_2, &gnorm));
     70:   PetscCheck(!PetscIsInfOrNanReal(f) && !PetscIsInfOrNanReal(gnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");

     72:   tao->reason = TAO_CONTINUE_ITERATING;
     73:   PetscCall(TaoLogConvergenceHistory(tao, f, gnorm, 0.0, tao->ksp_its));
     74:   PetscCall(TaoMonitor(tao, iter, f, gnorm, 0.0, step));
     75:   PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
     76:   if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(PETSC_SUCCESS);

     78:   /* Set initial scaling for the function */
     79:   delta = 2.0 * PetscMax(1.0, PetscAbsScalar(f)) / (gnorm * gnorm);
     80:   PetscCall(MatLMVMSetJ0Scale(lmP->M, delta));

     82:   /* Set counter for gradient/reset steps */
     83:   lmP->bfgs  = 0;
     84:   lmP->sgrad = 0;
     85:   lmP->grad  = 0;

     87:   /* Have not converged; continue with Newton method */
     88:   while (tao->reason == TAO_CONTINUE_ITERATING) {
     89:     /* Call general purpose update function */
     90:     PetscTryTypeMethod(tao, update, tao->niter, tao->user_update);

     92:     /* Compute direction */
     93:     PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient));
     94:     PetscCall(MatSolve(lmP->M, lmP->GV, lmP->D));

     96:     PetscCall(ProjDirect_OWLQN(lmP->D, lmP->GV));

     98:     ++lmP->bfgs;

    100:     /* Check for success (descent direction) */
    101:     PetscCall(VecDot(lmP->D, lmP->GV, &gdx));
    102:     if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
    103:       /* Step is not descent or direction produced not a number
    104:          We can assert bfgsUpdates > 1 in this case because
    105:          the first solve produces the scaled gradient direction,
    106:          which is guaranteed to be descent

    108:          Use steepest descent direction (scaled) */
    109:       ++lmP->grad;

    111:       delta = 2.0 * PetscMax(1.0, PetscAbsScalar(f)) / (gnorm * gnorm);
    112:       PetscCall(MatLMVMSetJ0Scale(lmP->M, delta));
    113:       PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE));
    114:       PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient));
    115:       PetscCall(MatSolve(lmP->M, lmP->GV, lmP->D));

    117:       PetscCall(ProjDirect_OWLQN(lmP->D, lmP->GV));

    119:       lmP->bfgs = 1;
    120:       ++lmP->sgrad;
    121:       stepType = OWLQN_SCALED_GRADIENT;
    122:     } else {
    123:       if (1 == lmP->bfgs) {
    124:         /* The first BFGS direction is always the scaled gradient */
    125:         ++lmP->sgrad;
    126:         stepType = OWLQN_SCALED_GRADIENT;
    127:       } else {
    128:         ++lmP->bfgs;
    129:         stepType = OWLQN_BFGS;
    130:       }
    131:     }

    133:     PetscCall(VecScale(lmP->D, -1.0));

    135:     /* Perform the linesearch */
    136:     fold = f;
    137:     PetscCall(VecCopy(tao->solution, lmP->Xold));
    138:     PetscCall(VecCopy(tao->gradient, lmP->Gold));

    140:     PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f, lmP->GV, lmP->D, &step, &ls_status));
    141:     PetscCall(TaoAddLineSearchCounts(tao));

    143:     while (((int)ls_status < 0) && (stepType != OWLQN_GRADIENT)) {
    144:       /* Reset factors and use scaled gradient step */
    145:       f = fold;
    146:       PetscCall(VecCopy(lmP->Xold, tao->solution));
    147:       PetscCall(VecCopy(lmP->Gold, tao->gradient));
    148:       PetscCall(VecCopy(tao->gradient, lmP->GV));

    150:       PetscCall(ComputePseudoGrad_OWLQN(tao->solution, lmP->GV, lmP->lambda));

    152:       switch (stepType) {
    153:       case OWLQN_BFGS:
    154:         /* Failed to obtain acceptable iterate with BFGS step
    155:            Attempt to use the scaled gradient direction */

    157:         delta = 2.0 * PetscMax(1.0, PetscAbsScalar(f)) / (gnorm * gnorm);
    158:         PetscCall(MatLMVMSetJ0Scale(lmP->M, delta));
    159:         PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE));
    160:         PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient));
    161:         PetscCall(MatSolve(lmP->M, lmP->GV, lmP->D));

    163:         PetscCall(ProjDirect_OWLQN(lmP->D, lmP->GV));

    165:         lmP->bfgs = 1;
    166:         ++lmP->sgrad;
    167:         stepType = OWLQN_SCALED_GRADIENT;
    168:         break;

    170:       case OWLQN_SCALED_GRADIENT:
    171:         /* The scaled gradient step did not produce a new iterate;
    172:            attempt to use the gradient direction.
    173:            Need to make sure we are not using a different diagonal scaling */
    174:         PetscCall(MatLMVMSetJ0Scale(lmP->M, 1.0));
    175:         PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE));
    176:         PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient));
    177:         PetscCall(MatSolve(lmP->M, lmP->GV, lmP->D));

    179:         PetscCall(ProjDirect_OWLQN(lmP->D, lmP->GV));

    181:         lmP->bfgs = 1;
    182:         ++lmP->grad;
    183:         stepType = OWLQN_GRADIENT;
    184:         break;
    185:       }
    186:       PetscCall(VecScale(lmP->D, -1.0));

    188:       /* Perform the linesearch */
    189:       PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f, lmP->GV, lmP->D, &step, &ls_status));
    190:       PetscCall(TaoAddLineSearchCounts(tao));
    191:     }

    193:     if ((int)ls_status < 0) {
    194:       /* Failed to find an improving point*/
    195:       f = fold;
    196:       PetscCall(VecCopy(lmP->Xold, tao->solution));
    197:       PetscCall(VecCopy(lmP->Gold, tao->gradient));
    198:       PetscCall(VecCopy(tao->gradient, lmP->GV));
    199:       step = 0.0;
    200:     } else {
    201:       /* a little hack here, because that gv is used to store g */
    202:       PetscCall(VecCopy(lmP->GV, tao->gradient));
    203:     }

    205:     PetscCall(ComputePseudoGrad_OWLQN(tao->solution, lmP->GV, lmP->lambda));

    207:     /* Check for termination */

    209:     PetscCall(VecNorm(lmP->GV, NORM_2, &gnorm));

    211:     iter++;
    212:     PetscCall(TaoLogConvergenceHistory(tao, f, gnorm, 0.0, tao->ksp_its));
    213:     PetscCall(TaoMonitor(tao, iter, f, gnorm, 0.0, step));
    214:     PetscUseTypeMethod(tao, convergencetest, tao->cnvP);

    216:     if ((int)ls_status < 0) break;
    217:   }
    218:   PetscFunctionReturn(PETSC_SUCCESS);
    219: }

    221: static PetscErrorCode TaoSetUp_OWLQN(Tao tao)
    222: {
    223:   TAO_OWLQN *lmP = (TAO_OWLQN *)tao->data;
    224:   PetscInt   n, N;

    226:   PetscFunctionBegin;
    227:   /* Existence of tao->solution checked in TaoSetUp() */
    228:   if (!tao->gradient) PetscCall(VecDuplicate(tao->solution, &tao->gradient));
    229:   if (!tao->stepdirection) PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));
    230:   if (!lmP->D) PetscCall(VecDuplicate(tao->solution, &lmP->D));
    231:   if (!lmP->GV) PetscCall(VecDuplicate(tao->solution, &lmP->GV));
    232:   if (!lmP->Xold) PetscCall(VecDuplicate(tao->solution, &lmP->Xold));
    233:   if (!lmP->Gold) PetscCall(VecDuplicate(tao->solution, &lmP->Gold));

    235:   /* Create matrix for the limited memory approximation */
    236:   PetscCall(VecGetLocalSize(tao->solution, &n));
    237:   PetscCall(VecGetSize(tao->solution, &N));
    238:   PetscCall(MatCreateLMVMBFGS(((PetscObject)tao)->comm, n, N, &lmP->M));
    239:   PetscCall(MatLMVMAllocate(lmP->M, tao->solution, tao->gradient));
    240:   PetscFunctionReturn(PETSC_SUCCESS);
    241: }

    243: /* ---------------------------------------------------------- */
    244: static PetscErrorCode TaoDestroy_OWLQN(Tao tao)
    245: {
    246:   TAO_OWLQN *lmP = (TAO_OWLQN *)tao->data;

    248:   PetscFunctionBegin;
    249:   if (tao->setupcalled) {
    250:     PetscCall(VecDestroy(&lmP->Xold));
    251:     PetscCall(VecDestroy(&lmP->Gold));
    252:     PetscCall(VecDestroy(&lmP->D));
    253:     PetscCall(MatDestroy(&lmP->M));
    254:     PetscCall(VecDestroy(&lmP->GV));
    255:   }
    256:   PetscCall(PetscFree(tao->data));
    257:   PetscFunctionReturn(PETSC_SUCCESS);
    258: }

    260: /*------------------------------------------------------------*/
    261: static PetscErrorCode TaoSetFromOptions_OWLQN(Tao tao, PetscOptionItems *PetscOptionsObject)
    262: {
    263:   TAO_OWLQN *lmP = (TAO_OWLQN *)tao->data;

    265:   PetscFunctionBegin;
    266:   PetscOptionsHeadBegin(PetscOptionsObject, "Orthant-Wise Limited-memory method for Quasi-Newton unconstrained optimization");
    267:   PetscCall(PetscOptionsReal("-tao_owlqn_lambda", "regulariser weight", "", 100, &lmP->lambda, NULL));
    268:   PetscOptionsHeadEnd();
    269:   PetscCall(TaoLineSearchSetFromOptions(tao->linesearch));
    270:   PetscFunctionReturn(PETSC_SUCCESS);
    271: }

    273: /*------------------------------------------------------------*/
    274: static PetscErrorCode TaoView_OWLQN(Tao tao, PetscViewer viewer)
    275: {
    276:   TAO_OWLQN *lm = (TAO_OWLQN *)tao->data;
    277:   PetscBool  isascii;

    279:   PetscFunctionBegin;
    280:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
    281:   if (isascii) {
    282:     PetscCall(PetscViewerASCIIPushTab(viewer));
    283:     PetscCall(PetscViewerASCIIPrintf(viewer, "BFGS steps: %" PetscInt_FMT "\n", lm->bfgs));
    284:     PetscCall(PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %" PetscInt_FMT "\n", lm->sgrad));
    285:     PetscCall(PetscViewerASCIIPrintf(viewer, "Gradient steps: %" PetscInt_FMT "\n", lm->grad));
    286:     PetscCall(PetscViewerASCIIPopTab(viewer));
    287:   }
    288:   PetscFunctionReturn(PETSC_SUCCESS);
    289: }

    291: /* ---------------------------------------------------------- */
    292: /*MC
    293:   TAOOWLQN - orthant-wise limited memory quasi-newton algorithm

    295: . - tao_owlqn_lambda - regulariser weight

    297:   Level: beginner
    298: M*/

    300: PETSC_EXTERN PetscErrorCode TaoCreate_OWLQN(Tao tao)
    301: {
    302:   TAO_OWLQN  *lmP;
    303:   const char *owarmijo_type = TAOLINESEARCHOWARMIJO;

    305:   PetscFunctionBegin;
    306:   tao->ops->setup          = TaoSetUp_OWLQN;
    307:   tao->ops->solve          = TaoSolve_OWLQN;
    308:   tao->ops->view           = TaoView_OWLQN;
    309:   tao->ops->setfromoptions = TaoSetFromOptions_OWLQN;
    310:   tao->ops->destroy        = TaoDestroy_OWLQN;

    312:   PetscCall(PetscNew(&lmP));
    313:   lmP->D      = NULL;
    314:   lmP->M      = NULL;
    315:   lmP->GV     = NULL;
    316:   lmP->Xold   = NULL;
    317:   lmP->Gold   = NULL;
    318:   lmP->lambda = 1.0;

    320:   tao->data = (void *)lmP;
    321:   /* Override default settings (unless already changed) */
    322:   PetscCall(TaoParametersInitialize(tao));
    323:   PetscObjectParameterSetDefault(tao, max_it, 2000);
    324:   PetscObjectParameterSetDefault(tao, max_funcs, 4000);

    326:   PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch));
    327:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1));
    328:   PetscCall(TaoLineSearchSetType(tao->linesearch, owarmijo_type));
    329:   PetscCall(TaoLineSearchUseTaoRoutines(tao->linesearch, tao));
    330:   PetscCall(TaoLineSearchSetOptionsPrefix(tao->linesearch, tao->hdr.prefix));
    331:   PetscFunctionReturn(PETSC_SUCCESS);
    332: }