Actual source code: pdipm.c

petsc-3.13.5 2020-09-01
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  1:  #include <petsctaolinesearch.h>
  2:  #include <../src/tao/constrained/impls/ipm/pdipm.h>
  3:  #include <petscsnes.h>

  5: /*
  6:    TaoPDIPMEvaluateFunctionsAndJacobians - Evaluate the objective function f, gradient fx, constraints, and all the Jacobians at current vector

  8:    Collective on tao

 10:    Input Parameter:
 11: +  tao - solver context
 12: -  x - vector at which all objects to be evaluated

 14:    Level: beginner

 16: .seealso: TaoPDIPMUpdateConstraints(), TaoPDIPMSetUpBounds()
 17: */
 18: PetscErrorCode TaoPDIPMEvaluateFunctionsAndJacobians(Tao tao,Vec x)
 19: {
 21:   TAO_PDIPM      *pdipm=(TAO_PDIPM*)tao->data;

 24:   /* Compute user objective function and gradient */
 25:   TaoComputeObjectiveAndGradient(tao,x,&pdipm->obj,tao->gradient);

 27:   /* Equality constraints and Jacobian */
 28:   if (pdipm->Ng) {
 29:     TaoComputeEqualityConstraints(tao,x,tao->constraints_equality);
 30:     TaoComputeJacobianEquality(tao,x,tao->jacobian_equality,tao->jacobian_equality_pre);
 31:   }

 33:   /* Inequality constraints and Jacobian */
 34:   if (pdipm->Nh) {
 35:     TaoComputeInequalityConstraints(tao,x,tao->constraints_inequality);
 36:     TaoComputeJacobianInequality(tao,x,tao->jacobian_inequality,tao->jacobian_inequality_pre);
 37:   }
 38:   return(0);
 39: }

 41: /*
 42:   TaoPDIPMUpdateConstraints - Update the vectors ce and ci at x

 44:   Collective

 46:   Input Parameter:
 47: + tao - Tao context
 48: - x - vector at which constraints to be evaluted

 50:    Level: beginner

 52: .seealso: TaoPDIPMEvaluateFunctionsAndJacobians()
 53: */
 54: PetscErrorCode TaoPDIPMUpdateConstraints(Tao tao,Vec x)
 55: {
 56:   PetscErrorCode    ierr;
 57:   TAO_PDIPM         *pdipm=(TAO_PDIPM*)tao->data;
 58:   PetscInt          i,offset,offset1,k,xstart;
 59:   PetscScalar       *carr;
 60:   const PetscInt    *ubptr,*lbptr,*bxptr,*fxptr;
 61:   const PetscScalar *xarr,*xuarr,*xlarr,*garr,*harr;

 64:   VecGetOwnershipRange(x,&xstart,NULL);

 66:   VecGetArrayRead(x,&xarr);
 67:   VecGetArrayRead(tao->XU,&xuarr);
 68:   VecGetArrayRead(tao->XL,&xlarr);

 70:   /* (1) Update ce vector */
 71:   VecGetArray(pdipm->ce,&carr);

 73:   /* (1.a) Inserting updated g(x) */
 74:   if (pdipm->Ng) {
 75:     VecGetArrayRead(tao->constraints_equality,&garr);
 76:     PetscMemcpy(carr,garr,pdipm->ng*sizeof(PetscScalar));
 77:     VecRestoreArrayRead(tao->constraints_equality,&garr);
 78:   }

 80:   /* (1.b) Update xfixed */
 81:   if (pdipm->Nxfixed) {
 82:     offset = pdipm->ng;
 83:     ISGetIndices(pdipm->isxfixed,&fxptr); /* global indices in x */
 84:     for (k=0;k < pdipm->nxfixed;k++){
 85:       i = fxptr[k]-xstart;
 86:       carr[offset + k] = xarr[i] - xuarr[i];
 87:     }
 88:   }
 89:   VecRestoreArray(pdipm->ce,&carr);

 91:   /* (2) Update ci vector */
 92:   VecGetArray(pdipm->ci,&carr);

 94:   if (pdipm->Nh) {
 95:     /* (2.a) Inserting updated h(x) */
 96:     VecGetArrayRead(tao->constraints_inequality,&harr);
 97:     PetscMemcpy(carr,harr,pdipm->nh*sizeof(PetscScalar));
 98:     VecRestoreArrayRead(tao->constraints_inequality,&harr);
 99:   }

101:   /* (2.b) Update xub */
102:   offset = pdipm->nh;
103:   if (pdipm->Nxub) {
104:     ISGetIndices(pdipm->isxub,&ubptr);
105:     for (k=0; k<pdipm->nxub; k++){
106:       i = ubptr[k]-xstart;
107:       carr[offset + k] = xuarr[i] - xarr[i];
108:     }
109:   }

111:   if (pdipm->Nxlb) {
112:     /* (2.c) Update xlb */
113:     offset += pdipm->nxub;
114:     ISGetIndices(pdipm->isxlb,&lbptr); /* global indices in x */
115:     for (k=0; k<pdipm->nxlb; k++){
116:       i = lbptr[k]-xstart;
117:       carr[offset + k] = xarr[i] - xlarr[i];
118:     }
119:   }

121:   if (pdipm->Nxbox) {
122:     /* (2.d) Update xbox */
123:     offset += pdipm->nxlb;
124:     offset1 = offset + pdipm->nxbox;
125:     ISGetIndices(pdipm->isxbox,&bxptr); /* global indices in x */
126:     for (k=0; k<pdipm->nxbox; k++){
127:       i = bxptr[k]-xstart; /* local indices in x */
128:       carr[offset+k]  = xuarr[i] - xarr[i];
129:       carr[offset1+k] = xarr[i]  - xlarr[i];
130:     }
131:   }
132:   VecRestoreArray(pdipm->ci,&carr);

134:   /* Restoring Vectors */
135:   VecRestoreArrayRead(x,&xarr);
136:   VecRestoreArrayRead(tao->XU,&xuarr);
137:   VecRestoreArrayRead(tao->XL,&xlarr);
138:   return(0);
139: }

141: /*
142:    TaoPDIPMSetUpBounds - Create upper and lower bound vectors of x

144:    Collective

146:    Input Parameter:
147: .  tao - holds pdipm and XL & XU

149:    Level: beginner

151: .seealso: TaoPDIPMUpdateConstraints
152: */
153: PetscErrorCode TaoPDIPMSetUpBounds(Tao tao)
154: {
155:   PetscErrorCode    ierr;
156:   TAO_PDIPM         *pdipm=(TAO_PDIPM*)tao->data;
157:   const PetscScalar *xl,*xu;
158:   PetscInt          n,*ixlb,*ixub,*ixfixed,*ixfree,*ixbox,i,low,high,idx;
159:   MPI_Comm          comm;
160:   PetscInt          sendbuf[5],recvbuf[5];

163:   /* Creates upper and lower bounds vectors on x, if not created already */
164:   TaoComputeVariableBounds(tao);

166:   VecGetLocalSize(tao->XL,&n);
167:   PetscMalloc5(n,&ixlb,n,&ixub,n,&ixfree,n,&ixfixed,n,&ixbox);

169:   VecGetOwnershipRange(tao->XL,&low,&high);
170:   VecGetArrayRead(tao->XL,&xl);
171:   VecGetArrayRead(tao->XU,&xu);
172:   for (i=0; i<n; i++) {
173:     idx = low + i;
174:     if ((PetscRealPart(xl[i]) > PETSC_NINFINITY) && (PetscRealPart(xu[i]) < PETSC_INFINITY)) {
175:       if (PetscRealPart(xl[i]) == PetscRealPart(xu[i])) {
176:         ixfixed[pdipm->nxfixed++]  = idx;
177:       } else ixbox[pdipm->nxbox++] = idx;
178:     } else {
179:       if ((PetscRealPart(xl[i]) > PETSC_NINFINITY) && (PetscRealPart(xu[i]) >= PETSC_INFINITY)) {
180:         ixlb[pdipm->nxlb++] = idx;
181:       } else if ((PetscRealPart(xl[i]) <= PETSC_NINFINITY) && (PetscRealPart(xu[i]) < PETSC_INFINITY)) {
182:         ixub[pdipm->nxlb++] = idx;
183:       } else  ixfree[pdipm->nxfree++] = idx;
184:     }
185:   }
186:   VecRestoreArrayRead(tao->XL,&xl);
187:   VecRestoreArrayRead(tao->XU,&xu);

189:   PetscObjectGetComm((PetscObject)tao,&comm);
190:   sendbuf[0] = pdipm->nxlb;
191:   sendbuf[1] = pdipm->nxub;
192:   sendbuf[2] = pdipm->nxfixed;
193:   sendbuf[3] = pdipm->nxbox;
194:   sendbuf[4] = pdipm->nxfree;

196:   MPI_Allreduce(sendbuf,recvbuf,5,MPIU_INT,MPI_SUM,comm);
197:   pdipm->Nxlb    = recvbuf[0];
198:   pdipm->Nxub    = recvbuf[1];
199:   pdipm->Nxfixed = recvbuf[2];
200:   pdipm->Nxbox   = recvbuf[3];
201:   pdipm->Nxfree  = recvbuf[4];

203:   if (pdipm->Nxlb) {
204:     ISCreateGeneral(comm,pdipm->nxlb,ixlb,PETSC_COPY_VALUES,&pdipm->isxlb);
205:   }
206:   if (pdipm->Nxub) {
207:     ISCreateGeneral(comm,pdipm->nxub,ixub,PETSC_COPY_VALUES,&pdipm->isxub);
208:   }
209:   if (pdipm->Nxfixed) {
210:     ISCreateGeneral(comm,pdipm->nxfixed,ixfixed,PETSC_COPY_VALUES,&pdipm->isxfixed);
211:   }
212:   if (pdipm->Nxbox) {
213:     ISCreateGeneral(comm,pdipm->nxbox,ixbox,PETSC_COPY_VALUES,&pdipm->isxbox);
214:   }
215:   if (pdipm->Nxfree) {
216:     ISCreateGeneral(comm,pdipm->nxfree,ixfree,PETSC_COPY_VALUES,&pdipm->isxfree);
217:   }
218:   PetscFree5(ixlb,ixub,ixfixed,ixbox,ixfree);
219:   return(0);
220: }

222: /*
223:    TaoPDIPMInitializeSolution - Initialize PDIPM solution X = [x; lambdae; lambdai; z].
224:    X consists of four subvectors in the order [x; lambdae; lambdai; z]. These
225:      four subvectors need to be initialized and its values copied over to X. Instead
226:      of copying, we use VecPlace/ResetArray functions to share the memory locations for
227:      X and the subvectors

229:    Collective

231:    Input Parameter:
232: .  tao - Tao context

234:    Level: beginner
235: */
236: PetscErrorCode TaoPDIPMInitializeSolution(Tao tao)
237: {
239:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;
240:   PetscScalar    *Xarr,*z,*lambdai;
241:   PetscInt       i;
242:   const PetscScalar *xarr,*h;

245:   VecGetArray(pdipm->X,&Xarr);

247:   /* Set Initialize X.x = tao->solution */
248:   VecGetArrayRead(tao->solution,&xarr);
249:   PetscMemcpy(Xarr,xarr,pdipm->nx*sizeof(PetscScalar));
250:   VecRestoreArrayRead(tao->solution,&xarr);

252:   /* Initialize X.lambdae = 0.0 */
253:   if (pdipm->lambdae) {
254:     VecSet(pdipm->lambdae,0.0);
255:   }
256:   /* Initialize X.lambdai = push_init_lambdai, X.z = push_init_slack */
257:   VecSet(pdipm->lambdai,pdipm->push_init_lambdai);
258:   VecSet(pdipm->z,pdipm->push_init_slack);

260:   /* Additional modification for X.lambdai and X.z */
261:   VecGetArray(pdipm->lambdai,&lambdai);
262:   VecGetArray(pdipm->z,&z);
263:   if (pdipm->Nh) {
264:     VecGetArrayRead(tao->constraints_inequality,&h);
265:     for (i=0; i < pdipm->nh; i++) {
266:       if (h[i] < -pdipm->push_init_slack) z[i] = -h[i];
267:       if (pdipm->mu/z[i] > pdipm->push_init_lambdai) lambdai[i] = pdipm->mu/z[i];
268:     }
269:     VecRestoreArrayRead(tao->constraints_inequality,&h);
270:   }
271:   VecRestoreArray(pdipm->lambdai,&lambdai);
272:   VecRestoreArray(pdipm->z,&z);

274:   VecRestoreArray(pdipm->X,&Xarr);
275:   return(0);
276: }

278: /*
279:    TaoSNESJacobian_PDIPM - Evaluate the Hessian matrix at X

281:    Input Parameter:
282:    snes - SNES context
283:    X - KKT Vector
284:    *ctx - pdipm context

286:    Output Parameter:
287:    J - Hessian matrix
288:    Jpre - Preconditioner
289: */
290: PetscErrorCode TaoSNESJacobian_PDIPM(SNES snes,Vec X, Mat J, Mat Jpre, void *ctx)
291: {
292:   PetscErrorCode    ierr;
293:   Tao               tao=(Tao)ctx;
294:   TAO_PDIPM         *pdipm = (TAO_PDIPM*)tao->data;
295:   PetscInt          i,row,cols[2],Jrstart,rjstart,nc,j;
296:   const PetscInt    *aj,*ranges,*Jranges,*rranges,*cranges;
297:   const PetscScalar *Xarr,*aa;
298:   PetscScalar       vals[2];
299:   PetscInt          proc,nx_all,*nce_all=pdipm->nce_all;
300:   MPI_Comm          comm;
301:   PetscMPIInt       rank,size;
302:   Mat               jac_equality_trans=pdipm->jac_equality_trans,jac_inequality_trans=pdipm->jac_inequality_trans;

305:   PetscObjectGetComm((PetscObject)snes,&comm);
306:   MPI_Comm_rank(comm,&rank);
307:   MPI_Comm_rank(comm,&size);

309:   MatGetOwnershipRanges(Jpre,&Jranges);
310:   MatGetOwnershipRange(Jpre,&Jrstart,NULL);
311:   MatGetOwnershipRangesColumn(tao->hessian,&rranges);
312:   MatGetOwnershipRangesColumn(tao->hessian,&cranges);

314:   VecGetArrayRead(X,&Xarr);

316:   /* (2) insert Z and Ci to Jpre -- overwrite existing values */
317:   for (i=0; i < pdipm->nci; i++) {
318:     row     = Jrstart + pdipm->off_z + i;
319:     cols[0] = Jrstart + pdipm->off_lambdai + i;
320:     cols[1] = row;
321:     vals[0] = Xarr[pdipm->off_z + i];
322:     vals[1] = Xarr[pdipm->off_lambdai + i];
323:     MatSetValues(Jpre,1,&row,2,cols,vals,INSERT_VALUES);
324:   }

326:   /* (3) insert 2nd row block of Jpre: [ grad g, 0, 0, 0] */
327:   if (pdipm->Ng) {
328:     MatGetOwnershipRange(tao->jacobian_equality,&rjstart,NULL);
329:     for (i=0; i<pdipm->ng; i++){
330:       row = Jrstart + pdipm->off_lambdae + i;
331:       
332:       MatGetRow(tao->jacobian_equality,i+rjstart,&nc,&aj,&aa);
333:       proc = 0;
334:       for (j=0; j < nc; j++) {
335:         while (aj[j] >= cranges[proc+1]) proc++;
336:         cols[0] = aj[j] - cranges[proc] + Jranges[proc];
337:         MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
338:       }
339:       MatRestoreRow(tao->jacobian_equality,i+rjstart,&nc,&aj,&aa);
340:     }
341:   }

343:   if (pdipm->Nh) {
344:     /* (4) insert 3nd row block of Jpre: [ grad h, 0, 0, 0] */
345:     MatGetOwnershipRange(tao->jacobian_inequality,&rjstart,NULL);
346:     for (i=0; i < pdipm->nh; i++){
347:       row = Jrstart + pdipm->off_lambdai + i;
348:       
349:       MatGetRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,&aa);
350:       proc = 0;
351:       for (j=0; j < nc; j++) {
352:         while (aj[j] >= cranges[proc+1]) proc++;
353:         cols[0] = aj[j] - cranges[proc] + Jranges[proc];
354:         MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
355:       }
356:     MatRestoreRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,&aa);
357:     }
358:   }

360:   /* (5) insert Wxx, grad g' and -grad h' to Jpre */
361:   if (pdipm->Ng) {
362:     MatTranspose(tao->jacobian_equality,MAT_REUSE_MATRIX,&jac_equality_trans);
363:   }
364:   if (pdipm->Nh) {
365:     MatTranspose(tao->jacobian_inequality,MAT_REUSE_MATRIX,&jac_inequality_trans);
366:   }

368:   VecPlaceArray(pdipm->x,Xarr);
369:   TaoComputeHessian(tao,pdipm->x,tao->hessian,tao->hessian_pre);
370:   VecResetArray(pdipm->x);

372:   MatGetOwnershipRange(tao->hessian,&rjstart,NULL);
373:   for (i=0; i<pdipm->nx; i++){
374:     row = Jrstart + i;

376:     /* insert Wxx */
377:     MatGetRow(tao->hessian,i+rjstart,&nc,&aj,&aa);
378:     proc = 0;
379:     for (j=0; j < nc; j++) {
380:       while (aj[j] >= cranges[proc+1]) proc++;
381:       cols[0] = aj[j] - cranges[proc] + Jranges[proc];
382:       MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
383:     }
384:     MatRestoreRow(tao->hessian,i+rjstart,&nc,&aj,&aa);

386:     if (pdipm->ng) {
387:       /* insert grad g' */
388:       MatGetRow(jac_equality_trans,i+rjstart,&nc,&aj,&aa);
389:       MatGetOwnershipRanges(tao->jacobian_equality,&ranges);
390:       proc = 0;
391:       for (j=0; j < nc; j++) {
392:         /* find row ownership of */
393:         while (aj[j] >= ranges[proc+1]) proc++;
394:         nx_all = rranges[proc+1] - rranges[proc];
395:         cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
396:         MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
397:       }
398:       MatRestoreRow(jac_equality_trans,i+rjstart,&nc,&aj,&aa);
399:     }

401:     if (pdipm->nh) {
402:       /* insert -grad h' */
403:       MatGetRow(jac_inequality_trans,i+rjstart,&nc,&aj,&aa);
404:       MatGetOwnershipRanges(tao->jacobian_inequality,&ranges);
405:       proc = 0;
406:       for (j=0; j < nc; j++) {
407:         /* find row ownership of */
408:         while (aj[j] >= ranges[proc+1]) proc++;
409:         nx_all = rranges[proc+1] - rranges[proc];
410:         cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
411:         MatSetValue(Jpre,row,cols[0],-aa[j],INSERT_VALUES);
412:       }
413:       MatRestoreRow(jac_inequality_trans,i+rjstart,&nc,&aj,&aa);
414:     }
415:   }
416:   VecRestoreArrayRead(X,&Xarr);

418:   /* (6) assemble Jpre and J */
419:   MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
420:   MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);

422:   if (J != Jpre) {
423:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
424:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
425:   }
426:   return(0);
427: }

429: /*
430:    TaoSnesFunction_PDIPM - Evaluate KKT function at X

432:    Input Parameter:
433:    snes - SNES context
434:    X - KKT Vector
435:    *ctx - pdipm

437:    Output Parameter:
438:    F - Updated Lagrangian vector
439: */
440: PetscErrorCode TaoSNESFunction_PDIPM(SNES snes,Vec X,Vec F,void *ctx)
441: {
443:   Tao            tao=(Tao)ctx;
444:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;
445:   PetscScalar    *Farr;
446:   Vec            x,L1;
447:   PetscInt       i;
448:   PetscReal      res[2],cnorm[2];
449:   const PetscScalar *Xarr,*carr,*zarr,*larr;

452:   VecSet(F,0.0);

454:   VecGetArrayRead(X,&Xarr);
455:   VecGetArray(F,&Farr);

457:   /* (0) Evaluate f, fx, Gx, Hx at X.x Note: pdipm->x is not changed below */
458:   x = pdipm->x;
459:   VecPlaceArray(x,Xarr);
460:   TaoPDIPMEvaluateFunctionsAndJacobians(tao,x);

462:   /* Update ce, ci, and Jci at X.x */
463:   TaoPDIPMUpdateConstraints(tao,x);
464:   VecResetArray(x);

466:   /* (1) L1 = fx + (gradG'*DE + Jce_xfixed'*lambdae_xfixed) - (gradH'*DI + Jci_xb'*lambdai_xb) */
467:   L1 = pdipm->x;
468:   VecPlaceArray(L1,Farr);
469:   if (pdipm->Nci) {
470:     if (pdipm->Nh) {
471:       /* L1 += gradH'*DI. Note: tao->DI is not changed below */
472:       VecPlaceArray(tao->DI,Xarr+pdipm->off_lambdai);
473:       MatMultTransposeAdd(tao->jacobian_inequality,tao->DI,L1,L1);
474:       VecResetArray(tao->DI);
475:     }

477:     /* L1 += Jci_xb'*lambdai_xb */
478:     VecPlaceArray(pdipm->lambdai_xb,Xarr+pdipm->off_lambdai+pdipm->nh);
479:     MatMultTransposeAdd(pdipm->Jci_xb,pdipm->lambdai_xb,L1,L1);
480:     VecResetArray(pdipm->lambdai_xb);

482:     /* (1.4) L1 = - (gradH'*DI + Jci_xb'*lambdai_xb) */
483:     VecScale(L1,-1.0);
484:   }

486:   /* L1 += fx */
487:   VecAXPY(L1,1.0,tao->gradient);

489:   if (pdipm->Nce) {
490:     if (pdipm->Ng) {
491:       /* L1 += gradG'*DE. Note: tao->DE is not changed below */
492:       VecPlaceArray(tao->DE,Xarr+pdipm->off_lambdae);
493:       MatMultTransposeAdd(tao->jacobian_equality,tao->DE,L1,L1);
494:       VecResetArray(tao->DE);
495:     }
496:     if (pdipm->Nxfixed) {
497:       /* L1 += Jce_xfixed'*lambdae_xfixed */
498:       VecPlaceArray(pdipm->lambdae_xfixed,Xarr+pdipm->off_lambdae+pdipm->ng);
499:       MatMultTransposeAdd(pdipm->Jce_xfixed,pdipm->lambdae_xfixed,L1,L1);
500:       VecResetArray(pdipm->lambdae_xfixed);
501:     }
502:   }
503:   VecNorm(L1,NORM_2,&res[0]);
504:   VecResetArray(L1);

506:   /* (2) L2 = ce(x) */
507:   if (pdipm->Nce) {
508:     VecGetArrayRead(pdipm->ce,&carr);
509:     for (i=0; i<pdipm->nce; i++) Farr[pdipm->off_lambdae + i] = carr[i];
510:     VecRestoreArrayRead(pdipm->ce,&carr);
511:   }
512:   VecNorm(pdipm->ce,NORM_2,&cnorm[0]);

514:   if (pdipm->Nci) {
515:     /* (3) L3 = ci(x) - z;
516:        (4) L4 = Z * Lambdai * e - mu * e
517:     */
518:     VecGetArrayRead(pdipm->ci,&carr);
519:     larr = Xarr+pdipm->off_lambdai;
520:     zarr = Xarr+pdipm->off_z;
521:     for (i=0; i<pdipm->nci; i++) {
522:       Farr[pdipm->off_lambdai + i] = carr[i] - zarr[i];
523:       Farr[pdipm->off_z       + i] = zarr[i]*larr[i] - pdipm->mu;
524:     }
525:     VecRestoreArrayRead(pdipm->ci,&carr);
526:   }

528:   VecPlaceArray(pdipm->ci,Farr+pdipm->off_lambdai);
529:   VecNorm(pdipm->ci,NORM_2,&cnorm[1]);
530:   VecResetArray(pdipm->ci);

532:   /* note: pdipm->z is not changed below */
533:   VecPlaceArray(pdipm->z,Farr+pdipm->off_z);
534:   VecNorm(pdipm->z,NORM_2,&res[1]);
535:   VecResetArray(pdipm->z);

537:   tao->residual = PetscSqrtReal(res[0]*res[0] + res[1]*res[1]);
538:   tao->cnorm    = PetscSqrtReal(cnorm[0]*cnorm[0] + cnorm[1]*cnorm[1]);

540:   VecRestoreArrayRead(X,&Xarr);
541:   VecRestoreArray(F,&Farr);
542:   return(0);
543: }

545: /*
546:    PDIPMLineSearch - Custom line search used with PDIPM.

548:    Collective on TAO

550:    Notes:
551:    PDIPMLineSearch employs a simple backtracking line-search to keep
552:    the slack variables (z) and inequality constraints lagrange multipliers
553:    (lambdai) positive, i.e., z,lambdai >=0. It does this by calculating scalars
554:    alpha_p and alpha_d to keep z,lambdai non-negative. The decision (x), and the 
555:    slack variables are updated as X = X + alpha_d*dx. The constraint multipliers
556:    are updated as Lambdai = Lambdai + alpha_p*dLambdai. The barrier parameter mu
557:    is also updated as mu = mu + z'lambdai/Nci
558: */
559: PetscErrorCode PDIPMLineSearch(SNESLineSearch linesearch,void *ctx)
560: {
562:   Tao            tao=(Tao)ctx;
563:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;
564:   SNES           snes;
565:   Vec            X,F,Y,W,G;
566:   PetscInt       i,iter;
567:   PetscReal      alpha_p=1.0,alpha_d=1.0,alpha[4];
568:   PetscScalar    *Xarr,*z,*lambdai,dot;
569:   const PetscScalar *dXarr,*dz,*dlambdai;
570:   PetscScalar    *taosolarr;

573:   SNESLineSearchGetSNES(linesearch,&snes);
574:   SNESGetIterationNumber(snes,&iter);

576:   SNESLineSearchSetReason(linesearch,SNES_LINESEARCH_SUCCEEDED);
577:   SNESLineSearchGetVecs(linesearch,&X,&F,&Y,&W,&G);

579:   VecGetArray(X,&Xarr);
580:   VecGetArrayRead(Y,&dXarr);
581:   z  = Xarr + pdipm->off_z;
582:   dz = dXarr + pdipm->off_z;
583:   for (i=0; i < pdipm->nci; i++) {
584:     if (z[i] - dz[i] < 0.0) {
585:       alpha_p = PetscMin(alpha_p,0.9999*z[i]/dz[i]);
586:     }
587:   }

589:   lambdai  = Xarr + pdipm->off_lambdai;
590:   dlambdai = dXarr + pdipm->off_lambdai;

592:   for (i=0; i<pdipm->nci; i++) {
593:     if (lambdai[i] - dlambdai[i] < 0.0) {
594:       alpha_d = PetscMin(0.9999*lambdai[i]/dlambdai[i],alpha_d);
595:     }
596:   }

598:   alpha[0] = alpha_p;
599:   alpha[1] = alpha_d;
600:   VecRestoreArrayRead(Y,&dXarr);
601:   VecRestoreArray(X,&Xarr);

603:   /* alpha = min(alpha) over all processes */
604:   MPI_Allreduce(alpha,alpha+2,2,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)tao));

606:   alpha_p = alpha[2];
607:   alpha_d = alpha[3];

609:   VecGetArray(X,&Xarr);
610:   VecGetArrayRead(Y,&dXarr);
611:   for (i=0; i<pdipm->nx; i++) {
612:     Xarr[i] = Xarr[i] - alpha_p * dXarr[i];
613:   }

615:   for (i=0; i<pdipm->nce; i++) {
616:     Xarr[i+pdipm->off_lambdae] = Xarr[i+pdipm->off_lambdae] - alpha_d * dXarr[i+pdipm->off_lambdae];
617:   }

619:   for (i=0; i<pdipm->nci; i++) {
620:     Xarr[i+pdipm->off_lambdai] = Xarr[i+pdipm->off_lambdai] - alpha_d * dXarr[i+pdipm->off_lambdai];
621:   }

623:   for (i=0; i<pdipm->nci; i++) {
624:     Xarr[i+pdipm->off_z] = Xarr[i+pdipm->off_z] - alpha_p * dXarr[i+pdipm->off_z];
625:   }

627:   VecGetArray(tao->solution,&taosolarr);
628:   PetscMemcpy(taosolarr,Xarr,pdipm->nx*sizeof(PetscScalar));
629:   VecRestoreArray(tao->solution,&taosolarr);


632:   VecRestoreArray(X,&Xarr);
633:   VecRestoreArrayRead(Y,&dXarr);

635:   /* Evaluate F at X */
636:   SNESComputeFunction(snes,X,F);
637:   SNESLineSearchComputeNorms(linesearch); /* must call this func, do not know why */

639:   /* update mu = mu_update_factor * dot(z,lambdai)/pdipm->nci at updated X */
640:   VecDot(pdipm->z,pdipm->lambdai,&dot);

642:   /* if (PetscAbsReal(pdipm->gradL) < 0.9*pdipm->mu)  */
643:   pdipm->mu = pdipm->mu_update_factor * dot/pdipm->Nci;

645:   /* Update F; get tao->residual and tao->cnorm */
646:   TaoSNESFunction_PDIPM(snes,X,F,(void*)tao);

648:   tao->niter++;
649:   TaoLogConvergenceHistory(tao,pdipm->obj,tao->residual,tao->cnorm,tao->niter);
650:   TaoMonitor(tao,tao->niter,pdipm->obj,tao->residual,tao->cnorm,pdipm->mu);

652:   (*tao->ops->convergencetest)(tao,tao->cnvP);
653:   if (tao->reason) {
654:     SNESSetConvergedReason(snes,SNES_CONVERGED_FNORM_ABS);
655:   }
656:   return(0);
657: }

659: /*
660:    TaoSolve_PDIPM

662:    Input Parameter:
663:    tao - TAO context

665:    Output Parameter:
666:    tao - TAO context
667: */
668: PetscErrorCode TaoSolve_PDIPM(Tao tao)
669: {
670:   PetscErrorCode     ierr;
671:   TAO_PDIPM          *pdipm = (TAO_PDIPM*)tao->data;
672:   SNESLineSearch     linesearch;  /* SNESLineSearch context */
673:   Vec                dummy;

676:   if (!tao->constraints_equality && !tao->constraints_inequality) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_ARG_NULL,"Equality and inequality contraints are not set. Either set them or switch to a different algorithm");

678:   /* Initialize all variables */
679:   TaoPDIPMInitializeSolution(tao);

681:   /* Set linesearch */
682:   SNESGetLineSearch(pdipm->snes,&linesearch);
683:   SNESLineSearchSetType(linesearch,SNESLINESEARCHSHELL);
684:   SNESLineSearchShellSetUserFunc(linesearch,PDIPMLineSearch,tao);
685:   SNESLineSearchSetFromOptions(linesearch);

687:   tao->reason = TAO_CONTINUE_ITERATING;

689:   /* -tao_monitor for iteration 0 and check convergence */
690:   VecDuplicate(pdipm->X,&dummy);
691:   TaoSNESFunction_PDIPM(pdipm->snes,pdipm->X,dummy,(void*)tao);

693:   TaoLogConvergenceHistory(tao,pdipm->obj,tao->residual,tao->cnorm,tao->niter);
694:   TaoMonitor(tao,tao->niter,pdipm->obj,tao->residual,tao->cnorm,pdipm->mu);
695:   VecDestroy(&dummy);
696:   (*tao->ops->convergencetest)(tao,tao->cnvP);
697:   if (tao->reason) {
698:     SNESSetConvergedReason(pdipm->snes,SNES_CONVERGED_FNORM_ABS);
699:   }

701:   while (tao->reason == TAO_CONTINUE_ITERATING) {
702:     SNESConvergedReason reason;
703:     SNESSolve(pdipm->snes,NULL,pdipm->X);

705:     /* Check SNES convergence */
706:     SNESGetConvergedReason(pdipm->snes,&reason);
707:     if (reason < 0) {
708:       PetscPrintf(PETSC_COMM_WORLD,"SNES solve did not converged due to reason %D\n",reason);
709:     }

711:     /* Check TAO convergence */
712:     if (PetscIsInfOrNanReal(pdipm->obj)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"User-provided compute function generated Inf or NaN");
713:   }
714:   return(0);
715: }

717: /*
718:    TaoSetup_PDIPM - Sets up tao and pdipm

720:    Input Parameter:
721:    tao - TAO object

723:    Output:   pdipm - initialized object
724: */
725: PetscErrorCode TaoSetup_PDIPM(Tao tao)
726: {
727:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;
729:   MPI_Comm       comm;
730:   PetscMPIInt    rank,size;
731:   PetscInt       row,col,Jcrstart,Jcrend,k,tmp,nc,proc,*nh_all,*ng_all;
732:   PetscInt       offset,*xa,*xb,i,j,rstart,rend;
733:   PetscScalar    one=1.0,neg_one=-1.0,*Xarr;
734:   const PetscInt    *cols,*rranges,*cranges,*aj,*ranges;
735:   const PetscScalar *aa;
736:   Mat            J,jac_equality_trans,jac_inequality_trans;
737:   Mat            Jce_xfixed_trans,Jci_xb_trans;
738:   PetscInt       *dnz,*onz,rjstart,nx_all,*nce_all,*Jranges,cols1[2];

741:   PetscObjectGetComm((PetscObject)tao,&comm);
742:   MPI_Comm_rank(comm,&rank);
743:   MPI_Comm_size(comm,&size);

745:   /* (1) Setup Bounds and create Tao vectors */
746:   TaoPDIPMSetUpBounds(tao);

748:   if (!tao->gradient) {
749:     VecDuplicate(tao->solution,&tao->gradient);
750:     VecDuplicate(tao->solution,&tao->stepdirection);
751:   }

753:   /* (2) Get sizes */
754:   /* Size of vector x - This is set by TaoSetInitialVector */
755:   VecGetSize(tao->solution,&pdipm->Nx);
756:   VecGetLocalSize(tao->solution,&pdipm->nx);

758:   /* Size of equality constraints and vectors */
759:   if (tao->constraints_equality) {
760:     VecGetSize(tao->constraints_equality,&pdipm->Ng);
761:     VecGetLocalSize(tao->constraints_equality,&pdipm->ng);
762:   } else {
763:     pdipm->ng = pdipm->Ng = 0;
764:   }

766:   pdipm->nce = pdipm->ng + pdipm->nxfixed;
767:   pdipm->Nce = pdipm->Ng + pdipm->Nxfixed;

769:   /* Size of inequality constraints and vectors */
770:   if (tao->constraints_inequality) {
771:     VecGetSize(tao->constraints_inequality,&pdipm->Nh);
772:     VecGetLocalSize(tao->constraints_inequality,&pdipm->nh);
773:   } else {
774:     pdipm->nh = pdipm->Nh = 0;
775:   }

777:   pdipm->nci = pdipm->nh + pdipm->nxlb + pdipm->nxub + 2*pdipm->nxbox;
778:   pdipm->Nci = pdipm->Nh + pdipm->Nxlb + pdipm->Nxub + 2*pdipm->Nxbox;

780:   /* Full size of the KKT system to be solved */
781:   pdipm->n = pdipm->nx + pdipm->nce + 2*pdipm->nci;
782:   pdipm->N = pdipm->Nx + pdipm->Nce + 2*pdipm->Nci;

784:   /* list below to TaoView_PDIPM()? */
785:   /* PetscPrintf(PETSC_COMM_SELF,"[%d] nce %d = ng %d + nxfixed %d\n",rank,pdipm->nce,pdipm->ng,pdipm->nxfixed); */
786:   /* PetscPrintf(PETSC_COMM_SELF,"[%d] nci %d = nh %d + nxlb %d + nxub %d + 2*nxbox %d\n",rank,pdipm->nci,pdipm->nh,pdipm->nxlb,pdipm->nxub,pdipm->nxbox); */
787:   /* PetscPrintf(PETSC_COMM_SELF,"[%d] n %d = nx %d + nce %d + 2*nci %d\n",rank,pdipm->n,pdipm->nx,pdipm->nce,pdipm->nci); */

789:   /* (3) Offsets for subvectors */
790:   pdipm->off_lambdae = pdipm->nx;
791:   pdipm->off_lambdai = pdipm->off_lambdae + pdipm->nce;
792:   pdipm->off_z       = pdipm->off_lambdai + pdipm->nci;

794:   /* (4) Create vectors and subvectors */
795:   /* Ce and Ci vectors */
796:   VecCreate(comm,&pdipm->ce);
797:   VecSetSizes(pdipm->ce,pdipm->nce,pdipm->Nce);
798:   VecSetFromOptions(pdipm->ce);

800:   VecCreate(comm,&pdipm->ci);
801:   VecSetSizes(pdipm->ci,pdipm->nci,pdipm->Nci);
802:   VecSetFromOptions(pdipm->ci);

804:   /* X=[x; lambdae; lambdai; z] for the big KKT system */
805:   VecCreate(comm,&pdipm->X);
806:   VecSetSizes(pdipm->X,pdipm->n,pdipm->N);
807:   VecSetFromOptions(pdipm->X);

809:   /* Subvectors; they share local arrays with X */
810:   VecGetArray(pdipm->X,&Xarr);
811:   /* x shares local array with X.x */
812:   if (pdipm->Nx) {
813:     VecCreateMPIWithArray(comm,1,pdipm->nx,pdipm->Nx,Xarr,&pdipm->x);
814:   }

816:   /* lambdae shares local array with X.lambdae */
817:   if (pdipm->Nce) {
818:     VecCreateMPIWithArray(comm,1,pdipm->nce,pdipm->Nce,Xarr+pdipm->off_lambdae,&pdipm->lambdae);
819:   }

821:   /* tao->DE shares local array with X.lambdae_g */
822:   if (pdipm->Ng) {
823:     VecCreateMPIWithArray(comm,1,pdipm->ng,pdipm->Ng,Xarr+pdipm->off_lambdae,&tao->DE);

825:     VecCreate(comm,&pdipm->lambdae_xfixed);
826:     VecSetSizes(pdipm->lambdae_xfixed,pdipm->nxfixed,PETSC_DECIDE);
827:     VecSetFromOptions(pdipm->lambdae_xfixed);
828:   }

830:   if (pdipm->Nci) {
831:     /* lambdai shares local array with X.lambdai */
832:     VecCreateMPIWithArray(comm,1,pdipm->nci,pdipm->Nci,Xarr+pdipm->off_lambdai,&pdipm->lambdai);

834:     /* z for slack variables; it shares local array with X.z */
835:     VecCreateMPIWithArray(comm,1,pdipm->nci,pdipm->Nci,Xarr+pdipm->off_z,&pdipm->z);
836:   }

838:   /* tao->DI which shares local array with X.lambdai_h */
839:   if (pdipm->Nh) {
840:     VecCreateMPIWithArray(comm,1,pdipm->nh,pdipm->Nh,Xarr+pdipm->off_lambdai,&tao->DI);
841:   }

843:   VecCreate(comm,&pdipm->lambdai_xb);
844:   VecSetSizes(pdipm->lambdai_xb,(pdipm->nci - pdipm->nh),PETSC_DECIDE);
845:   VecSetFromOptions(pdipm->lambdai_xb);

847:   VecRestoreArray(pdipm->X,&Xarr);

849:   /* (5) Create Jacobians Jce_xfixed and Jci */
850:   /* (5.1) PDIPM Jacobian of equality bounds cebound(x) = J_nxfixed */
851:   if (pdipm->Nxfixed) {
852:     /* Create Jce_xfixed */
853:     MatCreate(comm,&pdipm->Jce_xfixed);
854:     MatSetSizes(pdipm->Jce_xfixed,pdipm->nxfixed,pdipm->nx,PETSC_DECIDE,pdipm->Nx);
855:     MatSetFromOptions(pdipm->Jce_xfixed);
856:     MatSeqAIJSetPreallocation(pdipm->Jce_xfixed,1,NULL);
857:     MatMPIAIJSetPreallocation(pdipm->Jce_xfixed,1,NULL,1,NULL);

859:     MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,&Jcrend);
860:     ISGetIndices(pdipm->isxfixed,&cols);
861:     k = 0;
862:     for (row = Jcrstart; row < Jcrend; row++) {
863:       MatSetValues(pdipm->Jce_xfixed,1,&row,1,cols+k,&one,INSERT_VALUES);
864:       k++;
865:     }
866:     ISRestoreIndices(pdipm->isxfixed, &cols);
867:     MatAssemblyBegin(pdipm->Jce_xfixed,MAT_FINAL_ASSEMBLY);
868:     MatAssemblyEnd(pdipm->Jce_xfixed,MAT_FINAL_ASSEMBLY);
869:   }

871:   /* (5.2) PDIPM inequality Jacobian Jci = [tao->jacobian_inequality; ...] */
872:   MatCreate(comm,&pdipm->Jci_xb);
873:   MatSetSizes(pdipm->Jci_xb,pdipm->nci-pdipm->nh,pdipm->nx,PETSC_DECIDE,pdipm->Nx);
874:   MatSetFromOptions(pdipm->Jci_xb);
875:   MatSeqAIJSetPreallocation(pdipm->Jci_xb,1,NULL);
876:   MatMPIAIJSetPreallocation(pdipm->Jci_xb,1,NULL,1,NULL);

878:   MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,&Jcrend);
879:   offset = Jcrstart;
880:   if (pdipm->Nxub) {
881:     /* Add xub to Jci_xb */
882:     ISGetIndices(pdipm->isxub,&cols);
883:     k = 0;
884:     for (row = offset; row < offset + pdipm->nxub; row++) {
885:       MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&neg_one,INSERT_VALUES);
886:       k++;
887:     }
888:     ISRestoreIndices(pdipm->isxub, &cols);
889:   }

891:   if (pdipm->Nxlb) {
892:     /* Add xlb to Jci_xb */
893:     ISGetIndices(pdipm->isxlb,&cols);
894:     k = 0;
895:     offset += pdipm->nxub;
896:     for (row = offset; row < offset + pdipm->nxlb; row++) {
897:       MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&one,INSERT_VALUES);
898:       k++;
899:     }
900:     ISRestoreIndices(pdipm->isxlb, &cols);
901:   }

903:   /* Add xbox to Jci_xb */
904:   if (pdipm->Nxbox) {
905:     ISGetIndices(pdipm->isxbox,&cols);
906:     k = 0;
907:     offset += pdipm->nxlb;
908:     for (row = offset; row < offset + pdipm->nxbox; row++) {
909:       MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&neg_one,INSERT_VALUES);
910:       tmp = row + pdipm->nxbox;
911:       MatSetValues(pdipm->Jci_xb,1,&tmp,1,cols+k,&one,INSERT_VALUES);
912:       k++;
913:     }
914:     ISRestoreIndices(pdipm->isxbox, &cols);
915:   }

917:   MatAssemblyBegin(pdipm->Jci_xb,MAT_FINAL_ASSEMBLY);
918:   MatAssemblyEnd(pdipm->Jci_xb,MAT_FINAL_ASSEMBLY);
919:   /* MatView(pdipm->Jci_xb,PETSC_VIEWER_STDOUT_WORLD); */

921:   /* (6) Set up ISs for PC Fieldsplit */
922:   if (pdipm->solve_reduced_kkt) {
923:     PetscMalloc2(pdipm->nx+pdipm->nce,&xa,2*pdipm->nci,&xb);
924:     for(i=0; i < pdipm->nx + pdipm->nce; i++) xa[i] = i;
925:     for(i=0; i < 2*pdipm->nci; i++) xb[i] = pdipm->off_lambdai + i;

927:     ISCreateGeneral(comm,pdipm->nx+pdipm->nce,xa,PETSC_OWN_POINTER,&pdipm->is1);
928:     ISCreateGeneral(comm,2*pdipm->nci,xb,PETSC_OWN_POINTER,&pdipm->is2);
929:   }

931:   /* (7) Gather offsets from all processes */
932:   PetscMalloc1(size,&pdipm->nce_all);

934:   /* Get rstart of KKT matrix */
935:   MPI_Scan(&pdipm->n,&rstart,1,MPIU_INT,MPI_SUM,comm);
936:   rstart -= pdipm->n;

938:   MPI_Allgather(&pdipm->nce,1,MPIU_INT,pdipm->nce_all,1,MPIU_INT,comm);

940:   PetscMalloc3(size,&ng_all,size,&nh_all,size,&Jranges);
941:   MPI_Allgather(&rstart,1,MPIU_INT,Jranges,1,MPIU_INT,comm);
942:   MPI_Allgather(&pdipm->nh,1,MPIU_INT,nh_all,1,MPIU_INT,comm);
943:   MPI_Allgather(&pdipm->ng,1,MPIU_INT,ng_all,1,MPIU_INT,comm);

945:   MatGetOwnershipRanges(tao->hessian,&rranges);
946:   MatGetOwnershipRangesColumn(tao->hessian,&cranges);

948:   if (pdipm->Ng) {
949:     TaoComputeJacobianEquality(tao,tao->solution,tao->jacobian_equality,tao->jacobian_equality_pre);
950:     MatTranspose(tao->jacobian_equality,MAT_INITIAL_MATRIX,&pdipm->jac_equality_trans);
951:   }
952:   if (pdipm->Nh) {
953:     TaoComputeJacobianInequality(tao,tao->solution,tao->jacobian_inequality,tao->jacobian_inequality_pre);
954:     MatTranspose(tao->jacobian_inequality,MAT_INITIAL_MATRIX,&pdipm->jac_inequality_trans);
955:   }

957:   /* Count dnz,onz for preallocation of KKT matrix */
958:   jac_equality_trans   = pdipm->jac_equality_trans;
959:   jac_inequality_trans = pdipm->jac_inequality_trans;
960:   nce_all = pdipm->nce_all;

962:   if (pdipm->Nxfixed) {
963:     MatTranspose(pdipm->Jce_xfixed,MAT_INITIAL_MATRIX,&Jce_xfixed_trans);
964:   }
965:   MatTranspose(pdipm->Jci_xb,MAT_INITIAL_MATRIX,&Jci_xb_trans);

967:   MatPreallocateInitialize(comm,pdipm->n,pdipm->n,dnz,onz);

969:   /* 1st row block of KKT matrix: [Wxx; gradCe'; -gradCi'; 0] */
970:   TaoPDIPMEvaluateFunctionsAndJacobians(tao,pdipm->x);
971:   TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);

973:   /* Insert tao->hessian */
974:   MatGetOwnershipRange(tao->hessian,&rjstart,NULL);
975:   for (i=0; i<pdipm->nx; i++){
976:     row = rstart + i;

978:     MatGetRow(tao->hessian,i+rjstart,&nc,&aj,NULL);
979:     proc = 0;
980:     for (j=0; j < nc; j++) {
981:       while (aj[j] >= cranges[proc+1]) proc++;
982:       col = aj[j] - cranges[proc] + Jranges[proc];
983:       MatPreallocateSet(row,1,&col,dnz,onz);
984:     }
985:     MatRestoreRow(tao->hessian,i+rjstart,&nc,&aj,NULL);

987:     if (pdipm->ng) {
988:       /* Insert grad g' */
989:       MatGetRow(jac_equality_trans,i+rjstart,&nc,&aj,NULL);
990:       MatGetOwnershipRanges(tao->jacobian_equality,&ranges);
991:       proc = 0;
992:       for (j=0; j < nc; j++) {
993:         /* find row ownership of */
994:         while (aj[j] >= ranges[proc+1]) proc++;
995:         nx_all = rranges[proc+1] - rranges[proc];
996:         col = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
997:         MatPreallocateSet(row,1,&col,dnz,onz);
998:       }
999:       MatRestoreRow(jac_equality_trans,i+rjstart,&nc,&aj,NULL);
1000:     }

1002:     /* Insert Jce_xfixed^T' */
1003:     if (pdipm->nxfixed) {
1004:       MatGetRow(Jce_xfixed_trans,i+rjstart,&nc,&aj,NULL);
1005:       MatGetOwnershipRanges(pdipm->Jce_xfixed,&ranges);
1006:       proc = 0;
1007:       for (j=0; j < nc; j++) {
1008:         /* find row ownership of */
1009:         while (aj[j] >= ranges[proc+1]) proc++;
1010:         nx_all = rranges[proc+1] - rranges[proc];
1011:         col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + ng_all[proc];
1012:         MatPreallocateSet(row,1,&col,dnz,onz);
1013:       }
1014:       MatRestoreRow(Jce_xfixed_trans,i+rjstart,&nc,&aj,NULL);
1015:     }

1017:     if (pdipm->nh) {
1018:       /* Insert -grad h' */
1019:       MatGetRow(jac_inequality_trans,i+rjstart,&nc,&aj,NULL);
1020:       MatGetOwnershipRanges(tao->jacobian_inequality,&ranges);
1021:       proc = 0;
1022:       for (j=0; j < nc; j++) {
1023:         /* find row ownership of */
1024:         while (aj[j] >= ranges[proc+1]) proc++;
1025:         nx_all = rranges[proc+1] - rranges[proc];
1026:         col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
1027:         MatPreallocateSet(row,1,&col,dnz,onz);
1028:       }
1029:       MatRestoreRow(jac_inequality_trans,i+rjstart,&nc,&aj,NULL);
1030:     }

1032:     /* Insert Jci_xb^T' */
1033:     MatGetRow(Jci_xb_trans,i+rjstart,&nc,&aj,NULL);
1034:     MatGetOwnershipRanges(pdipm->Jci_xb,&ranges);
1035:     proc = 0;
1036:     for (j=0; j < nc; j++) {
1037:       /* find row ownership of */
1038:       while (aj[j] >= ranges[proc+1]) proc++;
1039:       nx_all = rranges[proc+1] - rranges[proc];
1040:       col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc] + nh_all[proc];
1041:       MatPreallocateSet(row,1,&col,dnz,onz);
1042:     }
1043:     MatRestoreRow(Jci_xb_trans,i+rjstart,&nc,&aj,NULL);
1044:   }

1046:   /* 2nd Row block of KKT matrix: [grad Ce, 0, 0, 0] */
1047:   if (pdipm->Ng) {
1048:     MatGetOwnershipRange(tao->jacobian_equality,&rjstart,NULL);
1049:     for (i=0; i < pdipm->ng; i++){
1050:       row = rstart + pdipm->off_lambdae + i;

1052:       MatGetRow(tao->jacobian_equality,i+rjstart,&nc,&aj,NULL);
1053:       proc = 0;
1054:       for (j=0; j < nc; j++) {
1055:         while (aj[j] >= cranges[proc+1]) proc++;
1056:         col = aj[j] - cranges[proc] + Jranges[proc];
1057:         MatPreallocateSet(row,1,&col,dnz,onz); /* grad g */
1058:       }
1059:       MatRestoreRow(tao->jacobian_equality,i+rjstart,&nc,&aj,NULL);
1060:     }
1061:   }
1062:   /* Jce_xfixed */
1063:   if (pdipm->Nxfixed) {
1064:     MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,NULL);
1065:     for (i=0; i < (pdipm->nce - pdipm->ng); i++ ){
1066:       row = rstart + pdipm->off_lambdae + pdipm->ng + i;

1068:       MatGetRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,NULL);
1069:       if (nc != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"nc != 1");

1071:       proc = 0;
1072:       j    = 0;
1073:       while (cols[j] >= cranges[proc+1]) proc++;
1074:       col = cols[j] - cranges[proc] + Jranges[proc];
1075:       MatPreallocateSet(row,1,&col,dnz,onz);
1076:       MatRestoreRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,NULL);
1077:     }
1078:   }

1080:   /* 3rd Row block of KKT matrix: [ gradCi, 0, 0, -I] */
1081:   if (pdipm->Nh) {
1082:     MatGetOwnershipRange(tao->jacobian_inequality,&rjstart,NULL);
1083:     for (i=0; i < pdipm->nh; i++){
1084:       row = rstart + pdipm->off_lambdai + i;

1086:       MatGetRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,NULL);
1087:       proc = 0;
1088:       for (j=0; j < nc; j++) {
1089:         while (aj[j] >= cranges[proc+1]) proc++;
1090:         col = aj[j] - cranges[proc] + Jranges[proc];
1091:         MatPreallocateSet(row,1,&col,dnz,onz); /* grad h */
1092:       }
1093:       MatRestoreRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,NULL);
1094:     }
1095:     /* -I */
1096:     for (i=0; i < pdipm->nh; i++){
1097:       row = rstart + pdipm->off_lambdai + i;
1098:       col = rstart + pdipm->off_z + i;
1099:       MatPreallocateSet(row,1,&col,dnz,onz);
1100:     }
1101:   }

1103:   /* Jci_xb */
1104:   MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,NULL);
1105:   for (i=0; i < (pdipm->nci - pdipm->nh); i++ ){
1106:     row = rstart + pdipm->off_lambdai + pdipm->nh + i;

1108:     MatGetRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,NULL);
1109:     if (nc != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"nc != 1");
1110:     proc = 0;
1111:     for (j=0; j < nc; j++) {
1112:       while (cols[j] >= cranges[proc+1]) proc++;
1113:       col = cols[j] - cranges[proc] + Jranges[proc];
1114:       MatPreallocateSet(row,1,&col,dnz,onz);
1115:     }
1116:     MatRestoreRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,NULL);
1117:     /* -I */
1118:     col = rstart + pdipm->off_z + pdipm->nh + i;
1119:     MatPreallocateSet(row,1,&col,dnz,onz);
1120:   }

1122:   /* 4-th Row block of KKT matrix: Z and Ci */
1123:   for (i=0; i < pdipm->nci; i++) {
1124:     row     = rstart + pdipm->off_z + i;
1125:     cols1[0] = rstart + pdipm->off_lambdai + i;
1126:     cols1[1] = row;
1127:     MatPreallocateSet(row,2,cols1,dnz,onz);
1128:   }

1130:   /* diagonal entry */
1131:   for (i=0; i<pdipm->n; i++) dnz[i]++; /* diagonal entry */

1133:   /* Create KKT matrix */
1134:   MatCreate(comm,&J);
1135:   MatSetSizes(J,pdipm->n,pdipm->n,PETSC_DECIDE,PETSC_DECIDE);
1136:   MatSetFromOptions(J);
1137:   MatSeqAIJSetPreallocation(J,0,dnz);
1138:   MatMPIAIJSetPreallocation(J,0,dnz,0,onz);
1139:   /* MatSetOption(J,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE); */
1140:   MatPreallocateFinalize(dnz,onz);
1141:   pdipm->K = J;

1143:   /* (8) Set up nonlinear solver SNES */
1144:   SNESSetFunction(pdipm->snes,NULL,TaoSNESFunction_PDIPM,(void*)tao);
1145:   SNESSetJacobian(pdipm->snes,J,J,TaoSNESJacobian_PDIPM,(void*)tao);

1147:   if (pdipm->solve_reduced_kkt) {
1148:     PC pc;
1149:     KSPGetPC(tao->ksp,&pc);
1150:     PCSetType(pc,PCFIELDSPLIT);
1151:     PCFieldSplitSetType(pc,PC_COMPOSITE_SCHUR);
1152:     PCFieldSplitSetIS(pc,"2",pdipm->is2);
1153:     PCFieldSplitSetIS(pc,"1",pdipm->is1);
1154:   }
1155:   SNESSetFromOptions(pdipm->snes);

1157:   /* (9) Insert constant entries to  K */
1158:   /* Set 0.0 to diagonal of K, so that the solver does not complain *about missing diagonal value */
1159:   MatGetOwnershipRange(J,&rstart,&rend);
1160:   for (i=rstart; i<rend; i++){
1161:     MatSetValue(J,i,i,0.0,INSERT_VALUES);
1162:   }

1164:   /* Row block of K: [ grad Ce, 0, 0, 0] */
1165:   if (pdipm->Nxfixed) {
1166:     MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,NULL);
1167:     for (i=0; i < (pdipm->nce - pdipm->ng); i++ ){
1168:       row = rstart + pdipm->off_lambdae + pdipm->ng + i;

1170:       MatGetRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,&aa);
1171:       proc = 0;
1172:       for (j=0; j < nc; j++) {
1173:         while (cols[j] >= cranges[proc+1]) proc++;
1174:         col = cols[j] - cranges[proc] + Jranges[proc];
1175:         MatSetValue(J,row,col,aa[j],INSERT_VALUES); /* grad Ce */
1176:         MatSetValue(J,col,row,aa[j],INSERT_VALUES); /* grad Ce' */
1177:       }
1178:       MatRestoreRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,&aa);
1179:     }
1180:   }

1182:   /* Row block of K: [ grad Ci, 0, 0, -I] */
1183:   MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,NULL);
1184:   for (i=0; i < (pdipm->nci - pdipm->nh); i++ ){
1185:     row = rstart + pdipm->off_lambdai + pdipm->nh + i;

1187:     MatGetRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,&aa);
1188:     proc = 0;
1189:     for (j=0; j < nc; j++) {
1190:       while (cols[j] >= cranges[proc+1]) proc++;
1191:       col = cols[j] - cranges[proc] + Jranges[proc];
1192:       MatSetValue(J,col,row,-aa[j],INSERT_VALUES);
1193:       MatSetValue(J,row,col,aa[j],INSERT_VALUES);
1194:     }
1195:     MatRestoreRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,&aa);

1197:     col = rstart + pdipm->off_z + pdipm->nh + i;
1198:     MatSetValue(J,row,col,-1,INSERT_VALUES);
1199:   }

1201:   for (i=0; i < pdipm->nh; i++){
1202:     row = rstart + pdipm->off_lambdai + i;
1203:     col = rstart + pdipm->off_z + i;
1204:     MatSetValue(J,row,col,-1,INSERT_VALUES);
1205:   }

1207:   if (pdipm->Nxfixed) {
1208:     MatDestroy(&Jce_xfixed_trans);
1209:   }
1210:   MatDestroy(&Jci_xb_trans);
1211:   PetscFree3(ng_all,nh_all,Jranges);
1212:   return(0);
1213: }

1215: /*
1216:    TaoDestroy_PDIPM - Destroys the pdipm object

1218:    Input:
1219:    full pdipm

1221:    Output:
1222:    Destroyed pdipm
1223: */
1224: PetscErrorCode TaoDestroy_PDIPM(Tao tao)
1225: {
1226:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;

1230:   /* Freeing Vectors assocaiated with KKT (X) */
1231:   VecDestroy(&pdipm->x); /* Solution x */
1232:   VecDestroy(&pdipm->lambdae); /* Equality constraints lagrangian multiplier*/
1233:   VecDestroy(&pdipm->lambdai); /* Inequality constraints lagrangian multiplier*/
1234:   VecDestroy(&pdipm->z);       /* Slack variables */
1235:   VecDestroy(&pdipm->X);       /* Big KKT system vector [x; lambdae; lambdai; z] */

1237:   /* work vectors */
1238:   VecDestroy(&pdipm->lambdae_xfixed);
1239:   VecDestroy(&pdipm->lambdai_xb);

1241:   /* Legrangian equality and inequality Vec */
1242:   VecDestroy(&pdipm->ce); /* Vec of equality constraints */
1243:   VecDestroy(&pdipm->ci); /* Vec of inequality constraints */

1245:   /* Matrices */
1246:   MatDestroy(&pdipm->Jce_xfixed);
1247:   MatDestroy(&pdipm->Jci_xb); /* Jacobian of inequality constraints Jci = [tao->jacobian_inequality ; J(nxub); J(nxlb); J(nxbx)] */
1248:   MatDestroy(&pdipm->K);

1250:   /* Index Sets */
1251:   if (pdipm->Nxub) {
1252:     ISDestroy(&pdipm->isxub);    /* Finite upper bound only -inf < x < ub */
1253:   }

1255:   if (pdipm->Nxlb) {
1256:     ISDestroy(&pdipm->isxlb);    /* Finite lower bound only  lb <= x < inf */
1257:   }

1259:   if (pdipm->Nxfixed) {
1260:     ISDestroy(&pdipm->isxfixed); /* Fixed variables         lb =  x = ub */
1261:   }

1263:   if (pdipm->Nxbox) {
1264:     ISDestroy(&pdipm->isxbox);   /* Boxed variables         lb <= x <= ub */
1265:   }

1267:   if (pdipm->Nxfree) {
1268:     ISDestroy(&pdipm->isxfree);  /* Free variables        -inf <= x <= inf */
1269:   }

1271:   if (pdipm->solve_reduced_kkt) {
1272:     ISDestroy(&pdipm->is1);
1273:     ISDestroy(&pdipm->is2);
1274:   }

1276:   /* SNES */
1277:   SNESDestroy(&pdipm->snes); /* Nonlinear solver */
1278:   PetscFree(pdipm->nce_all);
1279:   MatDestroy(&pdipm->jac_equality_trans);
1280:   MatDestroy(&pdipm->jac_inequality_trans);

1282:   /* Destroy pdipm */
1283:   PetscFree(tao->data); /* Holding locations of pdipm */

1285:   /* Destroy Dual */
1286:   VecDestroy(&tao->DE); /* equality dual */
1287:   VecDestroy(&tao->DI); /* dinequality dual */
1288:   return(0);
1289: }

1291: PetscErrorCode TaoSetFromOptions_PDIPM(PetscOptionItems *PetscOptionsObject,Tao tao)
1292: {
1293:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;

1297:   PetscOptionsHead(PetscOptionsObject,"PDIPM method for constrained optimization");
1298:   PetscOptionsReal("-tao_pdipm_push_init_slack","parameter to push initial slack variables away from bounds",NULL,pdipm->push_init_slack,&pdipm->push_init_slack,NULL);
1299:   PetscOptionsReal("-tao_pdipm_push_init_lambdai","parameter to push initial (inequality) dual variables away from bounds",NULL,pdipm->push_init_lambdai,&pdipm->push_init_lambdai,NULL);
1300:   PetscOptionsBool("-tao_pdipm_solve_reduced_kkt","Solve reduced KKT system using Schur-complement",NULL,pdipm->solve_reduced_kkt,&pdipm->solve_reduced_kkt,NULL);
1301:   PetscOptionsReal("-tao_pdipm_mu_update_factor","Update scalar for barrier parameter (mu) update",NULL,pdipm->mu_update_factor,&pdipm->mu_update_factor,NULL);
1302:   PetscOptionsTail();
1303:   return(0);
1304: }

1306: /*MC
1307:   TAOPDIPM - Barrier-based primal-dual interior point algorithm for generally constrained optimization.

1309:   Option Database Keys:
1310: +   -tao_pdipm_push_init_lambdai - parameter to push initial dual variables away from bounds (> 0)
1311: .   -tao_pdipm_push_init_slack  - parameter to push initial slack variables away from bounds (> 0)
1312: -   -tao_pdipm_mu_update_factor - update scalar for barrier parameter (mu) update (> 0)

1314:   Level: beginner
1315: M*/
1316: PETSC_EXTERN PetscErrorCode TaoCreate_PDIPM(Tao tao)
1317: {
1318:   TAO_PDIPM      *pdipm;

1322:   tao->ops->setup          = TaoSetup_PDIPM;
1323:   tao->ops->solve          = TaoSolve_PDIPM;
1324:   tao->ops->setfromoptions = TaoSetFromOptions_PDIPM;
1325:   tao->ops->destroy        = TaoDestroy_PDIPM;

1327:   PetscNewLog(tao,&pdipm);
1328:   tao->data = (void*)pdipm;

1330:   pdipm->nx      = pdipm->Nx      = 0;
1331:   pdipm->nxfixed = pdipm->Nxfixed = 0;
1332:   pdipm->nxlb    = pdipm->Nxlb    = 0;
1333:   pdipm->nxub    = pdipm->Nxub    = 0;
1334:   pdipm->nxbox   = pdipm->Nxbox   = 0;
1335:   pdipm->nxfree  = pdipm->Nxfree  = 0;

1337:   pdipm->ng = pdipm->Ng = pdipm->nce = pdipm->Nce = 0;
1338:   pdipm->nh = pdipm->Nh = pdipm->nci = pdipm->Nci = 0;
1339:   pdipm->n  = pdipm->N  = 0;
1340:   pdipm->mu = 1.0;
1341:   pdipm->mu_update_factor = 0.1;

1343:   pdipm->push_init_slack   = 1.0;
1344:   pdipm->push_init_lambdai = 1.0;
1345:   pdipm->solve_reduced_kkt = PETSC_FALSE;

1347:   /* Override default settings (unless already changed) */
1348:   if (!tao->max_it_changed) tao->max_it = 200;
1349:   if (!tao->max_funcs_changed) tao->max_funcs = 500;

1351:   SNESCreate(((PetscObject)tao)->comm,&pdipm->snes);
1352:   SNESSetOptionsPrefix(pdipm->snes,tao->hdr.prefix);
1353:   SNESGetKSP(pdipm->snes,&tao->ksp);
1354:   PetscObjectReference((PetscObject)tao->ksp);
1355:   return(0);
1356: }