Actual source code: isutil.c

  1: #include <petsctao.h>
  2: #include <petsc/private/vecimpl.h>
  3: #include <petsc/private/taoimpl.h>
  4: #include <../src/tao/matrix/submatfree.h>

  6: /*@C
  7:   TaoVecGetSubVec - Gets a subvector using the `IS`

  9:   Input Parameters:
 10: + vfull        - the full matrix
 11: . is           - the index set for the subvector
 12: . reduced_type - the method `Tao` is using for subsetting
 13: - maskvalue    - the value to set the unused vector elements to (for `TAO_SUBSET_MASK` or `TAO_SUBSET_MATRIXFREE`)

 15:   Output Parameter:
 16: . vreduced - the subvector

 18:   Level: developer

 20:   Notes:
 21:   `maskvalue` should usually be `0.0`, unless a pointwise divide will be used.

 23: .seealso: `TaoMatGetSubMat()`, `TaoSubsetType`
 24: @*/
 25: PetscErrorCode TaoVecGetSubVec(Vec vfull, IS is, TaoSubsetType reduced_type, PetscReal maskvalue, Vec *vreduced)
 26: {
 27:   PetscInt        nfull, nreduced, nreduced_local, rlow, rhigh, flow, fhigh;
 28:   PetscInt        i, nlocal;
 29:   PetscReal      *fv, *rv;
 30:   const PetscInt *s;
 31:   IS              ident;
 32:   VecType         vtype;
 33:   VecScatter      scatter;
 34:   MPI_Comm        comm;

 36:   PetscFunctionBegin;

 40:   PetscCall(VecGetSize(vfull, &nfull));
 41:   PetscCall(ISGetSize(is, &nreduced));

 43:   if (nreduced == nfull) {
 44:     PetscCall(VecDestroy(vreduced));
 45:     PetscCall(VecDuplicate(vfull, vreduced));
 46:     PetscCall(VecCopy(vfull, *vreduced));
 47:   } else {
 48:     switch (reduced_type) {
 49:     case TAO_SUBSET_SUBVEC:
 50:       PetscCall(VecGetType(vfull, &vtype));
 51:       PetscCall(VecGetOwnershipRange(vfull, &flow, &fhigh));
 52:       PetscCall(ISGetLocalSize(is, &nreduced_local));
 53:       PetscCall(PetscObjectGetComm((PetscObject)vfull, &comm));
 54:       if (*vreduced) PetscCall(VecDestroy(vreduced));
 55:       PetscCall(VecCreate(comm, vreduced));
 56:       PetscCall(VecSetType(*vreduced, vtype));

 58:       PetscCall(VecSetSizes(*vreduced, nreduced_local, nreduced));
 59:       PetscCall(VecGetOwnershipRange(*vreduced, &rlow, &rhigh));
 60:       PetscCall(ISCreateStride(comm, nreduced_local, rlow, 1, &ident));
 61:       PetscCall(VecScatterCreate(vfull, is, *vreduced, ident, &scatter));
 62:       PetscCall(VecScatterBegin(scatter, vfull, *vreduced, INSERT_VALUES, SCATTER_FORWARD));
 63:       PetscCall(VecScatterEnd(scatter, vfull, *vreduced, INSERT_VALUES, SCATTER_FORWARD));
 64:       PetscCall(VecScatterDestroy(&scatter));
 65:       PetscCall(ISDestroy(&ident));
 66:       break;

 68:     case TAO_SUBSET_MASK:
 69:     case TAO_SUBSET_MATRIXFREE:
 70:       /* vr[i] = vf[i]   if i in is
 71:        vr[i] = 0       otherwise */
 72:       if (!*vreduced) PetscCall(VecDuplicate(vfull, vreduced));

 74:       PetscCall(VecSet(*vreduced, maskvalue));
 75:       PetscCall(ISGetLocalSize(is, &nlocal));
 76:       PetscCall(VecGetOwnershipRange(vfull, &flow, &fhigh));
 77:       PetscCall(VecGetArray(vfull, &fv));
 78:       PetscCall(VecGetArray(*vreduced, &rv));
 79:       PetscCall(ISGetIndices(is, &s));
 80:       PetscCheck(nlocal <= (fhigh - flow), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "IS local size %" PetscInt_FMT " > Vec local size %" PetscInt_FMT, nlocal, fhigh - flow);
 81:       for (i = 0; i < nlocal; ++i) rv[s[i] - flow] = fv[s[i] - flow];
 82:       PetscCall(ISRestoreIndices(is, &s));
 83:       PetscCall(VecRestoreArray(vfull, &fv));
 84:       PetscCall(VecRestoreArray(*vreduced, &rv));
 85:       break;
 86:     }
 87:   }
 88:   PetscFunctionReturn(PETSC_SUCCESS);
 89: }

 91: /*@C
 92:   TaoMatGetSubMat - Gets a submatrix using the `IS`

 94:   Input Parameters:
 95: + M           - the full matrix (`n x n`)
 96: . is          - the index set for the submatrix (both row and column index sets need to be the same)
 97: . v1          - work vector of dimension n, needed for `TAO_SUBSET_MASK` option
 98: - subset_type - the method `Tao` is using for subsetting

100:   Output Parameter:
101: . Msub - the submatrix

103:   Level: developer

105: .seealso: `TaoVecGetSubVec()`, `TaoSubsetType`
106: @*/
107: PetscErrorCode TaoMatGetSubMat(Mat M, IS is, Vec v1, TaoSubsetType subset_type, Mat *Msub)
108: {
109:   IS        iscomp;
110:   PetscBool flg = PETSC_TRUE;

112:   PetscFunctionBegin;
115:   PetscCall(MatDestroy(Msub));
116:   switch (subset_type) {
117:   case TAO_SUBSET_SUBVEC:
118:     PetscCall(MatCreateSubMatrix(M, is, is, MAT_INITIAL_MATRIX, Msub));
119:     break;

121:   case TAO_SUBSET_MASK:
122:     /* Get Reduced Hessian
123:      Msub[i,j] = M[i,j] if i,j in Free_Local or i==j
124:      Msub[i,j] = 0      if i!=j and i or j not in Free_Local
125:      */
126:     PetscObjectOptionsBegin((PetscObject)M);
127:     PetscCall(PetscOptionsBool("-overwrite_hessian", "modify the existing hessian matrix when computing submatrices", "TaoSubsetType", flg, &flg, NULL));
128:     PetscOptionsEnd();
129:     if (flg) {
130:       PetscCall(MatDuplicate(M, MAT_COPY_VALUES, Msub));
131:     } else {
132:       /* Act on hessian directly (default) */
133:       PetscCall(PetscObjectReference((PetscObject)M));
134:       *Msub = M;
135:     }
136:     /* Save the diagonal to temporary vector */
137:     PetscCall(MatGetDiagonal(*Msub, v1));

139:     /* Zero out rows and columns */
140:     PetscCall(ISComplementVec(is, v1, &iscomp));

142:     /* Use v1 instead of 0 here because of PETSc bug */
143:     PetscCall(MatZeroRowsColumnsIS(*Msub, iscomp, 1.0, v1, v1));

145:     PetscCall(ISDestroy(&iscomp));
146:     break;
147:   case TAO_SUBSET_MATRIXFREE:
148:     PetscCall(ISComplementVec(is, v1, &iscomp));
149:     PetscCall(MatCreateSubMatrixFree(M, iscomp, iscomp, Msub));
150:     PetscCall(ISDestroy(&iscomp));
151:     break;
152:   }
153:   PetscFunctionReturn(PETSC_SUCCESS);
154: }

156: /*@C
157:   TaoEstimateActiveBounds - Generates index sets for variables at the lower and upper
158:   bounds, as well as fixed variables where lower and upper bounds equal each other.

160:   Input Parameters:
161: + X       - solution vector
162: . XL      - lower bound vector
163: . XU      - upper bound vector
164: . G       - unprojected gradient
165: . S       - step direction with which the active bounds will be estimated
166: . W       - work vector of type and size of `X`
167: - steplen - the step length at which the active bounds will be estimated (needs to be conservative)

169:   Output Parameters:
170: + bound_tol    - tolerance for the bound estimation
171: . active_lower - index set for active variables at the lower bound
172: . active_upper - index set for active variables at the upper bound
173: . active_fixed - index set for fixed variables
174: . active       - index set for all active variables
175: - inactive     - complementary index set for inactive variables

177:   Level: developer

179:   Notes:
180:   This estimation is based on Bertsekas' method, with a built in diagonal scaling value of `1.0e-3`.

182: .seealso: `TAOBNCG`, `TAOBNTL`, `TAOBNTR`, `TaoBoundSolution()`
183: @*/
184: PetscErrorCode TaoEstimateActiveBounds(Vec X, Vec XL, Vec XU, Vec G, Vec S, Vec W, PetscReal steplen, PetscReal *bound_tol, IS *active_lower, IS *active_upper, IS *active_fixed, IS *active, IS *inactive)
185: {
186:   PetscReal          wnorm;
187:   PetscReal          zero = PetscPowReal(PETSC_MACHINE_EPSILON, 2.0 / 3.0);
188:   PetscInt           i, n_isl = 0, n_isu = 0, n_isf = 0, n_isa = 0, n_isi = 0;
189:   PetscInt           N_isl, N_isu, N_isf, N_isa, N_isi;
190:   PetscInt           n, low, high, nDiff;
191:   PetscInt          *isl = NULL, *isu = NULL, *isf = NULL, *isa = NULL, *isi = NULL;
192:   const PetscScalar *xl, *xu, *x, *g;
193:   MPI_Comm           comm = PetscObjectComm((PetscObject)X);

195:   PetscFunctionBegin;

203:   if (XL) PetscCheckSameType(X, 1, XL, 2);
204:   if (XU) PetscCheckSameType(X, 1, XU, 3);
205:   PetscCheckSameType(X, 1, G, 4);
206:   PetscCheckSameType(X, 1, S, 5);
207:   PetscCheckSameType(X, 1, W, 6);
208:   if (XL) PetscCheckSameComm(X, 1, XL, 2);
209:   if (XU) PetscCheckSameComm(X, 1, XU, 3);
210:   PetscCheckSameComm(X, 1, G, 4);
211:   PetscCheckSameComm(X, 1, S, 5);
212:   PetscCheckSameComm(X, 1, W, 6);
213:   if (XL) VecCheckSameSize(X, 1, XL, 2);
214:   if (XU) VecCheckSameSize(X, 1, XU, 3);
215:   VecCheckSameSize(X, 1, G, 4);
216:   VecCheckSameSize(X, 1, S, 5);
217:   VecCheckSameSize(X, 1, W, 6);

219:   /* Update the tolerance for bound detection (this is based on Bertsekas' method) */
220:   PetscCall(VecCopy(X, W));
221:   PetscCall(VecAXPBY(W, steplen, 1.0, S));
222:   PetscCall(TaoBoundSolution(W, XL, XU, 0.0, &nDiff, W));
223:   PetscCall(VecAXPBY(W, 1.0, -1.0, X));
224:   PetscCall(VecNorm(W, NORM_2, &wnorm));
225:   *bound_tol = PetscMin(*bound_tol, wnorm);

227:   /* Clear all index sets */
228:   PetscCall(ISDestroy(active_lower));
229:   PetscCall(ISDestroy(active_upper));
230:   PetscCall(ISDestroy(active_fixed));
231:   PetscCall(ISDestroy(active));
232:   PetscCall(ISDestroy(inactive));

234:   PetscCall(VecGetOwnershipRange(X, &low, &high));
235:   PetscCall(VecGetLocalSize(X, &n));
236:   if (!XL && !XU) {
237:     PetscCall(ISCreateStride(comm, n, low, 1, inactive));
238:     PetscFunctionReturn(PETSC_SUCCESS);
239:   }
240:   if (n > 0) {
241:     PetscCall(VecGetArrayRead(X, &x));
242:     PetscCall(VecGetArrayRead(XL, &xl));
243:     PetscCall(VecGetArrayRead(XU, &xu));
244:     PetscCall(VecGetArrayRead(G, &g));

246:     /* Loop over variables and categorize the indexes */
247:     PetscCall(PetscMalloc1(n, &isl));
248:     PetscCall(PetscMalloc1(n, &isu));
249:     PetscCall(PetscMalloc1(n, &isf));
250:     PetscCall(PetscMalloc1(n, &isa));
251:     PetscCall(PetscMalloc1(n, &isi));
252:     for (i = 0; i < n; ++i) {
253:       if (xl[i] == xu[i]) {
254:         /* Fixed variables */
255:         isf[n_isf] = low + i;
256:         ++n_isf;
257:         isa[n_isa] = low + i;
258:         ++n_isa;
259:       } else if (xl[i] > PETSC_NINFINITY && x[i] <= xl[i] + *bound_tol && g[i] > zero) {
260:         /* Lower bounded variables */
261:         isl[n_isl] = low + i;
262:         ++n_isl;
263:         isa[n_isa] = low + i;
264:         ++n_isa;
265:       } else if (xu[i] < PETSC_INFINITY && x[i] >= xu[i] - *bound_tol && g[i] < zero) {
266:         /* Upper bounded variables */
267:         isu[n_isu] = low + i;
268:         ++n_isu;
269:         isa[n_isa] = low + i;
270:         ++n_isa;
271:       } else {
272:         /* Inactive variables */
273:         isi[n_isi] = low + i;
274:         ++n_isi;
275:       }
276:     }

278:     PetscCall(VecRestoreArrayRead(X, &x));
279:     PetscCall(VecRestoreArrayRead(XL, &xl));
280:     PetscCall(VecRestoreArrayRead(XU, &xu));
281:     PetscCall(VecRestoreArrayRead(G, &g));
282:   }

284:   /* Collect global sizes */
285:   PetscCall(MPIU_Allreduce(&n_isl, &N_isl, 1, MPIU_INT, MPI_SUM, comm));
286:   PetscCall(MPIU_Allreduce(&n_isu, &N_isu, 1, MPIU_INT, MPI_SUM, comm));
287:   PetscCall(MPIU_Allreduce(&n_isf, &N_isf, 1, MPIU_INT, MPI_SUM, comm));
288:   PetscCall(MPIU_Allreduce(&n_isa, &N_isa, 1, MPIU_INT, MPI_SUM, comm));
289:   PetscCall(MPIU_Allreduce(&n_isi, &N_isi, 1, MPIU_INT, MPI_SUM, comm));

291:   /* Create index set for lower bounded variables */
292:   if (N_isl > 0) {
293:     PetscCall(ISCreateGeneral(comm, n_isl, isl, PETSC_OWN_POINTER, active_lower));
294:   } else {
295:     PetscCall(PetscFree(isl));
296:   }
297:   /* Create index set for upper bounded variables */
298:   if (N_isu > 0) {
299:     PetscCall(ISCreateGeneral(comm, n_isu, isu, PETSC_OWN_POINTER, active_upper));
300:   } else {
301:     PetscCall(PetscFree(isu));
302:   }
303:   /* Create index set for fixed variables */
304:   if (N_isf > 0) {
305:     PetscCall(ISCreateGeneral(comm, n_isf, isf, PETSC_OWN_POINTER, active_fixed));
306:   } else {
307:     PetscCall(PetscFree(isf));
308:   }
309:   /* Create index set for all actively bounded variables */
310:   if (N_isa > 0) {
311:     PetscCall(ISCreateGeneral(comm, n_isa, isa, PETSC_OWN_POINTER, active));
312:   } else {
313:     PetscCall(PetscFree(isa));
314:   }
315:   /* Create index set for all inactive variables */
316:   if (N_isi > 0) {
317:     PetscCall(ISCreateGeneral(comm, n_isi, isi, PETSC_OWN_POINTER, inactive));
318:   } else {
319:     PetscCall(PetscFree(isi));
320:   }
321:   PetscFunctionReturn(PETSC_SUCCESS);
322: }

324: /*@C
325:   TaoBoundStep - Ensures the correct zero or adjusted step direction values for active
326:   variables.

328:   Input Parameters:
329: + X            - solution vector
330: . XL           - lower bound vector
331: . XU           - upper bound vector
332: . active_lower - index set for lower bounded active variables
333: . active_upper - index set for lower bounded active variables
334: . active_fixed - index set for fixed active variables
335: - scale        - amplification factor for the step that needs to be taken on actively bounded variables

337:   Output Parameter:
338: . S - step direction to be modified

340:   Level: developer

342: .seealso: `TAOBNCG`, `TAOBNTL`, `TAOBNTR`, `TaoBoundSolution()`
343: @*/
344: PetscErrorCode TaoBoundStep(Vec X, Vec XL, Vec XU, IS active_lower, IS active_upper, IS active_fixed, PetscReal scale, Vec S)
345: {
346:   Vec step_lower, step_upper, step_fixed;
347:   Vec x_lower, x_upper;
348:   Vec bound_lower, bound_upper;

350:   PetscFunctionBegin;
351:   /* Adjust step for variables at the estimated lower bound */
352:   if (active_lower) {
353:     PetscCall(VecGetSubVector(S, active_lower, &step_lower));
354:     PetscCall(VecGetSubVector(X, active_lower, &x_lower));
355:     PetscCall(VecGetSubVector(XL, active_lower, &bound_lower));
356:     PetscCall(VecCopy(bound_lower, step_lower));
357:     PetscCall(VecAXPY(step_lower, -1.0, x_lower));
358:     PetscCall(VecScale(step_lower, scale));
359:     PetscCall(VecRestoreSubVector(S, active_lower, &step_lower));
360:     PetscCall(VecRestoreSubVector(X, active_lower, &x_lower));
361:     PetscCall(VecRestoreSubVector(XL, active_lower, &bound_lower));
362:   }

364:   /* Adjust step for the variables at the estimated upper bound */
365:   if (active_upper) {
366:     PetscCall(VecGetSubVector(S, active_upper, &step_upper));
367:     PetscCall(VecGetSubVector(X, active_upper, &x_upper));
368:     PetscCall(VecGetSubVector(XU, active_upper, &bound_upper));
369:     PetscCall(VecCopy(bound_upper, step_upper));
370:     PetscCall(VecAXPY(step_upper, -1.0, x_upper));
371:     PetscCall(VecScale(step_upper, scale));
372:     PetscCall(VecRestoreSubVector(S, active_upper, &step_upper));
373:     PetscCall(VecRestoreSubVector(X, active_upper, &x_upper));
374:     PetscCall(VecRestoreSubVector(XU, active_upper, &bound_upper));
375:   }

377:   /* Zero out step for fixed variables */
378:   if (active_fixed) {
379:     PetscCall(VecGetSubVector(S, active_fixed, &step_fixed));
380:     PetscCall(VecSet(step_fixed, 0.0));
381:     PetscCall(VecRestoreSubVector(S, active_fixed, &step_fixed));
382:   }
383:   PetscFunctionReturn(PETSC_SUCCESS);
384: }

386: /*@C
387:   TaoBoundSolution - Ensures that the solution vector is snapped into the bounds within a given tolerance.

389:   Collective

391:   Input Parameters:
392: + X         - solution vector
393: . XL        - lower bound vector
394: . XU        - upper bound vector
395: - bound_tol - absolute tolerance in enforcing the bound

397:   Output Parameters:
398: + nDiff - total number of vector entries that have been bounded
399: - Xout  - modified solution vector satisfying bounds to `bound_tol`

401:   Level: developer

403: .seealso: `TAOBNCG`, `TAOBNTL`, `TAOBNTR`, `TaoBoundStep()`
404: @*/
405: PetscErrorCode TaoBoundSolution(Vec X, Vec XL, Vec XU, PetscReal bound_tol, PetscInt *nDiff, Vec Xout)
406: {
407:   PetscInt           i, n, low, high, nDiff_loc = 0;
408:   PetscScalar       *xout;
409:   const PetscScalar *x, *xl, *xu;

411:   PetscFunctionBegin;
416:   if (!XL && !XU) {
417:     PetscCall(VecCopy(X, Xout));
418:     *nDiff = 0.0;
419:     PetscFunctionReturn(PETSC_SUCCESS);
420:   }
421:   PetscCheckSameType(X, 1, XL, 2);
422:   PetscCheckSameType(X, 1, XU, 3);
423:   PetscCheckSameType(X, 1, Xout, 6);
424:   PetscCheckSameComm(X, 1, XL, 2);
425:   PetscCheckSameComm(X, 1, XU, 3);
426:   PetscCheckSameComm(X, 1, Xout, 6);
427:   VecCheckSameSize(X, 1, XL, 2);
428:   VecCheckSameSize(X, 1, XU, 3);
429:   VecCheckSameSize(X, 1, Xout, 4);

431:   PetscCall(VecGetOwnershipRange(X, &low, &high));
432:   PetscCall(VecGetLocalSize(X, &n));
433:   if (n > 0) {
434:     PetscCall(VecGetArrayRead(X, &x));
435:     PetscCall(VecGetArrayRead(XL, &xl));
436:     PetscCall(VecGetArrayRead(XU, &xu));
437:     PetscCall(VecGetArray(Xout, &xout));

439:     for (i = 0; i < n; ++i) {
440:       if (xl[i] > PETSC_NINFINITY && x[i] <= xl[i] + bound_tol) {
441:         xout[i] = xl[i];
442:         ++nDiff_loc;
443:       } else if (xu[i] < PETSC_INFINITY && x[i] >= xu[i] - bound_tol) {
444:         xout[i] = xu[i];
445:         ++nDiff_loc;
446:       }
447:     }

449:     PetscCall(VecRestoreArrayRead(X, &x));
450:     PetscCall(VecRestoreArrayRead(XL, &xl));
451:     PetscCall(VecRestoreArrayRead(XU, &xu));
452:     PetscCall(VecRestoreArray(Xout, &xout));
453:   }
454:   PetscCall(MPIU_Allreduce(&nDiff_loc, nDiff, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)X)));
455:   PetscFunctionReturn(PETSC_SUCCESS);
456: }