Actual source code: brgn.c

  1: #include <../src/tao/leastsquares/impls/brgn/brgn.h>

  3: const char *const TaoBRGNRegularizationTypes[] = {"user", "l2prox", "l2pure", "l1dict", "lm", "TaoBRGNRegularizationType", "TAOBRGN_REGULARIZATION_", NULL};

  5: static PetscErrorCode GNHessianProd(Mat H, Vec in, Vec out)
  6: {
  7:   TAO_BRGN *gn;

  9:   PetscFunctionBegin;
 10:   PetscCall(MatShellGetContext(H, &gn));
 11:   PetscCall(MatMult(gn->subsolver->ls_jac, in, gn->r_work));
 12:   PetscCall(MatMultTranspose(gn->subsolver->ls_jac, gn->r_work, out));
 13:   switch (gn->reg_type) {
 14:   case TAOBRGN_REGULARIZATION_USER:
 15:     PetscCall(MatMult(gn->Hreg, in, gn->x_work));
 16:     PetscCall(VecAXPY(out, gn->lambda, gn->x_work));
 17:     break;
 18:   case TAOBRGN_REGULARIZATION_L2PURE:
 19:     PetscCall(VecAXPY(out, gn->lambda, in));
 20:     break;
 21:   case TAOBRGN_REGULARIZATION_L2PROX:
 22:     PetscCall(VecAXPY(out, gn->lambda, in));
 23:     break;
 24:   case TAOBRGN_REGULARIZATION_L1DICT:
 25:     /* out = out + lambda*D'*(diag.*(D*in)) */
 26:     if (gn->D) {
 27:       PetscCall(MatMult(gn->D, in, gn->y)); /* y = D*in */
 28:     } else {
 29:       PetscCall(VecCopy(in, gn->y));
 30:     }
 31:     PetscCall(VecPointwiseMult(gn->y_work, gn->diag, gn->y)); /* y_work = diag.*(D*in), where diag = epsilon^2 ./ sqrt(x.^2+epsilon^2).^3 */
 32:     if (gn->D) {
 33:       PetscCall(MatMultTranspose(gn->D, gn->y_work, gn->x_work)); /* x_work = D'*(diag.*(D*in)) */
 34:     } else {
 35:       PetscCall(VecCopy(gn->y_work, gn->x_work));
 36:     }
 37:     PetscCall(VecAXPY(out, gn->lambda, gn->x_work));
 38:     break;
 39:   case TAOBRGN_REGULARIZATION_LM:
 40:     PetscCall(VecPointwiseMult(gn->x_work, gn->damping, in));
 41:     PetscCall(VecAXPY(out, 1, gn->x_work));
 42:     break;
 43:   }
 44:   PetscFunctionReturn(PETSC_SUCCESS);
 45: }
 46: static PetscErrorCode ComputeDamping(TAO_BRGN *gn)
 47: {
 48:   const PetscScalar *diag_ary;
 49:   PetscScalar       *damping_ary;
 50:   PetscInt           i, n;

 52:   PetscFunctionBegin;
 53:   /* update damping */
 54:   PetscCall(VecGetArray(gn->damping, &damping_ary));
 55:   PetscCall(VecGetArrayRead(gn->diag, &diag_ary));
 56:   PetscCall(VecGetLocalSize(gn->damping, &n));
 57:   for (i = 0; i < n; i++) damping_ary[i] = PetscClipInterval(diag_ary[i], PETSC_SQRT_MACHINE_EPSILON, PetscSqrtReal(PETSC_MAX_REAL));
 58:   PetscCall(VecScale(gn->damping, gn->lambda));
 59:   PetscCall(VecRestoreArray(gn->damping, &damping_ary));
 60:   PetscCall(VecRestoreArrayRead(gn->diag, &diag_ary));
 61:   PetscFunctionReturn(PETSC_SUCCESS);
 62: }
 63: /*@
 64:   TaoBRGNGetDampingVector - Get the damping vector $\mathrm{diag}(J^T J)$ from a `TAOBRGN` with `TAOBRGN_REGULARIZATION_LM` regularization

 66:   Collective

 68:   Input Parameter:
 69: . tao - a `Tao` of type `TAOBRGN` with `TAOBRGN_REGULARIZATION_LM` regularization

 71:   Output Parameter:
 72: . d - the damping vector

 74:   Level: developer

 76: .seealso: [](ch_tao), `Tao`, `TAOBRGN`, `TaoBRGNRegularzationTypes`
 77: @*/
 78: PetscErrorCode TaoBRGNGetDampingVector(Tao tao, Vec *d)
 79: {
 80:   PetscFunctionBegin;
 82:   PetscAssertPointer(d, 2);
 83:   PetscUseMethod((PetscObject)tao, "TaoBRGNGetDampingVector_C", (Tao, Vec *), (tao, d));
 84:   PetscFunctionReturn(PETSC_SUCCESS);
 85: }

 87: static PetscErrorCode TaoBRGNGetDampingVector_BRGN(Tao tao, Vec *d)
 88: {
 89:   TAO_BRGN *gn = (TAO_BRGN *)tao->data;

 91:   PetscFunctionBegin;
 92:   PetscCheck(gn->reg_type == TAOBRGN_REGULARIZATION_LM, PetscObjectComm((PetscObject)tao), PETSC_ERR_SUP, "Damping vector is only available if regularization type is lm.");
 93:   *d = gn->damping;
 94:   PetscFunctionReturn(PETSC_SUCCESS);
 95: }

 97: static PetscErrorCode GNObjectiveGradientEval(Tao tao, Vec X, PetscReal *fcn, Vec G, void *ptr)
 98: {
 99:   TAO_BRGN   *gn = (TAO_BRGN *)ptr;
100:   PetscInt    K; /* dimension of D*X */
101:   PetscScalar yESum;
102:   PetscReal   f_reg;

104:   PetscFunctionBegin;
105:   /* compute objective *fcn*/
106:   /* compute first term 0.5*||ls_res||_2^2 */
107:   PetscCall(TaoComputeResidual(tao, X, tao->ls_res));
108:   PetscCall(VecDot(tao->ls_res, tao->ls_res, fcn));
109:   *fcn *= 0.5;
110:   /* compute gradient G */
111:   PetscCall(TaoComputeResidualJacobian(tao, X, tao->ls_jac, tao->ls_jac_pre));
112:   PetscCall(MatMultTranspose(tao->ls_jac, tao->ls_res, G));
113:   /* add the regularization contribution */
114:   switch (gn->reg_type) {
115:   case TAOBRGN_REGULARIZATION_USER:
116:     PetscCall((*gn->regularizerobjandgrad)(tao, X, &f_reg, gn->x_work, gn->reg_obj_ctx));
117:     *fcn += gn->lambda * f_reg;
118:     PetscCall(VecAXPY(G, gn->lambda, gn->x_work));
119:     break;
120:   case TAOBRGN_REGULARIZATION_L2PURE:
121:     /* compute f = f + lambda*0.5*xk'*xk */
122:     PetscCall(VecDot(X, X, &f_reg));
123:     *fcn += gn->lambda * 0.5 * f_reg;
124:     /* compute G = G + lambda*xk */
125:     PetscCall(VecAXPY(G, gn->lambda, X));
126:     break;
127:   case TAOBRGN_REGULARIZATION_L2PROX:
128:     /* compute f = f + lambda*0.5*(xk - xkm1)'*(xk - xkm1) */
129:     PetscCall(VecAXPBYPCZ(gn->x_work, 1.0, -1.0, 0.0, X, gn->x_old));
130:     PetscCall(VecDot(gn->x_work, gn->x_work, &f_reg));
131:     *fcn += gn->lambda * 0.5 * f_reg;
132:     /* compute G = G + lambda*(xk - xkm1) */
133:     PetscCall(VecAXPBYPCZ(G, gn->lambda, -gn->lambda, 1.0, X, gn->x_old));
134:     break;
135:   case TAOBRGN_REGULARIZATION_L1DICT:
136:     /* compute f = f + lambda*sum(sqrt(y.^2+epsilon^2) - epsilon), where y = D*x*/
137:     if (gn->D) {
138:       PetscCall(MatMult(gn->D, X, gn->y)); /* y = D*x */
139:     } else {
140:       PetscCall(VecCopy(X, gn->y));
141:     }
142:     PetscCall(VecPointwiseMult(gn->y_work, gn->y, gn->y));
143:     PetscCall(VecShift(gn->y_work, gn->epsilon * gn->epsilon));
144:     PetscCall(VecSqrtAbs(gn->y_work)); /* gn->y_work = sqrt(y.^2+epsilon^2) */
145:     PetscCall(VecSum(gn->y_work, &yESum));
146:     PetscCall(VecGetSize(gn->y, &K));
147:     *fcn += gn->lambda * (yESum - K * gn->epsilon);
148:     /* compute G = G + lambda*D'*(y./sqrt(y.^2+epsilon^2)),where y = D*x */
149:     PetscCall(VecPointwiseDivide(gn->y_work, gn->y, gn->y_work)); /* reuse y_work = y./sqrt(y.^2+epsilon^2) */
150:     if (gn->D) {
151:       PetscCall(MatMultTranspose(gn->D, gn->y_work, gn->x_work));
152:     } else {
153:       PetscCall(VecCopy(gn->y_work, gn->x_work));
154:     }
155:     PetscCall(VecAXPY(G, gn->lambda, gn->x_work));
156:     break;
157:   case TAOBRGN_REGULARIZATION_LM:
158:     break;
159:   default:
160:     break;
161:   }
162:   PetscFunctionReturn(PETSC_SUCCESS);
163: }

165: static PetscErrorCode GNComputeHessian(Tao tao, Vec X, Mat H, Mat Hpre, void *ptr)
166: {
167:   TAO_BRGN    *gn = (TAO_BRGN *)ptr;
168:   PetscInt     i, n, cstart, cend;
169:   PetscScalar *cnorms, *diag_ary;

171:   PetscFunctionBegin;
172:   PetscCall(TaoComputeResidualJacobian(tao, X, tao->ls_jac, tao->ls_jac_pre));
173:   if (gn->mat_explicit) PetscCall(MatTransposeMatMult(tao->ls_jac, tao->ls_jac, MAT_REUSE_MATRIX, PETSC_DETERMINE, &gn->H));

175:   switch (gn->reg_type) {
176:   case TAOBRGN_REGULARIZATION_USER:
177:     PetscCall((*gn->regularizerhessian)(tao, X, gn->Hreg, gn->reg_hess_ctx));
178:     if (gn->mat_explicit) PetscCall(MatAXPY(gn->H, 1.0, gn->Hreg, DIFFERENT_NONZERO_PATTERN));
179:     break;
180:   case TAOBRGN_REGULARIZATION_L2PURE:
181:     if (gn->mat_explicit) PetscCall(MatShift(gn->H, gn->lambda));
182:     break;
183:   case TAOBRGN_REGULARIZATION_L2PROX:
184:     if (gn->mat_explicit) PetscCall(MatShift(gn->H, gn->lambda));
185:     break;
186:   case TAOBRGN_REGULARIZATION_L1DICT:
187:     /* calculate and store diagonal matrix as a vector: diag = epsilon^2 ./ sqrt(x.^2+epsilon^2).^3* --> diag = epsilon^2 ./ sqrt(y.^2+epsilon^2).^3,where y = D*x */
188:     if (gn->D) {
189:       PetscCall(MatMult(gn->D, X, gn->y)); /* y = D*x */
190:     } else {
191:       PetscCall(VecCopy(X, gn->y));
192:     }
193:     PetscCall(VecPointwiseMult(gn->y_work, gn->y, gn->y));
194:     PetscCall(VecShift(gn->y_work, gn->epsilon * gn->epsilon));
195:     PetscCall(VecCopy(gn->y_work, gn->diag));                    /* gn->diag = y.^2+epsilon^2 */
196:     PetscCall(VecSqrtAbs(gn->y_work));                           /* gn->y_work = sqrt(y.^2+epsilon^2) */
197:     PetscCall(VecPointwiseMult(gn->diag, gn->y_work, gn->diag)); /* gn->diag = sqrt(y.^2+epsilon^2).^3 */
198:     PetscCall(VecReciprocal(gn->diag));
199:     PetscCall(VecScale(gn->diag, gn->epsilon * gn->epsilon));
200:     if (gn->mat_explicit) PetscCall(MatDiagonalSet(gn->H, gn->diag, ADD_VALUES));
201:     break;
202:   case TAOBRGN_REGULARIZATION_LM:
203:     /* compute diagonal of J^T J */
204:     PetscCall(MatGetSize(gn->parent->ls_jac, NULL, &n));
205:     PetscCall(PetscMalloc1(n, &cnorms));
206:     PetscCall(MatGetColumnNorms(gn->parent->ls_jac, NORM_2, cnorms));
207:     PetscCall(MatGetOwnershipRangeColumn(gn->parent->ls_jac, &cstart, &cend));
208:     PetscCall(VecGetArray(gn->diag, &diag_ary));
209:     for (i = 0; i < cend - cstart; i++) diag_ary[i] = cnorms[cstart + i] * cnorms[cstart + i];
210:     PetscCall(VecRestoreArray(gn->diag, &diag_ary));
211:     PetscCall(PetscFree(cnorms));
212:     PetscCall(ComputeDamping(gn));
213:     if (gn->mat_explicit) PetscCall(MatDiagonalSet(gn->H, gn->damping, ADD_VALUES));
214:     break;
215:   default:
216:     break;
217:   }
218:   PetscFunctionReturn(PETSC_SUCCESS);
219: }

221: static PetscErrorCode GNHookFunction(Tao tao, PetscInt iter, void *ctx)
222: {
223:   TAO_BRGN *gn = (TAO_BRGN *)ctx;

225:   PetscFunctionBegin;
226:   /* Update basic tao information from the subsolver */
227:   gn->parent->nfuncs      = tao->nfuncs;
228:   gn->parent->ngrads      = tao->ngrads;
229:   gn->parent->nfuncgrads  = tao->nfuncgrads;
230:   gn->parent->nhess       = tao->nhess;
231:   gn->parent->niter       = tao->niter;
232:   gn->parent->ksp_its     = tao->ksp_its;
233:   gn->parent->ksp_tot_its = tao->ksp_tot_its;
234:   gn->parent->fc          = tao->fc;
235:   PetscCall(TaoGetConvergedReason(tao, &gn->parent->reason));
236:   /* Update the solution vectors */
237:   if (iter == 0) {
238:     PetscCall(VecSet(gn->x_old, 0.0));
239:   } else {
240:     PetscCall(VecCopy(tao->solution, gn->x_old));
241:     PetscCall(VecCopy(tao->solution, gn->parent->solution));
242:   }
243:   /* Update the gradient */
244:   PetscCall(VecCopy(tao->gradient, gn->parent->gradient));

246:   /* Update damping parameter for LM */
247:   if (gn->reg_type == TAOBRGN_REGULARIZATION_LM) {
248:     if (iter > 0) {
249:       if (gn->fc_old > tao->fc) {
250:         gn->lambda = gn->lambda * gn->downhill_lambda_change;
251:       } else {
252:         /* uphill step */
253:         gn->lambda = gn->lambda * gn->uphill_lambda_change;
254:       }
255:     }
256:     gn->fc_old = tao->fc;
257:   }

259:   /* Call general purpose update function */
260:   if (gn->parent->ops->update) PetscCall((*gn->parent->ops->update)(gn->parent, gn->parent->niter, gn->parent->user_update));
261:   PetscFunctionReturn(PETSC_SUCCESS);
262: }

264: static PetscErrorCode TaoBRGNGetRegularizationType_BRGN(Tao tao, TaoBRGNRegularizationType *type)
265: {
266:   TAO_BRGN *gn = (TAO_BRGN *)tao->data;

268:   PetscFunctionBegin;
269:   *type = gn->reg_type;
270:   PetscFunctionReturn(PETSC_SUCCESS);
271: }

273: /*@
274:   TaoBRGNGetRegularizationType - Get the `TaoBRGNRegularizationType` of a `TAOBRGN`

276:   Not collective

278:   Input Parameter:
279: . tao - a `Tao` of type `TAOBRGN`

281:   Output Parameter:
282: . type - the `TaoBRGNRegularizationType`

284:   Level: advanced

286: .seealso: [](ch_tao), `Tao`, `TAOBRGN`, `TaoBRGNRegularizationType`, `TaoBRGNSetRegularizationType()`
287: @*/
288: PetscErrorCode TaoBRGNGetRegularizationType(Tao tao, TaoBRGNRegularizationType *type)
289: {
290:   PetscFunctionBegin;
292:   PetscAssertPointer(type, 2);
293:   PetscUseMethod((PetscObject)tao, "TaoBRGNGetRegularizationType_C", (Tao, TaoBRGNRegularizationType *), (tao, type));
294:   PetscFunctionReturn(PETSC_SUCCESS);
295: }

297: static PetscErrorCode TaoBRGNSetRegularizationType_BRGN(Tao tao, TaoBRGNRegularizationType type)
298: {
299:   TAO_BRGN *gn = (TAO_BRGN *)tao->data;

301:   PetscFunctionBegin;
302:   gn->reg_type = type;
303:   PetscFunctionReturn(PETSC_SUCCESS);
304: }

306: /*@
307:   TaoBRGNSetRegularizationType - Set the `TaoBRGNRegularizationType` of a `TAOBRGN`

309:   Logically collective

311:   Input Parameters:
312: + tao  - a `Tao` of type `TAOBRGN`
313: - type - the `TaoBRGNRegularizationType`

315:   Level: advanced

317: .seealso: [](ch_tao), `Tao`, `TAOBRGN`, `TaoBRGNRegularizationType`, `TaoBRGNGetRegularizationType`
318: @*/
319: PetscErrorCode TaoBRGNSetRegularizationType(Tao tao, TaoBRGNRegularizationType type)
320: {
321:   PetscFunctionBegin;
324:   PetscTryMethod((PetscObject)tao, "TaoBRGNSetRegularizationType_C", (Tao, TaoBRGNRegularizationType), (tao, type));
325:   PetscFunctionReturn(PETSC_SUCCESS);
326: }

328: static PetscErrorCode TaoSolve_BRGN(Tao tao)
329: {
330:   TAO_BRGN *gn = (TAO_BRGN *)tao->data;

332:   PetscFunctionBegin;
333:   PetscCall(TaoSolve(gn->subsolver));
334:   /* Update basic tao information from the subsolver */
335:   tao->nfuncs      = gn->subsolver->nfuncs;
336:   tao->ngrads      = gn->subsolver->ngrads;
337:   tao->nfuncgrads  = gn->subsolver->nfuncgrads;
338:   tao->nhess       = gn->subsolver->nhess;
339:   tao->niter       = gn->subsolver->niter;
340:   tao->ksp_its     = gn->subsolver->ksp_its;
341:   tao->ksp_tot_its = gn->subsolver->ksp_tot_its;
342:   PetscCall(TaoGetConvergedReason(gn->subsolver, &tao->reason));
343:   /* Update vectors */
344:   PetscCall(VecCopy(gn->subsolver->solution, tao->solution));
345:   PetscCall(VecCopy(gn->subsolver->gradient, tao->gradient));
346:   PetscFunctionReturn(PETSC_SUCCESS);
347: }

349: static PetscErrorCode TaoSetFromOptions_BRGN(Tao tao, PetscOptionItems PetscOptionsObject)
350: {
351:   TAO_BRGN     *gn = (TAO_BRGN *)tao->data;
352:   TaoLineSearch ls;

354:   PetscFunctionBegin;
355:   PetscOptionsHeadBegin(PetscOptionsObject, "least-squares problems with regularizer: ||f(x)||^2 + lambda*g(x), g(x) = ||xk-xkm1||^2 or ||Dx||_1 or user defined function.");
356:   PetscCall(PetscOptionsBool("-tao_brgn_mat_explicit", "switches the Hessian construction to be an explicit matrix rather than MATSHELL", "", gn->mat_explicit, &gn->mat_explicit, NULL));
357:   PetscCall(PetscOptionsReal("-tao_brgn_regularizer_weight", "regularizer weight (default 1e-4)", "", gn->lambda, &gn->lambda, NULL));
358:   PetscCall(PetscOptionsReal("-tao_brgn_l1_smooth_epsilon", "L1-norm smooth approximation parameter: ||x||_1 = sum(sqrt(x.^2+epsilon^2)-epsilon) (default 1e-6)", "", gn->epsilon, &gn->epsilon, NULL));
359:   PetscCall(PetscOptionsReal("-tao_brgn_lm_downhill_lambda_change", "Factor to decrease trust region by on downhill steps", "", gn->downhill_lambda_change, &gn->downhill_lambda_change, NULL));
360:   PetscCall(PetscOptionsReal("-tao_brgn_lm_uphill_lambda_change", "Factor to increase trust region by on uphill steps", "", gn->uphill_lambda_change, &gn->uphill_lambda_change, NULL));
361:   PetscCall(PetscOptionsEnum("-tao_brgn_regularization_type", "regularization type", "", TaoBRGNRegularizationTypes, (PetscEnum)gn->reg_type, (PetscEnum *)&gn->reg_type, NULL));
362:   PetscOptionsHeadEnd();
363:   /* set unit line search direction as the default when using the lm regularizer */
364:   if (gn->reg_type == TAOBRGN_REGULARIZATION_LM) {
365:     PetscCall(TaoGetLineSearch(gn->subsolver, &ls));
366:     PetscCall(TaoLineSearchSetType(ls, TAOLINESEARCHUNIT));
367:   }
368:   PetscCall(TaoSetFromOptions(gn->subsolver));
369:   PetscFunctionReturn(PETSC_SUCCESS);
370: }

372: static PetscErrorCode TaoView_BRGN(Tao tao, PetscViewer viewer)
373: {
374:   TAO_BRGN *gn = (TAO_BRGN *)tao->data;
375:   PetscBool isascii;

377:   PetscFunctionBegin;
378:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
379:   if (isascii) {
380:     PetscCall(PetscViewerASCIIPushTab(viewer));
381:     PetscCall(PetscViewerASCIIPrintf(viewer, "Regularizer weight: %g\n", (double)gn->lambda));
382:     PetscCall(PetscViewerASCIIPrintf(viewer, "BRGN Regularization Type: %s\n", TaoBRGNRegularizationTypes[gn->reg_type]));
383:     switch (gn->reg_type) {
384:     case TAOBRGN_REGULARIZATION_L1DICT:
385:       PetscCall(PetscViewerASCIIPrintf(viewer, "L1 smooth epsilon: %g\n", (double)gn->epsilon));
386:       break;
387:     case TAOBRGN_REGULARIZATION_LM:
388:       PetscCall(PetscViewerASCIIPrintf(viewer, "Downhill trust region decrease factor:: %g\n", (double)gn->downhill_lambda_change));
389:       PetscCall(PetscViewerASCIIPrintf(viewer, "Uphill trust region increase factor:: %g\n", (double)gn->uphill_lambda_change));
390:       break;
391:     case TAOBRGN_REGULARIZATION_L2PROX:
392:     case TAOBRGN_REGULARIZATION_L2PURE:
393:     case TAOBRGN_REGULARIZATION_USER:
394:     default:
395:       break;
396:     }
397:     PetscCall(PetscViewerASCIIPopTab(viewer));
398:   }
399:   PetscCall(PetscViewerASCIIPushTab(viewer));
400:   PetscCall(TaoView(gn->subsolver, viewer));
401:   PetscCall(PetscViewerASCIIPopTab(viewer));
402:   PetscFunctionReturn(PETSC_SUCCESS);
403: }

405: static PetscErrorCode TaoSetUp_BRGN(Tao tao)
406: {
407:   TAO_BRGN *gn = (TAO_BRGN *)tao->data;
408:   PetscBool is_bnls, is_bntr, is_bntl;
409:   PetscInt  i, n, N, K; /* dict has size K*N*/

411:   PetscFunctionBegin;
412:   PetscCheck(tao->ls_res, PetscObjectComm((PetscObject)tao), PETSC_ERR_ORDER, "TaoSetResidualRoutine() must be called before setup!");
413:   PetscCall(PetscObjectTypeCompare((PetscObject)gn->subsolver, TAOBNLS, &is_bnls));
414:   PetscCall(PetscObjectTypeCompare((PetscObject)gn->subsolver, TAOBNTR, &is_bntr));
415:   PetscCall(PetscObjectTypeCompare((PetscObject)gn->subsolver, TAOBNTL, &is_bntl));
416:   PetscCheck((!is_bnls && !is_bntr && !is_bntl) || tao->ls_jac, PetscObjectComm((PetscObject)tao), PETSC_ERR_ORDER, "TaoSetResidualJacobianRoutine() must be called before setup!");
417:   if (!tao->gradient) PetscCall(VecDuplicate(tao->solution, &tao->gradient));
418:   if (!gn->x_work) PetscCall(VecDuplicate(tao->solution, &gn->x_work));
419:   if (!gn->r_work) PetscCall(VecDuplicate(tao->ls_res, &gn->r_work));
420:   if (!gn->x_old) {
421:     PetscCall(VecDuplicate(tao->solution, &gn->x_old));
422:     PetscCall(VecSet(gn->x_old, 0.0));
423:   }

425:   if (TAOBRGN_REGULARIZATION_L1DICT == gn->reg_type) {
426:     if (!gn->y) {
427:       if (gn->D) {
428:         PetscCall(MatGetSize(gn->D, &K, &N)); /* Shell matrices still must have sizes defined. K = N for identity matrix, K=N-1 or N for gradient matrix */
429:         PetscCall(MatCreateVecs(gn->D, NULL, &gn->y));
430:       } else {
431:         PetscCall(VecDuplicate(tao->solution, &gn->y)); /* If user does not setup dict matrix, use identity matrix, K=N */
432:       }
433:       PetscCall(VecSet(gn->y, 0.0));
434:     }
435:     if (!gn->y_work) PetscCall(VecDuplicate(gn->y, &gn->y_work));
436:     if (!gn->diag) {
437:       PetscCall(VecDuplicate(gn->y, &gn->diag));
438:       PetscCall(VecSet(gn->diag, 0.0));
439:     }
440:   }
441:   if (TAOBRGN_REGULARIZATION_LM == gn->reg_type) {
442:     if (!gn->diag) PetscCall(MatCreateVecs(tao->ls_jac, &gn->diag, NULL));
443:     if (!gn->damping) PetscCall(MatCreateVecs(tao->ls_jac, &gn->damping, NULL));
444:   }

446:   if (!tao->setupcalled) {
447:     /* Hessian setup */
448:     if (gn->mat_explicit) {
449:       PetscCall(TaoComputeResidualJacobian(tao, tao->solution, tao->ls_jac, tao->ls_jac_pre));
450:       PetscCall(MatTransposeMatMult(tao->ls_jac, tao->ls_jac, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &gn->H));
451:     } else {
452:       PetscCall(VecGetLocalSize(tao->solution, &n));
453:       PetscCall(VecGetSize(tao->solution, &N));
454:       PetscCall(MatCreate(PetscObjectComm((PetscObject)tao), &gn->H));
455:       PetscCall(MatSetSizes(gn->H, n, n, N, N));
456:       PetscCall(MatSetType(gn->H, MATSHELL));
457:       PetscCall(MatSetOption(gn->H, MAT_SYMMETRIC, PETSC_TRUE));
458:       PetscCall(MatShellSetOperation(gn->H, MATOP_MULT, (void (*)(void))GNHessianProd));
459:       PetscCall(MatShellSetContext(gn->H, gn));
460:     }
461:     PetscCall(MatSetUp(gn->H));
462:     /* Subsolver setup,include initial vector and dictionary D */
463:     PetscCall(TaoSetUpdate(gn->subsolver, GNHookFunction, gn));
464:     PetscCall(TaoSetSolution(gn->subsolver, tao->solution));
465:     if (tao->bounded) PetscCall(TaoSetVariableBounds(gn->subsolver, tao->XL, tao->XU));
466:     PetscCall(TaoSetResidualRoutine(gn->subsolver, tao->ls_res, tao->ops->computeresidual, tao->user_lsresP));
467:     PetscCall(TaoSetJacobianResidualRoutine(gn->subsolver, tao->ls_jac, tao->ls_jac, tao->ops->computeresidualjacobian, tao->user_lsjacP));
468:     PetscCall(TaoSetObjectiveAndGradient(gn->subsolver, NULL, GNObjectiveGradientEval, gn));
469:     PetscCall(TaoSetHessian(gn->subsolver, gn->H, gn->H, GNComputeHessian, gn));
470:     /* Propagate some options down */
471:     PetscCall(TaoSetTolerances(gn->subsolver, tao->gatol, tao->grtol, tao->gttol));
472:     PetscCall(TaoSetMaximumIterations(gn->subsolver, tao->max_it));
473:     PetscCall(TaoSetMaximumFunctionEvaluations(gn->subsolver, tao->max_funcs));
474:     for (i = 0; i < tao->numbermonitors; ++i) {
475:       PetscCall(TaoMonitorSet(gn->subsolver, tao->monitor[i], tao->monitorcontext[i], tao->monitordestroy[i]));
476:       PetscCall(PetscObjectReference((PetscObject)tao->monitorcontext[i]));
477:     }
478:     PetscCall(TaoSetUp(gn->subsolver));
479:   }
480:   PetscFunctionReturn(PETSC_SUCCESS);
481: }

483: static PetscErrorCode TaoDestroy_BRGN(Tao tao)
484: {
485:   TAO_BRGN *gn = (TAO_BRGN *)tao->data;

487:   PetscFunctionBegin;
488:   if (tao->setupcalled) {
489:     PetscCall(VecDestroy(&tao->gradient));
490:     PetscCall(VecDestroy(&gn->x_work));
491:     PetscCall(VecDestroy(&gn->r_work));
492:     PetscCall(VecDestroy(&gn->x_old));
493:     PetscCall(VecDestroy(&gn->diag));
494:     PetscCall(VecDestroy(&gn->y));
495:     PetscCall(VecDestroy(&gn->y_work));
496:   }
497:   PetscCall(VecDestroy(&gn->damping));
498:   PetscCall(VecDestroy(&gn->diag));
499:   PetscCall(MatDestroy(&gn->H));
500:   PetscCall(MatDestroy(&gn->D));
501:   PetscCall(MatDestroy(&gn->Hreg));
502:   PetscCall(TaoDestroy(&gn->subsolver));
503:   gn->parent = NULL;
504:   PetscCall(PetscFree(tao->data));
505:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNGetRegularizationType_C", NULL));
506:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNSetRegularizationType_C", NULL));
507:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNGetDampingVector_C", NULL));
508:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNSetDictionaryMatrix_C", NULL));
509:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNGetSubsolver_C", NULL));
510:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNSetRegularizerWeight_C", NULL));
511:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNSetL1SmoothEpsilon_C", NULL));
512:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNSetRegularizerObjectiveAndGradientRoutine_C", NULL));
513:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNSetRegularizerHessianRoutine_C", NULL));
514:   PetscFunctionReturn(PETSC_SUCCESS);
515: }

517: /*@
518:   TaoBRGNGetSubsolver - Get the pointer to the subsolver inside a `TAOBRGN`

520:   Collective

522:   Input Parameters:
523: + tao       - the Tao solver context
524: - subsolver - the `Tao` sub-solver context

526:   Level: advanced

528: .seealso: `Tao`, `Mat`, `TAOBRGN`
529: @*/
530: PetscErrorCode TaoBRGNGetSubsolver(Tao tao, Tao *subsolver)
531: {
532:   PetscFunctionBegin;
534:   PetscUseMethod((PetscObject)tao, "TaoBRGNGetSubsolver_C", (Tao, Tao *), (tao, subsolver));
535:   PetscFunctionReturn(PETSC_SUCCESS);
536: }

538: static PetscErrorCode TaoBRGNGetSubsolver_BRGN(Tao tao, Tao *subsolver)
539: {
540:   TAO_BRGN *gn = (TAO_BRGN *)tao->data;

542:   PetscFunctionBegin;
543:   *subsolver = gn->subsolver;
544:   PetscFunctionReturn(PETSC_SUCCESS);
545: }

547: /*@
548:   TaoBRGNSetRegularizerWeight - Set the regularizer weight for the Gauss-Newton least-squares algorithm

550:   Collective

552:   Input Parameters:
553: + tao    - the `Tao` solver context
554: - lambda - L1-norm regularizer weight

556:   Level: beginner

558: .seealso: `Tao`, `Mat`, `TAOBRGN`
559: @*/
560: PetscErrorCode TaoBRGNSetRegularizerWeight(Tao tao, PetscReal lambda)
561: {
562:   PetscFunctionBegin;
565:   PetscTryMethod((PetscObject)tao, "TaoBRGNSetRegularizerWeight_C", (Tao, PetscReal), (tao, lambda));
566:   PetscFunctionReturn(PETSC_SUCCESS);
567: }

569: static PetscErrorCode TaoBRGNSetRegularizerWeight_BRGN(Tao tao, PetscReal lambda)
570: {
571:   TAO_BRGN *gn = (TAO_BRGN *)tao->data;

573:   PetscFunctionBegin;
574:   gn->lambda = lambda;
575:   PetscFunctionReturn(PETSC_SUCCESS);
576: }

578: /*@
579:   TaoBRGNSetL1SmoothEpsilon - Set the L1-norm smooth approximation parameter for L1-regularized least-squares algorithm

581:   Collective

583:   Input Parameters:
584: + tao     - the `Tao` solver context
585: - epsilon - L1-norm smooth approximation parameter

587:   Level: advanced

589: .seealso: `Tao`, `Mat`, `TAOBRGN`
590: @*/
591: PetscErrorCode TaoBRGNSetL1SmoothEpsilon(Tao tao, PetscReal epsilon)
592: {
593:   PetscFunctionBegin;
596:   PetscTryMethod((PetscObject)tao, "TaoBRGNSetL1SmoothEpsilon_C", (Tao, PetscReal), (tao, epsilon));
597:   PetscFunctionReturn(PETSC_SUCCESS);
598: }

600: static PetscErrorCode TaoBRGNSetL1SmoothEpsilon_BRGN(Tao tao, PetscReal epsilon)
601: {
602:   TAO_BRGN *gn = (TAO_BRGN *)tao->data;

604:   PetscFunctionBegin;
605:   gn->epsilon = epsilon;
606:   PetscFunctionReturn(PETSC_SUCCESS);
607: }

609: /*@
610:   TaoBRGNSetDictionaryMatrix - bind the dictionary matrix from user application context to gn->D, for compressed sensing (with least-squares problem)

612:   Input Parameters:
613: + tao  - the `Tao` context
614: - dict - the user specified dictionary matrix.  We allow to set a `NULL` dictionary, which means identity matrix by default

616:   Level: advanced

618: .seealso: `Tao`, `Mat`, `TAOBRGN`
619: @*/
620: PetscErrorCode TaoBRGNSetDictionaryMatrix(Tao tao, Mat dict)
621: {
622:   PetscFunctionBegin;
624:   PetscTryMethod((PetscObject)tao, "TaoBRGNSetDictionaryMatrix_C", (Tao, Mat), (tao, dict));
625:   PetscFunctionReturn(PETSC_SUCCESS);
626: }

628: static PetscErrorCode TaoBRGNSetDictionaryMatrix_BRGN(Tao tao, Mat dict)
629: {
630:   TAO_BRGN *gn = (TAO_BRGN *)tao->data;

632:   PetscFunctionBegin;
633:   if (dict) {
635:     PetscCheckSameComm(tao, 1, dict, 2);
636:     PetscCall(PetscObjectReference((PetscObject)dict));
637:   }
638:   PetscCall(MatDestroy(&gn->D));
639:   gn->D = dict;
640:   PetscFunctionReturn(PETSC_SUCCESS);
641: }

643: /*@C
644:   TaoBRGNSetRegularizerObjectiveAndGradientRoutine - Sets the user-defined regularizer call-back
645:   function into the algorithm.

647:   Input Parameters:
648: + tao  - the Tao context
649: . func - function pointer for the regularizer value and gradient evaluation
650: - ctx  - user context for the regularizer

652:   Calling sequence:
653: + tao - the `Tao` context
654: . u   - the location at which to compute the objective and gradient
655: . val - location to store objective function value
656: . g   - location to store gradient
657: - ctx - user context for the regularizer Hessian

659:   Level: advanced

661: .seealso: `Tao`, `Mat`, `TAOBRGN`
662: @*/
663: PetscErrorCode TaoBRGNSetRegularizerObjectiveAndGradientRoutine(Tao tao, PetscErrorCode (*func)(Tao tao, Vec u, PetscReal *val, Vec g, void *ctx), void *ctx)
664: {
665:   PetscFunctionBegin;
667:   PetscTryMethod((PetscObject)tao, "TaoBRGNSetRegularizerObjectiveAndGradientRoutine_C", (Tao, PetscErrorCode (*)(Tao, Vec, PetscReal *, Vec, void *), void *), (tao, func, ctx));
668:   PetscFunctionReturn(PETSC_SUCCESS);
669: }

671: static PetscErrorCode TaoBRGNSetRegularizerObjectiveAndGradientRoutine_BRGN(Tao tao, PetscErrorCode (*func)(Tao tao, Vec u, PetscReal *val, Vec g, void *ctx), void *ctx)
672: {
673:   TAO_BRGN *gn = (TAO_BRGN *)tao->data;

675:   PetscFunctionBegin;
676:   if (ctx) gn->reg_obj_ctx = ctx;
677:   if (func) gn->regularizerobjandgrad = func;
678:   PetscFunctionReturn(PETSC_SUCCESS);
679: }

681: /*@C
682:   TaoBRGNSetRegularizerHessianRoutine - Sets the user-defined regularizer call-back
683:   function into the algorithm.

685:   Input Parameters:
686: + tao  - the `Tao` context
687: . Hreg - user-created matrix for the Hessian of the regularization term
688: . func - function pointer for the regularizer Hessian evaluation
689: - ctx  - user context for the regularizer Hessian

691:   Calling sequence:
692: + tao  - the `Tao` context
693: . u    - the location at which to compute the Hessian
694: . Hreg - user-created matrix for the Hessian of the regularization term
695: - ctx  - user context for the regularizer Hessian

697:   Level: advanced

699: .seealso: `Tao`, `Mat`, `TAOBRGN`
700: @*/
701: PetscErrorCode TaoBRGNSetRegularizerHessianRoutine(Tao tao, Mat Hreg, PetscErrorCode (*func)(Tao tao, Vec u, Mat Hreg, void *ctx), void *ctx)
702: {
703:   PetscFunctionBegin;
705:   PetscTryMethod((PetscObject)tao, "TaoBRGNSetRegularizerHessianRoutine_C", (Tao, Mat, PetscErrorCode (*)(Tao, Vec, Mat, void *), void *), (tao, Hreg, func, ctx));
706:   PetscFunctionReturn(PETSC_SUCCESS);
707: }

709: static PetscErrorCode TaoBRGNSetRegularizerHessianRoutine_BRGN(Tao tao, Mat Hreg, PetscErrorCode (*func)(Tao tao, Vec u, Mat Hreg, void *ctx), void *ctx)
710: {
711:   TAO_BRGN *gn = (TAO_BRGN *)tao->data;

713:   PetscFunctionBegin;
714:   if (Hreg) {
716:     PetscCheckSameComm(tao, 1, Hreg, 2);
717:   } else SETERRQ(PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_WRONG, "NULL Hessian detected! User must provide valid Hessian for the regularizer.");
718:   if (ctx) gn->reg_hess_ctx = ctx;
719:   if (func) gn->regularizerhessian = func;
720:   if (Hreg) {
721:     PetscCall(PetscObjectReference((PetscObject)Hreg));
722:     PetscCall(MatDestroy(&gn->Hreg));
723:     gn->Hreg = Hreg;
724:   }
725:   PetscFunctionReturn(PETSC_SUCCESS);
726: }

728: /*MC
729:   TAOBRGN - Bounded Regularized Gauss-Newton method for solving nonlinear least-squares
730:             problems with bound constraints. This algorithm is a thin wrapper around `TAOBNTL`
731:             that constructs the Gauss-Newton problem with the user-provided least-squares
732:             residual and Jacobian. The algorithm offers an L2-norm ("l2pure"), L2-norm proximal point ("l2prox")
733:             regularizer, and L1-norm dictionary regularizer ("l1dict"), where we approximate the
734:             L1-norm ||x||_1 by sum_i(sqrt(x_i^2+epsilon^2)-epsilon) with a small positive number epsilon.
735:             Also offered is the "lm" regularizer which uses a scaled diagonal of J^T J.
736:             With the "lm" regularizer, `TAOBRGN` is a Levenberg-Marquardt optimizer.
737:             The user can also provide own regularization function.

739:   Options Database Keys:
740: + -tao_brgn_regularization_type - regularization type ("user", "l2prox", "l2pure", "l1dict", "lm") (default "l2prox")
741: . -tao_brgn_regularizer_weight  - regularizer weight (default 1e-4)
742: - -tao_brgn_l1_smooth_epsilon   - L1-norm smooth approximation parameter: ||x||_1 = sum(sqrt(x.^2+epsilon^2)-epsilon) (default 1e-6)

744:   Level: beginner

746: .seealso: `Tao`, `TaoBRGNGetSubsolver()`, `TaoBRGNSetRegularizerWeight()`, `TaoBRGNSetL1SmoothEpsilon()`, `TaoBRGNSetDictionaryMatrix()`,
747:           `TaoBRGNSetRegularizerObjectiveAndGradientRoutine()`, `TaoBRGNSetRegularizerHessianRoutine()`
748: M*/
749: PETSC_EXTERN PetscErrorCode TaoCreate_BRGN(Tao tao)
750: {
751:   TAO_BRGN *gn;

753:   PetscFunctionBegin;
754:   PetscCall(PetscNew(&gn));

756:   tao->ops->destroy        = TaoDestroy_BRGN;
757:   tao->ops->setup          = TaoSetUp_BRGN;
758:   tao->ops->setfromoptions = TaoSetFromOptions_BRGN;
759:   tao->ops->view           = TaoView_BRGN;
760:   tao->ops->solve          = TaoSolve_BRGN;

762:   PetscCall(TaoParametersInitialize(tao));

764:   tao->data                  = gn;
765:   gn->reg_type               = TAOBRGN_REGULARIZATION_L2PROX;
766:   gn->lambda                 = 1e-4;
767:   gn->epsilon                = 1e-6;
768:   gn->downhill_lambda_change = 1. / 5.;
769:   gn->uphill_lambda_change   = 1.5;
770:   gn->parent                 = tao;

772:   PetscCall(TaoCreate(PetscObjectComm((PetscObject)tao), &gn->subsolver));
773:   PetscCall(TaoSetType(gn->subsolver, TAOBNLS));
774:   PetscCall(TaoSetOptionsPrefix(gn->subsolver, "tao_brgn_subsolver_"));
775:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNGetRegularizationType_C", TaoBRGNGetRegularizationType_BRGN));
776:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNSetRegularizationType_C", TaoBRGNSetRegularizationType_BRGN));
777:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNGetDampingVector_C", TaoBRGNGetDampingVector_BRGN));
778:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNSetDictionaryMatrix_C", TaoBRGNSetDictionaryMatrix_BRGN));
779:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNGetSubsolver_C", TaoBRGNGetSubsolver_BRGN));
780:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNSetRegularizerWeight_C", TaoBRGNSetRegularizerWeight_BRGN));
781:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNSetL1SmoothEpsilon_C", TaoBRGNSetL1SmoothEpsilon_BRGN));
782:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNSetRegularizerObjectiveAndGradientRoutine_C", TaoBRGNSetRegularizerObjectiveAndGradientRoutine_BRGN));
783:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoBRGNSetRegularizerHessianRoutine_C", TaoBRGNSetRegularizerHessianRoutine_BRGN));
784:   PetscFunctionReturn(PETSC_SUCCESS);
785: }