Actual source code: linesearchbisection.c

  1: #include <petsc/private/linesearchimpl.h>
  2: #include <petsc/private/snesimpl.h>

  4: static PetscErrorCode SNESLineSearchApply_Bisection(SNESLineSearch linesearch)
  5: {
  6:   PetscBool   changed_y, changed_w;
  7:   Vec         X, F, Y, W, G;
  8:   SNES        snes;
  9:   PetscReal   ynorm;
 10:   PetscReal   lambda_left, lambda, lambda_right, lambda_old, fnorm;
 11:   PetscScalar fty_left, fty, fty_initial;
 12:   PetscViewer monitor;
 13:   PetscReal   rtol, atol, ltol;
 14:   PetscInt    it, max_it;

 16:   PetscFunctionBegin;
 17:   PetscCall(SNESLineSearchGetVecs(linesearch, &X, &F, &Y, &W, &G));
 18:   PetscCall(SNESLineSearchGetLambda(linesearch, &lambda));
 19:   PetscCall(SNESLineSearchGetSNES(linesearch, &snes));
 20:   PetscCall(SNESLineSearchGetTolerances(linesearch, NULL, NULL, &rtol, &atol, &ltol, &max_it));
 21:   PetscCall(SNESLineSearchGetDefaultMonitor(linesearch, &monitor));

 23:   /* pre-check */
 24:   PetscCall(SNESLineSearchPreCheck(linesearch, X, Y, &changed_y));

 26:   /* compute ynorm to normalize search direction */
 27:   PetscCall(VecNorm(Y, NORM_2, &ynorm));

 29:   /* initialize interval for bisection */
 30:   lambda_left  = 0.0;
 31:   lambda_right = lambda;

 33:   /* compute fty at left end of interval */
 34:   if (linesearch->ops->vidirderiv) {
 35:     PetscCall((*linesearch->ops->vidirderiv)(snes, F, X, Y, &fty_left));
 36:   } else {
 37:     PetscCall(VecDot(F, Y, &fty_left));
 38:   }
 39:   fty_initial = fty_left;

 41:   /* compute fty at right end of interval (initial lambda) */
 42:   PetscCall(VecWAXPY(W, -lambda, Y, X));
 43:   if (linesearch->ops->viproject) PetscCall((*linesearch->ops->viproject)(snes, W));
 44:   PetscCall((*linesearch->ops->snesfunc)(snes, W, G));
 45:   if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
 46:     PetscCall(PetscInfo(snes, "Exceeded maximum function evaluations during line search!\n"));
 47:     snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
 48:     PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_FUNCTION));
 49:     PetscFunctionReturn(PETSC_SUCCESS);
 50:   }
 51:   if (linesearch->ops->vidirderiv) {
 52:     PetscCall((*linesearch->ops->vidirderiv)(snes, G, W, Y, &fty));
 53:   } else {
 54:     PetscCall(VecDot(G, Y, &fty));
 55:   }
 56:   /* check whether sign changes in interval */
 57:   if (!PetscIsInfOrNanScalar(fty) && (PetscRealPart(fty_left * fty) > 0.0)) {
 58:     /* no change of sign: accept full step */
 59:     if (monitor) {
 60:       PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
 61:       PetscCall(PetscViewerASCIIPrintf(monitor, "      Line search: sign of fty does not change in step interval, accepting full step\n"));
 62:       PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
 63:     }
 64:   } else {
 65:     /* change of sign: iteratively bisect interval */
 66:     lambda_old = 0.0;
 67:     it         = 0;

 69:     while (PETSC_TRUE) {
 70:       /* check for infinity or NaN */
 71:       if (PetscIsInfOrNanScalar(fty)) {
 72:         if (monitor) {
 73:           PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
 74:           PetscCall(PetscViewerASCIIPrintf(monitor, "      Line search fty is infinity or NaN!\n"));
 75:           PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
 76:         }
 77:         PetscCheck(!snes->errorifnotconverged, PetscObjectComm((PetscObject)snes), PETSC_ERR_CONV_FAILED, "infinity or NaN in function evaluation");
 78:         if (snes->functiondomainerror) {
 79:           PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_FUNCTION_DOMAIN));
 80:           snes->functiondomainerror = PETSC_FALSE;
 81:         } else PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_NANORINF));
 82:         PetscFunctionReturn(PETSC_SUCCESS);
 83:         break;
 84:       }

 86:       /* check absolute tolerance */
 87:       if (PetscAbsScalar(fty) <= atol * ynorm) {
 88:         if (monitor) {
 89:           PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
 90:           PetscCall(PetscViewerASCIIPrintf(monitor, "      Line search: abs(fty)/||y|| = %g <= atol = %g\n", (double)(PetscAbsScalar(fty) / ynorm), (double)atol));
 91:           PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
 92:         }
 93:         break;
 94:       }

 96:       /* check relative tolerance */
 97:       if (PetscAbsScalar(fty) / PetscAbsScalar(fty_initial) <= rtol) {
 98:         if (monitor) {
 99:           PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
100:           PetscCall(PetscViewerASCIIPrintf(monitor, "      Line search: abs(fty/fty_initial) = %g <= rtol  = %g\n", (double)(PetscAbsScalar(fty) / PetscAbsScalar(fty_initial)), (double)rtol));
101:           PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
102:         }
103:         break;
104:       }

106:       /* check maximum number of iterations */
107:       if (it > max_it) {
108:         if (monitor) {
109:           PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
110:           PetscCall(PetscViewerASCIIPrintf(monitor, "      Line search: maximum iterations reached\n"));
111:           PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
112:         }
113:         PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT));
114:         PetscFunctionReturn(PETSC_SUCCESS);
115:         break;
116:       }

118:       /* check change of lambda tolerance */
119:       if (PetscAbsReal(lambda - lambda_old) < ltol) {
120:         if (monitor) {
121:           PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
122:           PetscCall(PetscViewerASCIIPrintf(monitor, "      Line search: abs(dlambda) = %g < ltol = %g\n", (double)PetscAbsReal(lambda - lambda_old), (double)ltol));
123:           PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
124:         }
125:         break;
126:       }

128:       /* determine direction of bisection (not necessary for 0th iteration) */
129:       if (it > 0) {
130:         if (PetscRealPart(fty * fty_left) <= 0.0) {
131:           lambda_right = lambda;
132:         } else {
133:           lambda_left = lambda;
134:           /* also update fty_left for direction check in next iteration */
135:           fty_left = fty;
136:         }
137:       }

139:       /* bisect interval */
140:       lambda_old = lambda;
141:       lambda     = 0.5 * (lambda_left + lambda_right);

143:       /* compute fty at new lambda */
144:       PetscCall(VecWAXPY(W, -lambda, Y, X));
145:       if (linesearch->ops->viproject) PetscCall((*linesearch->ops->viproject)(snes, W));
146:       PetscCall((*linesearch->ops->snesfunc)(snes, W, G));
147:       if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
148:         PetscCall(PetscInfo(snes, "Exceeded maximum function evaluations during line search!\n"));
149:         snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
150:         PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_FUNCTION));
151:         PetscFunctionReturn(PETSC_SUCCESS);
152:       }
153:       if (linesearch->ops->vidirderiv) {
154:         PetscCall((*linesearch->ops->vidirderiv)(snes, G, W, Y, &fty));
155:       } else {
156:         PetscCall(VecDot(G, Y, &fty));
157:       }

159:       /* print iteration information */
160:       if (monitor) {
161:         PetscCall(PetscViewerASCIIAddTab(monitor, ((PetscObject)linesearch)->tablevel));
162:         PetscCall(PetscViewerASCIIPrintf(monitor, "      %3" PetscInt_FMT " Line search: fty/||y|| = %g, lambda = %g\n", it, (double)(PetscRealPart(fty) / ynorm), (double)lambda));
163:         PetscCall(PetscViewerASCIISubtractTab(monitor, ((PetscObject)linesearch)->tablevel));
164:       }

166:       /* count up iteration */
167:       it++;
168:     }
169:   }

171:   /* post-check */
172:   PetscCall(SNESLineSearchSetLambda(linesearch, lambda));
173:   PetscCall(SNESLineSearchPostCheck(linesearch, X, Y, W, &changed_y, &changed_w));
174:   if (changed_y) {
175:     if (!changed_w) PetscCall(VecWAXPY(W, -lambda, Y, X));
176:     if (linesearch->ops->viproject) PetscCall((*linesearch->ops->viproject)(snes, W));
177:   }

179:   /* update solution*/
180:   PetscCall(VecCopy(W, X));
181:   PetscCall((*linesearch->ops->snesfunc)(snes, X, F));
182:   PetscCall(SNESLineSearchComputeNorms(linesearch));
183:   PetscCall(SNESLineSearchGetNorms(linesearch, NULL, &fnorm, NULL));
184:   SNESLineSearchCheckFunctionDomainError(snes, linesearch, fnorm);

186:   /* finalization */
187:   PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_SUCCEEDED));
188:   PetscFunctionReturn(PETSC_SUCCESS);
189: }

191: /*MC
192:    SNESLINESEARCHBISECTION - Bisection line search.
193:    Similar to the critical point line search, `SNESLINESEARCHCP`, the bisection line search assumes that there exists some $G(x)$ for which the `SNESFunctionFn` $F(x) = grad G(x)$.
194:    This line search seeks to find the root of the directional derivative, that is $F(x_k - \lambda Y_k) \cdot Y_k / ||Y_k|| = 0$, along the search direction $Y_k$ through bisection.

196:    Options Database Keys:
197: +  -snes_linesearch_max_it <50>   - maximum number of bisection iterations for the line search
198: .  -snes_linesearch_damping <1.0> - initial `lambda` on entry to the line search
199: .  -snes_linesearch_rtol <1e\-8>  - relative tolerance for the directional derivative
200: .  -snes_linesearch_atol <1e\-6>  - absolute tolerance for the directional derivative
201: -  -snes_linesearch_ltol <1e\-6>  - minimum absolute change in `lambda` allowed

203:    Level: intermediate

205:    Notes:
206:    `lambda` is the scaling of the search direction (vector) that is computed by this algorithm.
207:    If there is no change of sign in the directional derivative from $\lambda=0$ to the initial `lambda` (the damping), then the initial `lambda` will be used.
208:    Hence, this line search will always give a `lambda` in the interval $[0, damping]$.
209:    This method does NOT use the objective function if it is provided with `SNESSetObjective()`.

211: .seealso: [](ch_snes), `SNESLineSearch`, `SNESLineSearchType`, `SNESLineSearchCreate()`, `SNESLineSearchSetType()`, `SNESLINESEARCHCP`
212: M*/
213: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_Bisection(SNESLineSearch linesearch)
214: {
215:   PetscFunctionBegin;
216:   linesearch->ops->apply          = SNESLineSearchApply_Bisection;
217:   linesearch->ops->destroy        = NULL;
218:   linesearch->ops->setfromoptions = NULL;
219:   linesearch->ops->reset          = NULL;
220:   linesearch->ops->view           = NULL;
221:   linesearch->ops->setup          = NULL;

223:   /* set default option values */
224:   linesearch->max_it = 50;
225:   linesearch->rtol   = 1e-8;
226:   linesearch->atol   = 1e-6;
227:   linesearch->ltol   = 1e-6;
228:   PetscFunctionReturn(PETSC_SUCCESS);
229: }