xref: /petsc/src/snes/linesearch/impls/bisection/linesearchbisection.c (revision bcd4bb4a4158aa96f212e9537e87b40407faf83e)
1 #include <petsc/private/linesearchimpl.h>
2 #include <petsc/private/snesimpl.h>
3 
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;
15 
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));
22 
23   /* pre-check */
24   PetscCall(SNESLineSearchPreCheck(linesearch, X, Y, &changed_y));
25 
26   /* compute ynorm to normalize search direction */
27   PetscCall(VecNorm(Y, NORM_2, &ynorm));
28 
29   /* initialize interval for bisection */
30   lambda_left  = 0.0;
31   lambda_right = lambda;
32 
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;
40 
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;
68 
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       }
85 
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       }
95 
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       }
105 
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       }
117 
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       }
127 
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       }
138 
139       /* bisect interval */
140       lambda_old = lambda;
141       lambda     = 0.5 * (lambda_left + lambda_right);
142 
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       }
158 
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       }
165 
166       /* count up iteration */
167       it++;
168     }
169   }
170 
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   }
178 
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);
185 
186   /* finalization */
187   PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_SUCCEEDED));
188   PetscFunctionReturn(PETSC_SUCCESS);
189 }
190 
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.
195 
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
202 
203    Level: intermediate
204 
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()`.
210 
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;
222 
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 }
230