xref: /petsc/src/snes/impls/qn/qn.c (revision 360c497dc2fe1f6322492a95ffc9e81167c14f18)
1 #include <private/snesimpl.h>
2 
3 
4 
5 typedef struct {
6   Vec         *dX;              /* The change in X */
7   Vec         *dF;              /* The change in F */
8   PetscInt    m;                /* the number of kept previous steps */
9   PetscScalar *alpha;
10   PetscScalar *beta;
11   PetscScalar *rho;
12   PetscViewer monitor;
13   PetscReal   powell_gamma;     /* Powell angle restart condition */
14   PetscReal   powell_downhill;  /* Powell descent restart condition */
15   PetscReal   scaling;          /* scaling of H0 */
16 } SNES_QN;
17 
18 #undef __FUNCT__
19 #define __FUNCT__ "LBGFSApplyJinv_Private"
20 PetscErrorCode LBGFSApplyJinv_Private(SNES snes, PetscInt it, Vec D, Vec Y) {
21 
22   PetscErrorCode ierr;
23 
24   SNES_QN *qn = (SNES_QN*)snes->data;
25 
26   Vec *dX = qn->dX;
27   Vec *dF = qn->dF;
28 
29   PetscScalar *alpha = qn->alpha;
30   PetscScalar *beta = qn->beta;
31   PetscScalar *rho = qn->rho;
32 
33   PetscInt k, i;
34   PetscInt m = qn->m;
35   PetscScalar t;
36   PetscInt l = m;
37 
38   PetscFunctionBegin;
39 
40   ierr = VecCopy(D, Y);CHKERRQ(ierr);
41 
42   if (it < m) l = it;
43 
44   /* outward recursion starting at iteration k's update and working back */
45   for (i = 0; i < l; i++) {
46     k = (it - i - 1) % l;
47     ierr = VecDot(dX[k], Y, &t);CHKERRQ(ierr);
48     alpha[k] = t*rho[k];
49     if (qn->monitor) {
50       ierr = PetscViewerASCIIAddTab(qn->monitor,((PetscObject)snes)->tablevel+2);CHKERRQ(ierr);
51       ierr = PetscViewerASCIIPrintf(qn->monitor, "it: %d k: %d alpha:        %14.12e\n", it, k, PetscRealPart(alpha[k]));CHKERRQ(ierr);
52       ierr = PetscViewerASCIISubtractTab(qn->monitor,((PetscObject)snes)->tablevel+2);CHKERRQ(ierr);
53     }
54     ierr = VecAXPY(Y, -alpha[k], dF[k]);CHKERRQ(ierr);
55   }
56 
57   ierr = VecScale(Y, qn->scaling);CHKERRQ(ierr);
58 
59   /* inward recursion starting at the first update and working forward */
60   for (i = 0; i < l; i++) {
61     k = (it + i - l) % l;
62     ierr = VecDot(dF[k], Y, &t);CHKERRQ(ierr);
63     beta[k] = rho[k]*t;
64     ierr = VecAXPY(Y, (alpha[k] - beta[k]), dX[k]);
65     if (qn->monitor) {
66       ierr = PetscViewerASCIIAddTab(qn->monitor,((PetscObject)snes)->tablevel+2);CHKERRQ(ierr);
67       ierr = PetscViewerASCIIPrintf(qn->monitor, "it: %d k: %d alpha - beta: %14.12e\n", it, k, PetscRealPart(alpha[k] - beta[k]));CHKERRQ(ierr);
68       ierr = PetscViewerASCIISubtractTab(qn->monitor,((PetscObject)snes)->tablevel+2);CHKERRQ(ierr);
69     }
70   }
71   PetscFunctionReturn(0);
72 }
73 
74 #undef __FUNCT__
75 #define __FUNCT__ "SNESSolve_QN"
76 static PetscErrorCode SNESSolve_QN(SNES snes)
77 {
78 
79   PetscErrorCode ierr;
80   SNES_QN *qn = (SNES_QN*) snes->data;
81 
82   Vec X, Xold;
83   Vec F, G, B;
84   Vec W, Y, FPC, Fold;
85   SNESConvergedReason reason;
86   PetscInt i, i_r, k;
87 
88   PetscReal fnorm, xnorm = 0, ynorm, gnorm;
89   PetscInt m = qn->m;
90   PetscBool lssucceed;
91 
92   PetscScalar rhosc;
93 
94   Vec *dX = qn->dX;
95   Vec *dF = qn->dF;
96   PetscScalar *rho = qn->rho;
97   PetscScalar FolddotF, FolddotFold, FdotF, YdotF, a;
98 
99   /* basically just a regular newton's method except for the application of the jacobian */
100   PetscFunctionBegin;
101 
102   X             = snes->vec_sol;        /* solution vector */
103   F             = snes->vec_func;       /* residual vector */
104   Y             = snes->vec_sol_update; /* search direction generated by J^-1D*/
105   B             = snes->vec_rhs;
106   G             = snes->work[0];
107   W             = snes->work[1];
108   Xold          = snes->work[2];
109 
110   /* directions generated by the preconditioned problem with F_pre = F or x - M(x, b) */
111   Fold          = snes->work[3];
112 
113   snes->reason = SNES_CONVERGED_ITERATING;
114 
115   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
116   snes->iter = 0;
117   snes->norm = 0.;
118   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
119   ierr = SNESComputeFunction(snes,X,F);CHKERRQ(ierr);
120   if (snes->domainerror) {
121     snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
122     PetscFunctionReturn(0);
123   }
124   ierr = VecNorm(F, NORM_2, &fnorm);CHKERRQ(ierr); /* fnorm <- ||F||  */
125   if (PetscIsInfOrNanReal(fnorm)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
126   ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr);
127   snes->norm = fnorm;
128   ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr);
129   SNESLogConvHistory(snes,fnorm,0);
130   ierr = SNESMonitor(snes,0,fnorm);CHKERRQ(ierr);
131 
132   /* set parameter for default relative tolerance convergence test */
133    snes->ttol = fnorm*snes->rtol;
134   /* test convergence */
135   ierr = (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
136   if (snes->reason) PetscFunctionReturn(0);
137 
138   /* initialize the search direction as steepest descent */
139   ierr = VecCopy(F, Y);CHKERRQ(ierr);
140 
141   for(i = 0, i_r = 0; i < snes->max_its; i++, i_r++) {
142     /* line search for lambda */
143     ynorm = 1; gnorm = fnorm;
144     ierr = VecCopy(F, Fold);CHKERRQ(ierr);
145     ierr = VecCopy(X, Xold);CHKERRQ(ierr);
146     ierr = (*snes->ops->linesearch)(snes,snes->lsP,X,F,Y,fnorm,xnorm,G,W,&ynorm,&gnorm,&lssucceed);CHKERRQ(ierr);
147     if (snes->reason == SNES_DIVERGED_FUNCTION_COUNT) break;
148     if (snes->domainerror) {
149       snes->reason = SNES_DIVERGED_FUNCTION_DOMAIN;
150       PetscFunctionReturn(0);
151       }
152     if (!lssucceed) {
153       if (++snes->numFailures >= snes->maxFailures) {
154         snes->reason = SNES_DIVERGED_LINE_SEARCH;
155         break;
156       }
157     }
158 
159     /* Update function and solution vectors */
160     fnorm = gnorm;
161     ierr = VecCopy(G,F);CHKERRQ(ierr);
162     ierr = VecCopy(W,X);CHKERRQ(ierr);
163 
164     if (snes->pc) {
165       ierr = SNESSolve(snes->pc, B, X);CHKERRQ(ierr);
166       ierr = SNESGetConvergedReason(snes->pc,&reason);CHKERRQ(ierr);
167       if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
168         snes->reason = SNES_DIVERGED_INNER;
169         PetscFunctionReturn(0);
170       }
171       ierr = SNESGetFunction(snes->pc, &FPC, PETSC_NULL, PETSC_NULL);CHKERRQ(ierr);
172       ierr = VecCopy(FPC, F);CHKERRQ(ierr);
173       ierr = SNESGetFunctionNorm(snes->pc, &fnorm);CHKERRQ(ierr);
174     }
175 
176     ierr = PetscInfo4(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lssucceed=%d\n",(double)fnorm,(double)gnorm,(double)ynorm,(int)lssucceed);CHKERRQ(ierr);
177 
178     ierr = SNESSetIterationNumber(snes, i+1);CHKERRQ(ierr);
179     ierr = SNESSetFunctionNorm(snes, fnorm);CHKERRQ(ierr);
180 
181     SNESLogConvHistory(snes,snes->norm,snes->iter);
182     ierr = SNESMonitor(snes,snes->iter,snes->norm);CHKERRQ(ierr);
183     /* set parameter for default relative tolerance convergence test */
184     ierr = (*snes->ops->converged)(snes,snes->iter,0.0,0.0,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
185     if (snes->reason) PetscFunctionReturn(0);
186 
187     /* check restart by Powell's Criterion: |F^T H_0 Fold| > 0.2 * |Fold^T H_0 Fold| */
188     ierr = VecDot(Fold, Fold, &FolddotFold);CHKERRQ(ierr);
189     ierr = VecDot(Fold, F, &FolddotF);CHKERRQ(ierr);
190     ierr = VecDot(F, F, &FdotF);CHKERRQ(ierr);
191     ierr = VecDot(Y, F, &YdotF);CHKERRQ(ierr);
192     if (PetscAbs(PetscRealPart(FolddotF)) > qn->powell_gamma*PetscAbs(PetscRealPart(FolddotFold))) {
193       if (qn->monitor) {
194         ierr = PetscViewerASCIIAddTab(qn->monitor,((PetscObject)snes)->tablevel+2);CHKERRQ(ierr);
195         ierr = PetscViewerASCIIPrintf(qn->monitor, "restart! |%14.12e| > %4.2f*|%14.12e|\n", k, PetscRealPart(FolddotF), qn->powell_gamma, PetscRealPart(FolddotFold));CHKERRQ(ierr);
196         ierr = PetscViewerASCIISubtractTab(qn->monitor,((PetscObject)snes)->tablevel+2);CHKERRQ(ierr);
197       }
198       i_r = -1;
199       /* general purpose update */
200       if (snes->ops->update) {
201         ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr);
202       }
203       ierr = VecCopy(F, Y);CHKERRQ(ierr);
204     } else {
205       /* set the differences */
206       k = i_r % m;
207       ierr = VecCopy(F, dF[k]);CHKERRQ(ierr);
208       ierr = VecAXPY(dF[k], -1.0, Fold);CHKERRQ(ierr);
209       ierr = VecCopy(X, dX[k]);CHKERRQ(ierr);
210       ierr = VecAXPY(dX[k], -1.0, Xold);CHKERRQ(ierr);
211       ierr = VecDot(dX[k], dF[k], &rhosc);CHKERRQ(ierr);
212 
213       /* set scaling to be shanno scaling */
214       rho[k] = 1. / rhosc;
215       ierr = VecDot(dF[k], dF[k], &a);CHKERRQ(ierr);
216       qn->scaling = PetscRealPart(rhosc) / PetscRealPart(a);
217 
218       /* general purpose update */
219       if (snes->ops->update) {
220         ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr);
221       }
222       /* apply the current iteration of the approximate jacobian in order to get the next search direction*/
223       ierr = LBGFSApplyJinv_Private(snes, i_r+1, F, Y);CHKERRQ(ierr);
224     }
225 }
226   if (i == snes->max_its) {
227     ierr = PetscInfo1(snes, "Maximum number of iterations has been reached: %D\n", snes->max_its);CHKERRQ(ierr);
228     if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
229   }
230   PetscFunctionReturn(0);
231 }
232 
233 
234 #undef __FUNCT__
235 #define __FUNCT__ "SNESSetUp_QN"
236 static PetscErrorCode SNESSetUp_QN(SNES snes)
237 {
238   SNES_QN *qn = (SNES_QN*)snes->data;
239   PetscErrorCode ierr;
240   PetscFunctionBegin;
241   ierr = VecDuplicateVecs(snes->vec_sol, qn->m, &qn->dX);CHKERRQ(ierr);
242   ierr = VecDuplicateVecs(snes->vec_sol, qn->m, &qn->dF);CHKERRQ(ierr);
243   ierr = PetscMalloc3(qn->m, PetscScalar, &qn->alpha, qn->m, PetscScalar, &qn->beta, qn->m, PetscScalar, &qn->rho);CHKERRQ(ierr);
244   ierr = SNESDefaultGetWork(snes,4);CHKERRQ(ierr);
245   PetscFunctionReturn(0);
246 }
247 
248 #undef __FUNCT__
249 #define __FUNCT__ "SNESReset_QN"
250 static PetscErrorCode SNESReset_QN(SNES snes)
251 {
252   PetscErrorCode ierr;
253   SNES_QN *qn;
254   PetscFunctionBegin;
255   if (snes->data) {
256     qn = (SNES_QN*)snes->data;
257     if (qn->dX) {
258       ierr = VecDestroyVecs(qn->m, &qn->dX);CHKERRQ(ierr);
259     }
260     if (qn->dF) {
261       ierr = VecDestroyVecs(qn->m, &qn->dF);CHKERRQ(ierr);
262     }
263     ierr = PetscFree3(qn->alpha, qn->beta, qn->rho);CHKERRQ(ierr);
264   }
265   PetscFunctionReturn(0);
266 }
267 
268 #undef __FUNCT__
269 #define __FUNCT__ "SNESDestroy_QN"
270 static PetscErrorCode SNESDestroy_QN(SNES snes)
271 {
272   PetscErrorCode ierr;
273   PetscFunctionBegin;
274   ierr = SNESReset_QN(snes);CHKERRQ(ierr);
275   ierr = PetscFree(snes->data);CHKERRQ(ierr);
276   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"","",PETSC_NULL);CHKERRQ(ierr);
277   PetscFunctionReturn(0);
278 }
279 
280 #undef __FUNCT__
281 #define __FUNCT__ "SNESSetFromOptions_QN"
282 static PetscErrorCode SNESSetFromOptions_QN(SNES snes)
283 {
284 
285   PetscErrorCode ierr;
286   SNES_QN *qn;
287   PetscBool monflg = PETSC_FALSE;
288   PetscFunctionBegin;
289 
290   qn = (SNES_QN*)snes->data;
291 
292   ierr = PetscOptionsHead("SNES QN options");CHKERRQ(ierr);
293   ierr = PetscOptionsInt("-snes_qn_m", "Number of past states saved for L-BFGS methods", "SNES", qn->m, &qn->m, PETSC_NULL);CHKERRQ(ierr);
294   ierr = PetscOptionsReal("-snes_qn_powell_gamma", "Powell angle tolerance",             "SNES", qn->powell_gamma, &qn->powell_gamma, PETSC_NULL);CHKERRQ(ierr);
295   ierr = PetscOptionsReal("-snes_qn_powell_downhill", "Powell descent tolerance",        "SNES", qn->powell_downhill, &qn->powell_downhill, PETSC_NULL);CHKERRQ(ierr);
296   ierr = PetscOptionsBool("-snes_qn_monitor", "Monitor for the QN methods",              "SNES", monflg, &monflg, PETSC_NULL);CHKERRQ(ierr);
297   ierr = PetscOptionsTail();CHKERRQ(ierr);
298   if (monflg) {
299     qn->monitor = PETSC_VIEWER_STDOUT_(((PetscObject)snes)->comm);CHKERRQ(ierr);
300   }
301   PetscFunctionReturn(0);
302 }
303 
304 EXTERN_C_BEGIN
305 #undef __FUNCT__
306 #define __FUNCT__ "SNESLineSearchSetType_QN"
307 PetscErrorCode  SNESLineSearchSetType_QN(SNES snes, SNESLineSearchType type)
308 {
309   PetscErrorCode ierr;
310   PetscFunctionBegin;
311 
312   switch (type) {
313   case SNES_LS_BASIC:
314     ierr = SNESLineSearchSet(snes,SNESLineSearchNo,PETSC_NULL);CHKERRQ(ierr);
315     break;
316   case SNES_LS_BASIC_NONORMS:
317     ierr = SNESLineSearchSet(snes,SNESLineSearchNoNorms,PETSC_NULL);CHKERRQ(ierr);
318     break;
319   case SNES_LS_QUADRATIC:
320     ierr = SNESLineSearchSet(snes,SNESLineSearchQuadraticSecant,PETSC_NULL);CHKERRQ(ierr);
321     break;
322   case SNES_LS_SECANT:
323     ierr = SNESLineSearchSet(snes,SNESLineSearchSecant,PETSC_NULL);CHKERRQ(ierr);
324     break;
325   default:
326     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP,"Unknown line search type");
327     break;
328   }
329   snes->ls_type = type;
330   PetscFunctionReturn(0);
331 }
332 EXTERN_C_END
333 
334 
335 /* -------------------------------------------------------------------------- */
336 /*MC
337       SNESQN - Limited-Memory Quasi-Newton methods for the solution of nonlinear systems.
338 
339       Options Database:
340 
341 +     -snes_qn_m - Number of past states saved for the L-Broyden methods.
342 -     -snes_qn_monitor - Monitors the quasi-newton jacobian.
343 
344       Notes: This implements the L-BFGS algorithm for the solution of F(x) = b using previous change in F(x) and x to
345       form the approximate inverse Jacobian using a series of multiplicative rank-one updates.  This will eventually be
346       generalized to implement several limited-memory Broyden methods.
347 
348       References:
349 
350       L-Broyden Methods: a generalization of the L-BFGS method to the limited memory Broyden family, M. B. Reed,
351       International Journal of Computer Mathematics, vol. 86, 2009.
352 
353 
354       Level: beginner
355 
356 .seealso:  SNESCreate(), SNES, SNESSetType(), SNESLS, SNESTR
357 
358 M*/
359 EXTERN_C_BEGIN
360 #undef __FUNCT__
361 #define __FUNCT__ "SNESCreate_QN"
362 PetscErrorCode  SNESCreate_QN(SNES snes)
363 {
364 
365   PetscErrorCode ierr;
366   SNES_QN *qn;
367 
368   PetscFunctionBegin;
369   snes->ops->setup           = SNESSetUp_QN;
370   snes->ops->solve           = SNESSolve_QN;
371   snes->ops->destroy         = SNESDestroy_QN;
372   snes->ops->setfromoptions  = SNESSetFromOptions_QN;
373   snes->ops->view            = 0;
374   snes->ops->reset           = SNESReset_QN;
375 
376   snes->usespc          = PETSC_TRUE;
377   snes->usesksp         = PETSC_FALSE;
378 
379   snes->max_funcs = 30000;
380   snes->max_its   = 10000;
381 
382   ierr = PetscNewLog(snes,SNES_QN,&qn);CHKERRQ(ierr);
383   snes->data = (void *) qn;
384   qn->m       = 10;
385   qn->scaling = 1.0;
386   qn->dX      = PETSC_NULL;
387   qn->dF      = PETSC_NULL;
388   qn->monitor = PETSC_NULL;
389   qn->powell_gamma   = 0.8;
390   qn->powell_downhill = 0.4;
391 
392   ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESLineSearchSetType_C","SNESLineSearchSetType_QN",SNESLineSearchSetType_QN);CHKERRQ(ierr);
393   ierr = SNESLineSearchSetType(snes, SNES_LS_SECANT);CHKERRQ(ierr);
394 
395   PetscFunctionReturn(0);
396 }
397 EXTERN_C_END
398