Actual source code: chwirut1.c
1: /*
2: Include "petsctao.h" so that we can use TAO solvers. Note that this
3: file automatically includes libraries such as:
4: petscsys.h - system routines
5: petscis.h - index sets
6: petscvec.h - vectors
7: petscmat.h - matrices
8: petscpc.h - preconditioners
9: petscksp.h - Krylov subspace methods
10: */
12: #include <petsctao.h>
14: /*
15: Description: These data are the result of a NIST study involving
16: ultrasonic calibration. The response variable is
17: ultrasonic response, and the predictor variable is
18: metal distance.
20: Reference: Chwirut, D., NIST (197?).
21: Ultrasonic Reference Block Study.
22: */
24: static char help[] = "Finds the nonlinear least-squares solution to the model \n\
25: y = exp[-b1*x]/(b2+b3*x) + e \n";
27: #define NOBSERVATIONS 214
28: #define NPARAMETERS 3
30: /* User-defined application context */
31: typedef struct {
32: /* Working space */
33: PetscReal t[NOBSERVATIONS]; /* array of independent variables of observation */
34: PetscReal y[NOBSERVATIONS]; /* array of dependent variables */
35: PetscReal j[NOBSERVATIONS][NPARAMETERS]; /* dense jacobian matrix array*/
36: PetscInt idm[NOBSERVATIONS]; /* Matrix indices for jacobian */
37: PetscInt idn[NPARAMETERS];
38: } AppCtx;
40: /* User provided Routines */
41: PetscErrorCode InitializeData(AppCtx *user);
42: PetscErrorCode FormStartingPoint(Vec);
43: PetscErrorCode EvaluateFunction(Tao, Vec, Vec, void *);
44: PetscErrorCode EvaluateJacobian(Tao, Vec, Mat, Mat, void *);
46: /*--------------------------------------------------------------------*/
47: int main(int argc, char **argv)
48: {
49: Vec x, f; /* solution, function */
50: Mat J; /* Jacobian matrix */
51: Tao tao; /* Tao solver context */
52: PetscInt i; /* iteration information */
53: PetscReal hist[100], resid[100];
54: PetscInt lits[100];
55: AppCtx user; /* user-defined work context */
57: PetscFunctionBeginUser;
58: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
59: /* Allocate vectors */
60: PetscCall(VecCreateSeq(MPI_COMM_SELF, NPARAMETERS, &x));
61: PetscCall(VecCreateSeq(MPI_COMM_SELF, NOBSERVATIONS, &f));
63: /* Create the Jacobian matrix. */
64: PetscCall(MatCreateSeqDense(MPI_COMM_SELF, NOBSERVATIONS, NPARAMETERS, NULL, &J));
66: for (i = 0; i < NOBSERVATIONS; i++) user.idm[i] = i;
68: for (i = 0; i < NPARAMETERS; i++) user.idn[i] = i;
70: /* Create TAO solver and set desired solution method */
71: PetscCall(TaoCreate(PETSC_COMM_SELF, &tao));
72: PetscCall(TaoSetType(tao, TAOPOUNDERS));
74: /* Set the function and Jacobian routines. */
75: PetscCall(InitializeData(&user));
76: PetscCall(FormStartingPoint(x));
77: PetscCall(TaoSetSolution(tao, x));
78: PetscCall(TaoSetResidualRoutine(tao, f, EvaluateFunction, (void *)&user));
79: PetscCall(TaoSetJacobianResidualRoutine(tao, J, J, EvaluateJacobian, (void *)&user));
81: /* Check for any TAO command line arguments */
82: PetscCall(TaoSetFromOptions(tao));
84: PetscCall(TaoSetConvergenceHistory(tao, hist, resid, NULL, lits, 100, PETSC_TRUE));
85: /* Perform the Solve */
86: PetscCall(TaoSolve(tao));
88: /* View the vector; then destroy it. */
89: PetscCall(VecView(x, PETSC_VIEWER_STDOUT_SELF));
91: /* Free TAO data structures */
92: PetscCall(TaoDestroy(&tao));
94: /* Free PETSc data structures */
95: PetscCall(VecDestroy(&x));
96: PetscCall(VecDestroy(&f));
97: PetscCall(MatDestroy(&J));
99: PetscCall(PetscFinalize());
100: return 0;
101: }
103: /*--------------------------------------------------------------------*/
104: PetscErrorCode EvaluateFunction(Tao tao, Vec X, Vec F, void *ptr)
105: {
106: AppCtx *user = (AppCtx *)ptr;
107: const PetscReal *x;
108: PetscReal *y = user->y, *f, *t = user->t;
110: PetscFunctionBegin;
111: PetscCall(VecGetArrayRead(X, &x));
112: PetscCall(VecGetArray(F, &f));
114: for (PetscInt i = 0; i < NOBSERVATIONS; i++) f[i] = y[i] - PetscExpScalar(-x[0] * t[i]) / (x[1] + x[2] * t[i]);
115: PetscCall(VecRestoreArrayRead(X, &x));
116: PetscCall(VecRestoreArray(F, &f));
117: PetscCall(PetscLogFlops(6 * NOBSERVATIONS));
118: PetscFunctionReturn(PETSC_SUCCESS);
119: }
121: /*------------------------------------------------------------*/
122: /* J[i][j] = df[i]/dt[j] */
123: PetscErrorCode EvaluateJacobian(Tao tao, Vec X, Mat J, Mat Jpre, void *ptr)
124: {
125: AppCtx *user = (AppCtx *)ptr;
126: const PetscReal *x;
127: PetscReal *t = user->t;
128: PetscReal base;
130: PetscFunctionBegin;
131: PetscCall(VecGetArrayRead(X, &x));
132: for (PetscInt i = 0; i < NOBSERVATIONS; i++) {
133: base = PetscExpScalar(-x[0] * t[i]) / (x[1] + x[2] * t[i]);
135: user->j[i][0] = t[i] * base;
136: user->j[i][1] = base / (x[1] + x[2] * t[i]);
137: user->j[i][2] = base * t[i] / (x[1] + x[2] * t[i]);
138: }
140: /* Assemble the matrix */
141: PetscCall(MatSetValues(J, NOBSERVATIONS, user->idm, NPARAMETERS, user->idn, (PetscReal *)user->j, INSERT_VALUES));
142: PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
143: PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
145: PetscCall(VecRestoreArrayRead(X, &x));
146: PetscCall(PetscLogFlops(NOBSERVATIONS * 13));
147: PetscFunctionReturn(PETSC_SUCCESS);
148: }
150: /* ------------------------------------------------------------ */
151: PetscErrorCode FormStartingPoint(Vec X)
152: {
153: PetscReal *x;
155: PetscFunctionBegin;
156: PetscCall(VecGetArray(X, &x));
157: x[0] = 0.15;
158: x[1] = 0.008;
159: x[2] = 0.010;
160: PetscCall(VecRestoreArray(X, &x));
161: PetscFunctionReturn(PETSC_SUCCESS);
162: }
164: /* ---------------------------------------------------------------------- */
165: PetscErrorCode InitializeData(AppCtx *user)
166: {
167: PetscReal *t = user->t, *y = user->y;
168: PetscInt i = 0;
170: PetscFunctionBegin;
171: y[i] = 92.9000;
172: t[i++] = 0.5000;
173: y[i] = 78.7000;
174: t[i++] = 0.6250;
175: y[i] = 64.2000;
176: t[i++] = 0.7500;
177: y[i] = 64.9000;
178: t[i++] = 0.8750;
179: y[i] = 57.1000;
180: t[i++] = 1.0000;
181: y[i] = 43.3000;
182: t[i++] = 1.2500;
183: y[i] = 31.1000;
184: t[i++] = 1.7500;
185: y[i] = 23.6000;
186: t[i++] = 2.2500;
187: y[i] = 31.0500;
188: t[i++] = 1.7500;
189: y[i] = 23.7750;
190: t[i++] = 2.2500;
191: y[i] = 17.7375;
192: t[i++] = 2.7500;
193: y[i] = 13.8000;
194: t[i++] = 3.2500;
195: y[i] = 11.5875;
196: t[i++] = 3.7500;
197: y[i] = 9.4125;
198: t[i++] = 4.2500;
199: y[i] = 7.7250;
200: t[i++] = 4.7500;
201: y[i] = 7.3500;
202: t[i++] = 5.2500;
203: y[i] = 8.0250;
204: t[i++] = 5.7500;
205: y[i] = 90.6000;
206: t[i++] = 0.5000;
207: y[i] = 76.9000;
208: t[i++] = 0.6250;
209: y[i] = 71.6000;
210: t[i++] = 0.7500;
211: y[i] = 63.6000;
212: t[i++] = 0.8750;
213: y[i] = 54.0000;
214: t[i++] = 1.0000;
215: y[i] = 39.2000;
216: t[i++] = 1.2500;
217: y[i] = 29.3000;
218: t[i++] = 1.7500;
219: y[i] = 21.4000;
220: t[i++] = 2.2500;
221: y[i] = 29.1750;
222: t[i++] = 1.7500;
223: y[i] = 22.1250;
224: t[i++] = 2.2500;
225: y[i] = 17.5125;
226: t[i++] = 2.7500;
227: y[i] = 14.2500;
228: t[i++] = 3.2500;
229: y[i] = 9.4500;
230: t[i++] = 3.7500;
231: y[i] = 9.1500;
232: t[i++] = 4.2500;
233: y[i] = 7.9125;
234: t[i++] = 4.7500;
235: y[i] = 8.4750;
236: t[i++] = 5.2500;
237: y[i] = 6.1125;
238: t[i++] = 5.7500;
239: y[i] = 80.0000;
240: t[i++] = 0.5000;
241: y[i] = 79.0000;
242: t[i++] = 0.6250;
243: y[i] = 63.8000;
244: t[i++] = 0.7500;
245: y[i] = 57.2000;
246: t[i++] = 0.8750;
247: y[i] = 53.2000;
248: t[i++] = 1.0000;
249: y[i] = 42.5000;
250: t[i++] = 1.2500;
251: y[i] = 26.8000;
252: t[i++] = 1.7500;
253: y[i] = 20.4000;
254: t[i++] = 2.2500;
255: y[i] = 26.8500;
256: t[i++] = 1.7500;
257: y[i] = 21.0000;
258: t[i++] = 2.2500;
259: y[i] = 16.4625;
260: t[i++] = 2.7500;
261: y[i] = 12.5250;
262: t[i++] = 3.2500;
263: y[i] = 10.5375;
264: t[i++] = 3.7500;
265: y[i] = 8.5875;
266: t[i++] = 4.2500;
267: y[i] = 7.1250;
268: t[i++] = 4.7500;
269: y[i] = 6.1125;
270: t[i++] = 5.2500;
271: y[i] = 5.9625;
272: t[i++] = 5.7500;
273: y[i] = 74.1000;
274: t[i++] = 0.5000;
275: y[i] = 67.3000;
276: t[i++] = 0.6250;
277: y[i] = 60.8000;
278: t[i++] = 0.7500;
279: y[i] = 55.5000;
280: t[i++] = 0.8750;
281: y[i] = 50.3000;
282: t[i++] = 1.0000;
283: y[i] = 41.0000;
284: t[i++] = 1.2500;
285: y[i] = 29.4000;
286: t[i++] = 1.7500;
287: y[i] = 20.4000;
288: t[i++] = 2.2500;
289: y[i] = 29.3625;
290: t[i++] = 1.7500;
291: y[i] = 21.1500;
292: t[i++] = 2.2500;
293: y[i] = 16.7625;
294: t[i++] = 2.7500;
295: y[i] = 13.2000;
296: t[i++] = 3.2500;
297: y[i] = 10.8750;
298: t[i++] = 3.7500;
299: y[i] = 8.1750;
300: t[i++] = 4.2500;
301: y[i] = 7.3500;
302: t[i++] = 4.7500;
303: y[i] = 5.9625;
304: t[i++] = 5.2500;
305: y[i] = 5.6250;
306: t[i++] = 5.7500;
307: y[i] = 81.5000;
308: t[i++] = .5000;
309: y[i] = 62.4000;
310: t[i++] = .7500;
311: y[i] = 32.5000;
312: t[i++] = 1.5000;
313: y[i] = 12.4100;
314: t[i++] = 3.0000;
315: y[i] = 13.1200;
316: t[i++] = 3.0000;
317: y[i] = 15.5600;
318: t[i++] = 3.0000;
319: y[i] = 5.6300;
320: t[i++] = 6.0000;
321: y[i] = 78.0000;
322: t[i++] = .5000;
323: y[i] = 59.9000;
324: t[i++] = .7500;
325: y[i] = 33.2000;
326: t[i++] = 1.5000;
327: y[i] = 13.8400;
328: t[i++] = 3.0000;
329: y[i] = 12.7500;
330: t[i++] = 3.0000;
331: y[i] = 14.6200;
332: t[i++] = 3.0000;
333: y[i] = 3.9400;
334: t[i++] = 6.0000;
335: y[i] = 76.8000;
336: t[i++] = .5000;
337: y[i] = 61.0000;
338: t[i++] = .7500;
339: y[i] = 32.9000;
340: t[i++] = 1.5000;
341: y[i] = 13.8700;
342: t[i++] = 3.0000;
343: y[i] = 11.8100;
344: t[i++] = 3.0000;
345: y[i] = 13.3100;
346: t[i++] = 3.0000;
347: y[i] = 5.4400;
348: t[i++] = 6.0000;
349: y[i] = 78.0000;
350: t[i++] = .5000;
351: y[i] = 63.5000;
352: t[i++] = .7500;
353: y[i] = 33.8000;
354: t[i++] = 1.5000;
355: y[i] = 12.5600;
356: t[i++] = 3.0000;
357: y[i] = 5.6300;
358: t[i++] = 6.0000;
359: y[i] = 12.7500;
360: t[i++] = 3.0000;
361: y[i] = 13.1200;
362: t[i++] = 3.0000;
363: y[i] = 5.4400;
364: t[i++] = 6.0000;
365: y[i] = 76.8000;
366: t[i++] = .5000;
367: y[i] = 60.0000;
368: t[i++] = .7500;
369: y[i] = 47.8000;
370: t[i++] = 1.0000;
371: y[i] = 32.0000;
372: t[i++] = 1.5000;
373: y[i] = 22.2000;
374: t[i++] = 2.0000;
375: y[i] = 22.5700;
376: t[i++] = 2.0000;
377: y[i] = 18.8200;
378: t[i++] = 2.5000;
379: y[i] = 13.9500;
380: t[i++] = 3.0000;
381: y[i] = 11.2500;
382: t[i++] = 4.0000;
383: y[i] = 9.0000;
384: t[i++] = 5.0000;
385: y[i] = 6.6700;
386: t[i++] = 6.0000;
387: y[i] = 75.8000;
388: t[i++] = .5000;
389: y[i] = 62.0000;
390: t[i++] = .7500;
391: y[i] = 48.8000;
392: t[i++] = 1.0000;
393: y[i] = 35.2000;
394: t[i++] = 1.5000;
395: y[i] = 20.0000;
396: t[i++] = 2.0000;
397: y[i] = 20.3200;
398: t[i++] = 2.0000;
399: y[i] = 19.3100;
400: t[i++] = 2.5000;
401: y[i] = 12.7500;
402: t[i++] = 3.0000;
403: y[i] = 10.4200;
404: t[i++] = 4.0000;
405: y[i] = 7.3100;
406: t[i++] = 5.0000;
407: y[i] = 7.4200;
408: t[i++] = 6.0000;
409: y[i] = 70.5000;
410: t[i++] = .5000;
411: y[i] = 59.5000;
412: t[i++] = .7500;
413: y[i] = 48.5000;
414: t[i++] = 1.0000;
415: y[i] = 35.8000;
416: t[i++] = 1.5000;
417: y[i] = 21.0000;
418: t[i++] = 2.0000;
419: y[i] = 21.6700;
420: t[i++] = 2.0000;
421: y[i] = 21.0000;
422: t[i++] = 2.5000;
423: y[i] = 15.6400;
424: t[i++] = 3.0000;
425: y[i] = 8.1700;
426: t[i++] = 4.0000;
427: y[i] = 8.5500;
428: t[i++] = 5.0000;
429: y[i] = 10.1200;
430: t[i++] = 6.0000;
431: y[i] = 78.0000;
432: t[i++] = .5000;
433: y[i] = 66.0000;
434: t[i++] = .6250;
435: y[i] = 62.0000;
436: t[i++] = .7500;
437: y[i] = 58.0000;
438: t[i++] = .8750;
439: y[i] = 47.7000;
440: t[i++] = 1.0000;
441: y[i] = 37.8000;
442: t[i++] = 1.2500;
443: y[i] = 20.2000;
444: t[i++] = 2.2500;
445: y[i] = 21.0700;
446: t[i++] = 2.2500;
447: y[i] = 13.8700;
448: t[i++] = 2.7500;
449: y[i] = 9.6700;
450: t[i++] = 3.2500;
451: y[i] = 7.7600;
452: t[i++] = 3.7500;
453: y[i] = 5.4400;
454: t[i++] = 4.2500;
455: y[i] = 4.8700;
456: t[i++] = 4.7500;
457: y[i] = 4.0100;
458: t[i++] = 5.2500;
459: y[i] = 3.7500;
460: t[i++] = 5.7500;
461: y[i] = 24.1900;
462: t[i++] = 3.0000;
463: y[i] = 25.7600;
464: t[i++] = 3.0000;
465: y[i] = 18.0700;
466: t[i++] = 3.0000;
467: y[i] = 11.8100;
468: t[i++] = 3.0000;
469: y[i] = 12.0700;
470: t[i++] = 3.0000;
471: y[i] = 16.1200;
472: t[i++] = 3.0000;
473: y[i] = 70.8000;
474: t[i++] = .5000;
475: y[i] = 54.7000;
476: t[i++] = .7500;
477: y[i] = 48.0000;
478: t[i++] = 1.0000;
479: y[i] = 39.8000;
480: t[i++] = 1.5000;
481: y[i] = 29.8000;
482: t[i++] = 2.0000;
483: y[i] = 23.7000;
484: t[i++] = 2.5000;
485: y[i] = 29.6200;
486: t[i++] = 2.0000;
487: y[i] = 23.8100;
488: t[i++] = 2.5000;
489: y[i] = 17.7000;
490: t[i++] = 3.0000;
491: y[i] = 11.5500;
492: t[i++] = 4.0000;
493: y[i] = 12.0700;
494: t[i++] = 5.0000;
495: y[i] = 8.7400;
496: t[i++] = 6.0000;
497: y[i] = 80.7000;
498: t[i++] = .5000;
499: y[i] = 61.3000;
500: t[i++] = .7500;
501: y[i] = 47.5000;
502: t[i++] = 1.0000;
503: y[i] = 29.0000;
504: t[i++] = 1.5000;
505: y[i] = 24.0000;
506: t[i++] = 2.0000;
507: y[i] = 17.7000;
508: t[i++] = 2.5000;
509: y[i] = 24.5600;
510: t[i++] = 2.0000;
511: y[i] = 18.6700;
512: t[i++] = 2.5000;
513: y[i] = 16.2400;
514: t[i++] = 3.0000;
515: y[i] = 8.7400;
516: t[i++] = 4.0000;
517: y[i] = 7.8700;
518: t[i++] = 5.0000;
519: y[i] = 8.5100;
520: t[i++] = 6.0000;
521: y[i] = 66.7000;
522: t[i++] = .5000;
523: y[i] = 59.2000;
524: t[i++] = .7500;
525: y[i] = 40.8000;
526: t[i++] = 1.0000;
527: y[i] = 30.7000;
528: t[i++] = 1.5000;
529: y[i] = 25.7000;
530: t[i++] = 2.0000;
531: y[i] = 16.3000;
532: t[i++] = 2.5000;
533: y[i] = 25.9900;
534: t[i++] = 2.0000;
535: y[i] = 16.9500;
536: t[i++] = 2.5000;
537: y[i] = 13.3500;
538: t[i++] = 3.0000;
539: y[i] = 8.6200;
540: t[i++] = 4.0000;
541: y[i] = 7.2000;
542: t[i++] = 5.0000;
543: y[i] = 6.6400;
544: t[i++] = 6.0000;
545: y[i] = 13.6900;
546: t[i++] = 3.0000;
547: y[i] = 81.0000;
548: t[i++] = .5000;
549: y[i] = 64.5000;
550: t[i++] = .7500;
551: y[i] = 35.5000;
552: t[i++] = 1.5000;
553: y[i] = 13.3100;
554: t[i++] = 3.0000;
555: y[i] = 4.8700;
556: t[i++] = 6.0000;
557: y[i] = 12.9400;
558: t[i++] = 3.0000;
559: y[i] = 5.0600;
560: t[i++] = 6.0000;
561: y[i] = 15.1900;
562: t[i++] = 3.0000;
563: y[i] = 14.6200;
564: t[i++] = 3.0000;
565: y[i] = 15.6400;
566: t[i++] = 3.0000;
567: y[i] = 25.5000;
568: t[i++] = 1.7500;
569: y[i] = 25.9500;
570: t[i++] = 1.7500;
571: y[i] = 81.7000;
572: t[i++] = .5000;
573: y[i] = 61.6000;
574: t[i++] = .7500;
575: y[i] = 29.8000;
576: t[i++] = 1.7500;
577: y[i] = 29.8100;
578: t[i++] = 1.7500;
579: y[i] = 17.1700;
580: t[i++] = 2.7500;
581: y[i] = 10.3900;
582: t[i++] = 3.7500;
583: y[i] = 28.4000;
584: t[i++] = 1.7500;
585: y[i] = 28.6900;
586: t[i++] = 1.7500;
587: y[i] = 81.3000;
588: t[i++] = .5000;
589: y[i] = 60.9000;
590: t[i++] = .7500;
591: y[i] = 16.6500;
592: t[i++] = 2.7500;
593: y[i] = 10.0500;
594: t[i++] = 3.7500;
595: y[i] = 28.9000;
596: t[i++] = 1.7500;
597: y[i] = 28.9500;
598: t[i++] = 1.7500;
599: PetscFunctionReturn(PETSC_SUCCESS);
600: }
602: /*TEST
604: build:
605: requires: !complex !single
607: test:
608: args: -tao_monitor -tao_max_it 100 -tao_type pounders -tao_gatol 1.e-5
610: test:
611: suffix: 2
612: args: -tao_monitor -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type l2prox -tao_brgn_regularizer_weight 1e-4 -tao_gatol 1.e-5 -tao_brgn_subsolver_tao_monitor
614: test:
615: suffix: 3
616: args: -tao_monitor -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type l1dict -tao_brgn_regularizer_weight 1e-4 -tao_brgn_l1_smooth_epsilon 1e-6 -tao_gatol 1.e-5 -tao_brgn_subsolver_tao_monitor
618: test:
619: suffix: 4
620: args: -tao_monitor -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type lm -tao_gatol 1.e-5 -tao_brgn_subsolver_tao_type bnls -tao_brgn_subsolver_tao_monitor
622: TEST*/