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: petsc.h - base PETSc routines petscvec.h - vectors
5: petscsys.h - system routines petscmat.h - matrices
6: petscis.h - index sets petscksp.h - Krylov subspace methods
7: petscviewer.h - viewers petscpc.h - preconditioners
9: */
11: #include <petsctao.h>
13: /*
14: Description: These data are the result of a NIST study involving
15: ultrasonic calibration. The response variable is
16: ultrasonic response, and the predictor variable is
17: metal distance.
19: Reference: Chwirut, D., NIST (197?).
20: Ultrasonic Reference Block Study.
21: */
23: static char help[] = "Finds the nonlinear least-squares solution to the model \n\
24: y = exp[-b1*x]/(b2+b3*x) + e \n";
26: #define NOBSERVATIONS 214
27: #define NPARAMETERS 3
29: /* User-defined application context */
30: typedef struct {
31: /* Working space */
32: PetscReal t[NOBSERVATIONS]; /* array of independent variables of observation */
33: PetscReal y[NOBSERVATIONS]; /* array of dependent variables */
34: PetscReal j[NOBSERVATIONS][NPARAMETERS]; /* dense jacobian matrix array*/
35: PetscInt idm[NOBSERVATIONS]; /* Matrix indices for jacobian */
36: PetscInt idn[NPARAMETERS];
37: } AppCtx;
39: /* User provided Routines */
40: PetscErrorCode InitializeData(AppCtx *user);
41: PetscErrorCode FormStartingPoint(Vec);
42: PetscErrorCode EvaluateFunction(Tao, Vec, Vec, void *);
43: PetscErrorCode EvaluateJacobian(Tao, Vec, Mat, Mat, void *);
45: /*--------------------------------------------------------------------*/
46: int main(int argc, char **argv)
47: {
48: Vec x, f; /* solution, function */
49: Mat J; /* Jacobian matrix */
50: Tao tao; /* Tao solver context */
51: PetscInt i; /* iteration information */
52: PetscReal hist[100], resid[100];
53: PetscInt lits[100];
54: AppCtx user; /* user-defined work context */
56: PetscFunctionBeginUser;
57: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
58: /* Allocate vectors */
59: PetscCall(VecCreateSeq(MPI_COMM_SELF, NPARAMETERS, &x));
60: PetscCall(VecCreateSeq(MPI_COMM_SELF, NOBSERVATIONS, &f));
62: /* Create the Jacobian matrix. */
63: PetscCall(MatCreateSeqDense(MPI_COMM_SELF, NOBSERVATIONS, NPARAMETERS, NULL, &J));
65: for (i = 0; i < NOBSERVATIONS; i++) user.idm[i] = i;
67: for (i = 0; i < NPARAMETERS; i++) user.idn[i] = i;
69: /* Create TAO solver and set desired solution method */
70: PetscCall(TaoCreate(PETSC_COMM_SELF, &tao));
71: PetscCall(TaoSetType(tao, TAOPOUNDERS));
73: /* Set the function and Jacobian routines. */
74: PetscCall(InitializeData(&user));
75: PetscCall(FormStartingPoint(x));
76: PetscCall(TaoSetSolution(tao, x));
77: PetscCall(TaoSetResidualRoutine(tao, f, EvaluateFunction, (void *)&user));
78: PetscCall(TaoSetJacobianResidualRoutine(tao, J, J, EvaluateJacobian, (void *)&user));
80: /* Check for any TAO command line arguments */
81: PetscCall(TaoSetFromOptions(tao));
83: PetscCall(TaoSetConvergenceHistory(tao, hist, resid, 0, lits, 100, PETSC_TRUE));
84: /* Perform the Solve */
85: PetscCall(TaoSolve(tao));
87: /* View the vector; then destroy it. */
88: PetscCall(VecView(x, PETSC_VIEWER_STDOUT_SELF));
90: /* Free TAO data structures */
91: PetscCall(TaoDestroy(&tao));
93: /* Free PETSc data structures */
94: PetscCall(VecDestroy(&x));
95: PetscCall(VecDestroy(&f));
96: PetscCall(MatDestroy(&J));
98: PetscCall(PetscFinalize());
99: return 0;
100: }
102: /*--------------------------------------------------------------------*/
103: PetscErrorCode EvaluateFunction(Tao tao, Vec X, Vec F, void *ptr)
104: {
105: AppCtx *user = (AppCtx *)ptr;
106: PetscInt i;
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 (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: PetscInt i;
127: const PetscReal *x;
128: PetscReal *t = user->t;
129: PetscReal base;
131: PetscFunctionBegin;
132: PetscCall(VecGetArrayRead(X, &x));
133: for (i = 0; i < NOBSERVATIONS; i++) {
134: base = PetscExpScalar(-x[0] * t[i]) / (x[1] + x[2] * t[i]);
136: user->j[i][0] = t[i] * base;
137: user->j[i][1] = base / (x[1] + x[2] * t[i]);
138: user->j[i][2] = base * t[i] / (x[1] + x[2] * t[i]);
139: }
141: /* Assemble the matrix */
142: PetscCall(MatSetValues(J, NOBSERVATIONS, user->idm, NPARAMETERS, user->idn, (PetscReal *)user->j, INSERT_VALUES));
143: PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
144: PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
146: PetscCall(VecRestoreArrayRead(X, &x));
147: PetscCall(PetscLogFlops(NOBSERVATIONS * 13));
148: PetscFunctionReturn(PETSC_SUCCESS);
149: }
151: /* ------------------------------------------------------------ */
152: PetscErrorCode FormStartingPoint(Vec X)
153: {
154: PetscReal *x;
156: PetscFunctionBegin;
157: PetscCall(VecGetArray(X, &x));
158: x[0] = 0.15;
159: x[1] = 0.008;
160: x[2] = 0.010;
161: PetscCall(VecRestoreArray(X, &x));
162: PetscFunctionReturn(PETSC_SUCCESS);
163: }
165: /* ---------------------------------------------------------------------- */
166: PetscErrorCode InitializeData(AppCtx *user)
167: {
168: PetscReal *t = user->t, *y = user->y;
169: PetscInt i = 0;
171: PetscFunctionBegin;
172: y[i] = 92.9000;
173: t[i++] = 0.5000;
174: y[i] = 78.7000;
175: t[i++] = 0.6250;
176: y[i] = 64.2000;
177: t[i++] = 0.7500;
178: y[i] = 64.9000;
179: t[i++] = 0.8750;
180: y[i] = 57.1000;
181: t[i++] = 1.0000;
182: y[i] = 43.3000;
183: t[i++] = 1.2500;
184: y[i] = 31.1000;
185: t[i++] = 1.7500;
186: y[i] = 23.6000;
187: t[i++] = 2.2500;
188: y[i] = 31.0500;
189: t[i++] = 1.7500;
190: y[i] = 23.7750;
191: t[i++] = 2.2500;
192: y[i] = 17.7375;
193: t[i++] = 2.7500;
194: y[i] = 13.8000;
195: t[i++] = 3.2500;
196: y[i] = 11.5875;
197: t[i++] = 3.7500;
198: y[i] = 9.4125;
199: t[i++] = 4.2500;
200: y[i] = 7.7250;
201: t[i++] = 4.7500;
202: y[i] = 7.3500;
203: t[i++] = 5.2500;
204: y[i] = 8.0250;
205: t[i++] = 5.7500;
206: y[i] = 90.6000;
207: t[i++] = 0.5000;
208: y[i] = 76.9000;
209: t[i++] = 0.6250;
210: y[i] = 71.6000;
211: t[i++] = 0.7500;
212: y[i] = 63.6000;
213: t[i++] = 0.8750;
214: y[i] = 54.0000;
215: t[i++] = 1.0000;
216: y[i] = 39.2000;
217: t[i++] = 1.2500;
218: y[i] = 29.3000;
219: t[i++] = 1.7500;
220: y[i] = 21.4000;
221: t[i++] = 2.2500;
222: y[i] = 29.1750;
223: t[i++] = 1.7500;
224: y[i] = 22.1250;
225: t[i++] = 2.2500;
226: y[i] = 17.5125;
227: t[i++] = 2.7500;
228: y[i] = 14.2500;
229: t[i++] = 3.2500;
230: y[i] = 9.4500;
231: t[i++] = 3.7500;
232: y[i] = 9.1500;
233: t[i++] = 4.2500;
234: y[i] = 7.9125;
235: t[i++] = 4.7500;
236: y[i] = 8.4750;
237: t[i++] = 5.2500;
238: y[i] = 6.1125;
239: t[i++] = 5.7500;
240: y[i] = 80.0000;
241: t[i++] = 0.5000;
242: y[i] = 79.0000;
243: t[i++] = 0.6250;
244: y[i] = 63.8000;
245: t[i++] = 0.7500;
246: y[i] = 57.2000;
247: t[i++] = 0.8750;
248: y[i] = 53.2000;
249: t[i++] = 1.0000;
250: y[i] = 42.5000;
251: t[i++] = 1.2500;
252: y[i] = 26.8000;
253: t[i++] = 1.7500;
254: y[i] = 20.4000;
255: t[i++] = 2.2500;
256: y[i] = 26.8500;
257: t[i++] = 1.7500;
258: y[i] = 21.0000;
259: t[i++] = 2.2500;
260: y[i] = 16.4625;
261: t[i++] = 2.7500;
262: y[i] = 12.5250;
263: t[i++] = 3.2500;
264: y[i] = 10.5375;
265: t[i++] = 3.7500;
266: y[i] = 8.5875;
267: t[i++] = 4.2500;
268: y[i] = 7.1250;
269: t[i++] = 4.7500;
270: y[i] = 6.1125;
271: t[i++] = 5.2500;
272: y[i] = 5.9625;
273: t[i++] = 5.7500;
274: y[i] = 74.1000;
275: t[i++] = 0.5000;
276: y[i] = 67.3000;
277: t[i++] = 0.6250;
278: y[i] = 60.8000;
279: t[i++] = 0.7500;
280: y[i] = 55.5000;
281: t[i++] = 0.8750;
282: y[i] = 50.3000;
283: t[i++] = 1.0000;
284: y[i] = 41.0000;
285: t[i++] = 1.2500;
286: y[i] = 29.4000;
287: t[i++] = 1.7500;
288: y[i] = 20.4000;
289: t[i++] = 2.2500;
290: y[i] = 29.3625;
291: t[i++] = 1.7500;
292: y[i] = 21.1500;
293: t[i++] = 2.2500;
294: y[i] = 16.7625;
295: t[i++] = 2.7500;
296: y[i] = 13.2000;
297: t[i++] = 3.2500;
298: y[i] = 10.8750;
299: t[i++] = 3.7500;
300: y[i] = 8.1750;
301: t[i++] = 4.2500;
302: y[i] = 7.3500;
303: t[i++] = 4.7500;
304: y[i] = 5.9625;
305: t[i++] = 5.2500;
306: y[i] = 5.6250;
307: t[i++] = 5.7500;
308: y[i] = 81.5000;
309: t[i++] = .5000;
310: y[i] = 62.4000;
311: t[i++] = .7500;
312: y[i] = 32.5000;
313: t[i++] = 1.5000;
314: y[i] = 12.4100;
315: t[i++] = 3.0000;
316: y[i] = 13.1200;
317: t[i++] = 3.0000;
318: y[i] = 15.5600;
319: t[i++] = 3.0000;
320: y[i] = 5.6300;
321: t[i++] = 6.0000;
322: y[i] = 78.0000;
323: t[i++] = .5000;
324: y[i] = 59.9000;
325: t[i++] = .7500;
326: y[i] = 33.2000;
327: t[i++] = 1.5000;
328: y[i] = 13.8400;
329: t[i++] = 3.0000;
330: y[i] = 12.7500;
331: t[i++] = 3.0000;
332: y[i] = 14.6200;
333: t[i++] = 3.0000;
334: y[i] = 3.9400;
335: t[i++] = 6.0000;
336: y[i] = 76.8000;
337: t[i++] = .5000;
338: y[i] = 61.0000;
339: t[i++] = .7500;
340: y[i] = 32.9000;
341: t[i++] = 1.5000;
342: y[i] = 13.8700;
343: t[i++] = 3.0000;
344: y[i] = 11.8100;
345: t[i++] = 3.0000;
346: y[i] = 13.3100;
347: t[i++] = 3.0000;
348: y[i] = 5.4400;
349: t[i++] = 6.0000;
350: y[i] = 78.0000;
351: t[i++] = .5000;
352: y[i] = 63.5000;
353: t[i++] = .7500;
354: y[i] = 33.8000;
355: t[i++] = 1.5000;
356: y[i] = 12.5600;
357: t[i++] = 3.0000;
358: y[i] = 5.6300;
359: t[i++] = 6.0000;
360: y[i] = 12.7500;
361: t[i++] = 3.0000;
362: y[i] = 13.1200;
363: t[i++] = 3.0000;
364: y[i] = 5.4400;
365: t[i++] = 6.0000;
366: y[i] = 76.8000;
367: t[i++] = .5000;
368: y[i] = 60.0000;
369: t[i++] = .7500;
370: y[i] = 47.8000;
371: t[i++] = 1.0000;
372: y[i] = 32.0000;
373: t[i++] = 1.5000;
374: y[i] = 22.2000;
375: t[i++] = 2.0000;
376: y[i] = 22.5700;
377: t[i++] = 2.0000;
378: y[i] = 18.8200;
379: t[i++] = 2.5000;
380: y[i] = 13.9500;
381: t[i++] = 3.0000;
382: y[i] = 11.2500;
383: t[i++] = 4.0000;
384: y[i] = 9.0000;
385: t[i++] = 5.0000;
386: y[i] = 6.6700;
387: t[i++] = 6.0000;
388: y[i] = 75.8000;
389: t[i++] = .5000;
390: y[i] = 62.0000;
391: t[i++] = .7500;
392: y[i] = 48.8000;
393: t[i++] = 1.0000;
394: y[i] = 35.2000;
395: t[i++] = 1.5000;
396: y[i] = 20.0000;
397: t[i++] = 2.0000;
398: y[i] = 20.3200;
399: t[i++] = 2.0000;
400: y[i] = 19.3100;
401: t[i++] = 2.5000;
402: y[i] = 12.7500;
403: t[i++] = 3.0000;
404: y[i] = 10.4200;
405: t[i++] = 4.0000;
406: y[i] = 7.3100;
407: t[i++] = 5.0000;
408: y[i] = 7.4200;
409: t[i++] = 6.0000;
410: y[i] = 70.5000;
411: t[i++] = .5000;
412: y[i] = 59.5000;
413: t[i++] = .7500;
414: y[i] = 48.5000;
415: t[i++] = 1.0000;
416: y[i] = 35.8000;
417: t[i++] = 1.5000;
418: y[i] = 21.0000;
419: t[i++] = 2.0000;
420: y[i] = 21.6700;
421: t[i++] = 2.0000;
422: y[i] = 21.0000;
423: t[i++] = 2.5000;
424: y[i] = 15.6400;
425: t[i++] = 3.0000;
426: y[i] = 8.1700;
427: t[i++] = 4.0000;
428: y[i] = 8.5500;
429: t[i++] = 5.0000;
430: y[i] = 10.1200;
431: t[i++] = 6.0000;
432: y[i] = 78.0000;
433: t[i++] = .5000;
434: y[i] = 66.0000;
435: t[i++] = .6250;
436: y[i] = 62.0000;
437: t[i++] = .7500;
438: y[i] = 58.0000;
439: t[i++] = .8750;
440: y[i] = 47.7000;
441: t[i++] = 1.0000;
442: y[i] = 37.8000;
443: t[i++] = 1.2500;
444: y[i] = 20.2000;
445: t[i++] = 2.2500;
446: y[i] = 21.0700;
447: t[i++] = 2.2500;
448: y[i] = 13.8700;
449: t[i++] = 2.7500;
450: y[i] = 9.6700;
451: t[i++] = 3.2500;
452: y[i] = 7.7600;
453: t[i++] = 3.7500;
454: y[i] = 5.4400;
455: t[i++] = 4.2500;
456: y[i] = 4.8700;
457: t[i++] = 4.7500;
458: y[i] = 4.0100;
459: t[i++] = 5.2500;
460: y[i] = 3.7500;
461: t[i++] = 5.7500;
462: y[i] = 24.1900;
463: t[i++] = 3.0000;
464: y[i] = 25.7600;
465: t[i++] = 3.0000;
466: y[i] = 18.0700;
467: t[i++] = 3.0000;
468: y[i] = 11.8100;
469: t[i++] = 3.0000;
470: y[i] = 12.0700;
471: t[i++] = 3.0000;
472: y[i] = 16.1200;
473: t[i++] = 3.0000;
474: y[i] = 70.8000;
475: t[i++] = .5000;
476: y[i] = 54.7000;
477: t[i++] = .7500;
478: y[i] = 48.0000;
479: t[i++] = 1.0000;
480: y[i] = 39.8000;
481: t[i++] = 1.5000;
482: y[i] = 29.8000;
483: t[i++] = 2.0000;
484: y[i] = 23.7000;
485: t[i++] = 2.5000;
486: y[i] = 29.6200;
487: t[i++] = 2.0000;
488: y[i] = 23.8100;
489: t[i++] = 2.5000;
490: y[i] = 17.7000;
491: t[i++] = 3.0000;
492: y[i] = 11.5500;
493: t[i++] = 4.0000;
494: y[i] = 12.0700;
495: t[i++] = 5.0000;
496: y[i] = 8.7400;
497: t[i++] = 6.0000;
498: y[i] = 80.7000;
499: t[i++] = .5000;
500: y[i] = 61.3000;
501: t[i++] = .7500;
502: y[i] = 47.5000;
503: t[i++] = 1.0000;
504: y[i] = 29.0000;
505: t[i++] = 1.5000;
506: y[i] = 24.0000;
507: t[i++] = 2.0000;
508: y[i] = 17.7000;
509: t[i++] = 2.5000;
510: y[i] = 24.5600;
511: t[i++] = 2.0000;
512: y[i] = 18.6700;
513: t[i++] = 2.5000;
514: y[i] = 16.2400;
515: t[i++] = 3.0000;
516: y[i] = 8.7400;
517: t[i++] = 4.0000;
518: y[i] = 7.8700;
519: t[i++] = 5.0000;
520: y[i] = 8.5100;
521: t[i++] = 6.0000;
522: y[i] = 66.7000;
523: t[i++] = .5000;
524: y[i] = 59.2000;
525: t[i++] = .7500;
526: y[i] = 40.8000;
527: t[i++] = 1.0000;
528: y[i] = 30.7000;
529: t[i++] = 1.5000;
530: y[i] = 25.7000;
531: t[i++] = 2.0000;
532: y[i] = 16.3000;
533: t[i++] = 2.5000;
534: y[i] = 25.9900;
535: t[i++] = 2.0000;
536: y[i] = 16.9500;
537: t[i++] = 2.5000;
538: y[i] = 13.3500;
539: t[i++] = 3.0000;
540: y[i] = 8.6200;
541: t[i++] = 4.0000;
542: y[i] = 7.2000;
543: t[i++] = 5.0000;
544: y[i] = 6.6400;
545: t[i++] = 6.0000;
546: y[i] = 13.6900;
547: t[i++] = 3.0000;
548: y[i] = 81.0000;
549: t[i++] = .5000;
550: y[i] = 64.5000;
551: t[i++] = .7500;
552: y[i] = 35.5000;
553: t[i++] = 1.5000;
554: y[i] = 13.3100;
555: t[i++] = 3.0000;
556: y[i] = 4.8700;
557: t[i++] = 6.0000;
558: y[i] = 12.9400;
559: t[i++] = 3.0000;
560: y[i] = 5.0600;
561: t[i++] = 6.0000;
562: y[i] = 15.1900;
563: t[i++] = 3.0000;
564: y[i] = 14.6200;
565: t[i++] = 3.0000;
566: y[i] = 15.6400;
567: t[i++] = 3.0000;
568: y[i] = 25.5000;
569: t[i++] = 1.7500;
570: y[i] = 25.9500;
571: t[i++] = 1.7500;
572: y[i] = 81.7000;
573: t[i++] = .5000;
574: y[i] = 61.6000;
575: t[i++] = .7500;
576: y[i] = 29.8000;
577: t[i++] = 1.7500;
578: y[i] = 29.8100;
579: t[i++] = 1.7500;
580: y[i] = 17.1700;
581: t[i++] = 2.7500;
582: y[i] = 10.3900;
583: t[i++] = 3.7500;
584: y[i] = 28.4000;
585: t[i++] = 1.7500;
586: y[i] = 28.6900;
587: t[i++] = 1.7500;
588: y[i] = 81.3000;
589: t[i++] = .5000;
590: y[i] = 60.9000;
591: t[i++] = .7500;
592: y[i] = 16.6500;
593: t[i++] = 2.7500;
594: y[i] = 10.0500;
595: t[i++] = 3.7500;
596: y[i] = 28.9000;
597: t[i++] = 1.7500;
598: y[i] = 28.9500;
599: t[i++] = 1.7500;
600: PetscFunctionReturn(PETSC_SUCCESS);
601: }
603: /*TEST
605: build:
606: requires: !complex !single
608: test:
609: args: -tao_monitor_short -tao_max_it 100 -tao_type pounders -tao_gatol 1.e-5
611: test:
612: suffix: 2
613: args: -tao_monitor_short -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type l2prox -tao_brgn_regularizer_weight 1e-4 -tao_gatol 1.e-5
615: test:
616: suffix: 3
617: args: -tao_monitor_short -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
619: test:
620: suffix: 4
621: args: -tao_monitor_short -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type lm -tao_gatol 1.e-5 -tao_brgn_subsolver_tao_type bnls
623: TEST*/