Actual source code: rosenbrock1.c
petsc-3.13.6 2020-09-29
1: /* Program usage: mpiexec -n 1 rosenbrock1 [-help] [all TAO options] */
3: /* Include "petsctao.h" so we can use TAO solvers. */
4: #include <petsctao.h>
6: static char help[] = "This example demonstrates use of the TAO package to \n\
7: solve an unconstrained minimization problem on a single processor. We \n\
8: minimize the extended Rosenbrock function: \n\
9: sum_{i=0}^{n/2-1} ( alpha*(x_{2i+1}-x_{2i}^2)^2 + (1-x_{2i})^2 ) \n\
10: or the chained Rosenbrock function:\n\
11: sum_{i=0}^{n-1} alpha*(x_{i+1} - x_i^2)^2 + (1 - x_i)^2\n";
13: /*T
14: Concepts: TAO^Solving an unconstrained minimization problem
15: Routines: TaoCreate();
16: Routines: TaoSetType(); TaoSetObjectiveAndGradientRoutine();
17: Routines: TaoSetHessianRoutine();
18: Routines: TaoSetInitialVector();
19: Routines: TaoSetFromOptions();
20: Routines: TaoSolve();
21: Routines: TaoDestroy();
22: Processors: 1
23: T*/
28: /*
29: User-defined Section 1.5 Writing Application Codes with PETSc context - contains data needed by the
30: Section 1.5 Writing Application Codes with PETSc-provided call-back routines that evaluate the function,
31: gradient, and hessian.
32: */
33: typedef struct {
34: PetscInt n; /* dimension */
35: PetscReal alpha; /* condition parameter */
36: PetscBool chained;
37: } AppCtx;
39: /* -------------- User-defined routines ---------- */
40: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
41: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,void*);
43: int main(int argc,char **argv)
44: {
45: PetscErrorCode ierr; /* used to check for functions returning nonzeros */
46: PetscReal zero=0.0;
47: Vec x; /* solution vector */
48: Mat H;
49: Tao tao; /* Tao solver context */
50: PetscBool flg, test_lmvm = PETSC_FALSE;
51: PetscMPIInt size; /* number of processes running */
52: AppCtx user; /* user-defined Section 1.5 Writing Application Codes with PETSc context */
53: KSP ksp;
54: PC pc;
55: Mat M;
56: Vec in, out, out2;
57: PetscReal mult_solve_dist;
59: /* Initialize TAO and PETSc */
60: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
61: MPI_Comm_size(PETSC_COMM_WORLD,&size);
62: if (size >1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"Incorrect number of processors");
64: /* Initialize problem parameters */
65: user.n = 2; user.alpha = 99.0; user.chained = PETSC_FALSE;
66: /* Check for command line arguments to override defaults */
67: PetscOptionsGetInt(NULL,NULL,"-n",&user.n,&flg);
68: PetscOptionsGetReal(NULL,NULL,"-alpha",&user.alpha,&flg);
69: PetscOptionsGetBool(NULL,NULL,"-chained",&user.chained,&flg);
70: PetscOptionsGetBool(NULL,NULL,"-test_lmvm",&test_lmvm,&flg);
72: /* Allocate vectors for the solution and gradient */
73: VecCreateSeq(PETSC_COMM_SELF,user.n,&x);
74: MatCreateSeqBAIJ(PETSC_COMM_SELF,2,user.n,user.n,1,NULL,&H);
76: /* The TAO code begins here */
78: /* Create TAO solver with desired solution method */
79: TaoCreate(PETSC_COMM_SELF,&tao);
80: TaoSetType(tao,TAOLMVM);
82: /* Set solution vec and an initial guess */
83: VecSet(x, zero);
84: TaoSetInitialVector(tao,x);
86: /* Set routines for function, gradient, hessian evaluation */
87: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);
88: TaoSetHessianRoutine(tao,H,H,FormHessian,&user);
89:
90: /* Test the LMVM matrix */
91: if (test_lmvm) {
92: PetscOptionsSetValue(NULL, "-tao_type", "bqnktr");
93: }
95: /* Check for TAO command line options */
96: TaoSetFromOptions(tao);
98: /* SOLVE THE APPLICATION */
99: TaoSolve(tao);
100:
101: /* Test the LMVM matrix */
102: if (test_lmvm) {
103: TaoGetKSP(tao, &ksp);
104: KSPGetPC(ksp, &pc);
105: PCLMVMGetMatLMVM(pc, &M);
106: VecDuplicate(x, &in);
107: VecDuplicate(x, &out);
108: VecDuplicate(x, &out2);
109: VecSet(in, 1.0);
110: MatMult(M, in, out);
111: MatSolve(M, out, out2);
112: VecAXPY(out2, -1.0, in);
113: VecNorm(out2, NORM_2, &mult_solve_dist);
114: if (mult_solve_dist < 1.e-11) {
115: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-11\n");
116: } else if(mult_solve_dist < 1.e-6) {
117: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-6\n");
118: } else {
119: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: %e\n", (double)mult_solve_dist);
120: }
121: VecDestroy(&in);
122: VecDestroy(&out);
123: VecDestroy(&out2);
124: }
126: TaoDestroy(&tao);
127: VecDestroy(&x);
128: MatDestroy(&H);
130: PetscFinalize();
131: return ierr;
132: }
134: /* -------------------------------------------------------------------- */
135: /*
136: FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).
138: Input Parameters:
139: . tao - the Tao context
140: . X - input vector
141: . ptr - optional user-defined context, as set by TaoSetFunctionGradient()
143: Output Parameters:
144: . G - vector containing the newly evaluated gradient
145: . f - function value
147: Note:
148: Some optimization methods ask for the function and the gradient evaluation
149: at the same time. Evaluating both at once may be more efficient that
150: evaluating each separately.
151: */
152: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
153: {
154: AppCtx *user = (AppCtx *) ptr;
155: PetscInt i,nn=user->n/2;
156: PetscErrorCode ierr;
157: PetscReal ff=0,t1,t2,alpha=user->alpha;
158: PetscScalar *g;
159: const PetscScalar *x;
162: /* Get pointers to vector data */
163: VecGetArrayRead(X,&x);
164: VecGetArray(G,&g);
166: /* Compute G(X) */
167: if (user->chained) {
168: g[0] = 0;
169: for (i=0; i<user->n-1; i++) {
170: t1 = x[i+1] - x[i]*x[i];
171: ff += PetscSqr(1 - x[i]) + alpha*t1*t1;
172: g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]);
173: g[i+1] = 2*alpha*t1;
174: }
175: } else {
176: for (i=0; i<nn; i++){
177: t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
178: ff += alpha*t1*t1 + t2*t2;
179: g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
180: g[2*i+1] = 2*alpha*t1;
181: }
182: }
184: /* Restore vectors */
185: VecRestoreArrayRead(X,&x);
186: VecRestoreArray(G,&g);
187: *f = ff;
189: PetscLogFlops(15.0*nn);
190: return(0);
191: }
193: /* ------------------------------------------------------------------- */
194: /*
195: FormHessian - Evaluates Hessian matrix.
197: Input Parameters:
198: . tao - the Tao context
199: . x - input vector
200: . ptr - optional user-defined context, as set by TaoSetHessian()
202: Output Parameters:
203: . H - Hessian matrix
205: Note: Providing the Hessian may not be necessary. Only some solvers
206: require this matrix.
207: */
208: PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
209: {
210: AppCtx *user = (AppCtx*)ptr;
211: PetscErrorCode ierr;
212: PetscInt i, ind[2];
213: PetscReal alpha=user->alpha;
214: PetscReal v[2][2];
215: const PetscScalar *x;
216: PetscBool assembled;
219: /* Zero existing matrix entries */
220: MatAssembled(H,&assembled);
221: if (assembled){MatZeroEntries(H); }
223: /* Get a pointer to vector data */
224: VecGetArrayRead(X,&x);
226: /* Compute H(X) entries */
227: if (user->chained) {
228: MatZeroEntries(H);
229: for (i=0; i<user->n-1; i++) {
230: PetscScalar t1 = x[i+1] - x[i]*x[i];
231: v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]);
232: v[0][1] = 2*alpha*(-2*x[i]);
233: v[1][0] = 2*alpha*(-2*x[i]);
234: v[1][1] = 2*alpha*t1;
235: ind[0] = i; ind[1] = i+1;
236: MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);
237: }
238: } else {
239: for (i=0; i<user->n/2; i++){
240: v[1][1] = 2*alpha;
241: v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
242: v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
243: ind[0]=2*i; ind[1]=2*i+1;
244: MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
245: }
246: }
247: VecRestoreArrayRead(X,&x);
249: /* Assemble matrix */
250: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
251: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
252: PetscLogFlops(9.0*user->n/2.0);
253: return(0);
254: }
257: /*TEST
259: build:
260: requires: !complex
262: test:
263: args: -tao_smonitor -tao_type nls -tao_gatol 1.e-4
264: requires: !single
266: test:
267: suffix: 2
268: args: -tao_smonitor -tao_type lmvm -tao_gatol 1.e-3
270: test:
271: suffix: 3
272: args: -tao_smonitor -tao_type ntr -tao_gatol 1.e-4
273: requires: !single
275: test:
276: suffix: 4
277: args: -tao_smonitor -tao_type ntr -tao_mf_hessian -tao_ntr_pc_type none -tao_gatol 1.e-4
278:
279: test:
280: suffix: 5
281: args: -tao_smonitor -tao_type bntr -tao_gatol 1.e-4
282:
283: test:
284: suffix: 6
285: args: -tao_smonitor -tao_type bntl -tao_gatol 1.e-4
286:
287: test:
288: suffix: 7
289: args: -tao_smonitor -tao_type bnls -tao_gatol 1.e-4
290:
291: test:
292: suffix: 8
293: args: -tao_smonitor -tao_type bntr -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
294:
295: test:
296: suffix: 9
297: args: -tao_smonitor -tao_type bntl -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
298:
299: test:
300: suffix: 10
301: args: -tao_smonitor -tao_type bnls -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
302:
303: test:
304: suffix: 11
305: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbroyden
306:
307: test:
308: suffix: 12
309: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbadbroyden
310:
311: test:
312: suffix: 13
313: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbroyden
315: test:
316: suffix: 14
317: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbfgs
318:
319: test:
320: suffix: 15
321: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmdfp
322:
323: test:
324: suffix: 16
325: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsr1
326:
327: test:
328: suffix: 17
329: args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnls
330:
331: test:
332: suffix: 18
333: args: -tao_smonitor -tao_gatol 1e-4 -tao_type blmvm
334:
335: test:
336: suffix: 19
337: args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1
338:
339: test:
340: suffix: 20
341: args: -tao_monitor -tao_gatol 1e-4 -tao_type blmvm -tao_ls_monitor
342:
343: test:
344: suffix: 21
345: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbadbroyden
347: test:
348: suffix: 22
349: args: -tao_max_it 1 -tao_converged_reason
351: test:
352: suffix: 23
353: args: -tao_max_funcs 0 -tao_converged_reason
355: test:
356: suffix: 24
357: args: -tao_gatol 10 -tao_converged_reason
359: test:
360: suffix: 25
361: args: -tao_grtol 10 -tao_converged_reason
363: test:
364: suffix: 26
365: args: -tao_gttol 10 -tao_converged_reason
367: test:
368: suffix: 27
369: args: -tao_steptol 10 -tao_converged_reason
371: test:
372: suffix: 28
373: args: -tao_fmin 10 -tao_converged_reason
375: TEST*/