Actual source code: rosenbrock1.c
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*/
25: /*
26: User-defined application context - contains data needed by the
27: application-provided call-back routines that evaluate the function,
28: gradient, and hessian.
29: */
30: typedef struct {
31: PetscInt n; /* dimension */
32: PetscReal alpha; /* condition parameter */
33: PetscBool chained;
34: } AppCtx;
36: /* -------------- User-defined routines ---------- */
37: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
38: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,void*);
40: int main(int argc,char **argv)
41: {
42: PetscErrorCode ierr; /* used to check for functions returning nonzeros */
43: PetscReal zero=0.0;
44: Vec x; /* solution vector */
45: Mat H;
46: Tao tao; /* Tao solver context */
47: PetscBool flg, test_lmvm = PETSC_FALSE;
48: PetscMPIInt size; /* number of processes running */
49: AppCtx user; /* user-defined application context */
50: KSP ksp;
51: PC pc;
52: Mat M;
53: Vec in, out, out2;
54: PetscReal mult_solve_dist;
56: /* Initialize TAO and PETSc */
57: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
58: MPI_Comm_size(PETSC_COMM_WORLD,&size);
59: if (size >1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"Incorrect number of processors");
61: /* Initialize problem parameters */
62: user.n = 2; user.alpha = 99.0; user.chained = PETSC_FALSE;
63: /* Check for command line arguments to override defaults */
64: PetscOptionsGetInt(NULL,NULL,"-n",&user.n,&flg);
65: PetscOptionsGetReal(NULL,NULL,"-alpha",&user.alpha,&flg);
66: PetscOptionsGetBool(NULL,NULL,"-chained",&user.chained,&flg);
67: PetscOptionsGetBool(NULL,NULL,"-test_lmvm",&test_lmvm,&flg);
69: /* Allocate vectors for the solution and gradient */
70: VecCreateSeq(PETSC_COMM_SELF,user.n,&x);
71: MatCreateSeqBAIJ(PETSC_COMM_SELF,2,user.n,user.n,1,NULL,&H);
73: /* The TAO code begins here */
75: /* Create TAO solver with desired solution method */
76: TaoCreate(PETSC_COMM_SELF,&tao);
77: TaoSetType(tao,TAOLMVM);
79: /* Set solution vec and an initial guess */
80: VecSet(x, zero);
81: TaoSetInitialVector(tao,x);
83: /* Set routines for function, gradient, hessian evaluation */
84: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);
85: TaoSetHessianRoutine(tao,H,H,FormHessian,&user);
87: /* Test the LMVM matrix */
88: if (test_lmvm) {
89: PetscOptionsSetValue(NULL, "-tao_type", "bqnktr");
90: }
92: /* Check for TAO command line options */
93: TaoSetFromOptions(tao);
95: /* SOLVE THE APPLICATION */
96: TaoSolve(tao);
98: /* Test the LMVM matrix */
99: if (test_lmvm) {
100: TaoGetKSP(tao, &ksp);
101: KSPGetPC(ksp, &pc);
102: PCLMVMGetMatLMVM(pc, &M);
103: VecDuplicate(x, &in);
104: VecDuplicate(x, &out);
105: VecDuplicate(x, &out2);
106: VecSet(in, 1.0);
107: MatMult(M, in, out);
108: MatSolve(M, out, out2);
109: VecAXPY(out2, -1.0, in);
110: VecNorm(out2, NORM_2, &mult_solve_dist);
111: if (mult_solve_dist < 1.e-11) {
112: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-11\n");
113: } else if (mult_solve_dist < 1.e-6) {
114: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-6\n");
115: } else {
116: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: %e\n", (double)mult_solve_dist);
117: }
118: VecDestroy(&in);
119: VecDestroy(&out);
120: VecDestroy(&out2);
121: }
123: TaoDestroy(&tao);
124: VecDestroy(&x);
125: MatDestroy(&H);
127: PetscFinalize();
128: return ierr;
129: }
131: /* -------------------------------------------------------------------- */
132: /*
133: FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).
135: Input Parameters:
136: . tao - the Tao context
137: . X - input vector
138: . ptr - optional user-defined context, as set by TaoSetFunctionGradient()
140: Output Parameters:
141: . G - vector containing the newly evaluated gradient
142: . f - function value
144: Note:
145: Some optimization methods ask for the function and the gradient evaluation
146: at the same time. Evaluating both at once may be more efficient that
147: evaluating each separately.
148: */
149: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
150: {
151: AppCtx *user = (AppCtx *) ptr;
152: PetscInt i,nn=user->n/2;
153: PetscErrorCode ierr;
154: PetscReal ff=0,t1,t2,alpha=user->alpha;
155: PetscScalar *g;
156: const PetscScalar *x;
159: /* Get pointers to vector data */
160: VecGetArrayRead(X,&x);
161: VecGetArray(G,&g);
163: /* Compute G(X) */
164: if (user->chained) {
165: g[0] = 0;
166: for (i=0; i<user->n-1; i++) {
167: t1 = x[i+1] - x[i]*x[i];
168: ff += PetscSqr(1 - x[i]) + alpha*t1*t1;
169: g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]);
170: g[i+1] = 2*alpha*t1;
171: }
172: } else {
173: for (i=0; i<nn; i++) {
174: t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
175: ff += alpha*t1*t1 + t2*t2;
176: g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
177: g[2*i+1] = 2*alpha*t1;
178: }
179: }
181: /* Restore vectors */
182: VecRestoreArrayRead(X,&x);
183: VecRestoreArray(G,&g);
184: *f = ff;
186: PetscLogFlops(15.0*nn);
187: return(0);
188: }
190: /* ------------------------------------------------------------------- */
191: /*
192: FormHessian - Evaluates Hessian matrix.
194: Input Parameters:
195: . tao - the Tao context
196: . x - input vector
197: . ptr - optional user-defined context, as set by TaoSetHessian()
199: Output Parameters:
200: . H - Hessian matrix
202: Note: Providing the Hessian may not be necessary. Only some solvers
203: require this matrix.
204: */
205: PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
206: {
207: AppCtx *user = (AppCtx*)ptr;
208: PetscErrorCode ierr;
209: PetscInt i, ind[2];
210: PetscReal alpha=user->alpha;
211: PetscReal v[2][2];
212: const PetscScalar *x;
213: PetscBool assembled;
216: /* Zero existing matrix entries */
217: MatAssembled(H,&assembled);
218: if (assembled) {MatZeroEntries(H);}
220: /* Get a pointer to vector data */
221: VecGetArrayRead(X,&x);
223: /* Compute H(X) entries */
224: if (user->chained) {
225: MatZeroEntries(H);
226: for (i=0; i<user->n-1; i++) {
227: PetscScalar t1 = x[i+1] - x[i]*x[i];
228: v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]);
229: v[0][1] = 2*alpha*(-2*x[i]);
230: v[1][0] = 2*alpha*(-2*x[i]);
231: v[1][1] = 2*alpha*t1;
232: ind[0] = i; ind[1] = i+1;
233: MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);
234: }
235: } else {
236: for (i=0; i<user->n/2; i++) {
237: v[1][1] = 2*alpha;
238: v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
239: v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
240: ind[0]=2*i; ind[1]=2*i+1;
241: MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
242: }
243: }
244: VecRestoreArrayRead(X,&x);
246: /* Assemble matrix */
247: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
248: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
249: PetscLogFlops(9.0*user->n/2.0);
250: return(0);
251: }
253: /*TEST
255: build:
256: requires: !complex
258: test:
259: args: -tao_smonitor -tao_type nls -tao_gatol 1.e-4
260: requires: !single
262: test:
263: suffix: 2
264: args: -tao_smonitor -tao_type lmvm -tao_gatol 1.e-3
266: test:
267: suffix: 3
268: args: -tao_smonitor -tao_type ntr -tao_gatol 1.e-4
269: requires: !single
271: test:
272: suffix: 4
273: args: -tao_smonitor -tao_type ntr -tao_mf_hessian -tao_ntr_pc_type none -tao_gatol 1.e-4
275: test:
276: suffix: 5
277: args: -tao_smonitor -tao_type bntr -tao_gatol 1.e-4
279: test:
280: suffix: 6
281: args: -tao_smonitor -tao_type bntl -tao_gatol 1.e-4
283: test:
284: suffix: 7
285: args: -tao_smonitor -tao_type bnls -tao_gatol 1.e-4
287: test:
288: suffix: 8
289: args: -tao_smonitor -tao_type bntr -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
291: test:
292: suffix: 9
293: args: -tao_smonitor -tao_type bntl -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
295: test:
296: suffix: 10
297: args: -tao_smonitor -tao_type bnls -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
299: test:
300: suffix: 11
301: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbroyden
303: test:
304: suffix: 12
305: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbadbroyden
307: test:
308: suffix: 13
309: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbroyden
311: test:
312: suffix: 14
313: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbfgs
315: test:
316: suffix: 15
317: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmdfp
319: test:
320: suffix: 16
321: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsr1
323: test:
324: suffix: 17
325: args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnls
327: test:
328: suffix: 18
329: args: -tao_smonitor -tao_gatol 1e-4 -tao_type blmvm
331: test:
332: suffix: 19
333: args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1
335: test:
336: suffix: 20
337: args: -tao_monitor -tao_gatol 1e-4 -tao_type blmvm -tao_ls_monitor
339: test:
340: suffix: 21
341: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbadbroyden
343: test:
344: suffix: 22
345: args: -tao_max_it 1 -tao_converged_reason
347: test:
348: suffix: 23
349: args: -tao_max_funcs 0 -tao_converged_reason
351: test:
352: suffix: 24
353: args: -tao_gatol 10 -tao_converged_reason
355: test:
356: suffix: 25
357: args: -tao_grtol 10 -tao_converged_reason
359: test:
360: suffix: 26
361: args: -tao_gttol 10 -tao_converged_reason
363: test:
364: suffix: 27
365: args: -tao_steptol 10 -tao_converged_reason
367: test:
368: suffix: 28
369: args: -tao_fmin 10 -tao_converged_reason
371: TEST*/