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(); TaoSetObjectiveAndGradient();
17: Routines: TaoSetHessian();
18: Routines: TaoSetSolution();
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: PetscReal zero=0.0;
43: Vec x; /* solution vector */
44: Mat H;
45: Tao tao; /* Tao solver context */
46: PetscBool flg, test_lmvm = PETSC_FALSE;
47: PetscMPIInt size; /* number of processes running */
48: AppCtx user; /* user-defined application context */
49: KSP ksp;
50: PC pc;
51: Mat M;
52: Vec in, out, out2;
53: PetscReal mult_solve_dist;
55: /* Initialize TAO and PETSc */
56: PetscInitialize(&argc,&argv,(char*)0,help);
57: MPI_Comm_size(PETSC_COMM_WORLD,&size);
60: /* Initialize problem parameters */
61: user.n = 2; user.alpha = 99.0; user.chained = PETSC_FALSE;
62: /* Check for command line arguments to override defaults */
63: PetscOptionsGetInt(NULL,NULL,"-n",&user.n,&flg);
64: PetscOptionsGetReal(NULL,NULL,"-alpha",&user.alpha,&flg);
65: PetscOptionsGetBool(NULL,NULL,"-chained",&user.chained,&flg);
66: PetscOptionsGetBool(NULL,NULL,"-test_lmvm",&test_lmvm,&flg);
68: /* Allocate vectors for the solution and gradient */
69: VecCreateSeq(PETSC_COMM_SELF,user.n,&x);
70: MatCreateSeqBAIJ(PETSC_COMM_SELF,2,user.n,user.n,1,NULL,&H);
72: /* The TAO code begins here */
74: /* Create TAO solver with desired solution method */
75: TaoCreate(PETSC_COMM_SELF,&tao);
76: TaoSetType(tao,TAOLMVM);
78: /* Set solution vec and an initial guess */
79: VecSet(x, zero);
80: TaoSetSolution(tao,x);
82: /* Set routines for function, gradient, hessian evaluation */
83: TaoSetObjectiveAndGradient(tao,NULL,FormFunctionGradient,&user);
84: TaoSetHessian(tao,H,H,FormHessian,&user);
86: /* Test the LMVM matrix */
87: if (test_lmvm) {
88: PetscOptionsSetValue(NULL, "-tao_type", "bqnktr");
89: }
91: /* Check for TAO command line options */
92: TaoSetFromOptions(tao);
94: /* SOLVE THE APPLICATION */
95: TaoSolve(tao);
97: /* Test the LMVM matrix */
98: if (test_lmvm) {
99: TaoGetKSP(tao, &ksp);
100: KSPGetPC(ksp, &pc);
101: PCLMVMGetMatLMVM(pc, &M);
102: VecDuplicate(x, &in);
103: VecDuplicate(x, &out);
104: VecDuplicate(x, &out2);
105: VecSet(in, 1.0);
106: MatMult(M, in, out);
107: MatSolve(M, out, out2);
108: VecAXPY(out2, -1.0, in);
109: VecNorm(out2, NORM_2, &mult_solve_dist);
110: if (mult_solve_dist < 1.e-11) {
111: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-11\n");
112: } else if (mult_solve_dist < 1.e-6) {
113: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-6\n");
114: } else {
115: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: %e\n", (double)mult_solve_dist);
116: }
117: VecDestroy(&in);
118: VecDestroy(&out);
119: VecDestroy(&out2);
120: }
122: TaoDestroy(&tao);
123: VecDestroy(&x);
124: MatDestroy(&H);
126: PetscFinalize();
127: return 0;
128: }
130: /* -------------------------------------------------------------------- */
131: /*
132: FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).
134: Input Parameters:
135: . tao - the Tao context
136: . X - input vector
137: . ptr - optional user-defined context, as set by TaoSetFunctionGradient()
139: Output Parameters:
140: . G - vector containing the newly evaluated gradient
141: . f - function value
143: Note:
144: Some optimization methods ask for the function and the gradient evaluation
145: at the same time. Evaluating both at once may be more efficient that
146: evaluating each separately.
147: */
148: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
149: {
150: AppCtx *user = (AppCtx *) ptr;
151: PetscInt i,nn=user->n/2;
152: PetscReal ff=0,t1,t2,alpha=user->alpha;
153: PetscScalar *g;
154: const PetscScalar *x;
157: /* Get pointers to vector data */
158: VecGetArrayRead(X,&x);
159: VecGetArray(G,&g);
161: /* Compute G(X) */
162: if (user->chained) {
163: g[0] = 0;
164: for (i=0; i<user->n-1; i++) {
165: t1 = x[i+1] - x[i]*x[i];
166: ff += PetscSqr(1 - x[i]) + alpha*t1*t1;
167: g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]);
168: g[i+1] = 2*alpha*t1;
169: }
170: } else {
171: for (i=0; i<nn; i++) {
172: t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
173: ff += alpha*t1*t1 + t2*t2;
174: g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
175: g[2*i+1] = 2*alpha*t1;
176: }
177: }
179: /* Restore vectors */
180: VecRestoreArrayRead(X,&x);
181: VecRestoreArray(G,&g);
182: *f = ff;
184: PetscLogFlops(15.0*nn);
185: return 0;
186: }
188: /* ------------------------------------------------------------------- */
189: /*
190: FormHessian - Evaluates Hessian matrix.
192: Input Parameters:
193: . tao - the Tao context
194: . x - input vector
195: . ptr - optional user-defined context, as set by TaoSetHessian()
197: Output Parameters:
198: . H - Hessian matrix
200: Note: Providing the Hessian may not be necessary. Only some solvers
201: require this matrix.
202: */
203: PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
204: {
205: AppCtx *user = (AppCtx*)ptr;
206: PetscInt i, ind[2];
207: PetscReal alpha=user->alpha;
208: PetscReal v[2][2];
209: const PetscScalar *x;
210: PetscBool assembled;
213: /* Zero existing matrix entries */
214: MatAssembled(H,&assembled);
215: if (assembled) MatZeroEntries(H);
217: /* Get a pointer to vector data */
218: VecGetArrayRead(X,&x);
220: /* Compute H(X) entries */
221: if (user->chained) {
222: MatZeroEntries(H);
223: for (i=0; i<user->n-1; i++) {
224: PetscScalar t1 = x[i+1] - x[i]*x[i];
225: v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]);
226: v[0][1] = 2*alpha*(-2*x[i]);
227: v[1][0] = 2*alpha*(-2*x[i]);
228: v[1][1] = 2*alpha*t1;
229: ind[0] = i; ind[1] = i+1;
230: MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);
231: }
232: } else {
233: for (i=0; i<user->n/2; i++) {
234: v[1][1] = 2*alpha;
235: v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
236: v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
237: ind[0]=2*i; ind[1]=2*i+1;
238: MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
239: }
240: }
241: VecRestoreArrayRead(X,&x);
243: /* Assemble matrix */
244: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
245: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
246: PetscLogFlops(9.0*user->n/2.0);
247: return 0;
248: }
250: /*TEST
252: build:
253: requires: !complex
255: test:
256: args: -tao_smonitor -tao_type nls -tao_gatol 1.e-4
257: requires: !single
259: test:
260: suffix: 2
261: args: -tao_smonitor -tao_type lmvm -tao_gatol 1.e-3
263: test:
264: suffix: 3
265: args: -tao_smonitor -tao_type ntr -tao_gatol 1.e-4
266: requires: !single
268: test:
269: suffix: 4
270: args: -tao_smonitor -tao_type ntr -tao_mf_hessian -tao_ntr_pc_type none -tao_gatol 1.e-4
272: test:
273: suffix: 5
274: args: -tao_smonitor -tao_type bntr -tao_gatol 1.e-4
276: test:
277: suffix: 6
278: args: -tao_smonitor -tao_type bntl -tao_gatol 1.e-4
280: test:
281: suffix: 7
282: args: -tao_smonitor -tao_type bnls -tao_gatol 1.e-4
284: test:
285: suffix: 8
286: args: -tao_smonitor -tao_type bntr -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
288: test:
289: suffix: 9
290: args: -tao_smonitor -tao_type bntl -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
292: test:
293: suffix: 10
294: args: -tao_smonitor -tao_type bnls -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
296: test:
297: suffix: 11
298: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbroyden
300: test:
301: suffix: 12
302: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbadbroyden
304: test:
305: suffix: 13
306: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbroyden
308: test:
309: suffix: 14
310: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbfgs
312: test:
313: suffix: 15
314: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmdfp
316: test:
317: suffix: 16
318: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsr1
320: test:
321: suffix: 17
322: args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnls
324: test:
325: suffix: 18
326: args: -tao_smonitor -tao_gatol 1e-4 -tao_type blmvm
328: test:
329: suffix: 19
330: args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1
332: test:
333: suffix: 20
334: args: -tao_monitor -tao_gatol 1e-4 -tao_type blmvm -tao_ls_monitor
336: test:
337: suffix: 21
338: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbadbroyden
340: test:
341: suffix: 22
342: args: -tao_max_it 1 -tao_converged_reason
344: test:
345: suffix: 23
346: args: -tao_max_funcs 0 -tao_converged_reason
348: test:
349: suffix: 24
350: args: -tao_gatol 10 -tao_converged_reason
352: test:
353: suffix: 25
354: args: -tao_grtol 10 -tao_converged_reason
356: test:
357: suffix: 26
358: args: -tao_gttol 10 -tao_converged_reason
360: test:
361: suffix: 27
362: args: -tao_steptol 10 -tao_converged_reason
364: test:
365: suffix: 28
366: args: -tao_fmin 10 -tao_converged_reason
368: TEST*/