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: /*
14: User-defined application context - contains data needed by the
15: application-provided call-back routines that evaluate the function,
16: gradient, and hessian.
17: */
18: typedef struct {
19: PetscInt n; /* dimension */
20: PetscReal alpha; /* condition parameter */
21: PetscBool chained;
22: } AppCtx;
24: /* -------------- User-defined routines ---------- */
25: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
26: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,void*);
28: int main(int argc,char **argv)
29: {
30: PetscReal zero=0.0;
31: Vec x; /* solution vector */
32: Mat H;
33: Tao tao; /* Tao solver context */
34: PetscBool flg, test_lmvm = PETSC_FALSE;
35: PetscMPIInt size; /* number of processes running */
36: AppCtx user; /* user-defined application context */
37: KSP ksp;
38: PC pc;
39: Mat M;
40: Vec in, out, out2;
41: PetscReal mult_solve_dist;
43: /* Initialize TAO and PETSc */
44: PetscInitialize(&argc,&argv,(char*)0,help);
45: MPI_Comm_size(PETSC_COMM_WORLD,&size);
48: /* Initialize problem parameters */
49: user.n = 2; user.alpha = 99.0; user.chained = PETSC_FALSE;
50: /* Check for command line arguments to override defaults */
51: PetscOptionsGetInt(NULL,NULL,"-n",&user.n,&flg);
52: PetscOptionsGetReal(NULL,NULL,"-alpha",&user.alpha,&flg);
53: PetscOptionsGetBool(NULL,NULL,"-chained",&user.chained,&flg);
54: PetscOptionsGetBool(NULL,NULL,"-test_lmvm",&test_lmvm,&flg);
56: /* Allocate vectors for the solution and gradient */
57: VecCreateSeq(PETSC_COMM_SELF,user.n,&x);
58: MatCreateSeqBAIJ(PETSC_COMM_SELF,2,user.n,user.n,1,NULL,&H);
60: /* The TAO code begins here */
62: /* Create TAO solver with desired solution method */
63: TaoCreate(PETSC_COMM_SELF,&tao);
64: TaoSetType(tao,TAOLMVM);
66: /* Set solution vec and an initial guess */
67: VecSet(x, zero);
68: TaoSetSolution(tao,x);
70: /* Set routines for function, gradient, hessian evaluation */
71: TaoSetObjectiveAndGradient(tao,NULL,FormFunctionGradient,&user);
72: TaoSetHessian(tao,H,H,FormHessian,&user);
74: /* Test the LMVM matrix */
75: if (test_lmvm) {
76: PetscOptionsSetValue(NULL, "-tao_type", "bqnktr");
77: }
79: /* Check for TAO command line options */
80: TaoSetFromOptions(tao);
82: /* SOLVE THE APPLICATION */
83: TaoSolve(tao);
85: /* Test the LMVM matrix */
86: if (test_lmvm) {
87: TaoGetKSP(tao, &ksp);
88: KSPGetPC(ksp, &pc);
89: PCLMVMGetMatLMVM(pc, &M);
90: VecDuplicate(x, &in);
91: VecDuplicate(x, &out);
92: VecDuplicate(x, &out2);
93: VecSet(in, 1.0);
94: MatMult(M, in, out);
95: MatSolve(M, out, out2);
96: VecAXPY(out2, -1.0, in);
97: VecNorm(out2, NORM_2, &mult_solve_dist);
98: if (mult_solve_dist < 1.e-11) {
99: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-11\n");
100: } else if (mult_solve_dist < 1.e-6) {
101: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-6\n");
102: } else {
103: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: %e\n", (double)mult_solve_dist);
104: }
105: VecDestroy(&in);
106: VecDestroy(&out);
107: VecDestroy(&out2);
108: }
110: TaoDestroy(&tao);
111: VecDestroy(&x);
112: MatDestroy(&H);
114: PetscFinalize();
115: return 0;
116: }
118: /* -------------------------------------------------------------------- */
119: /*
120: FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).
122: Input Parameters:
123: . tao - the Tao context
124: . X - input vector
125: . ptr - optional user-defined context, as set by TaoSetFunctionGradient()
127: Output Parameters:
128: . G - vector containing the newly evaluated gradient
129: . f - function value
131: Note:
132: Some optimization methods ask for the function and the gradient evaluation
133: at the same time. Evaluating both at once may be more efficient that
134: evaluating each separately.
135: */
136: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
137: {
138: AppCtx *user = (AppCtx *) ptr;
139: PetscInt i,nn=user->n/2;
140: PetscReal ff=0,t1,t2,alpha=user->alpha;
141: PetscScalar *g;
142: const PetscScalar *x;
145: /* Get pointers to vector data */
146: VecGetArrayRead(X,&x);
147: VecGetArray(G,&g);
149: /* Compute G(X) */
150: if (user->chained) {
151: g[0] = 0;
152: for (i=0; i<user->n-1; i++) {
153: t1 = x[i+1] - x[i]*x[i];
154: ff += PetscSqr(1 - x[i]) + alpha*t1*t1;
155: g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]);
156: g[i+1] = 2*alpha*t1;
157: }
158: } else {
159: for (i=0; i<nn; i++) {
160: t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
161: ff += alpha*t1*t1 + t2*t2;
162: g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
163: g[2*i+1] = 2*alpha*t1;
164: }
165: }
167: /* Restore vectors */
168: VecRestoreArrayRead(X,&x);
169: VecRestoreArray(G,&g);
170: *f = ff;
172: PetscLogFlops(15.0*nn);
173: return 0;
174: }
176: /* ------------------------------------------------------------------- */
177: /*
178: FormHessian - Evaluates Hessian matrix.
180: Input Parameters:
181: . tao - the Tao context
182: . x - input vector
183: . ptr - optional user-defined context, as set by TaoSetHessian()
185: Output Parameters:
186: . H - Hessian matrix
188: Note: Providing the Hessian may not be necessary. Only some solvers
189: require this matrix.
190: */
191: PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
192: {
193: AppCtx *user = (AppCtx*)ptr;
194: PetscInt i, ind[2];
195: PetscReal alpha=user->alpha;
196: PetscReal v[2][2];
197: const PetscScalar *x;
198: PetscBool assembled;
201: /* Zero existing matrix entries */
202: MatAssembled(H,&assembled);
203: if (assembled) MatZeroEntries(H);
205: /* Get a pointer to vector data */
206: VecGetArrayRead(X,&x);
208: /* Compute H(X) entries */
209: if (user->chained) {
210: MatZeroEntries(H);
211: for (i=0; i<user->n-1; i++) {
212: PetscScalar t1 = x[i+1] - x[i]*x[i];
213: v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]);
214: v[0][1] = 2*alpha*(-2*x[i]);
215: v[1][0] = 2*alpha*(-2*x[i]);
216: v[1][1] = 2*alpha*t1;
217: ind[0] = i; ind[1] = i+1;
218: MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);
219: }
220: } else {
221: for (i=0; i<user->n/2; i++) {
222: v[1][1] = 2*alpha;
223: v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
224: v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
225: ind[0]=2*i; ind[1]=2*i+1;
226: MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
227: }
228: }
229: VecRestoreArrayRead(X,&x);
231: /* Assemble matrix */
232: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
233: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
234: PetscLogFlops(9.0*user->n/2.0);
235: return 0;
236: }
238: /*TEST
240: build:
241: requires: !complex
243: test:
244: args: -tao_smonitor -tao_type nls -tao_gatol 1.e-4
245: requires: !single
247: test:
248: suffix: 2
249: args: -tao_smonitor -tao_type lmvm -tao_gatol 1.e-3
251: test:
252: suffix: 3
253: args: -tao_smonitor -tao_type ntr -tao_gatol 1.e-4
254: requires: !single
256: test:
257: suffix: 4
258: args: -tao_smonitor -tao_type ntr -tao_mf_hessian -tao_ntr_pc_type none -tao_gatol 1.e-4
260: test:
261: suffix: 5
262: args: -tao_smonitor -tao_type bntr -tao_gatol 1.e-4
264: test:
265: suffix: 6
266: args: -tao_smonitor -tao_type bntl -tao_gatol 1.e-4
268: test:
269: suffix: 7
270: args: -tao_smonitor -tao_type bnls -tao_gatol 1.e-4
272: test:
273: suffix: 8
274: args: -tao_smonitor -tao_type bntr -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
276: test:
277: suffix: 9
278: args: -tao_smonitor -tao_type bntl -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
280: test:
281: suffix: 10
282: args: -tao_smonitor -tao_type bnls -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
284: test:
285: suffix: 11
286: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbroyden
288: test:
289: suffix: 12
290: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbadbroyden
292: test:
293: suffix: 13
294: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbroyden
296: test:
297: suffix: 14
298: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbfgs
300: test:
301: suffix: 15
302: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmdfp
304: test:
305: suffix: 16
306: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsr1
308: test:
309: suffix: 17
310: args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnls
312: test:
313: suffix: 18
314: args: -tao_smonitor -tao_gatol 1e-4 -tao_type blmvm
316: test:
317: suffix: 19
318: args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1
320: test:
321: suffix: 20
322: args: -tao_monitor -tao_gatol 1e-4 -tao_type blmvm -tao_ls_monitor
324: test:
325: suffix: 21
326: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbadbroyden
328: test:
329: suffix: 22
330: args: -tao_max_it 1 -tao_converged_reason
332: test:
333: suffix: 23
334: args: -tao_max_funcs 0 -tao_converged_reason
336: test:
337: suffix: 24
338: args: -tao_gatol 10 -tao_converged_reason
340: test:
341: suffix: 25
342: args: -tao_grtol 10 -tao_converged_reason
344: test:
345: suffix: 26
346: args: -tao_gttol 10 -tao_converged_reason
348: test:
349: suffix: 27
350: args: -tao_steptol 10 -tao_converged_reason
352: test:
353: suffix: 28
354: args: -tao_fmin 10 -tao_converged_reason
356: TEST*/