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 */
 45:   PetscInitialize(&argc, &argv, (char *)0, help);
 46:   MPI_Comm_size(PETSC_COMM_WORLD, &size);

 49:   /* Initialize problem parameters */
 50:   user.n       = 2;
 51:   user.alpha   = 99.0;
 52:   user.chained = PETSC_FALSE;
 53:   /* Check for command line arguments to override defaults */
 54:   PetscOptionsGetInt(NULL, NULL, "-n", &user.n, &flg);
 55:   PetscOptionsGetReal(NULL, NULL, "-alpha", &user.alpha, &flg);
 56:   PetscOptionsGetBool(NULL, NULL, "-chained", &user.chained, &flg);
 57:   PetscOptionsGetBool(NULL, NULL, "-test_lmvm", &test_lmvm, &flg);

 59:   /* Allocate vectors for the solution and gradient */
 60:   VecCreateSeq(PETSC_COMM_SELF, user.n, &x);
 61:   MatCreateSeqBAIJ(PETSC_COMM_SELF, 2, user.n, user.n, 1, NULL, &H);

 63:   /* The TAO code begins here */

 65:   /* Create TAO solver with desired solution method */
 66:   TaoCreate(PETSC_COMM_SELF, &tao);
 67:   TaoSetType(tao, TAOLMVM);

 69:   /* Set solution vec and an initial guess */
 70:   VecSet(x, zero);
 71:   TaoSetSolution(tao, x);

 73:   /* Set routines for function, gradient, hessian evaluation */
 74:   TaoSetObjectiveAndGradient(tao, NULL, FormFunctionGradient, &user);
 75:   TaoSetHessian(tao, H, H, FormHessian, &user);

 77:   /* Test the LMVM matrix */
 78:   if (test_lmvm) PetscOptionsSetValue(NULL, "-tao_type", "bqnktr");

 80:   /* Check for TAO command line options */
 81:   TaoSetFromOptions(tao);

 83:   /* SOLVE THE APPLICATION */
 84:   TaoSolve(tao);

 86:   /* Test the LMVM matrix */
 87:   if (test_lmvm) {
 88:     TaoGetKSP(tao, &ksp);
 89:     KSPGetPC(ksp, &pc);
 90:     PCLMVMGetMatLMVM(pc, &M);
 91:     VecDuplicate(x, &in);
 92:     VecDuplicate(x, &out);
 93:     VecDuplicate(x, &out2);
 94:     VecSet(in, 1.0);
 95:     MatMult(M, in, out);
 96:     MatSolve(M, out, out2);
 97:     VecAXPY(out2, -1.0, in);
 98:     VecNorm(out2, NORM_2, &mult_solve_dist);
 99:     if (mult_solve_dist < 1.e-11) {
100:       PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-11\n");
101:     } else if (mult_solve_dist < 1.e-6) {
102:       PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-6\n");
103:     } else {
104:       PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: %e\n", (double)mult_solve_dist);
105:     }
106:     VecDestroy(&in);
107:     VecDestroy(&out);
108:     VecDestroy(&out2);
109:   }

111:   TaoDestroy(&tao);
112:   VecDestroy(&x);
113:   MatDestroy(&H);

115:   PetscFinalize();
116:   return 0;
117: }

119: /* -------------------------------------------------------------------- */
120: /*
121:     FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).

123:     Input Parameters:
124: .   tao  - the Tao context
125: .   X    - input vector
126: .   ptr  - optional user-defined context, as set by TaoSetFunctionGradient()

128:     Output Parameters:
129: .   G - vector containing the newly evaluated gradient
130: .   f - function value

132:     Note:
133:     Some optimization methods ask for the function and the gradient evaluation
134:     at the same time.  Evaluating both at once may be more efficient that
135:     evaluating each separately.
136: */
137: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
138: {
139:   AppCtx            *user = (AppCtx *)ptr;
140:   PetscInt           i, nn = user->n / 2;
141:   PetscReal          ff = 0, t1, t2, alpha = user->alpha;
142:   PetscScalar       *g;
143:   const PetscScalar *x;

146:   /* Get pointers to vector data */
147:   VecGetArrayRead(X, &x);
148:   VecGetArray(G, &g);

150:   /* Compute G(X) */
151:   if (user->chained) {
152:     g[0] = 0;
153:     for (i = 0; i < user->n - 1; i++) {
154:       t1 = x[i + 1] - x[i] * x[i];
155:       ff += PetscSqr(1 - x[i]) + alpha * t1 * t1;
156:       g[i] += -2 * (1 - x[i]) + 2 * alpha * t1 * (-2 * x[i]);
157:       g[i + 1] = 2 * alpha * t1;
158:     }
159:   } else {
160:     for (i = 0; i < nn; i++) {
161:       t1 = x[2 * i + 1] - x[2 * i] * x[2 * i];
162:       t2 = 1 - x[2 * i];
163:       ff += alpha * t1 * t1 + t2 * t2;
164:       g[2 * i]     = -4 * alpha * t1 * x[2 * i] - 2.0 * t2;
165:       g[2 * i + 1] = 2 * alpha * t1;
166:     }
167:   }

169:   /* Restore vectors */
170:   VecRestoreArrayRead(X, &x);
171:   VecRestoreArray(G, &g);
172:   *f = ff;

174:   PetscLogFlops(15.0 * nn);
175:   return 0;
176: }

178: /* ------------------------------------------------------------------- */
179: /*
180:    FormHessian - Evaluates Hessian matrix.

182:    Input Parameters:
183: .  tao   - the Tao context
184: .  x     - input vector
185: .  ptr   - optional user-defined context, as set by TaoSetHessian()

187:    Output Parameters:
188: .  H     - Hessian matrix

190:    Note:  Providing the Hessian may not be necessary.  Only some solvers
191:    require this matrix.
192: */
193: PetscErrorCode FormHessian(Tao tao, Vec X, Mat H, Mat Hpre, void *ptr)
194: {
195:   AppCtx            *user = (AppCtx *)ptr;
196:   PetscInt           i, ind[2];
197:   PetscReal          alpha = user->alpha;
198:   PetscReal          v[2][2];
199:   const PetscScalar *x;
200:   PetscBool          assembled;

203:   /* Zero existing matrix entries */
204:   MatAssembled(H, &assembled);
205:   if (assembled) MatZeroEntries(H);

207:   /* Get a pointer to vector data */
208:   VecGetArrayRead(X, &x);

210:   /* Compute H(X) entries */
211:   if (user->chained) {
212:     MatZeroEntries(H);
213:     for (i = 0; i < user->n - 1; i++) {
214:       PetscScalar t1 = x[i + 1] - x[i] * x[i];
215:       v[0][0]        = 2 + 2 * alpha * (t1 * (-2) - 2 * x[i]);
216:       v[0][1]        = 2 * alpha * (-2 * x[i]);
217:       v[1][0]        = 2 * alpha * (-2 * x[i]);
218:       v[1][1]        = 2 * alpha * t1;
219:       ind[0]         = i;
220:       ind[1]         = i + 1;
221:       MatSetValues(H, 2, ind, 2, ind, v[0], ADD_VALUES);
222:     }
223:   } else {
224:     for (i = 0; i < user->n / 2; i++) {
225:       v[1][1] = 2 * alpha;
226:       v[0][0] = -4 * alpha * (x[2 * i + 1] - 3 * x[2 * i] * x[2 * i]) + 2;
227:       v[1][0] = v[0][1] = -4.0 * alpha * x[2 * i];
228:       ind[0]            = 2 * i;
229:       ind[1]            = 2 * i + 1;
230:       MatSetValues(H, 2, ind, 2, ind, v[0], INSERT_VALUES);
231:     }
232:   }
233:   VecRestoreArrayRead(X, &x);

235:   /* Assemble matrix */
236:   MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY);
237:   MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY);
238:   PetscLogFlops(9.0 * user->n / 2.0);
239:   return 0;
240: }

242: /*TEST

244:    build:
245:       requires: !complex

247:    test:
248:       args: -tao_smonitor -tao_type nls -tao_gatol 1.e-4
249:       requires: !single

251:    test:
252:       suffix: 2
253:       args: -tao_smonitor -tao_type lmvm -tao_gatol 1.e-3

255:    test:
256:       suffix: 3
257:       args: -tao_smonitor -tao_type ntr -tao_gatol 1.e-4
258:       requires: !single

260:    test:
261:       suffix: 4
262:       args: -tao_smonitor -tao_type ntr -tao_mf_hessian -tao_ntr_pc_type none -tao_gatol 1.e-4

264:    test:
265:       suffix: 5
266:       args: -tao_smonitor -tao_type bntr -tao_gatol 1.e-4

268:    test:
269:       suffix: 6
270:       args: -tao_smonitor -tao_type bntl -tao_gatol 1.e-4

272:    test:
273:       suffix: 7
274:       args: -tao_smonitor -tao_type bnls -tao_gatol 1.e-4

276:    test:
277:       suffix: 8
278:       args: -tao_smonitor -tao_type bntr -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

280:    test:
281:       suffix: 9
282:       args: -tao_smonitor -tao_type bntl -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

284:    test:
285:       suffix: 10
286:       args: -tao_smonitor -tao_type bnls -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

288:    test:
289:       suffix: 11
290:       args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbroyden

292:    test:
293:       suffix: 12
294:       args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbadbroyden

296:    test:
297:      suffix: 13
298:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbroyden

300:    test:
301:      suffix: 14
302:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbfgs

304:    test:
305:      suffix: 15
306:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmdfp

308:    test:
309:      suffix: 16
310:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsr1

312:    test:
313:      suffix: 17
314:      args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnls

316:    test:
317:      suffix: 18
318:      args: -tao_smonitor -tao_gatol 1e-4 -tao_type blmvm

320:    test:
321:      suffix: 19
322:      args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1

324:    test:
325:      suffix: 20
326:      args: -tao_monitor -tao_gatol 1e-4 -tao_type blmvm -tao_ls_monitor

328:    test:
329:      suffix: 21
330:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbadbroyden

332:    test:
333:      suffix: 22
334:      args: -tao_max_it 1 -tao_converged_reason

336:    test:
337:      suffix: 23
338:      args: -tao_max_funcs 0 -tao_converged_reason

340:    test:
341:      suffix: 24
342:      args: -tao_gatol 10 -tao_converged_reason

344:    test:
345:      suffix: 25
346:      args: -tao_grtol 10 -tao_converged_reason

348:    test:
349:      suffix: 26
350:      args: -tao_gttol 10 -tao_converged_reason

352:    test:
353:      suffix: 27
354:      args: -tao_steptol 10 -tao_converged_reason

356:    test:
357:      suffix: 28
358:      args: -tao_fmin 10 -tao_converged_reason

360: TEST*/