Actual source code: rosenbrock3.c

  1: /* Program usage: mpiexec -n 1 rosenbrock2 [-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:   TaoConvergedReason reason;
 38:   PetscInt           its, recycled_its = 0, oneshot_its = 0;

 40:   /* Initialize TAO and PETSc */
 42:   PetscInitialize(&argc, &argv, (char *)0, help);
 43:   MPI_Comm_size(PETSC_COMM_WORLD, &size);

 46:   /* Initialize problem parameters */
 47:   user.n       = 2;
 48:   user.alpha   = 99.0;
 49:   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, TAOBQNLS);

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

 77:   /* Solve the problem */
 78:   TaoSetTolerances(tao, 1.e-5, 0.0, 0.0);
 79:   TaoSetMaximumIterations(tao, 5);
 80:   TaoSetRecycleHistory(tao, PETSC_TRUE);
 81:   reason = TAO_CONTINUE_ITERATING;
 82:   flg    = PETSC_FALSE;
 83:   TaoGetRecycleHistory(tao, &flg);
 84:   if (flg) PetscPrintf(PETSC_COMM_SELF, "Recycle: enabled\n");
 85:   while (reason != TAO_CONVERGED_GATOL) {
 86:     TaoSolve(tao);
 87:     TaoGetConvergedReason(tao, &reason);
 88:     TaoGetIterationNumber(tao, &its);
 89:     recycled_its += its;
 90:     PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");
 91:   }

 93:   /* Disable recycling and solve again! */
 94:   TaoSetMaximumIterations(tao, 100);
 95:   TaoSetRecycleHistory(tao, PETSC_FALSE);
 96:   VecSet(x, zero);
 97:   TaoGetRecycleHistory(tao, &flg);
 98:   if (!flg) PetscPrintf(PETSC_COMM_SELF, "Recycle: disabled\n");
 99:   TaoSolve(tao);
100:   TaoGetConvergedReason(tao, &reason);
102:   TaoGetIterationNumber(tao, &oneshot_its);
103:   PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");
104:   PetscPrintf(PETSC_COMM_SELF, "recycled its: %" PetscInt_FMT " | oneshot its: %" PetscInt_FMT "\n", recycled_its, oneshot_its);

107:   TaoDestroy(&tao);
108:   VecDestroy(&x);
109:   MatDestroy(&H);

111:   PetscFinalize();
112:   return 0;
113: }

115: /* -------------------------------------------------------------------- */
116: /*
117:     FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).

119:     Input Parameters:
120: .   tao  - the Tao context
121: .   X    - input vector
122: .   ptr  - optional user-defined context, as set by TaoSetFunctionGradient()

124:     Output Parameters:
125: .   G - vector containing the newly evaluated gradient
126: .   f - function value

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

142:   /* Get pointers to vector data */
143:   VecGetArrayRead(X, &x);
144:   VecGetArrayWrite(G, &g);

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

165:   /* Restore vectors */
166:   VecRestoreArrayRead(X, &x);
167:   VecRestoreArrayWrite(G, &g);
168:   *f = ff;

170:   PetscLogFlops(15.0 * nn);
171:   return 0;
172: }

174: /* ------------------------------------------------------------------- */
175: /*
176:    FormHessian - Evaluates Hessian matrix.

178:    Input Parameters:
179: .  tao   - the Tao context
180: .  x     - input vector
181: .  ptr   - optional user-defined context, as set by TaoSetHessian()

183:    Output Parameters:
184: .  H     - Hessian matrix

186:    Note:  Providing the Hessian may not be necessary.  Only some solvers
187:    require this matrix.
188: */
189: PetscErrorCode FormHessian(Tao tao, Vec X, Mat H, Mat Hpre, void *ptr)
190: {
191:   AppCtx            *user = (AppCtx *)ptr;
192:   PetscInt           i, ind[2];
193:   PetscReal          alpha = user->alpha;
194:   PetscReal          v[2][2];
195:   const PetscScalar *x;
196:   PetscBool          assembled;

199:   /* Zero existing matrix entries */
200:   MatAssembled(H, &assembled);
201:   if (assembled || user->chained) MatZeroEntries(H);

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

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

230:   /* Assemble matrix */
231:   MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY);
232:   MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY);
233:   PetscLogFlops(9.0 * user->n / 2.0);
234:   return 0;
235: }

237: /*TEST

239:    build:
240:       requires: !complex

242:    test:
243:       args: -tao_type bqnls -tao_monitor
244:       requires: !single

246: TEST*/