Date: 2026-07-30T21:14:29+00:00

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 */
     41:   PetscFunctionBeginUser;
     42:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
     43:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
     44:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Incorrect number of processors");

     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:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &user.n, &flg));
     52:   PetscCall(PetscOptionsGetReal(NULL, NULL, "-alpha", &user.alpha, &flg));
     53:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-chained", &user.chained, &flg));
     54:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_lmvm", &test_lmvm, &flg));

     56:   /* Allocate vectors for the solution and gradient */
     57:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, user.n, &x));
     58:   PetscCall(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:   PetscCall(TaoCreate(PETSC_COMM_SELF, &tao));
     64:   PetscCall(TaoSetType(tao, TAOBQNLS));

     66:   /* Set solution vec and an initial guess */
     67:   PetscCall(VecSet(x, zero));
     68:   PetscCall(TaoSetSolution(tao, x));

     70:   /* Set routines for function, gradient, hessian evaluation */
     71:   PetscCall(TaoSetObjectiveAndGradient(tao, NULL, FormFunctionGradient, &user));
     72:   PetscCall(TaoSetHessian(tao, H, H, FormHessian, &user));

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

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

     93:   /* Disable recycling and solve again! */
     94:   PetscCall(TaoSetMaximumIterations(tao, 100));
     95:   PetscCall(TaoSetRecycleHistory(tao, PETSC_FALSE));
     96:   PetscCall(VecSet(x, zero));
     97:   PetscCall(TaoGetRecycleHistory(tao, &flg));
     98:   if (!flg) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Recycle: disabled\n"));
     99:   PetscCall(TaoSolve(tao));
    100:   PetscCall(TaoGetConvergedReason(tao, &reason));
    101:   PetscCheck(reason == TAO_CONVERGED_GATOL, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "Solution failed to converge!");
    102:   PetscCall(TaoGetIterationNumber(tao, &oneshot_its));
    103:   PetscCall(PetscPrintf(PETSC_COMM_SELF, "-----------------------\n"));
    104:   PetscCall(PetscPrintf(PETSC_COMM_SELF, "recycled its: %" PetscInt_FMT " | oneshot its: %" PetscInt_FMT "\n", recycled_its, oneshot_its));
    105:   PetscCheck(recycled_its == oneshot_its, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "Recycled solution does not match oneshot solution!");

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

    111:   PetscCall(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;

    141:   PetscFunctionBeginUser;
    142:   /* Get pointers to vector data */
    143:   PetscCall(VecGetArrayRead(X, &x));
    144:   PetscCall(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:   PetscCall(VecRestoreArrayRead(X, &x));
    167:   PetscCall(VecRestoreArrayWrite(G, &g));
    168:   *f = ff;

    170:   PetscCall(PetscLogFlops(15.0 * nn));
    171:   PetscFunctionReturn(PETSC_SUCCESS);
    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;

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

    203:   /* Get a pointer to vector data */
    204:   PetscCall(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:       PetscCall(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:       PetscCall(MatSetValues(H, 2, ind, 2, ind, v[0], INSERT_VALUES));
    226:     }
    227:   }
    228:   PetscCall(VecRestoreArrayRead(X, &x));

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

    237: /*TEST

    239:    build:
    240:       requires: !complex

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

    246: TEST*/