Date: 2022-08-02T03:15:12+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:   PetscInitialize(&argc,&argv,(char*)0,help);
     42:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

     45:   /* Initialize problem parameters */
     46:   user.n = 2; user.alpha = 99.0; user.chained = PETSC_FALSE;
     47:   /* Check for command line arguments to override defaults */
     48:   PetscOptionsGetInt(NULL,NULL,"-n",&user.n,&flg);
     49:   PetscOptionsGetReal(NULL,NULL,"-alpha",&user.alpha,&flg);
     50:   PetscOptionsGetBool(NULL,NULL,"-chained",&user.chained,&flg);
     51:   PetscOptionsGetBool(NULL,NULL,"-test_lmvm",&test_lmvm,&flg);

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

     57:   /* The TAO code begins here */

     59:   /* Create TAO solver with desired solution method */
     60:   TaoCreate(PETSC_COMM_SELF,&tao);
     61:   TaoSetType(tao,TAOBQNLS);

     63:   /* Set solution vec and an initial guess */
     64:   VecSet(x, zero);
     65:   TaoSetSolution(tao,x);

     67:   /* Set routines for function, gradient, hessian evaluation */
     68:   TaoSetObjectiveAndGradient(tao,NULL,FormFunctionGradient,&user);
     69:   TaoSetHessian(tao,H,H,FormHessian,&user);

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

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

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

    104:   TaoDestroy(&tao);
    105:   VecDestroy(&x);
    106:   MatDestroy(&H);

    108:   PetscFinalize();
    109:   return 0;
    110: }

    112: /* -------------------------------------------------------------------- */
    113: /*
    114:     FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).

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

    121:     Output Parameters:
    122: .   G - vector containing the newly evaluated gradient
    123: .   f - function value

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

    139:   /* Get pointers to vector data */
    140:   VecGetArrayRead(X,&x);
    141:   VecGetArrayWrite(G,&g);

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

    161:   /* Restore vectors */
    162:   VecRestoreArrayRead(X,&x);
    163:   VecRestoreArrayWrite(G,&g);
    164:   *f   = ff;

    166:   PetscLogFlops(15.0*nn);
    167:   return 0;
    168: }

    170: /* ------------------------------------------------------------------- */
    171: /*
    172:    FormHessian - Evaluates Hessian matrix.

    174:    Input Parameters:
    175: .  tao   - the Tao context
    176: .  x     - input vector
    177: .  ptr   - optional user-defined context, as set by TaoSetHessian()

    179:    Output Parameters:
    180: .  H     - Hessian matrix

    182:    Note:  Providing the Hessian may not be necessary.  Only some solvers
    183:    require this matrix.
    184: */
    185: PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
    186: {
    187:   AppCtx            *user = (AppCtx*)ptr;
    188:   PetscInt          i, ind[2];
    189:   PetscReal         alpha=user->alpha;
    190:   PetscReal         v[2][2];
    191:   const PetscScalar *x;
    192:   PetscBool         assembled;

    195:   /* Zero existing matrix entries */
    196:   MatAssembled(H,&assembled);
    197:   if (assembled || user->chained) MatZeroEntries(H);

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

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

    224:   /* Assemble matrix */
    225:   MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
    226:   MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
    227:   PetscLogFlops(9.0*user->n/2.0);
    228:   return 0;
    229: }

    231: /*TEST

    233:    build:
    234:       requires: !complex

    236:    test:
    237:       args: -tao_type bqnls -tao_monitor
    238:       requires: !single

    240: TEST*/