Date: 2022-03-31T04:48:59+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: /*T
     14:    Concepts: TAO^Solving an unconstrained minimization problem
     15:    Routines: TaoCreate();
     16:    Routines: TaoSetType(); TaoSetObjectiveAndGradient();
     17:    Routines: TaoSetHessian();
     18:    Routines: TaoSetSolution();
     19:    Routines: TaoSetFromOptions();
     20:    Routines: TaoSolve();
     21:    Routines: TaoDestroy();
     22:    Processors: 1
     23: T*/

     25: /*
     26:    User-defined application context - contains data needed by the
     27:    application-provided call-back routines that evaluate the function,
     28:    gradient, and hessian.
     29: */
     30: typedef struct {
     31:   PetscInt  n;          /* dimension */
     32:   PetscReal alpha;   /* condition parameter */
     33:   PetscBool chained;
     34: } AppCtx;

     36: /* -------------- User-defined routines ---------- */
     37: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
     38: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,void*);

     40: int main(int argc,char **argv)
     41: {
     42:   PetscReal          zero=0.0;
     43:   Vec                x;                     /* solution vector */
     44:   Mat                H;
     45:   Tao                tao;                   /* Tao solver context */
     46:   PetscBool          flg, test_lmvm = PETSC_FALSE;
     47:   PetscMPIInt        size;                  /* number of processes running */
     48:   AppCtx             user;                  /* user-defined application context */
     49:   TaoConvergedReason reason;
     50:   PetscInt           its, recycled_its=0, oneshot_its=0;

     52:   /* Initialize TAO and PETSc */
     53:   PetscInitialize(&argc,&argv,(char*)0,help);
     54:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

     57:   /* Initialize problem parameters */
     58:   user.n = 2; user.alpha = 99.0; user.chained = PETSC_FALSE;
     59:   /* Check for command line arguments to override defaults */
     60:   PetscOptionsGetInt(NULL,NULL,"-n",&user.n,&flg);
     61:   PetscOptionsGetReal(NULL,NULL,"-alpha",&user.alpha,&flg);
     62:   PetscOptionsGetBool(NULL,NULL,"-chained",&user.chained,&flg);
     63:   PetscOptionsGetBool(NULL,NULL,"-test_lmvm",&test_lmvm,&flg);

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

     69:   /* The TAO code begins here */

     71:   /* Create TAO solver with desired solution method */
     72:   TaoCreate(PETSC_COMM_SELF,&tao);
     73:   TaoSetType(tao,TAOBQNLS);

     75:   /* Set solution vec and an initial guess */
     76:   VecSet(x, zero);
     77:   TaoSetSolution(tao,x);

     79:   /* Set routines for function, gradient, hessian evaluation */
     80:   TaoSetObjectiveAndGradient(tao,NULL,FormFunctionGradient,&user);
     81:   TaoSetHessian(tao,H,H,FormHessian,&user);

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

     86:   /* Solve the problem */
     87:   TaoSetTolerances(tao, 1.e-5, 0.0, 0.0);
     88:   TaoSetMaximumIterations(tao, 5);
     89:   TaoSetRecycleHistory(tao, PETSC_TRUE);
     90:   reason = TAO_CONTINUE_ITERATING;
     91:   flg = PETSC_FALSE;
     92:   TaoGetRecycleHistory(tao, &flg);
     93:   if (flg) PetscPrintf(PETSC_COMM_SELF, "Recycle: enabled\n");
     94:   while (reason != TAO_CONVERGED_GATOL) {
     95:     TaoSolve(tao);
     96:     TaoGetConvergedReason(tao, &reason);
     97:     TaoGetIterationNumber(tao, &its);
     98:     recycled_its += its;
     99:     PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");
    100:   }

    102:   /* Disable recycling and solve again! */
    103:   TaoSetMaximumIterations(tao, 100);
    104:   TaoSetRecycleHistory(tao, PETSC_FALSE);
    105:   VecSet(x, zero);
    106:   TaoGetRecycleHistory(tao, &flg);
    107:   if (!flg) PetscPrintf(PETSC_COMM_SELF, "Recycle: disabled\n");
    108:   TaoSolve(tao);
    109:   TaoGetConvergedReason(tao, &reason);
    111:   TaoGetIterationNumber(tao, &oneshot_its);
    112:   PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");
    113:   PetscPrintf(PETSC_COMM_SELF, "recycled its: %D | oneshot its: %D\n", recycled_its, oneshot_its);

    116:   TaoDestroy(&tao);
    117:   VecDestroy(&x);
    118:   MatDestroy(&H);

    120:   PetscFinalize();
    121:   return 0;
    122: }

    124: /* -------------------------------------------------------------------- */
    125: /*
    126:     FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).

    128:     Input Parameters:
    129: .   tao  - the Tao context
    130: .   X    - input vector
    131: .   ptr  - optional user-defined context, as set by TaoSetFunctionGradient()

    133:     Output Parameters:
    134: .   G - vector containing the newly evaluated gradient
    135: .   f - function value

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

    151:   /* Get pointers to vector data */
    152:   VecGetArrayRead(X,&x);
    153:   VecGetArrayWrite(G,&g);

    155:   /* Compute G(X) */
    156:   if (user->chained) {
    157:     g[0] = 0;
    158:     for (i=0; i<user->n-1; i++) {
    159:       t1 = x[i+1] - x[i]*x[i];
    160:       ff += PetscSqr(1 - x[i]) + alpha*t1*t1;
    161:       g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]);
    162:       g[i+1] = 2*alpha*t1;
    163:     }
    164:   } else {
    165:     for (i=0; i<nn; i++) {
    166:       t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
    167:       ff += alpha*t1*t1 + t2*t2;
    168:       g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
    169:       g[2*i+1] = 2*alpha*t1;
    170:     }
    171:   }

    173:   /* Restore vectors */
    174:   VecRestoreArrayRead(X,&x);
    175:   VecRestoreArrayWrite(G,&g);
    176:   *f   = ff;

    178:   PetscLogFlops(15.0*nn);
    179:   return 0;
    180: }

    182: /* ------------------------------------------------------------------- */
    183: /*
    184:    FormHessian - Evaluates Hessian matrix.

    186:    Input Parameters:
    187: .  tao   - the Tao context
    188: .  x     - input vector
    189: .  ptr   - optional user-defined context, as set by TaoSetHessian()

    191:    Output Parameters:
    192: .  H     - Hessian matrix

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

    207:   /* Zero existing matrix entries */
    208:   MatAssembled(H,&assembled);
    209:   if (assembled || user->chained) MatZeroEntries(H);

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

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

    236:   /* Assemble matrix */
    237:   MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
    238:   MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
    239:   PetscLogFlops(9.0*user->n/2.0);
    240:   return 0;
    241: }

    243: /*TEST

    245:    build:
    246:       requires: !complex

    248:    test:
    249:       args: -tao_type bqnls -tao_monitor
    250:       requires: !single

    252: TEST*/