Date: 2022-03-04T17:39:50+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(); TaoSetObjectiveAndGradientRoutine();
     17:    Routines: TaoSetHessianRoutine();
     18:    Routines: TaoSetInitialVector();
     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:   PetscErrorCode     ierr;                  /* used to check for functions returning nonzeros */
     43:   PetscReal          zero=0.0;
     44:   Vec                x;                     /* solution vector */
     45:   Mat                H;
     46:   Tao                tao;                   /* Tao solver context */
     47:   PetscBool          flg, test_lmvm = PETSC_FALSE;
     48:   PetscMPIInt        size;                  /* number of processes running */
     49:   AppCtx             user;                  /* user-defined application context */
     50:   TaoConvergedReason reason;
     51:   PetscInt           its, recycled_its=0, oneshot_its=0;

     53:   /* Initialize TAO and PETSc */
     54:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     55:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     56:   if (size >1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"Incorrect number of processors");

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

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

     70:   /* The TAO code begins here */

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

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

     80:   /* Set routines for function, gradient, hessian evaluation */
     81:   TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);
     82:   TaoSetHessianRoutine(tao,H,H,FormHessian,&user);

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

     87:   /* Solve the problem */
     88:   TaoSetTolerances(tao, 1.e-5, 0.0, 0.0);
     89:   TaoSetMaximumIterations(tao, 5);
     90:   TaoSetRecycleHistory(tao, PETSC_TRUE);
     91:   reason = TAO_CONTINUE_ITERATING;
     92:   flg = PETSC_FALSE;
     93:   TaoGetRecycleHistory(tao, &flg);
     94:   if (flg) {PetscPrintf(PETSC_COMM_SELF, "Recycle: enabled\n");}
     95:   while (reason != TAO_CONVERGED_GATOL) {
     96:     TaoSolve(tao);
     97:     TaoGetConvergedReason(tao, &reason);
     98:     TaoGetIterationNumber(tao, &its);
     99:     recycled_its += its;
    100:     PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");
    101:   }

    103:   /* Disable recycling and solve again! */
    104:   TaoSetMaximumIterations(tao, 100);
    105:   TaoSetRecycleHistory(tao, PETSC_FALSE);
    106:   VecSet(x, zero);
    107:   TaoGetRecycleHistory(tao, &flg);
    108:   if (!flg) {PetscPrintf(PETSC_COMM_SELF, "Recycle: disabled\n");}
    109:   TaoSolve(tao);
    110:   TaoGetConvergedReason(tao, &reason);
    111:   if (reason != TAO_CONVERGED_GATOL) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "Solution failed to converge!");
    112:   TaoGetIterationNumber(tao, &oneshot_its);
    113:   PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");
    114:   PetscPrintf(PETSC_COMM_SELF, "recycled its: %D | oneshot its: %D\n", recycled_its, oneshot_its);
    115:   if (recycled_its != oneshot_its) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "Recycled solution does not match oneshot solution!");

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

    121:   PetscFinalize();
    122:   return ierr;
    123: }

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

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

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

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

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

    157:   /* Compute G(X) */
    158:   if (user->chained) {
    159:     g[0] = 0;
    160:     for (i=0; i<user->n-1; i++) {
    161:       t1 = x[i+1] - x[i]*x[i];
    162:       ff += PetscSqr(1 - x[i]) + alpha*t1*t1;
    163:       g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]);
    164:       g[i+1] = 2*alpha*t1;
    165:     }
    166:   } else {
    167:     for (i=0; i<nn; i++) {
    168:       t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
    169:       ff += alpha*t1*t1 + t2*t2;
    170:       g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
    171:       g[2*i+1] = 2*alpha*t1;
    172:     }
    173:   }

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

    180:   PetscLogFlops(15.0*nn);
    181:   return(0);
    182: }

    184: /* ------------------------------------------------------------------- */
    185: /*
    186:    FormHessian - Evaluates Hessian matrix.

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

    193:    Output Parameters:
    194: .  H     - Hessian matrix

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

    210:   /* Zero existing matrix entries */
    211:   MatAssembled(H,&assembled);
    212:   if (assembled || user->chained) {MatZeroEntries(H);}

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

    217:   /* Compute H(X) entries */
    218:   if (user->chained) {
    219:     for (i=0; i<user->n-1; i++) {
    220:       PetscScalar t1 = x[i+1] - x[i]*x[i];
    221:       v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]);
    222:       v[0][1] = 2*alpha*(-2*x[i]);
    223:       v[1][0] = 2*alpha*(-2*x[i]);
    224:       v[1][1] = 2*alpha*t1;
    225:       ind[0] = i; ind[1] = i+1;
    226:       MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);
    227:     }
    228:   } else {
    229:     for (i=0; i<user->n/2; i++) {
    230:       v[1][1] = 2*alpha;
    231:       v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
    232:       v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
    233:       ind[0]=2*i; ind[1]=2*i+1;
    234:       MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
    235:     }
    236:   }
    237:   VecRestoreArrayRead(X,&x);

    239:   /* Assemble matrix */
    240:   MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
    241:   MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
    242:   PetscLogFlops(9.0*user->n/2.0);
    243:   return(0);
    244: }

    246: /*TEST

    248:    build:
    249:       requires: !complex

    251:    test:
    252:       args: -tao_type bqnls -tao_monitor
    253:       requires: !single

    255: TEST*/