Actual source code: rosenbrock1.c

      1: /* Program usage: mpiexec -n 1 rosenbrock1 [-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*/

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

     39: /* -------------- User-defined routines ---------- */
     40: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
     41: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,void*);

     43: int main(int argc,char **argv)
     44: {
     45:   PetscErrorCode     ierr;                  /* used to check for functions returning nonzeros */
     46:   PetscReal          zero=0.0;
     47:   Vec                x;                     /* solution vector */
     48:   Mat                H;
     49:   Tao                tao;                   /* Tao solver context */
     50:   PetscBool          flg, test_lmvm = PETSC_FALSE;
     51:   PetscMPIInt        size;                  /* number of processes running */
     52:   AppCtx             user;                  /* user-defined application context */
     53:   KSP                ksp;
     54:   PC                 pc;
     55:   Mat                M;
     56:   Vec                in, out, out2;
     57:   PetscReal          mult_solve_dist;

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

     64:   /* Initialize problem parameters */
     65:   user.n = 2; user.alpha = 99.0; user.chained = PETSC_FALSE;
     66:   /* Check for command line arguments to override defaults */
     67:   PetscOptionsGetInt(NULL,NULL,"-n",&user.n,&flg);
     68:   PetscOptionsGetReal(NULL,NULL,"-alpha",&user.alpha,&flg);
     69:   PetscOptionsGetBool(NULL,NULL,"-chained",&user.chained,&flg);
     70:   PetscOptionsGetBool(NULL,NULL,"-test_lmvm",&test_lmvm,&flg);

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

     76:   /* The TAO code begins here */

     78:   /* Create TAO solver with desired solution method */
     79:   TaoCreate(PETSC_COMM_SELF,&tao);
     80:   TaoSetType(tao,TAOLMVM);

     82:   /* Set solution vec and an initial guess */
     83:   VecSet(x, zero);
     84:   TaoSetInitialVector(tao,x);

     86:   /* Set routines for function, gradient, hessian evaluation */
     87:   TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);
     88:   TaoSetHessianRoutine(tao,H,H,FormHessian,&user);

     90:   /* Test the LMVM matrix */
     91:   if (test_lmvm) {
     92:     PetscOptionsSetValue(NULL, "-tao_type", "bqnktr");
     93:   }

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

     98:   /* SOLVE THE APPLICATION */
     99:   TaoSolve(tao);

    101:   /* Test the LMVM matrix */
    102:   if (test_lmvm) {
    103:     TaoGetKSP(tao, &ksp);
    104:     KSPGetPC(ksp, &pc);
    105:     PCLMVMGetMatLMVM(pc, &M);
    106:     VecDuplicate(x, &in);
    107:     VecDuplicate(x, &out);
    108:     VecDuplicate(x, &out2);
    109:     VecSet(in, 1.0);
    110:     MatMult(M, in, out);
    111:     MatSolve(M, out, out2);
    112:     VecAXPY(out2, -1.0, in);
    113:     VecNorm(out2, NORM_2, &mult_solve_dist);
    114:     if (mult_solve_dist < 1.e-11) {
    115:       PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-11\n");
    116:     } else if (mult_solve_dist < 1.e-6) {
    117:       PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-6\n");
    118:     } else {
    119:       PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: %e\n", (double)mult_solve_dist);
    120:     }
    121:     VecDestroy(&in);
    122:     VecDestroy(&out);
    123:     VecDestroy(&out2);
    124:   }

    126:   TaoDestroy(&tao);
    127:   VecDestroy(&x);
    128:   MatDestroy(&H);

    130:   PetscFinalize();
    131:   return ierr;
    132: }

    134: /* -------------------------------------------------------------------- */
    135: /*
    136:     FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).

    138:     Input Parameters:
    139: .   tao  - the Tao context
    140: .   X    - input vector
    141: .   ptr  - optional user-defined context, as set by TaoSetFunctionGradient()

    143:     Output Parameters:
    144: .   G - vector containing the newly evaluated gradient
    145: .   f - function value

    147:     Note:
    148:     Some optimization methods ask for the function and the gradient evaluation
    149:     at the same time.  Evaluating both at once may be more efficient that
    150:     evaluating each separately.
    151: */
    152: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
    153: {
    154:   AppCtx            *user = (AppCtx *) ptr;
    155:   PetscInt          i,nn=user->n/2;
    156:   PetscErrorCode    ierr;
    157:   PetscReal         ff=0,t1,t2,alpha=user->alpha;
    158:   PetscScalar       *g;
    159:   const PetscScalar *x;

    162:   /* Get pointers to vector data */
    163:   VecGetArrayRead(X,&x);
    164:   VecGetArray(G,&g);

    166:   /* Compute G(X) */
    167:   if (user->chained) {
    168:     g[0] = 0;
    169:     for (i=0; i<user->n-1; i++) {
    170:       t1 = x[i+1] - x[i]*x[i];
    171:       ff += PetscSqr(1 - x[i]) + alpha*t1*t1;
    172:       g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]);
    173:       g[i+1] = 2*alpha*t1;
    174:     }
    175:   } else {
    176:     for (i=0; i<nn; i++){
    177:       t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
    178:       ff += alpha*t1*t1 + t2*t2;
    179:       g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
    180:       g[2*i+1] = 2*alpha*t1;
    181:     }
    182:   }

    184:   /* Restore vectors */
    185:   VecRestoreArrayRead(X,&x);
    186:   VecRestoreArray(G,&g);
    187:   *f   = ff;

    189:   PetscLogFlops(15.0*nn);
    190:   return(0);
    191: }

    193: /* ------------------------------------------------------------------- */
    194: /*
    195:    FormHessian - Evaluates Hessian matrix.

    197:    Input Parameters:
    198: .  tao   - the Tao context
    199: .  x     - input vector
    200: .  ptr   - optional user-defined context, as set by TaoSetHessian()

    202:    Output Parameters:
    203: .  H     - Hessian matrix

    205:    Note:  Providing the Hessian may not be necessary.  Only some solvers
    206:    require this matrix.
    207: */
    208: PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
    209: {
    210:   AppCtx            *user = (AppCtx*)ptr;
    211:   PetscErrorCode    ierr;
    212:   PetscInt          i, ind[2];
    213:   PetscReal         alpha=user->alpha;
    214:   PetscReal         v[2][2];
    215:   const PetscScalar *x;
    216:   PetscBool         assembled;

    219:   /* Zero existing matrix entries */
    220:   MatAssembled(H,&assembled);
    221:   if (assembled){MatZeroEntries(H);}

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

    226:   /* Compute H(X) entries */
    227:   if (user->chained) {
    228:     MatZeroEntries(H);
    229:     for (i=0; i<user->n-1; i++) {
    230:       PetscScalar t1 = x[i+1] - x[i]*x[i];
    231:       v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]);
    232:       v[0][1] = 2*alpha*(-2*x[i]);
    233:       v[1][0] = 2*alpha*(-2*x[i]);
    234:       v[1][1] = 2*alpha*t1;
    235:       ind[0] = i; ind[1] = i+1;
    236:       MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);
    237:     }
    238:   } else {
    239:     for (i=0; i<user->n/2; i++){
    240:       v[1][1] = 2*alpha;
    241:       v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
    242:       v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
    243:       ind[0]=2*i; ind[1]=2*i+1;
    244:       MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
    245:     }
    246:   }
    247:   VecRestoreArrayRead(X,&x);

    249:   /* Assemble matrix */
    250:   MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
    251:   MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
    252:   PetscLogFlops(9.0*user->n/2.0);
    253:   return(0);
    254: }

    257: /*TEST

    259:    build:
    260:       requires: !complex

    262:    test:
    263:       args: -tao_smonitor -tao_type nls -tao_gatol 1.e-4
    264:       requires: !single

    266:    test:
    267:       suffix: 2
    268:       args: -tao_smonitor -tao_type lmvm -tao_gatol 1.e-3

    270:    test:
    271:       suffix: 3
    272:       args: -tao_smonitor -tao_type ntr -tao_gatol 1.e-4
    273:       requires: !single

    275:    test:
    276:       suffix: 4
    277:       args: -tao_smonitor -tao_type ntr -tao_mf_hessian -tao_ntr_pc_type none -tao_gatol 1.e-4

    279:    test:
    280:       suffix: 5
    281:       args: -tao_smonitor -tao_type bntr -tao_gatol 1.e-4

    283:    test:
    284:       suffix: 6
    285:       args: -tao_smonitor -tao_type bntl -tao_gatol 1.e-4

    287:    test:
    288:       suffix: 7
    289:       args: -tao_smonitor -tao_type bnls -tao_gatol 1.e-4

    291:    test:
    292:       suffix: 8
    293:       args: -tao_smonitor -tao_type bntr -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

    295:    test:
    296:       suffix: 9
    297:       args: -tao_smonitor -tao_type bntl -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

    299:    test:
    300:       suffix: 10
    301:       args: -tao_smonitor -tao_type bnls -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

    303:    test:
    304:       suffix: 11
    305:       args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbroyden

    307:    test:
    308:       suffix: 12
    309:       args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbadbroyden

    311:    test:
    312:      suffix: 13
    313:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbroyden

    315:    test:
    316:      suffix: 14
    317:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbfgs

    319:    test:
    320:      suffix: 15
    321:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmdfp

    323:    test:
    324:      suffix: 16
    325:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsr1

    327:    test:
    328:      suffix: 17
    329:      args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnls

    331:    test:
    332:      suffix: 18
    333:      args: -tao_smonitor -tao_gatol 1e-4 -tao_type blmvm

    335:    test:
    336:      suffix: 19
    337:      args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1

    339:    test:
    340:      suffix: 20
    341:      args: -tao_monitor -tao_gatol 1e-4 -tao_type blmvm -tao_ls_monitor

    343:    test:
    344:      suffix: 21
    345:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbadbroyden

    347:    test:
    348:      suffix: 22
    349:      args: -tao_max_it 1 -tao_converged_reason

    351:    test:
    352:      suffix: 23
    353:      args: -tao_max_funcs 0 -tao_converged_reason

    355:    test:
    356:      suffix: 24
    357:      args: -tao_gatol 10 -tao_converged_reason

    359:    test:
    360:      suffix: 25
    361:      args: -tao_grtol 10 -tao_converged_reason

    363:    test:
    364:      suffix: 26
    365:      args: -tao_gttol 10 -tao_converged_reason

    367:    test:
    368:      suffix: 27
    369:      args: -tao_steptol 10 -tao_converged_reason

    371:    test:
    372:      suffix: 28
    373:      args: -tao_fmin 10 -tao_converged_reason

    375: TEST*/