Date: 2022-03-04T17:39:50+00:00

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*/

     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:   KSP                ksp;
     51:   PC                 pc;
     52:   Mat                M;
     53:   Vec                in, out, out2;
     54:   PetscReal          mult_solve_dist;

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

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

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

     73:   /* The TAO code begins here */

     75:   /* Create TAO solver with desired solution method */
     76:   TaoCreate(PETSC_COMM_SELF,&tao);
     77:   TaoSetType(tao,TAOLMVM);

     79:   /* Set solution vec and an initial guess */
     80:   VecSet(x, zero);
     81:   TaoSetInitialVector(tao,x);

     83:   /* Set routines for function, gradient, hessian evaluation */
     84:   TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);
     85:   TaoSetHessianRoutine(tao,H,H,FormHessian,&user);

     87:   /* Test the LMVM matrix */
     88:   if (test_lmvm) {
     89:     PetscOptionsSetValue(NULL, "-tao_type", "bqnktr");
     90:   }

     92:   /* Check for TAO command line options */
     93:   TaoSetFromOptions(tao);

     95:   /* SOLVE THE APPLICATION */
     96:   TaoSolve(tao);

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

    123:   TaoDestroy(&tao);
    124:   VecDestroy(&x);
    125:   MatDestroy(&H);

    127:   PetscFinalize();
    128:   return ierr;
    129: }

    131: /* -------------------------------------------------------------------- */
    132: /*
    133:     FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).

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

    140:     Output Parameters:
    141: .   G - vector containing the newly evaluated gradient
    142: .   f - function value

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

    159:   /* Get pointers to vector data */
    160:   VecGetArrayRead(X,&x);
    161:   VecGetArray(G,&g);

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

    181:   /* Restore vectors */
    182:   VecRestoreArrayRead(X,&x);
    183:   VecRestoreArray(G,&g);
    184:   *f   = ff;

    186:   PetscLogFlops(15.0*nn);
    187:   return(0);
    188: }

    190: /* ------------------------------------------------------------------- */
    191: /*
    192:    FormHessian - Evaluates Hessian matrix.

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

    199:    Output Parameters:
    200: .  H     - Hessian matrix

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

    216:   /* Zero existing matrix entries */
    217:   MatAssembled(H,&assembled);
    218:   if (assembled) {MatZeroEntries(H);}

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

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

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

    253: /*TEST

    255:    build:
    256:       requires: !complex

    258:    test:
    259:       args: -tao_smonitor -tao_type nls -tao_gatol 1.e-4
    260:       requires: !single

    262:    test:
    263:       suffix: 2
    264:       args: -tao_smonitor -tao_type lmvm -tao_gatol 1.e-3

    266:    test:
    267:       suffix: 3
    268:       args: -tao_smonitor -tao_type ntr -tao_gatol 1.e-4
    269:       requires: !single

    271:    test:
    272:       suffix: 4
    273:       args: -tao_smonitor -tao_type ntr -tao_mf_hessian -tao_ntr_pc_type none -tao_gatol 1.e-4

    275:    test:
    276:       suffix: 5
    277:       args: -tao_smonitor -tao_type bntr -tao_gatol 1.e-4

    279:    test:
    280:       suffix: 6
    281:       args: -tao_smonitor -tao_type bntl -tao_gatol 1.e-4

    283:    test:
    284:       suffix: 7
    285:       args: -tao_smonitor -tao_type bnls -tao_gatol 1.e-4

    287:    test:
    288:       suffix: 8
    289:       args: -tao_smonitor -tao_type bntr -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

    291:    test:
    292:       suffix: 9
    293:       args: -tao_smonitor -tao_type bntl -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

    295:    test:
    296:       suffix: 10
    297:       args: -tao_smonitor -tao_type bnls -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

    299:    test:
    300:       suffix: 11
    301:       args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbroyden

    303:    test:
    304:       suffix: 12
    305:       args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbadbroyden

    307:    test:
    308:      suffix: 13
    309:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbroyden

    311:    test:
    312:      suffix: 14
    313:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbfgs

    315:    test:
    316:      suffix: 15
    317:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmdfp

    319:    test:
    320:      suffix: 16
    321:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsr1

    323:    test:
    324:      suffix: 17
    325:      args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnls

    327:    test:
    328:      suffix: 18
    329:      args: -tao_smonitor -tao_gatol 1e-4 -tao_type blmvm

    331:    test:
    332:      suffix: 19
    333:      args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1

    335:    test:
    336:      suffix: 20
    337:      args: -tao_monitor -tao_gatol 1e-4 -tao_type blmvm -tao_ls_monitor

    339:    test:
    340:      suffix: 21
    341:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbadbroyden

    343:    test:
    344:      suffix: 22
    345:      args: -tao_max_it 1 -tao_converged_reason

    347:    test:
    348:      suffix: 23
    349:      args: -tao_max_funcs 0 -tao_converged_reason

    351:    test:
    352:      suffix: 24
    353:      args: -tao_gatol 10 -tao_converged_reason

    355:    test:
    356:      suffix: 25
    357:      args: -tao_grtol 10 -tao_converged_reason

    359:    test:
    360:      suffix: 26
    361:      args: -tao_gttol 10 -tao_converged_reason

    363:    test:
    364:      suffix: 27
    365:      args: -tao_steptol 10 -tao_converged_reason

    367:    test:
    368:      suffix: 28
    369:      args: -tao_fmin 10 -tao_converged_reason

    371: TEST*/