Date: 2022-08-02T03:15:12+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: /*
     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:   KSP                ksp;
     38:   PC                 pc;
     39:   Mat                M;
     40:   Vec                in, out, out2;
     41:   PetscReal          mult_solve_dist;

     43:   /* Initialize TAO and PETSc */
     44:   PetscInitialize(&argc,&argv,(char*)0,help);
     45:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

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

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

     60:   /* The TAO code begins here */

     62:   /* Create TAO solver with desired solution method */
     63:   TaoCreate(PETSC_COMM_SELF,&tao);
     64:   TaoSetType(tao,TAOLMVM);

     66:   /* Set solution vec and an initial guess */
     67:   VecSet(x, zero);
     68:   TaoSetSolution(tao,x);

     70:   /* Set routines for function, gradient, hessian evaluation */
     71:   TaoSetObjectiveAndGradient(tao,NULL,FormFunctionGradient,&user);
     72:   TaoSetHessian(tao,H,H,FormHessian,&user);

     74:   /* Test the LMVM matrix */
     75:   if (test_lmvm) {
     76:     PetscOptionsSetValue(NULL, "-tao_type", "bqnktr");
     77:   }

     79:   /* Check for TAO command line options */
     80:   TaoSetFromOptions(tao);

     82:   /* SOLVE THE APPLICATION */
     83:   TaoSolve(tao);

     85:   /* Test the LMVM matrix */
     86:   if (test_lmvm) {
     87:     TaoGetKSP(tao, &ksp);
     88:     KSPGetPC(ksp, &pc);
     89:     PCLMVMGetMatLMVM(pc, &M);
     90:     VecDuplicate(x, &in);
     91:     VecDuplicate(x, &out);
     92:     VecDuplicate(x, &out2);
     93:     VecSet(in, 1.0);
     94:     MatMult(M, in, out);
     95:     MatSolve(M, out, out2);
     96:     VecAXPY(out2, -1.0, in);
     97:     VecNorm(out2, NORM_2, &mult_solve_dist);
     98:     if (mult_solve_dist < 1.e-11) {
     99:       PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-11\n");
    100:     } else if (mult_solve_dist < 1.e-6) {
    101:       PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-6\n");
    102:     } else {
    103:       PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: %e\n", (double)mult_solve_dist);
    104:     }
    105:     VecDestroy(&in);
    106:     VecDestroy(&out);
    107:     VecDestroy(&out2);
    108:   }

    110:   TaoDestroy(&tao);
    111:   VecDestroy(&x);
    112:   MatDestroy(&H);

    114:   PetscFinalize();
    115:   return 0;
    116: }

    118: /* -------------------------------------------------------------------- */
    119: /*
    120:     FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).

    122:     Input Parameters:
    123: .   tao  - the Tao context
    124: .   X    - input vector
    125: .   ptr  - optional user-defined context, as set by TaoSetFunctionGradient()

    127:     Output Parameters:
    128: .   G - vector containing the newly evaluated gradient
    129: .   f - function value

    131:     Note:
    132:     Some optimization methods ask for the function and the gradient evaluation
    133:     at the same time.  Evaluating both at once may be more efficient that
    134:     evaluating each separately.
    135: */
    136: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
    137: {
    138:   AppCtx            *user = (AppCtx *) ptr;
    139:   PetscInt          i,nn=user->n/2;
    140:   PetscReal         ff=0,t1,t2,alpha=user->alpha;
    141:   PetscScalar       *g;
    142:   const PetscScalar *x;

    145:   /* Get pointers to vector data */
    146:   VecGetArrayRead(X,&x);
    147:   VecGetArray(G,&g);

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

    167:   /* Restore vectors */
    168:   VecRestoreArrayRead(X,&x);
    169:   VecRestoreArray(G,&g);
    170:   *f   = ff;

    172:   PetscLogFlops(15.0*nn);
    173:   return 0;
    174: }

    176: /* ------------------------------------------------------------------- */
    177: /*
    178:    FormHessian - Evaluates Hessian matrix.

    180:    Input Parameters:
    181: .  tao   - the Tao context
    182: .  x     - input vector
    183: .  ptr   - optional user-defined context, as set by TaoSetHessian()

    185:    Output Parameters:
    186: .  H     - Hessian matrix

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

    201:   /* Zero existing matrix entries */
    202:   MatAssembled(H,&assembled);
    203:   if (assembled) MatZeroEntries(H);

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

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

    231:   /* Assemble matrix */
    232:   MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
    233:   MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
    234:   PetscLogFlops(9.0*user->n/2.0);
    235:   return 0;
    236: }

    238: /*TEST

    240:    build:
    241:       requires: !complex

    243:    test:
    244:       args: -tao_smonitor -tao_type nls -tao_gatol 1.e-4
    245:       requires: !single

    247:    test:
    248:       suffix: 2
    249:       args: -tao_smonitor -tao_type lmvm -tao_gatol 1.e-3

    251:    test:
    252:       suffix: 3
    253:       args: -tao_smonitor -tao_type ntr -tao_gatol 1.e-4
    254:       requires: !single

    256:    test:
    257:       suffix: 4
    258:       args: -tao_smonitor -tao_type ntr -tao_mf_hessian -tao_ntr_pc_type none -tao_gatol 1.e-4

    260:    test:
    261:       suffix: 5
    262:       args: -tao_smonitor -tao_type bntr -tao_gatol 1.e-4

    264:    test:
    265:       suffix: 6
    266:       args: -tao_smonitor -tao_type bntl -tao_gatol 1.e-4

    268:    test:
    269:       suffix: 7
    270:       args: -tao_smonitor -tao_type bnls -tao_gatol 1.e-4

    272:    test:
    273:       suffix: 8
    274:       args: -tao_smonitor -tao_type bntr -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

    276:    test:
    277:       suffix: 9
    278:       args: -tao_smonitor -tao_type bntl -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

    280:    test:
    281:       suffix: 10
    282:       args: -tao_smonitor -tao_type bnls -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

    284:    test:
    285:       suffix: 11
    286:       args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbroyden

    288:    test:
    289:       suffix: 12
    290:       args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbadbroyden

    292:    test:
    293:      suffix: 13
    294:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbroyden

    296:    test:
    297:      suffix: 14
    298:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbfgs

    300:    test:
    301:      suffix: 15
    302:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmdfp

    304:    test:
    305:      suffix: 16
    306:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsr1

    308:    test:
    309:      suffix: 17
    310:      args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnls

    312:    test:
    313:      suffix: 18
    314:      args: -tao_smonitor -tao_gatol 1e-4 -tao_type blmvm

    316:    test:
    317:      suffix: 19
    318:      args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1

    320:    test:
    321:      suffix: 20
    322:      args: -tao_monitor -tao_gatol 1e-4 -tao_type blmvm -tao_ls_monitor

    324:    test:
    325:      suffix: 21
    326:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbadbroyden

    328:    test:
    329:      suffix: 22
    330:      args: -tao_max_it 1 -tao_converged_reason

    332:    test:
    333:      suffix: 23
    334:      args: -tao_max_funcs 0 -tao_converged_reason

    336:    test:
    337:      suffix: 24
    338:      args: -tao_gatol 10 -tao_converged_reason

    340:    test:
    341:      suffix: 25
    342:      args: -tao_grtol 10 -tao_converged_reason

    344:    test:
    345:      suffix: 26
    346:      args: -tao_gttol 10 -tao_converged_reason

    348:    test:
    349:      suffix: 27
    350:      args: -tao_steptol 10 -tao_converged_reason

    352:    test:
    353:      suffix: 28
    354:      args: -tao_fmin 10 -tao_converged_reason

    356: TEST*/