Date: 2026-03-01T05:25:17+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:   PetscFunctionBeginUser;
     45:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
     46:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
     47:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Incorrect number of processors");

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

     59:   /* Allocate vectors for the solution and gradient */
     60:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, user.n, &x));
     61:   PetscCall(MatCreateSeqBAIJ(PETSC_COMM_SELF, 2, user.n, user.n, 1, NULL, &H));

     63:   /* The TAO code begins here */

     65:   /* Create TAO solver with desired solution method */
     66:   PetscCall(TaoCreate(PETSC_COMM_SELF, &tao));
     67:   PetscCall(TaoSetType(tao, TAOLMVM));

     69:   /* Set solution vec and an initial guess */
     70:   PetscCall(VecSet(x, zero));
     71:   PetscCall(TaoSetSolution(tao, x));

     73:   /* Set routines for function, gradient, hessian evaluation */
     74:   PetscCall(TaoSetObjectiveAndGradient(tao, NULL, FormFunctionGradient, &user));
     75:   PetscCall(TaoSetHessian(tao, H, H, FormHessian, &user));

     77:   /* Test the LMVM matrix */
     78:   if (test_lmvm) PetscCall(PetscOptionsSetValue(NULL, "-tao_type", "bqnktr"));

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

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

     86:   /* Test the LMVM matrix */
     87:   if (test_lmvm) {
     88:     PetscCall(TaoGetKSP(tao, &ksp));
     89:     PetscCall(KSPGetPC(ksp, &pc));
     90:     PetscCall(PCLMVMGetMatLMVM(pc, &M));
     91:     PetscCall(VecDuplicate(x, &in));
     92:     PetscCall(VecDuplicate(x, &out));
     93:     PetscCall(VecDuplicate(x, &out2));
     94:     PetscCall(VecSet(in, 1.0));
     95:     PetscCall(MatMult(M, in, out));
     96:     PetscCall(MatSolve(M, out, out2));
     97:     PetscCall(VecAXPY(out2, -1.0, in));
     98:     PetscCall(VecNorm(out2, NORM_2, &mult_solve_dist));
     99:     if (mult_solve_dist < 1.e-11) {
    100:       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)tao), "Inverse error of LMVM MatMult and MatSolve: < 1.e-11\n"));
    101:     } else if (mult_solve_dist < 1.e-6) {
    102:       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)tao), "Inverse error of LMVM MatMult and MatSolve: < 1.e-6\n"));
    103:     } else {
    104:       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)tao), "Inverse error of LMVM MatMult and MatSolve is not small: %e\n", (double)mult_solve_dist));
    105:     }
    106:     PetscCall(VecDestroy(&in));
    107:     PetscCall(VecDestroy(&out));
    108:     PetscCall(VecDestroy(&out2));
    109:   }

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

    115:   PetscCall(PetscFinalize());
    116:   return 0;
    117: }

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

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

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

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

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

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

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

    174:   PetscCall(PetscLogFlops(15.0 * nn));
    175:   PetscFunctionReturn(PETSC_SUCCESS);
    176: }

    178: /* ------------------------------------------------------------------- */
    179: /*
    180:    FormHessian - Evaluates Hessian matrix.

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

    187:    Output Parameters:
    188: .  H     - Hessian matrix

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

    202:   PetscFunctionBeginUser;
    203:   /* Zero existing matrix entries */
    204:   PetscCall(MatAssembled(H, &assembled));
    205:   if (assembled) PetscCall(MatZeroEntries(H));

    207:   /* Get a pointer to vector data */
    208:   PetscCall(VecGetArrayRead(X, &x));

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

    235:   /* Assemble matrix */
    236:   PetscCall(MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY));
    237:   PetscCall(MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY));
    238:   PetscCall(PetscLogFlops(9.0 * user->n / 2.0));
    239:   PetscFunctionReturn(PETSC_SUCCESS);
    240: }

    242: /*TEST

    244:    build:
    245:      requires: !complex

    247:    test:
    248:      requires: !single
    249:      args: -tao_monitor_short -tao_type nls -tao_gatol 1.e-4

    251:    test:
    252:      suffix: 2
    253:      requires: !single
    254:      args: -tao_monitor_short -tao_type lmvm -tao_gatol 1.e-3

    256:    test:
    257:      suffix: 3
    258:      requires: !single
    259:      args: -tao_monitor_short -tao_type ntr -tao_gatol 1.e-4

    261:    test:
    262:      suffix: 4
    263:      requires: !single
    264:      args: -tao_monitor_short -tao_type ntr -tao_mf_hessian -tao_ntr_pc_type none -tao_gatol 1.e-4

    266:    test:
    267:      suffix: 5
    268:      requires: !single
    269:      args: -tao_monitor_short -tao_type bntr -tao_gatol 1.e-4

    271:    test:
    272:      suffix: 6
    273:      requires: !single
    274:      args: -tao_monitor_short -tao_type bntl -tao_gatol 1.e-4

    276:    test:
    277:      suffix: 7
    278:      requires: !single
    279:      args: -tao_monitor_short -tao_type bnls -tao_gatol 1.e-4

    281:    test:
    282:      suffix: 8
    283:      requires: !single
    284:      args: -tao_monitor_short -tao_type bntr -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

    286:    test:
    287:      suffix: 9
    288:      requires: !single
    289:      args: -tao_monitor_short -tao_type bntl -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

    291:    test:
    292:      suffix: 10
    293:      requires: !single
    294:      args: -tao_monitor_short -tao_type bnls -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4

    296:    test:
    297:      suffix: 11
    298:      requires: !single
    299:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbroyden

    301:    test:
    302:      suffix: 12
    303:      requires: !single
    304:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbadbroyden

    306:    test:
    307:      suffix: 13
    308:      requires: !single
    309:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbroyden -tao_bqnk_mat_lmvm_beta {{0.0 0.25 1.0}} -tao_bqnk_mat_lmvm_rho 0.75 -tao_bqnk_mat_lmvm_sigma_hist 2

    311:    test:
    312:      suffix: 14
    313:      requires: !single
    314:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbfgs -tao_bqnk_mat_lmvm_scale_type {{scalar diagonal}} -tao_bqnk_mat_lmvm_alpha {{0.0 0.25 0.5}} -tao_bqnk_mat_lmvm_theta 1.0

    316:    test:
    317:      suffix: 15
    318:      requires: !single
    319:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmdfp

    321:    test:
    322:      suffix: 16
    323:      requires: !single
    324:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsr1

    326:    test:
    327:      suffix: 17
    328:      requires: !single
    329:      args: -tao_monitor_short -tao_gatol 1e-4 -tao_type bqnls

    331:    test:
    332:      suffix: 18
    333:      requires: !single
    334:      args: -tao_monitor_short -tao_gatol 1e-4 -tao_type blmvm

    336:    test:
    337:      suffix: 19
    338:      requires: !single
    339:      args: -tao_monitor_short -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1

    341:    test:
    342:      suffix: 20
    343:      requires: !single
    344:      args: -tao_monitor -tao_gatol 1e-4 -tao_type blmvm -tao_ls_monitor

    346:    test:
    347:      suffix: 21
    348:      requires: !single
    349:      args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbadbroyden

    351:    test:
    352:      suffix: 22
    353:      requires: !single
    354:      args: -tao_max_it 1 -tao_converged_reason

    356:    test:
    357:      suffix: 23
    358:      requires: !single
    359:      args: -tao_max_funcs 0 -tao_converged_reason

    361:    test:
    362:      suffix: 24
    363:      requires: !single
    364:      args: -tao_gatol 10 -tao_converged_reason

    366:    test:
    367:      suffix: 25
    368:      requires: !single
    369:      args: -tao_grtol 10 -tao_converged_reason

    371:    test:
    372:      suffix: 26
    373:      requires: !single
    374:      args: -tao_gttol 10 -tao_converged_reason

    376:    test:
    377:      suffix: 27
    378:      requires: !single
    379:      args: -tao_steptol 10 -tao_converged_reason

    381:    test:
    382:      suffix: 28
    383:      requires: !single
    384:      args: -tao_fmin 10 -tao_converged_reason

    386:    test:
    387:      suffix: snes
    388:      requires: !single
    389:      args: -snes_monitor ::ascii_info_detail -tao_type snes -snes_type newtontr -snes_atol 1.e-4 -pc_type none -tao_mf_hessian -ksp_type cg

    391:    test:
    392:      suffix: snes_ls_armijo
    393:      requires: !single
    394:      args: -snes_monitor ::ascii_info_detail -tao_type snes -snes_type newtonls -snes_atol 1.e-4 -pc_type none -tao_mf_hessian -snes_linesearch_monitor -snes_linesearch_order 1

    396:    test:
    397:      suffix: snes_tr_cgnegcurve_kmdc
    398:      requires: !single
    399:      args: -snes_monitor ::ascii_info_detail -tao_type snes -snes_type newtontr -snes_atol 1.e-4 -pc_type none -ksp_type cg -snes_tr_kmdc 0.9 -ksp_converged_neg_curve -ksp_converged_reason

    401:    test:
    402:      suffix: snes_ls_lmvm
    403:      requires: !single
    404:      args: -snes_monitor ::ascii_info_detail -tao_type snes -snes_type newtonls -snes_atol 1.e-4 -pc_type lmvm -tao_mf_hessian

    406: TEST*/