Date: 2026-03-01T05:25:16+00:00

Actual source code: ex1.c

      1: /* Program usage: mpiexec -n 2 ./ex1 [-help] [all TAO options] */

      3: /* ----------------------------------------------------------------------
      4: min f(x) = (x0 - 2)^2 + (x1 - 2)^2 - 2*(x0 + x1)
      5: s.t.  x0^2 + x1 - 2 = 0
      6:       0  <= x0^2 - x1 <= 1
      7:       -1 <= x0, x1 <= 2
      8: -->
      9:       g(x)  = 0
     10:       h(x) >= 0
     11:       -1 <= x0, x1 <= 2
     12: where
     13:       g(x) = x0^2 + x1 - 2
     14:       h(x) = [x0^2 - x1
     15:               1 -(x0^2 - x1)]
     16: ---------------------------------------------------------------------- */

     18: #include <petsctao.h>

     20: static char help[] = "Solves constrained optimization problem using pdipm.\n\
     21: Input parameters include:\n\
     22:   -tao_type pdipm    : sets Tao solver\n\
     23:   -no_eq             : removes the equaility constraints from the problem\n\
     24:   -no_bound          : removes the bound constraints from the problem\n\
     25:   -init_view         : view initial object setup\n\
     26:   -snes_fd           : snes with finite difference Jacobian (needed for pdipm)\n\
     27:   -snes_compare_explicit : compare user Jacobian with finite difference Jacobian \n\
     28:   -tao_monitor_constraint_norm : convergence monitor with constraint norm \n\
     29:   -tao_monitor_solution : view exact solution at each iteration\n\
     30:   Note: external package MUMPS is required to run pdipm in parallel. This is designed for a maximum of 2 processors, the code will error if size > 2.\n";

     32: /*
     33:    User-defined application context - contains data needed by the application
     34: */
     35: typedef struct {
     36:   PetscInt   n;  /* Global length of x */
     37:   PetscInt   ne; /* Global number of equality constraints */
     38:   PetscInt   ni; /* Global number of inequality constraints */
     39:   PetscBool  noeqflag, noboundflag, initview;
     40:   Vec        x, xl, xu;
     41:   Vec        ce, ci, bl, bu, Xseq;
     42:   Mat        Ae, Ai, H;
     43:   VecScatter scat;
     44: } AppCtx;

     46: /* -------- User-defined Routines --------- */
     47: PetscErrorCode InitializeProblem(AppCtx *);
     48: PetscErrorCode DestroyProblem(AppCtx *);
     49: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal *, Vec, void *);
     50: PetscErrorCode FormPDIPMHessian(Tao, Vec, Mat, Mat, void *);
     51: PetscErrorCode FormInequalityConstraints(Tao, Vec, Vec, void *);
     52: PetscErrorCode FormEqualityConstraints(Tao, Vec, Vec, void *);
     53: PetscErrorCode FormInequalityJacobian(Tao, Vec, Mat, Mat, void *);
     54: PetscErrorCode FormEqualityJacobian(Tao, Vec, Mat, Mat, void *);

     56: int main(int argc, char **argv)
     57: {
     58:   Tao         tao;
     59:   KSP         ksp;
     60:   PC          pc;
     61:   AppCtx      user; /* application context */
     62:   Vec         x, G, CI, CE;
     63:   PetscMPIInt size;
     64:   PetscReal   f;
     65:   PetscBool   pdipm;

     67:   PetscFunctionBeginUser;
     68:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
     69:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
     70:   PetscCheck(size <= 2, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "More than 2 processes detected. Example written to use at most 2 processes.");

     72:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "---- Constrained Problem -----\n"));
     73:   PetscCall(InitializeProblem(&user)); /* sets up problem, function below */

     75:   PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
     76:   PetscCall(TaoSetType(tao, TAOALMM));
     77:   PetscCall(TaoSetSolution(tao, user.x));
     78:   if (!user.noboundflag) PetscCall(TaoSetVariableBounds(tao, user.xl, user.xu));
     79:   PetscCall(TaoSetObjectiveAndGradient(tao, NULL, FormFunctionGradient, (void *)&user));
     80:   PetscCall(TaoSetTolerances(tao, 1.e-4, 0.0, 0.0));
     81:   PetscCall(TaoSetConstraintTolerances(tao, 1.e-4, 0.0));
     82:   PetscCall(TaoSetMaximumFunctionEvaluations(tao, 1e6));
     83:   PetscCall(TaoSetFromOptions(tao));

     85:   if (!user.noeqflag) {
     86:     PetscCall(TaoSetEqualityConstraintsRoutine(tao, user.ce, FormEqualityConstraints, (void *)&user));
     87:     PetscCall(TaoSetJacobianEqualityRoutine(tao, user.Ae, user.Ae, FormEqualityJacobian, (void *)&user));
     88:   }
     89:   PetscCall(TaoSetInequalityConstraintsRoutine(tao, user.ci, FormInequalityConstraints, (void *)&user));
     90:   PetscCall(TaoSetJacobianInequalityRoutine(tao, user.Ai, user.Ai, FormInequalityJacobian, (void *)&user));

     92:   PetscCall(PetscObjectTypeCompare((PetscObject)tao, TAOPDIPM, &pdipm));
     93:   if (pdipm) {
     94:     /*
     95:       PDIPM produces an indefinite KKT matrix with some zeros along the diagonal
     96:       Inverting this indefinite matrix requires PETSc to be configured with MUMPS
     97:     */
     98:     PetscCheck(PetscDefined(HAVE_MUMPS), PetscObjectComm((PetscObject)tao), PETSC_ERR_SUP, "TAOPDIPM requires PETSc to be configured with MUMPS (--download-mumps)");
     99:     PetscCall(TaoGetKSP(tao, &ksp));
    100:     PetscCall(KSPGetPC(ksp, &pc));
    101:     PetscCall(PCFactorSetMatSolverType(pc, MATSOLVERMUMPS));
    102:     PetscCall(KSPSetType(ksp, KSPPREONLY));
    103:     PetscCall(PCSetType(pc, PCCHOLESKY));
    104:     PetscCall(KSPSetFromOptions(ksp));
    105:     PetscCall(TaoSetHessian(tao, user.H, user.H, FormPDIPMHessian, (void *)&user));
    106:   }

    108:   /* Print out an initial view of the problem */
    109:   if (user.initview) {
    110:     PetscCall(TaoSetUp(tao));
    111:     PetscCall(VecDuplicate(user.x, &G));
    112:     PetscCall(FormFunctionGradient(tao, user.x, &f, G, (void *)&user));
    113:     if (pdipm) PetscCall(FormPDIPMHessian(tao, user.x, user.H, user.H, (void *)&user));
    114:     PetscCall(PetscViewerASCIIPushTab(PETSC_VIEWER_STDOUT_WORLD));
    115:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\nInitial point X:\n"));
    116:     PetscCall(VecView(user.x, PETSC_VIEWER_STDOUT_WORLD));
    117:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\nInitial objective f(x) = %g\n", (double)f));
    118:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\nInitial gradient and Hessian:\n"));
    119:     PetscCall(VecView(G, PETSC_VIEWER_STDOUT_WORLD));
    120:     if (pdipm) PetscCall(MatView(user.H, PETSC_VIEWER_STDOUT_WORLD));
    121:     PetscCall(VecDestroy(&G));
    122:     PetscCall(FormInequalityJacobian(tao, user.x, user.Ai, user.Ai, (void *)&user));
    123:     PetscCall(MatCreateVecs(user.Ai, NULL, &CI));
    124:     PetscCall(FormInequalityConstraints(tao, user.x, CI, (void *)&user));
    125:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\nInitial inequality constraints and Jacobian:\n"));
    126:     PetscCall(VecView(CI, PETSC_VIEWER_STDOUT_WORLD));
    127:     PetscCall(MatView(user.Ai, PETSC_VIEWER_STDOUT_WORLD));
    128:     PetscCall(VecDestroy(&CI));
    129:     if (!user.noeqflag) {
    130:       PetscCall(FormEqualityJacobian(tao, user.x, user.Ae, user.Ae, (void *)&user));
    131:       PetscCall(MatCreateVecs(user.Ae, NULL, &CE));
    132:       PetscCall(FormEqualityConstraints(tao, user.x, CE, (void *)&user));
    133:       PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\nInitial equality constraints and Jacobian:\n"));
    134:       PetscCall(VecView(CE, PETSC_VIEWER_STDOUT_WORLD));
    135:       PetscCall(MatView(user.Ae, PETSC_VIEWER_STDOUT_WORLD));
    136:       PetscCall(VecDestroy(&CE));
    137:     }
    138:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n"));
    139:     PetscCall(PetscViewerASCIIPopTab(PETSC_VIEWER_STDOUT_WORLD));
    140:   }

    142:   PetscCall(TaoSolve(tao));
    143:   PetscCall(TaoGetSolution(tao, &x));
    144:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Found solution:\n"));
    145:   PetscCall(VecView(x, PETSC_VIEWER_STDOUT_WORLD));

    147:   /* Free objects */
    148:   PetscCall(DestroyProblem(&user));
    149:   PetscCall(TaoDestroy(&tao));
    150:   PetscCall(PetscFinalize());
    151:   return PETSC_SUCCESS;
    152: }

    154: PetscErrorCode InitializeProblem(AppCtx *user)
    155: {
    156:   PetscMPIInt size;
    157:   PetscMPIInt rank;
    158:   PetscInt    nloc, neloc, niloc;

    160:   PetscFunctionBegin;
    161:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
    162:   PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
    163:   user->noeqflag    = PETSC_FALSE;
    164:   user->noboundflag = PETSC_FALSE;
    165:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-no_eq", &user->noeqflag, NULL));
    166:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-no_bound", &user->noboundflag, NULL));
    167:   user->initview = PETSC_FALSE;
    168:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-init_view", &user->initview, NULL));

    170:   /* Tell user the correct solution, not an error checking */
    171:   if (!user->noeqflag) {
    172:     /* With equality constraint, bound or no bound makes no different to the solution */
    173:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Expected solution: f(1, 1) = -2\n"));
    174:   } else {
    175:     if (user->noboundflag) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Expected solution (-no_eq, -no_bound): f(2.05655, 3.22938) = -9.05728\n"));
    176:     else PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Expected solution (-no_eq): f(1.73205, 2) = -7.3923\n"));
    177:   }

    179:   /* create vector x and set initial values */
    180:   user->n = 2; /* global length */
    181:   nloc    = (size == 1) ? user->n : 1;
    182:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->x));
    183:   PetscCall(VecSetSizes(user->x, nloc, user->n));
    184:   PetscCall(VecSetFromOptions(user->x));
    185:   PetscCall(VecSet(user->x, 0.0));

    187:   /* create and set lower and upper bound vectors */
    188:   PetscCall(VecDuplicate(user->x, &user->xl));
    189:   PetscCall(VecDuplicate(user->x, &user->xu));
    190:   PetscCall(VecSet(user->xl, -1.0));
    191:   PetscCall(VecSet(user->xu, 2.0));

    193:   /* create scater to zero */
    194:   PetscCall(VecScatterCreateToZero(user->x, &user->scat, &user->Xseq));

    196:   user->ne = 1;
    197:   user->ni = 2;
    198:   neloc    = (rank == 0) ? user->ne : 0;
    199:   niloc    = (size == 1) ? user->ni : 1;

    201:   if (!user->noeqflag) {
    202:     PetscCall(VecCreate(PETSC_COMM_WORLD, &user->ce)); /* a 1x1 vec for equality constraints */
    203:     PetscCall(VecSetSizes(user->ce, neloc, user->ne));
    204:     PetscCall(VecSetFromOptions(user->ce));
    205:     PetscCall(VecSetUp(user->ce));
    206:   }

    208:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->ci)); /* a 2x1 vec for inequality constraints */
    209:   PetscCall(VecSetSizes(user->ci, niloc, user->ni));
    210:   PetscCall(VecSetFromOptions(user->ci));
    211:   PetscCall(VecSetUp(user->ci));

    213:   /* nexn & nixn matrices for equally and inequalty constraints */
    214:   if (!user->noeqflag) {
    215:     PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Ae));
    216:     PetscCall(MatSetSizes(user->Ae, neloc, nloc, user->ne, user->n));
    217:     PetscCall(MatSetFromOptions(user->Ae));
    218:     PetscCall(MatSetUp(user->Ae));
    219:   }

    221:   PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Ai));
    222:   PetscCall(MatSetSizes(user->Ai, niloc, nloc, user->ni, user->n));
    223:   PetscCall(MatSetFromOptions(user->Ai));
    224:   PetscCall(MatSetUp(user->Ai));

    226:   PetscCall(MatCreate(PETSC_COMM_WORLD, &user->H));
    227:   PetscCall(MatSetSizes(user->H, nloc, nloc, user->n, user->n));
    228:   PetscCall(MatSetFromOptions(user->H));
    229:   PetscCall(MatSetUp(user->H));
    230:   PetscFunctionReturn(PETSC_SUCCESS);
    231: }

    233: PetscErrorCode DestroyProblem(AppCtx *user)
    234: {
    235:   PetscFunctionBegin;
    236:   if (!user->noeqflag) PetscCall(MatDestroy(&user->Ae));
    237:   PetscCall(MatDestroy(&user->Ai));
    238:   PetscCall(MatDestroy(&user->H));

    240:   PetscCall(VecDestroy(&user->x));
    241:   if (!user->noeqflag) PetscCall(VecDestroy(&user->ce));
    242:   PetscCall(VecDestroy(&user->ci));
    243:   PetscCall(VecDestroy(&user->xl));
    244:   PetscCall(VecDestroy(&user->xu));
    245:   PetscCall(VecDestroy(&user->Xseq));
    246:   PetscCall(VecScatterDestroy(&user->scat));
    247:   PetscFunctionReturn(PETSC_SUCCESS);
    248: }

    250: /* Evaluate
    251:    f(x) = (x0 - 2)^2 + (x1 - 2)^2 - 2*(x0 + x1)
    252:    G = grad f = [2*(x0 - 2) - 2, 2*(x1 - 2) - 2] = 2*X - 6
    253: */
    254: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ctx)
    255: {
    256:   const PetscScalar *x;
    257:   MPI_Comm           comm;
    258:   PetscMPIInt        rank;
    259:   PetscReal          fin;
    260:   AppCtx            *user = (AppCtx *)ctx;
    261:   Vec                Xseq = user->Xseq;
    262:   VecScatter         scat = user->scat;

    264:   PetscFunctionBegin;
    265:   /* f = (x0 - 2)^2 + (x1 - 2)^2 - 2*(x0 + x1) */
    266:   PetscCall(PetscObjectGetComm((PetscObject)tao, &comm));
    267:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    269:   PetscCall(VecScatterBegin(scat, X, Xseq, INSERT_VALUES, SCATTER_FORWARD));
    270:   PetscCall(VecScatterEnd(scat, X, Xseq, INSERT_VALUES, SCATTER_FORWARD));

    272:   fin = 0.0;
    273:   if (rank == 0) {
    274:     PetscCall(VecGetArrayRead(Xseq, &x));
    275:     fin = (x[0] - 2.0) * (x[0] - 2.0) + (x[1] - 2.0) * (x[1] - 2.0) - 2.0 * (x[0] + x[1]);
    276:     PetscCall(VecRestoreArrayRead(Xseq, &x));
    277:   }
    278:   PetscCallMPI(MPIU_Allreduce(&fin, f, 1, MPIU_REAL, MPIU_SUM, comm));

    280:   /* G = 2*X - 6 */
    281:   PetscCall(VecSet(G, -6.0));
    282:   PetscCall(VecAXPY(G, 2.0, X));
    283:   PetscFunctionReturn(PETSC_SUCCESS);
    284: }

    286: /* Evaluate PDIPM Hessian, see Eqn(22) in http://doi.org/10.1049/gtd2.12708
    287:    H = Wxx = fxx        + Jacobian(grad g^T*DE)   - Jacobian(grad h^T*DI)]
    288:            = fxx        + Jacobin([2*x0; 1]de[0]) - Jacobian([2*x0, -2*x0; -1, 1][di[0] di[1]]^T)
    289:            = [2 0; 0 2] + [2*de[0]  0;      0  0] - [2*di[0]-2*di[1], 0; 0, 0]
    290:            = [ 2*(1+de[0]-di[0]+di[1]), 0;
    291:                           0,            2]
    292: */
    293: PetscErrorCode FormPDIPMHessian(Tao tao, Vec x, Mat H, Mat Hpre, void *ctx)
    294: {
    295:   AppCtx            *user = (AppCtx *)ctx;
    296:   Vec                DE, DI;
    297:   const PetscScalar *de, *di;
    298:   PetscInt           zero = 0, one = 1;
    299:   PetscScalar        two = 2.0;
    300:   PetscScalar        val = 0.0;
    301:   Vec                Deseq, Diseq;
    302:   VecScatter         Descat, Discat;
    303:   PetscMPIInt        rank;
    304:   MPI_Comm           comm;

    306:   PetscFunctionBegin;
    307:   PetscCall(TaoGetDualVariables(tao, &DE, &DI));

    309:   PetscCall(PetscObjectGetComm((PetscObject)tao, &comm));
    310:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    312:   if (!user->noeqflag) {
    313:     PetscCall(VecScatterCreateToZero(DE, &Descat, &Deseq));
    314:     PetscCall(VecScatterBegin(Descat, DE, Deseq, INSERT_VALUES, SCATTER_FORWARD));
    315:     PetscCall(VecScatterEnd(Descat, DE, Deseq, INSERT_VALUES, SCATTER_FORWARD));
    316:   }
    317:   PetscCall(VecScatterCreateToZero(DI, &Discat, &Diseq));
    318:   PetscCall(VecScatterBegin(Discat, DI, Diseq, INSERT_VALUES, SCATTER_FORWARD));
    319:   PetscCall(VecScatterEnd(Discat, DI, Diseq, INSERT_VALUES, SCATTER_FORWARD));

    321:   if (rank == 0) {
    322:     if (!user->noeqflag) PetscCall(VecGetArrayRead(Deseq, &de)); /* places equality constraint dual into array */
    323:     PetscCall(VecGetArrayRead(Diseq, &di));                      /* places inequality constraint dual into array */

    325:     if (!user->noeqflag) {
    326:       val = 2.0 * (1 + de[0] - di[0] + di[1]);
    327:       PetscCall(VecRestoreArrayRead(Deseq, &de));
    328:       PetscCall(VecRestoreArrayRead(Diseq, &di));
    329:     } else {
    330:       val = 2.0 * (1 - di[0] + di[1]);
    331:     }
    332:     PetscCall(VecRestoreArrayRead(Diseq, &di));
    333:     PetscCall(MatSetValues(H, 1, &zero, 1, &zero, &val, INSERT_VALUES));
    334:     PetscCall(MatSetValues(H, 1, &one, 1, &one, &two, INSERT_VALUES));
    335:   }
    336:   PetscCall(MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY));
    337:   PetscCall(MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY));
    338:   if (!user->noeqflag) {
    339:     PetscCall(VecScatterDestroy(&Descat));
    340:     PetscCall(VecDestroy(&Deseq));
    341:   }
    342:   PetscCall(VecScatterDestroy(&Discat));
    343:   PetscCall(VecDestroy(&Diseq));
    344:   PetscFunctionReturn(PETSC_SUCCESS);
    345: }

    347: /* Evaluate
    348:    h = [ x0^2 - x1;
    349:          1 -(x0^2 - x1)]
    350: */
    351: PetscErrorCode FormInequalityConstraints(Tao tao, Vec X, Vec CI, void *ctx)
    352: {
    353:   const PetscScalar *x;
    354:   PetscScalar        ci;
    355:   MPI_Comm           comm;
    356:   PetscMPIInt        rank;
    357:   AppCtx            *user = (AppCtx *)ctx;
    358:   Vec                Xseq = user->Xseq;
    359:   VecScatter         scat = user->scat;

    361:   PetscFunctionBegin;
    362:   PetscCall(PetscObjectGetComm((PetscObject)tao, &comm));
    363:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    365:   PetscCall(VecScatterBegin(scat, X, Xseq, INSERT_VALUES, SCATTER_FORWARD));
    366:   PetscCall(VecScatterEnd(scat, X, Xseq, INSERT_VALUES, SCATTER_FORWARD));

    368:   if (rank == 0) {
    369:     PetscCall(VecGetArrayRead(Xseq, &x));
    370:     ci = x[0] * x[0] - x[1];
    371:     PetscCall(VecSetValue(CI, 0, ci, INSERT_VALUES));
    372:     ci = -x[0] * x[0] + x[1] + 1.0;
    373:     PetscCall(VecSetValue(CI, 1, ci, INSERT_VALUES));
    374:     PetscCall(VecRestoreArrayRead(Xseq, &x));
    375:   }
    376:   PetscCall(VecAssemblyBegin(CI));
    377:   PetscCall(VecAssemblyEnd(CI));
    378:   PetscFunctionReturn(PETSC_SUCCESS);
    379: }

    381: /* Evaluate
    382:    g = [ x0^2 + x1 - 2]
    383: */
    384: PetscErrorCode FormEqualityConstraints(Tao tao, Vec X, Vec CE, void *ctx)
    385: {
    386:   const PetscScalar *x;
    387:   PetscScalar        ce;
    388:   MPI_Comm           comm;
    389:   PetscMPIInt        rank;
    390:   AppCtx            *user = (AppCtx *)ctx;
    391:   Vec                Xseq = user->Xseq;
    392:   VecScatter         scat = user->scat;

    394:   PetscFunctionBegin;
    395:   PetscCall(PetscObjectGetComm((PetscObject)tao, &comm));
    396:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    398:   PetscCall(VecScatterBegin(scat, X, Xseq, INSERT_VALUES, SCATTER_FORWARD));
    399:   PetscCall(VecScatterEnd(scat, X, Xseq, INSERT_VALUES, SCATTER_FORWARD));

    401:   if (rank == 0) {
    402:     PetscCall(VecGetArrayRead(Xseq, &x));
    403:     ce = x[0] * x[0] + x[1] - 2.0;
    404:     PetscCall(VecSetValue(CE, 0, ce, INSERT_VALUES));
    405:     PetscCall(VecRestoreArrayRead(Xseq, &x));
    406:   }
    407:   PetscCall(VecAssemblyBegin(CE));
    408:   PetscCall(VecAssemblyEnd(CE));
    409:   PetscFunctionReturn(PETSC_SUCCESS);
    410: }

    412: /*
    413:   grad h = [  2*x0, -1;
    414:              -2*x0,  1]
    415: */
    416: PetscErrorCode FormInequalityJacobian(Tao tao, Vec X, Mat JI, Mat JIpre, void *ctx)
    417: {
    418:   AppCtx            *user = (AppCtx *)ctx;
    419:   PetscInt           zero = 0, one = 1, cols[2];
    420:   PetscScalar        vals[2];
    421:   const PetscScalar *x;
    422:   Vec                Xseq = user->Xseq;
    423:   VecScatter         scat = user->scat;
    424:   MPI_Comm           comm;
    425:   PetscMPIInt        rank;

    427:   PetscFunctionBegin;
    428:   PetscCall(PetscObjectGetComm((PetscObject)tao, &comm));
    429:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    430:   PetscCall(VecScatterBegin(scat, X, Xseq, INSERT_VALUES, SCATTER_FORWARD));
    431:   PetscCall(VecScatterEnd(scat, X, Xseq, INSERT_VALUES, SCATTER_FORWARD));

    433:   PetscCall(VecGetArrayRead(Xseq, &x));
    434:   if (rank == 0) {
    435:     cols[0] = 0;
    436:     cols[1] = 1;
    437:     vals[0] = 2 * x[0];
    438:     vals[1] = -1.0;
    439:     PetscCall(MatSetValues(JI, 1, &zero, 2, cols, vals, INSERT_VALUES));
    440:     vals[0] = -2 * x[0];
    441:     vals[1] = 1.0;
    442:     PetscCall(MatSetValues(JI, 1, &one, 2, cols, vals, INSERT_VALUES));
    443:   }
    444:   PetscCall(VecRestoreArrayRead(Xseq, &x));
    445:   PetscCall(MatAssemblyBegin(JI, MAT_FINAL_ASSEMBLY));
    446:   PetscCall(MatAssemblyEnd(JI, MAT_FINAL_ASSEMBLY));
    447:   PetscFunctionReturn(PETSC_SUCCESS);
    448: }

    450: /*
    451:   grad g = [2*x0, 1.0]
    452: */
    453: PetscErrorCode FormEqualityJacobian(Tao tao, Vec X, Mat JE, Mat JEpre, void *ctx)
    454: {
    455:   PetscInt           zero = 0, cols[2];
    456:   PetscScalar        vals[2];
    457:   const PetscScalar *x;
    458:   PetscMPIInt        rank;
    459:   MPI_Comm           comm;

    461:   PetscFunctionBegin;
    462:   PetscCall(PetscObjectGetComm((PetscObject)tao, &comm));
    463:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    465:   if (rank == 0) {
    466:     PetscCall(VecGetArrayRead(X, &x));
    467:     cols[0] = 0;
    468:     cols[1] = 1;
    469:     vals[0] = 2 * x[0];
    470:     vals[1] = 1.0;
    471:     PetscCall(MatSetValues(JE, 1, &zero, 2, cols, vals, INSERT_VALUES));
    472:     PetscCall(VecRestoreArrayRead(X, &x));
    473:   }
    474:   PetscCall(MatAssemblyBegin(JE, MAT_FINAL_ASSEMBLY));
    475:   PetscCall(MatAssemblyEnd(JE, MAT_FINAL_ASSEMBLY));
    476:   PetscFunctionReturn(PETSC_SUCCESS);
    477: }

    479: /*TEST

    481:    build:
    482:       requires: !complex !defined(PETSC_USE_CXX)

    484:    test:
    485:       args: -tao_converged_reason -tao_gatol 1.e-6 -tao_type pdipm -tao_pdipm_kkt_shift_pd
    486:       requires: mumps !single
    487:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    489:    test:
    490:       suffix: pdipm_2
    491:       requires: mumps
    492:       nsize: 2
    493:       args: -tao_converged_reason -tao_gatol 1.e-6 -tao_type pdipm
    494:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    496:    test:
    497:       suffix: 2
    498:       args: -tao_converged_reason
    499:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    501:    test:
    502:       suffix: 3
    503:       args: -tao_converged_reason -no_eq
    504:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    506:    test:
    507:       suffix: 4
    508:       args: -tao_converged_reason -tao_almm_type classic
    509:       requires: !single
    510:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    512:    test:
    513:       suffix: 5
    514:       args: -tao_converged_reason -tao_almm_type classic -no_eq
    515:       requires: !single
    516:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    518:    test:
    519:       suffix: 6
    520:       args: -tao_converged_reason -tao_almm_subsolver_tao_type bqnktr
    521:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    523:    test:
    524:       suffix: 7
    525:       args: -tao_converged_reason -tao_almm_subsolver_tao_type bncg
    526:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    528:    test:
    529:       suffix: 8
    530:       nsize: 2
    531:       args: -tao_converged_reason
    532:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    534:    test:
    535:       suffix: 9
    536:       nsize: 2
    537:       args: -tao_converged_reason -vec_type cuda -mat_type aijcusparse
    538:       requires: cuda
    539:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    541:    test:
    542:       suffix: 10
    543:       args: -tao_converged_reason -tao_almm_type classic -no_eq -no_bound
    544:       requires: !single
    545:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    547:    test:
    548:       suffix: 11
    549:       args: -tao_converged_reason -tao_almm_type classic -no_bound
    550:       requires: !single
    551:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    553:    test:
    554:       suffix: 12
    555:       args: -tao_converged_reason -tao_almm_type phr -no_eq -no_bound
    556:       requires: !single
    557:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    559:    test:
    560:       suffix: 13
    561:       args: -tao_converged_reason -tao_almm_type phr -no_bound
    562:       requires: !single
    563:       filter: sed  -e "s/CONVERGED_GATOL iterations *[0-9]\{1,\}/CONVERGED_GATOL/g"

    565: TEST*/