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*/