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

Actual source code: elliptic.c

      1: #include <petsc/private/taoimpl.h>

      3: typedef struct {
      4:   PetscInt n; /* Number of total variables */
      5:   PetscInt m; /* Number of constraints */
      6:   PetscInt nstate;
      7:   PetscInt ndesign;
      8:   PetscInt mx;    /* grid points in each direction */
      9:   PetscInt ns;    /* Number of data samples (1<=ns<=8)
     10:                   Currently only ns=1 is supported */
     11:   PetscInt ndata; /* Number of data points per sample */
     12:   IS       s_is;
     13:   IS       d_is;

     15:   VecScatter  state_scatter;
     16:   VecScatter  design_scatter;
     17:   VecScatter *yi_scatter, *di_scatter;
     18:   Vec         suby, subq, subd;
     19:   Mat         Js, Jd, JsPrec, JsInv, JsBlock;

     21:   PetscReal  alpha; /* Regularization parameter */
     22:   PetscReal  beta;  /* Weight attributed to ||u||^2 in regularization functional */
     23:   PetscReal  noise; /* Amount of noise to add to data */
     24:   PetscReal *ones;
     25:   Mat        Q;
     26:   Mat        MQ;
     27:   Mat        L;

     29:   Mat Grad;
     30:   Mat Av, Avwork;
     31:   Mat Div, Divwork;
     32:   Mat DSG;
     33:   Mat Diag, Ones;

     35:   Vec q;
     36:   Vec ur; /* reference */

     38:   Vec d;
     39:   Vec dwork;

     41:   Vec x; /* super vec of y,u */

     43:   Vec y; /* state variables */
     44:   Vec ywork;

     46:   Vec ytrue;

     48:   Vec u; /* design variables */
     49:   Vec uwork;

     51:   Vec utrue;

     53:   Vec js_diag;

     55:   Vec c; /* constraint vector */
     56:   Vec cwork;

     58:   Vec lwork;
     59:   Vec S;
     60:   Vec Swork, Twork, Sdiag, Ywork;
     61:   Vec Av_u;

     63:   KSP solver;
     64:   PC  prec;

     66:   PetscReal     tola, tolb, tolc, told;
     67:   PetscInt      ksp_its;
     68:   PetscInt      ksp_its_initial;
     69:   PetscLogStage stages[10];
     70:   PetscBool     use_ptap;
     71:   PetscBool     use_lrc;
     72: } AppCtx;

     74: PetscErrorCode FormFunction(Tao, Vec, PetscReal *, void *);
     75: PetscErrorCode FormGradient(Tao, Vec, Vec, void *);
     76: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal *, Vec, void *);
     77: PetscErrorCode FormJacobianState(Tao, Vec, Mat, Mat, Mat, void *);
     78: PetscErrorCode FormJacobianDesign(Tao, Vec, Mat, void *);
     79: PetscErrorCode FormConstraints(Tao, Vec, Vec, void *);
     80: PetscErrorCode FormHessian(Tao, Vec, Mat, Mat, void *);
     81: PetscErrorCode Gather(Vec, Vec, VecScatter, Vec, VecScatter);
     82: PetscErrorCode Scatter(Vec, Vec, VecScatter, Vec, VecScatter);
     83: PetscErrorCode EllipticInitialize(AppCtx *);
     84: PetscErrorCode EllipticDestroy(AppCtx *);
     85: PetscErrorCode EllipticMonitor(Tao, void *);

     87: PetscErrorCode StateBlockMatMult(Mat, Vec, Vec);
     88: PetscErrorCode StateMatMult(Mat, Vec, Vec);

     90: PetscErrorCode StateInvMatMult(Mat, Vec, Vec);
     91: PetscErrorCode DesignMatMult(Mat, Vec, Vec);
     92: PetscErrorCode DesignMatMultTranspose(Mat, Vec, Vec);

     94: PetscErrorCode QMatMult(Mat, Vec, Vec);
     95: PetscErrorCode QMatMultTranspose(Mat, Vec, Vec);

     97: static char help[] = "";

     99: int main(int argc, char **argv)
    100: {
    101:   Vec      x0;
    102:   Tao      tao;
    103:   AppCtx   user;
    104:   PetscInt ntests = 1;
    105:   PetscInt i;

    107:   PetscFunctionBeginUser;
    108:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
    109:   user.mx = 8;
    110:   PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "elliptic example", NULL);
    111:   PetscCall(PetscOptionsInt("-mx", "Number of grid points in each direction", "", user.mx, &user.mx, NULL));
    112:   user.ns = 6;
    113:   PetscCall(PetscOptionsInt("-ns", "Number of data samples (1<=ns<=8)", "", user.ns, &user.ns, NULL));
    114:   user.ndata = 64;
    115:   PetscCall(PetscOptionsInt("-ndata", "Numbers of data points per sample", "", user.ndata, &user.ndata, NULL));
    116:   user.alpha = 0.1;
    117:   PetscCall(PetscOptionsReal("-alpha", "Regularization parameter", "", user.alpha, &user.alpha, NULL));
    118:   user.beta = 0.00001;
    119:   PetscCall(PetscOptionsReal("-beta", "Weight attributed to ||u||^2 in regularization functional", "", user.beta, &user.beta, NULL));
    120:   user.noise = 0.01;
    121:   PetscCall(PetscOptionsReal("-noise", "Amount of noise to add to data", "", user.noise, &user.noise, NULL));

    123:   user.use_ptap = PETSC_FALSE;
    124:   PetscCall(PetscOptionsBool("-use_ptap", "Use ptap matrix for DSG", "", user.use_ptap, &user.use_ptap, NULL));
    125:   user.use_lrc = PETSC_FALSE;
    126:   PetscCall(PetscOptionsBool("-use_lrc", "Use lrc matrix for Js", "", user.use_lrc, &user.use_lrc, NULL));
    127:   PetscCall(PetscOptionsInt("-ntests", "Number of times to repeat TaoSolve", "", ntests, &ntests, NULL));
    128:   PetscOptionsEnd();

    130:   user.m       = user.ns * user.mx * user.mx * user.mx; /* number of constraints */
    131:   user.nstate  = user.m;
    132:   user.ndesign = user.mx * user.mx * user.mx;
    133:   user.n       = user.nstate + user.ndesign; /* number of variables */

    135:   /* Create TAO solver and set desired solution method */
    136:   PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
    137:   PetscCall(TaoSetType(tao, TAOLCL));

    139:   /* Set up initial vectors and matrices */
    140:   PetscCall(EllipticInitialize(&user));

    142:   PetscCall(Gather(user.x, user.y, user.state_scatter, user.u, user.design_scatter));
    143:   PetscCall(VecDuplicate(user.x, &x0));
    144:   PetscCall(VecCopy(user.x, x0));

    146:   /* Set solution vector with an initial guess */
    147:   PetscCall(TaoSetSolution(tao, user.x));
    148:   PetscCall(TaoSetObjective(tao, FormFunction, &user));
    149:   PetscCall(TaoSetGradient(tao, NULL, FormGradient, &user));
    150:   PetscCall(TaoSetConstraintsRoutine(tao, user.c, FormConstraints, &user));

    152:   PetscCall(TaoSetJacobianStateRoutine(tao, user.Js, NULL, user.JsInv, FormJacobianState, &user));
    153:   PetscCall(TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, &user));

    155:   PetscCall(TaoSetStateDesignIS(tao, user.s_is, user.d_is));
    156:   PetscCall(TaoSetFromOptions(tao));

    158:   /* SOLVE THE APPLICATION */
    159:   PetscCall(PetscLogStageRegister("Trials", &user.stages[1]));
    160:   PetscCall(PetscLogStagePush(user.stages[1]));
    161:   for (i = 0; i < ntests; i++) {
    162:     PetscCall(TaoSolve(tao));
    163:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "KSP Iterations = %" PetscInt_FMT "\n", user.ksp_its));
    164:     PetscCall(VecCopy(x0, user.x));
    165:   }
    166:   PetscCall(PetscLogStagePop());
    167:   PetscCall(PetscBarrier((PetscObject)user.x));
    168:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "KSP iterations within initialization: "));
    169:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "\n", user.ksp_its_initial));

    171:   PetscCall(TaoDestroy(&tao));
    172:   PetscCall(VecDestroy(&x0));
    173:   PetscCall(EllipticDestroy(&user));
    174:   PetscCall(PetscFinalize());
    175:   return 0;
    176: }
    177: /* ------------------------------------------------------------------- */
    178: /*
    179:    dwork = Qy - d
    180:    lwork = L*(u-ur)
    181:    f = 1/2 * (dwork.dwork + alpha*lwork.lwork)
    182: */
    183: PetscErrorCode FormFunction(Tao tao, Vec X, PetscReal *f, void *ptr)
    184: {
    185:   PetscReal d1 = 0, d2 = 0;
    186:   AppCtx   *user = (AppCtx *)ptr;

    188:   PetscFunctionBegin;
    189:   PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
    190:   PetscCall(MatMult(user->MQ, user->y, user->dwork));
    191:   PetscCall(VecAXPY(user->dwork, -1.0, user->d));
    192:   PetscCall(VecDot(user->dwork, user->dwork, &d1));
    193:   PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
    194:   PetscCall(MatMult(user->L, user->uwork, user->lwork));
    195:   PetscCall(VecDot(user->lwork, user->lwork, &d2));
    196:   *f = 0.5 * (d1 + user->alpha * d2);
    197:   PetscFunctionReturn(PETSC_SUCCESS);
    198: }

    200: /* ------------------------------------------------------------------- */
    201: /*
    202:     state: g_s = Q' *(Qy - d)
    203:     design: g_d = alpha*L'*L*(u-ur)
    204: */
    205: PetscErrorCode FormGradient(Tao tao, Vec X, Vec G, void *ptr)
    206: {
    207:   AppCtx *user = (AppCtx *)ptr;

    209:   PetscFunctionBegin;
    210:   PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
    211:   PetscCall(MatMult(user->MQ, user->y, user->dwork));
    212:   PetscCall(VecAXPY(user->dwork, -1.0, user->d));
    213:   PetscCall(MatMultTranspose(user->MQ, user->dwork, user->ywork));
    214:   PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
    215:   PetscCall(MatMult(user->L, user->uwork, user->lwork));
    216:   PetscCall(MatMultTranspose(user->L, user->lwork, user->uwork));
    217:   PetscCall(VecScale(user->uwork, user->alpha));
    218:   PetscCall(Gather(G, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
    219:   PetscFunctionReturn(PETSC_SUCCESS);
    220: }

    222: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
    223: {
    224:   PetscReal d1, d2;
    225:   AppCtx   *user = (AppCtx *)ptr;

    227:   PetscFunctionBegin;
    228:   PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
    229:   PetscCall(MatMult(user->MQ, user->y, user->dwork));
    230:   PetscCall(VecAXPY(user->dwork, -1.0, user->d));
    231:   PetscCall(VecDot(user->dwork, user->dwork, &d1));
    232:   PetscCall(MatMultTranspose(user->MQ, user->dwork, user->ywork));

    234:   PetscCall(VecWAXPY(user->uwork, -1.0, user->ur, user->u));
    235:   PetscCall(MatMult(user->L, user->uwork, user->lwork));
    236:   PetscCall(VecDot(user->lwork, user->lwork, &d2));
    237:   PetscCall(MatMultTranspose(user->L, user->lwork, user->uwork));
    238:   PetscCall(VecScale(user->uwork, user->alpha));
    239:   *f = 0.5 * (d1 + user->alpha * d2);
    240:   PetscCall(Gather(G, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
    241:   PetscFunctionReturn(PETSC_SUCCESS);
    242: }

    244: /* ------------------------------------------------------------------- */
    245: /* A
    246: MatShell object
    247: */
    248: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
    249: {
    250:   AppCtx *user = (AppCtx *)ptr;

    252:   PetscFunctionBegin;
    253:   PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
    254:   /* DSG = Div * (1/Av_u) * Grad */
    255:   PetscCall(VecSet(user->uwork, 0));
    256:   PetscCall(VecAXPY(user->uwork, -1.0, user->u));
    257:   PetscCall(VecExp(user->uwork));
    258:   PetscCall(MatMult(user->Av, user->uwork, user->Av_u));
    259:   PetscCall(VecCopy(user->Av_u, user->Swork));
    260:   PetscCall(VecReciprocal(user->Swork));
    261:   if (user->use_ptap) {
    262:     PetscCall(MatDiagonalSet(user->Diag, user->Swork, INSERT_VALUES));
    263:     PetscCall(MatPtAP(user->Diag, user->Grad, MAT_REUSE_MATRIX, 1.0, &user->DSG));
    264:   } else {
    265:     PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
    266:     PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Swork));
    267:     PetscCall(MatProductNumeric(user->DSG));
    268:   }
    269:   PetscFunctionReturn(PETSC_SUCCESS);
    270: }
    271: /* ------------------------------------------------------------------- */
    272: /* B */
    273: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
    274: {
    275:   AppCtx *user = (AppCtx *)ptr;

    277:   PetscFunctionBegin;
    278:   PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
    279:   PetscFunctionReturn(PETSC_SUCCESS);
    280: }

    282: PetscErrorCode StateBlockMatMult(Mat J_shell, Vec X, Vec Y)
    283: {
    284:   PetscReal sum;
    285:   AppCtx   *user;

    287:   PetscFunctionBegin;
    288:   PetscCall(MatShellGetContext(J_shell, &user));
    289:   PetscCall(MatMult(user->DSG, X, Y));
    290:   PetscCall(VecSum(X, &sum));
    291:   sum /= user->ndesign;
    292:   PetscCall(VecShift(Y, sum));
    293:   PetscFunctionReturn(PETSC_SUCCESS);
    294: }

    296: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
    297: {
    298:   PetscInt i;
    299:   AppCtx  *user;

    301:   PetscFunctionBegin;
    302:   PetscCall(MatShellGetContext(J_shell, &user));
    303:   if (user->ns == 1) {
    304:     PetscCall(MatMult(user->JsBlock, X, Y));
    305:   } else {
    306:     for (i = 0; i < user->ns; i++) {
    307:       PetscCall(Scatter(X, user->subq, user->yi_scatter[i], 0, 0));
    308:       PetscCall(Scatter(Y, user->suby, user->yi_scatter[i], 0, 0));
    309:       PetscCall(MatMult(user->JsBlock, user->subq, user->suby));
    310:       PetscCall(Gather(Y, user->suby, user->yi_scatter[i], 0, 0));
    311:     }
    312:   }
    313:   PetscFunctionReturn(PETSC_SUCCESS);
    314: }

    316: PetscErrorCode StateInvMatMult(Mat J_shell, Vec X, Vec Y)
    317: {
    318:   PetscInt its, i;
    319:   AppCtx  *user;

    321:   PetscFunctionBegin;
    322:   PetscCall(MatShellGetContext(J_shell, &user));
    323:   PetscCall(KSPSetOperators(user->solver, user->JsBlock, user->DSG));
    324:   if (Y == user->ytrue) {
    325:     /* First solve is done using true solution to set up problem */
    326:     PetscCall(KSPSetTolerances(user->solver, 1e-8, PETSC_CURRENT, PETSC_CURRENT, PETSC_CURRENT));
    327:   } else {
    328:     PetscCall(KSPSetTolerances(user->solver, PETSC_CURRENT, PETSC_CURRENT, PETSC_CURRENT, PETSC_CURRENT));
    329:   }
    330:   if (user->ns == 1) {
    331:     PetscCall(KSPSolve(user->solver, X, Y));
    332:     PetscCall(KSPGetIterationNumber(user->solver, &its));
    333:     user->ksp_its += its;
    334:   } else {
    335:     for (i = 0; i < user->ns; i++) {
    336:       PetscCall(Scatter(X, user->subq, user->yi_scatter[i], 0, 0));
    337:       PetscCall(Scatter(Y, user->suby, user->yi_scatter[i], 0, 0));
    338:       PetscCall(KSPSolve(user->solver, user->subq, user->suby));
    339:       PetscCall(KSPGetIterationNumber(user->solver, &its));
    340:       user->ksp_its += its;
    341:       PetscCall(Gather(Y, user->suby, user->yi_scatter[i], 0, 0));
    342:     }
    343:   }
    344:   PetscFunctionReturn(PETSC_SUCCESS);
    345: }
    346: PetscErrorCode QMatMult(Mat J_shell, Vec X, Vec Y)
    347: {
    348:   AppCtx  *user;
    349:   PetscInt i;

    351:   PetscFunctionBegin;
    352:   PetscCall(MatShellGetContext(J_shell, &user));
    353:   if (user->ns == 1) {
    354:     PetscCall(MatMult(user->Q, X, Y));
    355:   } else {
    356:     for (i = 0; i < user->ns; i++) {
    357:       PetscCall(Scatter(X, user->subq, user->yi_scatter[i], 0, 0));
    358:       PetscCall(Scatter(Y, user->subd, user->di_scatter[i], 0, 0));
    359:       PetscCall(MatMult(user->Q, user->subq, user->subd));
    360:       PetscCall(Gather(Y, user->subd, user->di_scatter[i], 0, 0));
    361:     }
    362:   }
    363:   PetscFunctionReturn(PETSC_SUCCESS);
    364: }

    366: PetscErrorCode QMatMultTranspose(Mat J_shell, Vec X, Vec Y)
    367: {
    368:   AppCtx  *user;
    369:   PetscInt i;

    371:   PetscFunctionBegin;
    372:   PetscCall(MatShellGetContext(J_shell, &user));
    373:   if (user->ns == 1) {
    374:     PetscCall(MatMultTranspose(user->Q, X, Y));
    375:   } else {
    376:     for (i = 0; i < user->ns; i++) {
    377:       PetscCall(Scatter(X, user->subd, user->di_scatter[i], 0, 0));
    378:       PetscCall(Scatter(Y, user->suby, user->yi_scatter[i], 0, 0));
    379:       PetscCall(MatMultTranspose(user->Q, user->subd, user->suby));
    380:       PetscCall(Gather(Y, user->suby, user->yi_scatter[i], 0, 0));
    381:     }
    382:   }
    383:   PetscFunctionReturn(PETSC_SUCCESS);
    384: }

    386: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
    387: {
    388:   PetscInt i;
    389:   AppCtx  *user;

    391:   PetscFunctionBegin;
    392:   PetscCall(MatShellGetContext(J_shell, &user));

    394:   /* sdiag(1./v) */
    395:   PetscCall(VecSet(user->uwork, 0));
    396:   PetscCall(VecAXPY(user->uwork, -1.0, user->u));
    397:   PetscCall(VecExp(user->uwork));

    399:   /* sdiag(1./((Av*(1./v)).^2)) */
    400:   PetscCall(MatMult(user->Av, user->uwork, user->Swork));
    401:   PetscCall(VecPointwiseMult(user->Swork, user->Swork, user->Swork));
    402:   PetscCall(VecReciprocal(user->Swork));

    404:   /* (Av * (sdiag(1./v) * b)) */
    405:   PetscCall(VecPointwiseMult(user->uwork, user->uwork, X));
    406:   PetscCall(MatMult(user->Av, user->uwork, user->Twork));

    408:   /* (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b))) */
    409:   PetscCall(VecPointwiseMult(user->Swork, user->Twork, user->Swork));

    411:   if (user->ns == 1) {
    412:     /* (sdiag(Grad*y(:,i)) */
    413:     PetscCall(MatMult(user->Grad, user->y, user->Twork));

    415:     /* Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
    416:     PetscCall(VecPointwiseMult(user->Swork, user->Twork, user->Swork));
    417:     PetscCall(MatMultTranspose(user->Grad, user->Swork, Y));
    418:   } else {
    419:     for (i = 0; i < user->ns; i++) {
    420:       PetscCall(Scatter(user->y, user->suby, user->yi_scatter[i], 0, 0));
    421:       PetscCall(Scatter(Y, user->subq, user->yi_scatter[i], 0, 0));

    423:       PetscCall(MatMult(user->Grad, user->suby, user->Twork));
    424:       PetscCall(VecPointwiseMult(user->Twork, user->Twork, user->Swork));
    425:       PetscCall(MatMultTranspose(user->Grad, user->Twork, user->subq));
    426:       PetscCall(Gather(user->y, user->suby, user->yi_scatter[i], 0, 0));
    427:       PetscCall(Gather(Y, user->subq, user->yi_scatter[i], 0, 0));
    428:     }
    429:   }
    430:   PetscFunctionReturn(PETSC_SUCCESS);
    431: }

    433: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
    434: {
    435:   PetscInt i;
    436:   AppCtx  *user;

    438:   PetscFunctionBegin;
    439:   PetscCall(MatShellGetContext(J_shell, &user));
    440:   PetscCall(VecZeroEntries(Y));

    442:   /* Sdiag = 1./((Av*(1./v)).^2) */
    443:   PetscCall(VecSet(user->uwork, 0));
    444:   PetscCall(VecAXPY(user->uwork, -1.0, user->u));
    445:   PetscCall(VecExp(user->uwork));
    446:   PetscCall(MatMult(user->Av, user->uwork, user->Swork));
    447:   PetscCall(VecPointwiseMult(user->Sdiag, user->Swork, user->Swork));
    448:   PetscCall(VecReciprocal(user->Sdiag));

    450:   for (i = 0; i < user->ns; i++) {
    451:     PetscCall(Scatter(X, user->subq, user->yi_scatter[i], 0, 0));
    452:     PetscCall(Scatter(user->y, user->suby, user->yi_scatter[i], 0, 0));

    454:     /* Swork = (Div' * b(:,i)) */
    455:     PetscCall(MatMult(user->Grad, user->subq, user->Swork));

    457:     /* Twork = Grad*y(:,i) */
    458:     PetscCall(MatMult(user->Grad, user->suby, user->Twork));

    460:     /* Twork = sdiag(Twork) * Swork */
    461:     PetscCall(VecPointwiseMult(user->Twork, user->Swork, user->Twork));

    463:     /* Swork = pointwisemult(Sdiag,Twork) */
    464:     PetscCall(VecPointwiseMult(user->Swork, user->Twork, user->Sdiag));

    466:     /* Ywork = Av' * Swork */
    467:     PetscCall(MatMultTranspose(user->Av, user->Swork, user->Ywork));

    469:     /* Ywork = pointwisemult(uwork,Ywork) */
    470:     PetscCall(VecPointwiseMult(user->Ywork, user->uwork, user->Ywork));
    471:     PetscCall(VecAXPY(Y, 1.0, user->Ywork));
    472:     PetscCall(Gather(user->y, user->suby, user->yi_scatter[i], 0, 0));
    473:   }
    474:   PetscFunctionReturn(PETSC_SUCCESS);
    475: }

    477: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
    478: {
    479:   /* C=Ay - q      A = Div * Sigma * Grad + hx*hx*hx*ones(n,n) */
    480:   PetscReal sum;
    481:   PetscInt  i;
    482:   AppCtx   *user = (AppCtx *)ptr;

    484:   PetscFunctionBegin;
    485:   PetscCall(Scatter(X, user->y, user->state_scatter, user->u, user->design_scatter));
    486:   if (user->ns == 1) {
    487:     PetscCall(MatMult(user->Grad, user->y, user->Swork));
    488:     PetscCall(VecPointwiseDivide(user->Swork, user->Swork, user->Av_u));
    489:     PetscCall(MatMultTranspose(user->Grad, user->Swork, C));
    490:     PetscCall(VecSum(user->y, &sum));
    491:     sum /= user->ndesign;
    492:     PetscCall(VecShift(C, sum));
    493:   } else {
    494:     for (i = 0; i < user->ns; i++) {
    495:       PetscCall(Scatter(user->y, user->suby, user->yi_scatter[i], 0, 0));
    496:       PetscCall(Scatter(C, user->subq, user->yi_scatter[i], 0, 0));
    497:       PetscCall(MatMult(user->Grad, user->suby, user->Swork));
    498:       PetscCall(VecPointwiseDivide(user->Swork, user->Swork, user->Av_u));
    499:       PetscCall(MatMultTranspose(user->Grad, user->Swork, user->subq));

    501:       PetscCall(VecSum(user->suby, &sum));
    502:       sum /= user->ndesign;
    503:       PetscCall(VecShift(user->subq, sum));

    505:       PetscCall(Gather(user->y, user->suby, user->yi_scatter[i], 0, 0));
    506:       PetscCall(Gather(C, user->subq, user->yi_scatter[i], 0, 0));
    507:     }
    508:   }
    509:   PetscCall(VecAXPY(C, -1.0, user->q));
    510:   PetscFunctionReturn(PETSC_SUCCESS);
    511: }

    513: PetscErrorCode Scatter(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
    514: {
    515:   PetscFunctionBegin;
    516:   PetscCall(VecScatterBegin(scat1, x, sub1, INSERT_VALUES, SCATTER_FORWARD));
    517:   PetscCall(VecScatterEnd(scat1, x, sub1, INSERT_VALUES, SCATTER_FORWARD));
    518:   if (sub2) {
    519:     PetscCall(VecScatterBegin(scat2, x, sub2, INSERT_VALUES, SCATTER_FORWARD));
    520:     PetscCall(VecScatterEnd(scat2, x, sub2, INSERT_VALUES, SCATTER_FORWARD));
    521:   }
    522:   PetscFunctionReturn(PETSC_SUCCESS);
    523: }

    525: PetscErrorCode Gather(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
    526: {
    527:   PetscFunctionBegin;
    528:   PetscCall(VecScatterBegin(scat1, sub1, x, INSERT_VALUES, SCATTER_REVERSE));
    529:   PetscCall(VecScatterEnd(scat1, sub1, x, INSERT_VALUES, SCATTER_REVERSE));
    530:   if (sub2) {
    531:     PetscCall(VecScatterBegin(scat2, sub2, x, INSERT_VALUES, SCATTER_REVERSE));
    532:     PetscCall(VecScatterEnd(scat2, sub2, x, INSERT_VALUES, SCATTER_REVERSE));
    533:   }
    534:   PetscFunctionReturn(PETSC_SUCCESS);
    535: }

    537: PetscErrorCode EllipticInitialize(AppCtx *user)
    538: {
    539:   PetscInt        m, n, i, j, k, l, linear_index, is, js, ks, ls, istart, iend, iblock;
    540:   Vec             XX, YY, ZZ, XXwork, YYwork, ZZwork, UTwork;
    541:   PetscReal      *x, *y, *z;
    542:   PetscReal       h, meanut;
    543:   PetscScalar     hinv, neg_hinv, half = 0.5, sqrt_beta;
    544:   PetscInt        im, indx1, indx2, indy1, indy2, indz1, indz2, nx, ny, nz;
    545:   IS              is_alldesign, is_allstate;
    546:   IS              is_from_d;
    547:   IS              is_from_y;
    548:   PetscInt        lo, hi, hi2, lo2, ysubnlocal, dsubnlocal;
    549:   const PetscInt *ranges, *subranges;
    550:   PetscMPIInt     size;
    551:   PetscReal       xri, yri, zri, xim, yim, zim, dx1, dx2, dy1, dy2, dz1, dz2, Dx, Dy, Dz;
    552:   PetscScalar     v, vx, vy, vz;
    553:   PetscInt        offset, subindex, subvec, nrank, kk;

    555:   PetscScalar xr[64] = {0.4970, 0.8498, 0.7814, 0.6268, 0.7782, 0.6402, 0.3617, 0.3160, 0.3610, 0.5298, 0.6987, 0.3331, 0.7962, 0.5596, 0.3866, 0.6774, 0.5407, 0.4518, 0.6702, 0.6061, 0.7580, 0.8997,
    556:                         0.5198, 0.8326, 0.2138, 0.9198, 0.3000, 0.2833, 0.8288, 0.7076, 0.1820, 0.0728, 0.8447, 0.2367, 0.3239, 0.6413, 0.3114, 0.4731, 0.1192, 0.9273, 0.5724, 0.4331, 0.5136, 0.3547,
    557:                         0.4413, 0.2602, 0.5698, 0.7278, 0.5261, 0.6230, 0.2454, 0.3948, 0.7479, 0.6582, 0.4660, 0.5594, 0.7574, 0.1143, 0.5900, 0.1065, 0.4260, 0.3294, 0.8276, 0.0756};

    559:   PetscScalar yr[64] = {0.7345, 0.9120, 0.9288, 0.7528, 0.4463, 0.4985, 0.2497, 0.6256, 0.3425, 0.9026, 0.6983, 0.4230, 0.7140, 0.2970, 0.4474, 0.8792, 0.6604, 0.2485, 0.7968, 0.6127, 0.1796, 0.2437,
    560:                         0.5938, 0.6137, 0.3867, 0.5658, 0.4575, 0.1009, 0.0863, 0.3361, 0.0738, 0.3985, 0.6602, 0.1437, 0.0934, 0.5983, 0.5950, 0.0763, 0.0768, 0.2288, 0.5761, 0.1129, 0.3841, 0.6150,
    561:                         0.6904, 0.6686, 0.1361, 0.4601, 0.4491, 0.3716, 0.1969, 0.6537, 0.6743, 0.6991, 0.4811, 0.5480, 0.1684, 0.4569, 0.6889, 0.8437, 0.3015, 0.2854, 0.8199, 0.2658};

    563:   PetscScalar zr[64] = {0.7668, 0.8573, 0.2654, 0.2719, 0.1060, 0.1311, 0.6232, 0.2295, 0.8009, 0.2147, 0.2119, 0.9325, 0.4473, 0.3600, 0.3374, 0.3819, 0.4066, 0.5801, 0.1673, 0.0959, 0.4638, 0.8236,
    564:                         0.8800, 0.2939, 0.2028, 0.8262, 0.2706, 0.6276, 0.9085, 0.6443, 0.8241, 0.0712, 0.1824, 0.7789, 0.4389, 0.8415, 0.7055, 0.6639, 0.3653, 0.2078, 0.1987, 0.2297, 0.4321, 0.8115,
    565:                         0.4915, 0.7764, 0.4657, 0.4627, 0.4569, 0.4232, 0.8514, 0.0674, 0.3227, 0.1055, 0.6690, 0.6313, 0.9226, 0.5461, 0.4126, 0.2364, 0.6096, 0.7042, 0.3914, 0.0711};

    567:   PetscFunctionBegin;
    568:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
    569:   PetscCall(PetscLogStageRegister("Elliptic Setup", &user->stages[0]));
    570:   PetscCall(PetscLogStagePush(user->stages[0]));

    572:   /* Create u,y,c,x */
    573:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->u));
    574:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->y));
    575:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->c));
    576:   PetscCall(VecSetSizes(user->u, PETSC_DECIDE, user->ndesign));
    577:   PetscCall(VecSetFromOptions(user->u));
    578:   PetscCall(VecGetLocalSize(user->u, &ysubnlocal));
    579:   PetscCall(VecSetSizes(user->y, ysubnlocal * user->ns, user->nstate));
    580:   PetscCall(VecSetSizes(user->c, ysubnlocal * user->ns, user->m));
    581:   PetscCall(VecSetFromOptions(user->y));
    582:   PetscCall(VecSetFromOptions(user->c));

    584:   /*
    585:      *******************************
    586:      Create scatters for x <-> y,u
    587:      *******************************

    589:      If the state vector y and design vector u are partitioned as
    590:      [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
    591:      then the solution vector x is organized as
    592:      [y_1; u_1; y_2; u_2; ...; y_np; u_np].
    593:      The index sets user->s_is and user->d_is correspond to the indices of the
    594:      state and design variables owned by the current processor.
    595:   */
    596:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->x));

    598:   PetscCall(VecGetOwnershipRange(user->y, &lo, &hi));
    599:   PetscCall(VecGetOwnershipRange(user->u, &lo2, &hi2));

    601:   PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo, 1, &is_allstate));
    602:   PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo + lo2, 1, &user->s_is));
    603:   PetscCall(ISCreateStride(PETSC_COMM_SELF, hi2 - lo2, lo2, 1, &is_alldesign));
    604:   PetscCall(ISCreateStride(PETSC_COMM_SELF, hi2 - lo2, hi + lo2, 1, &user->d_is));

    606:   PetscCall(VecSetSizes(user->x, hi - lo + hi2 - lo2, user->n));
    607:   PetscCall(VecSetFromOptions(user->x));

    609:   PetscCall(VecScatterCreate(user->x, user->s_is, user->y, is_allstate, &user->state_scatter));
    610:   PetscCall(VecScatterCreate(user->x, user->d_is, user->u, is_alldesign, &user->design_scatter));
    611:   PetscCall(ISDestroy(&is_alldesign));
    612:   PetscCall(ISDestroy(&is_allstate));
    613:   /*
    614:      *******************************
    615:      Create scatter from y to y_1,y_2,...,y_ns
    616:      *******************************
    617:   */
    618:   PetscCall(PetscMalloc1(user->ns, &user->yi_scatter));
    619:   PetscCall(VecDuplicate(user->u, &user->suby));
    620:   PetscCall(VecDuplicate(user->u, &user->subq));

    622:   PetscCall(VecGetOwnershipRange(user->y, &lo2, &hi2));
    623:   istart = 0;
    624:   for (i = 0; i < user->ns; i++) {
    625:     PetscCall(VecGetOwnershipRange(user->suby, &lo, &hi));
    626:     PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo2 + istart, 1, &is_from_y));
    627:     PetscCall(VecScatterCreate(user->y, is_from_y, user->suby, NULL, &user->yi_scatter[i]));
    628:     istart = istart + hi - lo;
    629:     PetscCall(ISDestroy(&is_from_y));
    630:   }
    631:   /*
    632:      *******************************
    633:      Create scatter from d to d_1,d_2,...,d_ns
    634:      *******************************
    635:   */
    636:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->subd));
    637:   PetscCall(VecSetSizes(user->subd, PETSC_DECIDE, user->ndata));
    638:   PetscCall(VecSetFromOptions(user->subd));
    639:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->d));
    640:   PetscCall(VecGetLocalSize(user->subd, &dsubnlocal));
    641:   PetscCall(VecSetSizes(user->d, dsubnlocal * user->ns, user->ndata * user->ns));
    642:   PetscCall(VecSetFromOptions(user->d));
    643:   PetscCall(PetscMalloc1(user->ns, &user->di_scatter));

    645:   PetscCall(VecGetOwnershipRange(user->d, &lo2, &hi2));
    646:   istart = 0;
    647:   for (i = 0; i < user->ns; i++) {
    648:     PetscCall(VecGetOwnershipRange(user->subd, &lo, &hi));
    649:     PetscCall(ISCreateStride(PETSC_COMM_SELF, hi - lo, lo2 + istart, 1, &is_from_d));
    650:     PetscCall(VecScatterCreate(user->d, is_from_d, user->subd, NULL, &user->di_scatter[i]));
    651:     istart = istart + hi - lo;
    652:     PetscCall(ISDestroy(&is_from_d));
    653:   }

    655:   PetscCall(PetscMalloc1(user->mx, &x));
    656:   PetscCall(PetscMalloc1(user->mx, &y));
    657:   PetscCall(PetscMalloc1(user->mx, &z));

    659:   user->ksp_its         = 0;
    660:   user->ksp_its_initial = 0;

    662:   n         = user->mx * user->mx * user->mx;
    663:   m         = 3 * user->mx * user->mx * (user->mx - 1);
    664:   sqrt_beta = PetscSqrtScalar(user->beta);

    666:   PetscCall(VecCreate(PETSC_COMM_WORLD, &XX));
    667:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->q));
    668:   PetscCall(VecSetSizes(XX, ysubnlocal, n));
    669:   PetscCall(VecSetSizes(user->q, ysubnlocal * user->ns, user->m));
    670:   PetscCall(VecSetFromOptions(XX));
    671:   PetscCall(VecSetFromOptions(user->q));

    673:   PetscCall(VecDuplicate(XX, &YY));
    674:   PetscCall(VecDuplicate(XX, &ZZ));
    675:   PetscCall(VecDuplicate(XX, &XXwork));
    676:   PetscCall(VecDuplicate(XX, &YYwork));
    677:   PetscCall(VecDuplicate(XX, &ZZwork));
    678:   PetscCall(VecDuplicate(XX, &UTwork));
    679:   PetscCall(VecDuplicate(XX, &user->utrue));

    681:   /* map for striding q */
    682:   PetscCall(VecGetOwnershipRanges(user->q, &ranges));
    683:   PetscCall(VecGetOwnershipRanges(user->u, &subranges));

    685:   PetscCall(VecGetOwnershipRange(user->q, &lo2, &hi2));
    686:   PetscCall(VecGetOwnershipRange(user->u, &lo, &hi));
    687:   /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
    688:   h        = 1.0 / user->mx;
    689:   hinv     = user->mx;
    690:   neg_hinv = -hinv;

    692:   PetscCall(VecGetOwnershipRange(XX, &istart, &iend));
    693:   for (linear_index = istart; linear_index < iend; linear_index++) {
    694:     i  = linear_index % user->mx;
    695:     j  = ((linear_index - i) / user->mx) % user->mx;
    696:     k  = ((linear_index - i) / user->mx - j) / user->mx;
    697:     vx = h * (i + 0.5);
    698:     vy = h * (j + 0.5);
    699:     vz = h * (k + 0.5);
    700:     PetscCall(VecSetValues(XX, 1, &linear_index, &vx, INSERT_VALUES));
    701:     PetscCall(VecSetValues(YY, 1, &linear_index, &vy, INSERT_VALUES));
    702:     PetscCall(VecSetValues(ZZ, 1, &linear_index, &vz, INSERT_VALUES));
    703:     for (is = 0; is < 2; is++) {
    704:       for (js = 0; js < 2; js++) {
    705:         for (ks = 0; ks < 2; ks++) {
    706:           ls = is * 4 + js * 2 + ks;
    707:           if (ls < user->ns) {
    708:             l = ls * n + linear_index;
    709:             /* remap */
    710:             subindex = l % n;
    711:             subvec   = l / n;
    712:             nrank    = 0;
    713:             while (subindex >= subranges[nrank + 1]) nrank++;
    714:             offset = subindex - subranges[nrank];
    715:             istart = 0;
    716:             for (kk = 0; kk < nrank; kk++) istart += user->ns * (subranges[kk + 1] - subranges[kk]);
    717:             istart += (subranges[nrank + 1] - subranges[nrank]) * subvec;
    718:             l = istart + offset;
    719:             v = 100 * PetscSinScalar(2 * PETSC_PI * (vx + 0.25 * is)) * PetscSinScalar(2 * PETSC_PI * (vy + 0.25 * js)) * PetscSinScalar(2 * PETSC_PI * (vz + 0.25 * ks));
    720:             PetscCall(VecSetValues(user->q, 1, &l, &v, INSERT_VALUES));
    721:           }
    722:         }
    723:       }
    724:     }
    725:   }

    727:   PetscCall(VecAssemblyBegin(XX));
    728:   PetscCall(VecAssemblyEnd(XX));
    729:   PetscCall(VecAssemblyBegin(YY));
    730:   PetscCall(VecAssemblyEnd(YY));
    731:   PetscCall(VecAssemblyBegin(ZZ));
    732:   PetscCall(VecAssemblyEnd(ZZ));
    733:   PetscCall(VecAssemblyBegin(user->q));
    734:   PetscCall(VecAssemblyEnd(user->q));

    736:   /* Compute true parameter function
    737:      ut = exp(-((x-0.25)^2+(y-0.25)^2+(z-0.25)^2)/0.05) - exp((x-0.75)^2-(y-0.75)^2-(z-0.75))^2/0.05) */
    738:   PetscCall(VecCopy(XX, XXwork));
    739:   PetscCall(VecCopy(YY, YYwork));
    740:   PetscCall(VecCopy(ZZ, ZZwork));

    742:   PetscCall(VecShift(XXwork, -0.25));
    743:   PetscCall(VecShift(YYwork, -0.25));
    744:   PetscCall(VecShift(ZZwork, -0.25));

    746:   PetscCall(VecPointwiseMult(XXwork, XXwork, XXwork));
    747:   PetscCall(VecPointwiseMult(YYwork, YYwork, YYwork));
    748:   PetscCall(VecPointwiseMult(ZZwork, ZZwork, ZZwork));

    750:   PetscCall(VecCopy(XXwork, UTwork));
    751:   PetscCall(VecAXPY(UTwork, 1.0, YYwork));
    752:   PetscCall(VecAXPY(UTwork, 1.0, ZZwork));
    753:   PetscCall(VecScale(UTwork, -20.0));
    754:   PetscCall(VecExp(UTwork));
    755:   PetscCall(VecCopy(UTwork, user->utrue));

    757:   PetscCall(VecCopy(XX, XXwork));
    758:   PetscCall(VecCopy(YY, YYwork));
    759:   PetscCall(VecCopy(ZZ, ZZwork));

    761:   PetscCall(VecShift(XXwork, -0.75));
    762:   PetscCall(VecShift(YYwork, -0.75));
    763:   PetscCall(VecShift(ZZwork, -0.75));

    765:   PetscCall(VecPointwiseMult(XXwork, XXwork, XXwork));
    766:   PetscCall(VecPointwiseMult(YYwork, YYwork, YYwork));
    767:   PetscCall(VecPointwiseMult(ZZwork, ZZwork, ZZwork));

    769:   PetscCall(VecCopy(XXwork, UTwork));
    770:   PetscCall(VecAXPY(UTwork, 1.0, YYwork));
    771:   PetscCall(VecAXPY(UTwork, 1.0, ZZwork));
    772:   PetscCall(VecScale(UTwork, -20.0));
    773:   PetscCall(VecExp(UTwork));

    775:   PetscCall(VecAXPY(user->utrue, -1.0, UTwork));

    777:   PetscCall(VecDestroy(&XX));
    778:   PetscCall(VecDestroy(&YY));
    779:   PetscCall(VecDestroy(&ZZ));
    780:   PetscCall(VecDestroy(&XXwork));
    781:   PetscCall(VecDestroy(&YYwork));
    782:   PetscCall(VecDestroy(&ZZwork));
    783:   PetscCall(VecDestroy(&UTwork));

    785:   /* Initial guess and reference model */
    786:   PetscCall(VecDuplicate(user->utrue, &user->ur));
    787:   PetscCall(VecSum(user->utrue, &meanut));
    788:   meanut = meanut / n;
    789:   PetscCall(VecSet(user->ur, meanut));
    790:   PetscCall(VecCopy(user->ur, user->u));

    792:   /* Generate Grad matrix */
    793:   PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Grad));
    794:   PetscCall(MatSetSizes(user->Grad, PETSC_DECIDE, ysubnlocal, m, n));
    795:   PetscCall(MatSetFromOptions(user->Grad));
    796:   PetscCall(MatMPIAIJSetPreallocation(user->Grad, 2, NULL, 2, NULL));
    797:   PetscCall(MatSeqAIJSetPreallocation(user->Grad, 2, NULL));
    798:   PetscCall(MatGetOwnershipRange(user->Grad, &istart, &iend));

    800:   for (i = istart; i < iend; i++) {
    801:     if (i < m / 3) {
    802:       iblock = i / (user->mx - 1);
    803:       j      = iblock * user->mx + (i % (user->mx - 1));
    804:       PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
    805:       j = j + 1;
    806:       PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
    807:     }
    808:     if (i >= m / 3 && i < 2 * m / 3) {
    809:       iblock = (i - m / 3) / (user->mx * (user->mx - 1));
    810:       j      = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
    811:       PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
    812:       j = j + user->mx;
    813:       PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
    814:     }
    815:     if (i >= 2 * m / 3) {
    816:       j = i - 2 * m / 3;
    817:       PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
    818:       j = j + user->mx * user->mx;
    819:       PetscCall(MatSetValues(user->Grad, 1, &i, 1, &j, &hinv, INSERT_VALUES));
    820:     }
    821:   }

    823:   PetscCall(MatAssemblyBegin(user->Grad, MAT_FINAL_ASSEMBLY));
    824:   PetscCall(MatAssemblyEnd(user->Grad, MAT_FINAL_ASSEMBLY));

    826:   /* Generate arithmetic averaging matrix Av */
    827:   PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Av));
    828:   PetscCall(MatSetSizes(user->Av, PETSC_DECIDE, ysubnlocal, m, n));
    829:   PetscCall(MatSetFromOptions(user->Av));
    830:   PetscCall(MatMPIAIJSetPreallocation(user->Av, 2, NULL, 2, NULL));
    831:   PetscCall(MatSeqAIJSetPreallocation(user->Av, 2, NULL));
    832:   PetscCall(MatGetOwnershipRange(user->Av, &istart, &iend));

    834:   for (i = istart; i < iend; i++) {
    835:     if (i < m / 3) {
    836:       iblock = i / (user->mx - 1);
    837:       j      = iblock * user->mx + (i % (user->mx - 1));
    838:       PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
    839:       j = j + 1;
    840:       PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
    841:     }
    842:     if (i >= m / 3 && i < 2 * m / 3) {
    843:       iblock = (i - m / 3) / (user->mx * (user->mx - 1));
    844:       j      = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
    845:       PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
    846:       j = j + user->mx;
    847:       PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
    848:     }
    849:     if (i >= 2 * m / 3) {
    850:       j = i - 2 * m / 3;
    851:       PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
    852:       j = j + user->mx * user->mx;
    853:       PetscCall(MatSetValues(user->Av, 1, &i, 1, &j, &half, INSERT_VALUES));
    854:     }
    855:   }

    857:   PetscCall(MatAssemblyBegin(user->Av, MAT_FINAL_ASSEMBLY));
    858:   PetscCall(MatAssemblyEnd(user->Av, MAT_FINAL_ASSEMBLY));

    860:   PetscCall(MatCreate(PETSC_COMM_WORLD, &user->L));
    861:   PetscCall(MatSetSizes(user->L, PETSC_DECIDE, ysubnlocal, m + n, n));
    862:   PetscCall(MatSetFromOptions(user->L));
    863:   PetscCall(MatMPIAIJSetPreallocation(user->L, 2, NULL, 2, NULL));
    864:   PetscCall(MatSeqAIJSetPreallocation(user->L, 2, NULL));
    865:   PetscCall(MatGetOwnershipRange(user->L, &istart, &iend));

    867:   for (i = istart; i < iend; i++) {
    868:     if (i < m / 3) {
    869:       iblock = i / (user->mx - 1);
    870:       j      = iblock * user->mx + (i % (user->mx - 1));
    871:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
    872:       j = j + 1;
    873:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
    874:     }
    875:     if (i >= m / 3 && i < 2 * m / 3) {
    876:       iblock = (i - m / 3) / (user->mx * (user->mx - 1));
    877:       j      = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
    878:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
    879:       j = j + user->mx;
    880:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
    881:     }
    882:     if (i >= 2 * m / 3 && i < m) {
    883:       j = i - 2 * m / 3;
    884:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &neg_hinv, INSERT_VALUES));
    885:       j = j + user->mx * user->mx;
    886:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &hinv, INSERT_VALUES));
    887:     }
    888:     if (i >= m) {
    889:       j = i - m;
    890:       PetscCall(MatSetValues(user->L, 1, &i, 1, &j, &sqrt_beta, INSERT_VALUES));
    891:     }
    892:   }
    893:   PetscCall(MatAssemblyBegin(user->L, MAT_FINAL_ASSEMBLY));
    894:   PetscCall(MatAssemblyEnd(user->L, MAT_FINAL_ASSEMBLY));
    895:   PetscCall(MatScale(user->L, PetscPowScalar(h, 1.5)));

    897:   /* Generate Div matrix */
    898:   if (!user->use_ptap) {
    899:     /* Generate Div matrix */
    900:     PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Div));
    901:     PetscCall(MatSetSizes(user->Div, ysubnlocal, PETSC_DECIDE, n, m));
    902:     PetscCall(MatSetFromOptions(user->Div));
    903:     PetscCall(MatMPIAIJSetPreallocation(user->Div, 4, NULL, 4, NULL));
    904:     PetscCall(MatSeqAIJSetPreallocation(user->Div, 6, NULL));
    905:     PetscCall(MatGetOwnershipRange(user->Grad, &istart, &iend));

    907:     for (i = istart; i < iend; i++) {
    908:       if (i < m / 3) {
    909:         iblock = i / (user->mx - 1);
    910:         j      = iblock * user->mx + (i % (user->mx - 1));
    911:         PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &neg_hinv, INSERT_VALUES));
    912:         j = j + 1;
    913:         PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &hinv, INSERT_VALUES));
    914:       }
    915:       if (i >= m / 3 && i < 2 * m / 3) {
    916:         iblock = (i - m / 3) / (user->mx * (user->mx - 1));
    917:         j      = iblock * user->mx * user->mx + ((i - m / 3) % (user->mx * (user->mx - 1)));
    918:         PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &neg_hinv, INSERT_VALUES));
    919:         j = j + user->mx;
    920:         PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &hinv, INSERT_VALUES));
    921:       }
    922:       if (i >= 2 * m / 3) {
    923:         j = i - 2 * m / 3;
    924:         PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &neg_hinv, INSERT_VALUES));
    925:         j = j + user->mx * user->mx;
    926:         PetscCall(MatSetValues(user->Div, 1, &j, 1, &i, &hinv, INSERT_VALUES));
    927:       }
    928:     }

    930:     PetscCall(MatAssemblyBegin(user->Div, MAT_FINAL_ASSEMBLY));
    931:     PetscCall(MatAssemblyEnd(user->Div, MAT_FINAL_ASSEMBLY));
    932:     PetscCall(MatDuplicate(user->Div, MAT_SHARE_NONZERO_PATTERN, &user->Divwork));
    933:   } else {
    934:     PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Diag));
    935:     PetscCall(MatSetSizes(user->Diag, PETSC_DECIDE, PETSC_DECIDE, m, m));
    936:     PetscCall(MatSetFromOptions(user->Diag));
    937:     PetscCall(MatMPIAIJSetPreallocation(user->Diag, 1, NULL, 0, NULL));
    938:     PetscCall(MatSeqAIJSetPreallocation(user->Diag, 1, NULL));
    939:   }

    941:   /* Build work vectors and matrices */
    942:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->S));
    943:   PetscCall(VecSetSizes(user->S, PETSC_DECIDE, m));
    944:   PetscCall(VecSetFromOptions(user->S));

    946:   PetscCall(VecCreate(PETSC_COMM_WORLD, &user->lwork));
    947:   PetscCall(VecSetSizes(user->lwork, PETSC_DECIDE, m + user->mx * user->mx * user->mx));
    948:   PetscCall(VecSetFromOptions(user->lwork));

    950:   PetscCall(MatDuplicate(user->Av, MAT_SHARE_NONZERO_PATTERN, &user->Avwork));

    952:   PetscCall(VecDuplicate(user->S, &user->Swork));
    953:   PetscCall(VecDuplicate(user->S, &user->Sdiag));
    954:   PetscCall(VecDuplicate(user->S, &user->Av_u));
    955:   PetscCall(VecDuplicate(user->S, &user->Twork));
    956:   PetscCall(VecDuplicate(user->y, &user->ywork));
    957:   PetscCall(VecDuplicate(user->u, &user->Ywork));
    958:   PetscCall(VecDuplicate(user->u, &user->uwork));
    959:   PetscCall(VecDuplicate(user->u, &user->js_diag));
    960:   PetscCall(VecDuplicate(user->c, &user->cwork));
    961:   PetscCall(VecDuplicate(user->d, &user->dwork));

    963:   /* Create a matrix-free shell user->Jd for computing B*x */
    964:   PetscCall(MatCreateShell(PETSC_COMM_WORLD, ysubnlocal * user->ns, ysubnlocal, user->nstate, user->ndesign, user, &user->Jd));
    965:   PetscCall(MatShellSetOperation(user->Jd, MATOP_MULT, (PetscErrorCodeFn *)DesignMatMult));
    966:   PetscCall(MatShellSetOperation(user->Jd, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)DesignMatMultTranspose));

    968:   /* Compute true state function ytrue given utrue */
    969:   PetscCall(VecDuplicate(user->y, &user->ytrue));

    971:   /* First compute Av_u = Av*exp(-u) */
    972:   PetscCall(VecSet(user->uwork, 0));
    973:   PetscCall(VecAXPY(user->uwork, -1.0, user->utrue)); /* Note: user->utrue */
    974:   PetscCall(VecExp(user->uwork));
    975:   PetscCall(MatMult(user->Av, user->uwork, user->Av_u));

    977:   /* Next form DSG = Div*S*Grad */
    978:   PetscCall(VecCopy(user->Av_u, user->Swork));
    979:   PetscCall(VecReciprocal(user->Swork));
    980:   if (user->use_ptap) {
    981:     PetscCall(MatDiagonalSet(user->Diag, user->Swork, INSERT_VALUES));
    982:     PetscCall(MatPtAP(user->Diag, user->Grad, MAT_INITIAL_MATRIX, 1.0, &user->DSG));
    983:   } else {
    984:     PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
    985:     PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Swork));

    987:     PetscCall(MatMatMult(user->Divwork, user->Grad, MAT_INITIAL_MATRIX, 1.0, &user->DSG));
    988:   }

    990:   PetscCall(MatSetOption(user->DSG, MAT_SYMMETRIC, PETSC_TRUE));
    991:   PetscCall(MatSetOption(user->DSG, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));

    993:   if (user->use_lrc == PETSC_TRUE) {
    994:     v = PetscSqrtReal(1.0 / user->ndesign);
    995:     PetscCall(PetscMalloc1(user->ndesign, &user->ones));

    997:     for (i = 0; i < user->ndesign; i++) user->ones[i] = v;
    998:     PetscCall(MatCreateDense(PETSC_COMM_WORLD, ysubnlocal, PETSC_DECIDE, user->ndesign, 1, user->ones, &user->Ones));
    999:     PetscCall(MatCreateLRC(user->DSG, user->Ones, NULL, user->Ones, &user->JsBlock));
    1000:     PetscCall(MatSetUp(user->JsBlock));
    1001:   } else {
    1002:     /* Create matrix-free shell user->Js for computing (A + h^3*e*e^T)*x */
    1003:     PetscCall(MatCreateShell(PETSC_COMM_WORLD, ysubnlocal, ysubnlocal, user->ndesign, user->ndesign, user, &user->JsBlock));
    1004:     PetscCall(MatShellSetOperation(user->JsBlock, MATOP_MULT, (PetscErrorCodeFn *)StateBlockMatMult));
    1005:     PetscCall(MatShellSetOperation(user->JsBlock, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)StateBlockMatMult));
    1006:   }
    1007:   PetscCall(MatSetOption(user->JsBlock, MAT_SYMMETRIC, PETSC_TRUE));
    1008:   PetscCall(MatSetOption(user->JsBlock, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
    1009:   PetscCall(MatCreateShell(PETSC_COMM_WORLD, ysubnlocal * user->ns, ysubnlocal * user->ns, user->nstate, user->nstate, user, &user->Js));
    1010:   PetscCall(MatShellSetOperation(user->Js, MATOP_MULT, (PetscErrorCodeFn *)StateMatMult));
    1011:   PetscCall(MatShellSetOperation(user->Js, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)StateMatMult));
    1012:   PetscCall(MatSetOption(user->Js, MAT_SYMMETRIC, PETSC_TRUE));
    1013:   PetscCall(MatSetOption(user->Js, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));

    1015:   PetscCall(MatCreateShell(PETSC_COMM_WORLD, ysubnlocal * user->ns, ysubnlocal * user->ns, user->nstate, user->nstate, user, &user->JsInv));
    1016:   PetscCall(MatShellSetOperation(user->JsInv, MATOP_MULT, (PetscErrorCodeFn *)StateInvMatMult));
    1017:   PetscCall(MatShellSetOperation(user->JsInv, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)StateInvMatMult));
    1018:   PetscCall(MatSetOption(user->JsInv, MAT_SYMMETRIC, PETSC_TRUE));
    1019:   PetscCall(MatSetOption(user->JsInv, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));

    1021:   PetscCall(MatSetOption(user->DSG, MAT_SYMMETRIC, PETSC_TRUE));
    1022:   PetscCall(MatSetOption(user->DSG, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
    1023:   /* Now solve for ytrue */
    1024:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &user->solver));
    1025:   PetscCall(KSPSetFromOptions(user->solver));

    1027:   PetscCall(KSPSetOperators(user->solver, user->JsBlock, user->DSG));

    1029:   PetscCall(MatMult(user->JsInv, user->q, user->ytrue));
    1030:   /* First compute Av_u = Av*exp(-u) */
    1031:   PetscCall(VecSet(user->uwork, 0));
    1032:   PetscCall(VecAXPY(user->uwork, -1.0, user->u)); /* Note: user->u */
    1033:   PetscCall(VecExp(user->uwork));
    1034:   PetscCall(MatMult(user->Av, user->uwork, user->Av_u));

    1036:   /* Next update DSG = Div*S*Grad  with user->u */
    1037:   PetscCall(VecCopy(user->Av_u, user->Swork));
    1038:   PetscCall(VecReciprocal(user->Swork));
    1039:   if (user->use_ptap) {
    1040:     PetscCall(MatDiagonalSet(user->Diag, user->Swork, INSERT_VALUES));
    1041:     PetscCall(MatPtAP(user->Diag, user->Grad, MAT_REUSE_MATRIX, 1.0, &user->DSG));
    1042:   } else {
    1043:     PetscCall(MatCopy(user->Div, user->Divwork, SAME_NONZERO_PATTERN));
    1044:     PetscCall(MatDiagonalScale(user->Divwork, NULL, user->Av_u));
    1045:     PetscCall(MatProductNumeric(user->DSG));
    1046:   }

    1048:   /* Now solve for y */

    1050:   PetscCall(MatMult(user->JsInv, user->q, user->y));

    1052:   user->ksp_its_initial = user->ksp_its;
    1053:   user->ksp_its         = 0;
    1054:   /* Construct projection matrix Q (blocks) */
    1055:   PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Q));
    1056:   PetscCall(MatSetSizes(user->Q, dsubnlocal, ysubnlocal, user->ndata, user->ndesign));
    1057:   PetscCall(MatSetFromOptions(user->Q));
    1058:   PetscCall(MatMPIAIJSetPreallocation(user->Q, 8, NULL, 8, NULL));
    1059:   PetscCall(MatSeqAIJSetPreallocation(user->Q, 8, NULL));

    1061:   for (i = 0; i < user->mx; i++) {
    1062:     x[i] = h * (i + 0.5);
    1063:     y[i] = h * (i + 0.5);
    1064:     z[i] = h * (i + 0.5);
    1065:   }
    1066:   PetscCall(MatGetOwnershipRange(user->Q, &istart, &iend));

    1068:   nx = user->mx;
    1069:   ny = user->mx;
    1070:   nz = user->mx;
    1071:   for (i = istart; i < iend; i++) {
    1072:     xri = xr[i];
    1073:     im  = 0;
    1074:     xim = x[im];
    1075:     while (xri > xim && im < nx) {
    1076:       im  = im + 1;
    1077:       xim = x[im];
    1078:     }
    1079:     indx1 = im - 1;
    1080:     indx2 = im;
    1081:     dx1   = xri - x[indx1];
    1082:     dx2   = x[indx2] - xri;

    1084:     yri = yr[i];
    1085:     im  = 0;
    1086:     yim = y[im];
    1087:     while (yri > yim && im < ny) {
    1088:       im  = im + 1;
    1089:       yim = y[im];
    1090:     }
    1091:     indy1 = im - 1;
    1092:     indy2 = im;
    1093:     dy1   = yri - y[indy1];
    1094:     dy2   = y[indy2] - yri;

    1096:     zri = zr[i];
    1097:     im  = 0;
    1098:     zim = z[im];
    1099:     while (zri > zim && im < nz) {
    1100:       im  = im + 1;
    1101:       zim = z[im];
    1102:     }
    1103:     indz1 = im - 1;
    1104:     indz2 = im;
    1105:     dz1   = zri - z[indz1];
    1106:     dz2   = z[indz2] - zri;

    1108:     Dx = x[indx2] - x[indx1];
    1109:     Dy = y[indy2] - y[indy1];
    1110:     Dz = z[indz2] - z[indz1];

    1112:     j = indx1 + indy1 * nx + indz1 * nx * ny;
    1113:     v = (1 - dx1 / Dx) * (1 - dy1 / Dy) * (1 - dz1 / Dz);
    1114:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

    1116:     j = indx1 + indy1 * nx + indz2 * nx * ny;
    1117:     v = (1 - dx1 / Dx) * (1 - dy1 / Dy) * (1 - dz2 / Dz);
    1118:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

    1120:     j = indx1 + indy2 * nx + indz1 * nx * ny;
    1121:     v = (1 - dx1 / Dx) * (1 - dy2 / Dy) * (1 - dz1 / Dz);
    1122:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

    1124:     j = indx1 + indy2 * nx + indz2 * nx * ny;
    1125:     v = (1 - dx1 / Dx) * (1 - dy2 / Dy) * (1 - dz2 / Dz);
    1126:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

    1128:     j = indx2 + indy1 * nx + indz1 * nx * ny;
    1129:     v = (1 - dx2 / Dx) * (1 - dy1 / Dy) * (1 - dz1 / Dz);
    1130:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

    1132:     j = indx2 + indy1 * nx + indz2 * nx * ny;
    1133:     v = (1 - dx2 / Dx) * (1 - dy1 / Dy) * (1 - dz2 / Dz);
    1134:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

    1136:     j = indx2 + indy2 * nx + indz1 * nx * ny;
    1137:     v = (1 - dx2 / Dx) * (1 - dy2 / Dy) * (1 - dz1 / Dz);
    1138:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));

    1140:     j = indx2 + indy2 * nx + indz2 * nx * ny;
    1141:     v = (1 - dx2 / Dx) * (1 - dy2 / Dy) * (1 - dz2 / Dz);
    1142:     PetscCall(MatSetValues(user->Q, 1, &i, 1, &j, &v, INSERT_VALUES));
    1143:   }

    1145:   PetscCall(MatAssemblyBegin(user->Q, MAT_FINAL_ASSEMBLY));
    1146:   PetscCall(MatAssemblyEnd(user->Q, MAT_FINAL_ASSEMBLY));
    1147:   /* Create MQ (composed of blocks of Q */
    1148:   PetscCall(MatCreateShell(PETSC_COMM_WORLD, dsubnlocal * user->ns, PETSC_DECIDE, user->ndata * user->ns, user->nstate, user, &user->MQ));
    1149:   PetscCall(MatShellSetOperation(user->MQ, MATOP_MULT, (PetscErrorCodeFn *)QMatMult));
    1150:   PetscCall(MatShellSetOperation(user->MQ, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)QMatMultTranspose));

    1152:   /* Add noise to the measurement data */
    1153:   PetscCall(VecSet(user->ywork, 1.0));
    1154:   PetscCall(VecAYPX(user->ywork, user->noise, user->ytrue));
    1155:   PetscCall(MatMult(user->MQ, user->ywork, user->d));

    1157:   /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
    1158:   PetscCall(PetscFree(x));
    1159:   PetscCall(PetscFree(y));
    1160:   PetscCall(PetscFree(z));
    1161:   PetscCall(PetscLogStagePop());
    1162:   PetscFunctionReturn(PETSC_SUCCESS);
    1163: }

    1165: PetscErrorCode EllipticDestroy(AppCtx *user)
    1166: {
    1167:   PetscInt i;

    1169:   PetscFunctionBegin;
    1170:   PetscCall(MatDestroy(&user->DSG));
    1171:   PetscCall(KSPDestroy(&user->solver));
    1172:   PetscCall(MatDestroy(&user->Q));
    1173:   PetscCall(MatDestroy(&user->MQ));
    1174:   if (!user->use_ptap) {
    1175:     PetscCall(MatDestroy(&user->Div));
    1176:     PetscCall(MatDestroy(&user->Divwork));
    1177:   } else {
    1178:     PetscCall(MatDestroy(&user->Diag));
    1179:   }
    1180:   if (user->use_lrc) PetscCall(MatDestroy(&user->Ones));

    1182:   PetscCall(MatDestroy(&user->Grad));
    1183:   PetscCall(MatDestroy(&user->Av));
    1184:   PetscCall(MatDestroy(&user->Avwork));
    1185:   PetscCall(MatDestroy(&user->L));
    1186:   PetscCall(MatDestroy(&user->Js));
    1187:   PetscCall(MatDestroy(&user->Jd));
    1188:   PetscCall(MatDestroy(&user->JsBlock));
    1189:   PetscCall(MatDestroy(&user->JsInv));

    1191:   PetscCall(VecDestroy(&user->x));
    1192:   PetscCall(VecDestroy(&user->u));
    1193:   PetscCall(VecDestroy(&user->uwork));
    1194:   PetscCall(VecDestroy(&user->utrue));
    1195:   PetscCall(VecDestroy(&user->y));
    1196:   PetscCall(VecDestroy(&user->ywork));
    1197:   PetscCall(VecDestroy(&user->ytrue));
    1198:   PetscCall(VecDestroy(&user->c));
    1199:   PetscCall(VecDestroy(&user->cwork));
    1200:   PetscCall(VecDestroy(&user->ur));
    1201:   PetscCall(VecDestroy(&user->q));
    1202:   PetscCall(VecDestroy(&user->d));
    1203:   PetscCall(VecDestroy(&user->dwork));
    1204:   PetscCall(VecDestroy(&user->lwork));
    1205:   PetscCall(VecDestroy(&user->S));
    1206:   PetscCall(VecDestroy(&user->Swork));
    1207:   PetscCall(VecDestroy(&user->Sdiag));
    1208:   PetscCall(VecDestroy(&user->Ywork));
    1209:   PetscCall(VecDestroy(&user->Twork));
    1210:   PetscCall(VecDestroy(&user->Av_u));
    1211:   PetscCall(VecDestroy(&user->js_diag));
    1212:   PetscCall(ISDestroy(&user->s_is));
    1213:   PetscCall(ISDestroy(&user->d_is));
    1214:   PetscCall(VecDestroy(&user->suby));
    1215:   PetscCall(VecDestroy(&user->subd));
    1216:   PetscCall(VecDestroy(&user->subq));
    1217:   PetscCall(VecScatterDestroy(&user->state_scatter));
    1218:   PetscCall(VecScatterDestroy(&user->design_scatter));
    1219:   for (i = 0; i < user->ns; i++) {
    1220:     PetscCall(VecScatterDestroy(&user->yi_scatter[i]));
    1221:     PetscCall(VecScatterDestroy(&user->di_scatter[i]));
    1222:   }
    1223:   PetscCall(PetscFree(user->yi_scatter));
    1224:   PetscCall(PetscFree(user->di_scatter));
    1225:   if (user->use_lrc) {
    1226:     PetscCall(PetscFree(user->ones));
    1227:     PetscCall(MatDestroy(&user->Ones));
    1228:   }
    1229:   PetscFunctionReturn(PETSC_SUCCESS);
    1230: }

    1232: PetscErrorCode EllipticMonitor(Tao tao, void *ptr)
    1233: {
    1234:   Vec       X;
    1235:   PetscReal unorm, ynorm;
    1236:   AppCtx   *user = (AppCtx *)ptr;

    1238:   PetscFunctionBegin;
    1239:   PetscCall(TaoGetSolution(tao, &X));
    1240:   PetscCall(Scatter(X, user->ywork, user->state_scatter, user->uwork, user->design_scatter));
    1241:   PetscCall(VecAXPY(user->ywork, -1.0, user->ytrue));
    1242:   PetscCall(VecAXPY(user->uwork, -1.0, user->utrue));
    1243:   PetscCall(VecNorm(user->uwork, NORM_2, &unorm));
    1244:   PetscCall(VecNorm(user->ywork, NORM_2, &ynorm));
    1245:   PetscCall(PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n", (double)unorm, (double)ynorm));
    1246:   PetscFunctionReturn(PETSC_SUCCESS);
    1247: }

    1249: /*TEST

    1251:    build:
    1252:       requires: !complex

    1254:    test:
    1255:       args: -tao_monitor_constraint_norm -ns 1 -tao_type lcl -tao_gatol 1.e-3 -tao_max_it 11
    1256:       requires: !single

    1258:    test:
    1259:       suffix: 2
    1260:       args: -tao_monitor_constraint_norm -tao_type lcl -tao_max_it 11 -use_ptap -use_lrc -ns 1 -tao_gatol 1.e-3
    1261:       requires: !single

    1263: TEST*/