Date: 2021-03-03T22:28:16+00:00

Actual source code: elliptic.c
petsc-3.14.5 2021-03-03
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      1: #include <petsc/private/taoimpl.h>

      3: /*T
      4:    Concepts: TAO^Solving a system of nonlinear equations, nonlinear least squares
      5:    Routines: TaoCreate();
      6:    Routines: TaoSetType();
      7:    Routines: TaoSetInitialVector();
      8:    Routines: TaoSetObjectiveRoutine();
      9:    Routines: TaoSetGradientRoutine();
     10:    Routines: TaoSetConstraintsRoutine();
     11:    Routines: TaoSetJacobianStateRoutine();
     12:    Routines: TaoSetJacobianDesignRoutine();
     13:    Routines: TaoSetStateDesignIS();
     14:    Routines: TaoSetFromOptions();
     15:    Routines: TaoSolve();
     16:    Routines: TaoDestroy();
     17:    Processors: n
     18: T*/

     22: typedef struct {
     23:   PetscInt n; /* Number of total variables */
     24:   PetscInt m; /* Number of constraints */
     25:   PetscInt nstate;
     26:   PetscInt ndesign;
     27:   PetscInt mx; /* grid points in each direction */
     28:   PetscInt ns; /* Number of data samples (1<=ns<=8)
     29:                   Currently only ns=1 is supported */
     30:   PetscInt ndata; /* Number of data points per sample */
     31:   IS       s_is;
     32:   IS       d_is;

     34:   VecScatter state_scatter;
     35:   VecScatter design_scatter;
     36:   VecScatter *yi_scatter, *di_scatter;
     37:   Vec        suby,subq,subd;
     38:   Mat        Js,Jd,JsPrec,JsInv,JsBlock;

     40:   PetscReal alpha; /* Regularization parameter */
     41:   PetscReal beta; /* Weight attributed to ||u||^2 in regularization functional */
     42:   PetscReal noise; /* Amount of noise to add to data */
     43:   PetscReal *ones;
     44:   Mat       Q;
     45:   Mat       MQ;
     46:   Mat       L;

     48:   Mat Grad;
     49:   Mat Av,Avwork;
     50:   Mat Div, Divwork;
     51:   Mat DSG;
     52:   Mat Diag,Ones;

     55:   Vec q;
     56:   Vec ur; /* reference */

     58:   Vec d;
     59:   Vec dwork;

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

     63:   Vec y; /* state variables */
     64:   Vec ywork;

     66:   Vec ytrue;

     68:   Vec u; /* design variables */
     69:   Vec uwork;

     71:   Vec utrue;

     73:   Vec js_diag;

     75:   Vec c; /* constraint vector */
     76:   Vec cwork;

     78:   Vec lwork;
     79:   Vec S;
     80:   Vec Swork,Twork,Sdiag,Ywork;
     81:   Vec Av_u;

     83:   KSP solver;
     84:   PC  prec;

     86:   PetscReal tola,tolb,tolc,told;
     87:   PetscInt  ksp_its;
     88:   PetscInt  ksp_its_initial;
     89:   PetscLogStage stages[10];
     90:   PetscBool use_ptap;
     91:   PetscBool use_lrc;
     92: } AppCtx;

     94: PetscErrorCode FormFunction(Tao, Vec, PetscReal*, void*);
     95: PetscErrorCode FormGradient(Tao, Vec, Vec, void*);
     96: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal*, Vec, void*);
     97: PetscErrorCode FormJacobianState(Tao, Vec, Mat, Mat, Mat, void*);
     98: PetscErrorCode FormJacobianDesign(Tao, Vec, Mat,void*);
     99: PetscErrorCode FormConstraints(Tao, Vec, Vec, void*);
    100: PetscErrorCode FormHessian(Tao, Vec, Mat, Mat, void*);
    101: PetscErrorCode Gather(Vec, Vec, VecScatter, Vec, VecScatter);
    102: PetscErrorCode Scatter(Vec, Vec, VecScatter, Vec, VecScatter);
    103: PetscErrorCode EllipticInitialize(AppCtx*);
    104: PetscErrorCode EllipticDestroy(AppCtx*);
    105: PetscErrorCode EllipticMonitor(Tao, void*);

    107: PetscErrorCode StateBlockMatMult(Mat,Vec,Vec);
    108: PetscErrorCode StateMatMult(Mat,Vec,Vec);

    110: PetscErrorCode StateInvMatMult(Mat,Vec,Vec);
    111: PetscErrorCode DesignMatMult(Mat,Vec,Vec);
    112: PetscErrorCode DesignMatMultTranspose(Mat,Vec,Vec);

    114: PetscErrorCode QMatMult(Mat,Vec,Vec);
    115: PetscErrorCode QMatMultTranspose(Mat,Vec,Vec);

    117: static  char help[]="";

    119: int main(int argc, char **argv)
    120: {
    121:   PetscErrorCode     ierr;
    122:   Vec                x0;
    123:   Tao                tao;
    124:   AppCtx             user;
    125:   PetscInt           ntests = 1;
    126:   PetscInt           i;

    128:   PetscInitialize(&argc, &argv, (char*)0,help);if (ierr) return ierr;
    129:   user.mx = 8;
    130:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"elliptic example",NULL);
    131:   PetscOptionsInt("-mx","Number of grid points in each direction","",user.mx,&user.mx,NULL);
    132:   user.ns = 6;
    133:   PetscOptionsInt("-ns","Number of data samples (1<=ns<=8)","",user.ns,&user.ns,NULL);
    134:   user.ndata = 64;
    135:   PetscOptionsInt("-ndata","Numbers of data points per sample","",user.ndata,&user.ndata,NULL);
    136:   user.alpha = 0.1;
    137:   PetscOptionsReal("-alpha","Regularization parameter","",user.alpha,&user.alpha,NULL);
    138:   user.beta = 0.00001;
    139:   PetscOptionsReal("-beta","Weight attributed to ||u||^2 in regularization functional","",user.beta,&user.beta,NULL);
    140:   user.noise = 0.01;
    141:   PetscOptionsReal("-noise","Amount of noise to add to data","",user.noise,&user.noise,NULL);

    143:   user.use_ptap = PETSC_FALSE;
    144:   PetscOptionsBool("-use_ptap","Use ptap matrix for DSG","",user.use_ptap,&user.use_ptap,NULL);
    145:   user.use_lrc = PETSC_FALSE;
    146:   PetscOptionsBool("-use_lrc","Use lrc matrix for Js","",user.use_lrc,&user.use_lrc,NULL);
    147:   PetscOptionsInt("-ntests","Number of times to repeat TaoSolve","",ntests,&ntests,NULL);
    148:   PetscOptionsEnd();

    150:   user.m = user.ns*user.mx*user.mx*user.mx; /* number of constraints */
    151:   user.nstate =  user.m;
    152:   user.ndesign = user.mx*user.mx*user.mx;
    153:   user.n = user.nstate + user.ndesign; /* number of variables */

    155:   /* Create TAO solver and set desired solution method */
    156:   TaoCreate(PETSC_COMM_WORLD,&tao);
    157:   TaoSetType(tao,TAOLCL);

    159:   /* Set up initial vectors and matrices */
    160:   EllipticInitialize(&user);

    162:   Gather(user.x,user.y,user.state_scatter,user.u,user.design_scatter);
    163:   VecDuplicate(user.x,&x0);
    164:   VecCopy(user.x,x0);

    166:   /* Set solution vector with an initial guess */
    167:   TaoSetInitialVector(tao,user.x);
    168:   TaoSetObjectiveRoutine(tao, FormFunction, (void *)&user);
    169:   TaoSetGradientRoutine(tao, FormGradient, (void *)&user);
    170:   TaoSetConstraintsRoutine(tao, user.c, FormConstraints, (void *)&user);

    172:   TaoSetJacobianStateRoutine(tao, user.Js, NULL, user.JsInv, FormJacobianState, (void *)&user);
    173:   TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, (void *)&user);

    175:   TaoSetStateDesignIS(tao,user.s_is,user.d_is);
    176:   TaoSetFromOptions(tao);

    178:   /* SOLVE THE APPLICATION */
    179:   PetscLogStageRegister("Trials",&user.stages[1]);
    180:   PetscLogStagePush(user.stages[1]);
    181:   for (i=0; i<ntests; i++){
    182:     TaoSolve(tao);
    183:     PetscPrintf(PETSC_COMM_WORLD,"KSP Iterations = %D\n",user.ksp_its);
    184:     VecCopy(x0,user.x);
    185:   }
    186:   PetscLogStagePop();
    187:   PetscBarrier((PetscObject)user.x);
    188:   PetscPrintf(PETSC_COMM_WORLD,"KSP iterations within initialization: ");
    189:   PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its_initial);

    191:   TaoDestroy(&tao);
    192:   VecDestroy(&x0);
    193:   EllipticDestroy(&user);
    194:   PetscFinalize();
    195:   return ierr;
    196: }
    197: /* ------------------------------------------------------------------- */
    198: /*
    199:    dwork = Qy - d
    200:    lwork = L*(u-ur)
    201:    f = 1/2 * (dwork.dwork + alpha*lwork.lwork)
    202: */
    203: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
    204: {
    206:   PetscReal      d1=0,d2=0;
    207:   AppCtx         *user = (AppCtx*)ptr;

    210:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
    211:   MatMult(user->MQ,user->y,user->dwork);
    212:   VecAXPY(user->dwork,-1.0,user->d);
    213:   VecDot(user->dwork,user->dwork,&d1);
    214:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
    215:   MatMult(user->L,user->uwork,user->lwork);
    216:   VecDot(user->lwork,user->lwork,&d2);
    217:   *f = 0.5 * (d1 + user->alpha*d2);
    218:   return(0);
    219: }

    221: /* ------------------------------------------------------------------- */
    222: /*
    223:     state: g_s = Q' *(Qy - d)
    224:     design: g_d = alpha*L'*L*(u-ur)
    225: */
    226: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
    227: {
    229:   AppCtx         *user = (AppCtx*)ptr;

    232:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
    233:   MatMult(user->MQ,user->y,user->dwork);
    234:   VecAXPY(user->dwork,-1.0,user->d);
    235:   MatMultTranspose(user->MQ,user->dwork,user->ywork);
    236:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
    237:   MatMult(user->L,user->uwork,user->lwork);
    238:   MatMultTranspose(user->L,user->lwork,user->uwork);
    239:   VecScale(user->uwork, user->alpha);
    240:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
    241:   return(0);
    242: }

    244: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
    245: {
    247:   PetscReal      d1,d2;
    248:   AppCtx         *user = (AppCtx*)ptr;

    251:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
    252:   MatMult(user->MQ,user->y,user->dwork);
    253:   VecAXPY(user->dwork,-1.0,user->d);
    254:   VecDot(user->dwork,user->dwork,&d1);
    255:   MatMultTranspose(user->MQ,user->dwork,user->ywork);

    257:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
    258:   MatMult(user->L,user->uwork,user->lwork);
    259:   VecDot(user->lwork,user->lwork,&d2);
    260:   MatMultTranspose(user->L,user->lwork,user->uwork);
    261:   VecScale(user->uwork, user->alpha);
    262:   *f = 0.5 * (d1 + user->alpha*d2);
    263:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
    264:   return(0);
    265: }

    267: /* ------------------------------------------------------------------- */
    268: /* A
    269: MatShell object
    270: */
    271: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
    272: {
    274:   AppCtx         *user = (AppCtx*)ptr;

    277:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
    278:   /* DSG = Div * (1/Av_u) * Grad */
    279:   VecSet(user->uwork,0);
    280:   VecAXPY(user->uwork,-1.0,user->u);
    281:   VecExp(user->uwork);
    282:   MatMult(user->Av,user->uwork,user->Av_u);
    283:   VecCopy(user->Av_u,user->Swork);
    284:   VecReciprocal(user->Swork);
    285:   if (user->use_ptap) {
    286:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
    287:     MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
    288:   } else {
    289:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
    290:     MatDiagonalScale(user->Divwork,NULL,user->Swork);
    291:     MatProductNumeric(user->DSG);
    292:   }
    293:   return(0);
    294: }
    295: /* ------------------------------------------------------------------- */
    296: /* B */
    297: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
    298: {
    300:   AppCtx         *user = (AppCtx*)ptr;

    303:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
    304:   return(0);
    305: }

    307: PetscErrorCode StateBlockMatMult(Mat J_shell, Vec X, Vec Y)
    308: {
    310:   PetscReal      sum;
    311:   AppCtx         *user;

    314:   MatShellGetContext(J_shell,(void**)&user);
    315:   MatMult(user->DSG,X,Y);
    316:   VecSum(X,&sum);
    317:   sum /= user->ndesign;
    318:   VecShift(Y,sum);
    319:   return(0);
    320: }

    322: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
    323: {
    325:   PetscInt       i;
    326:   AppCtx         *user;

    329:   MatShellGetContext(J_shell,(void**)&user);
    330:   if (user->ns == 1) {
    331:     MatMult(user->JsBlock,X,Y);
    332:   } else {
    333:     for (i=0;i<user->ns;i++) {
    334:       Scatter(X,user->subq,user->yi_scatter[i],0,0);
    335:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
    336:       MatMult(user->JsBlock,user->subq,user->suby);
    337:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
    338:     }
    339:   }
    340:   return(0);
    341: }

    343: PetscErrorCode StateInvMatMult(Mat J_shell, Vec X, Vec Y)
    344: {
    346:   PetscInt       its,i;
    347:   AppCtx         *user;

    350:   MatShellGetContext(J_shell,(void**)&user);
    351:   KSPSetOperators(user->solver,user->JsBlock,user->DSG);
    352:   if (Y == user->ytrue) {
    353:     /* First solve is done using true solution to set up problem */
    354:     KSPSetTolerances(user->solver,1e-8,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    355:   } else {
    356:     KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    357:   }
    358:   if (user->ns == 1) {
    359:     KSPSolve(user->solver,X,Y);
    360:     KSPGetIterationNumber(user->solver,&its);
    361:     user->ksp_its+=its;
    362:   } else {
    363:     for (i=0;i<user->ns;i++) {
    364:       Scatter(X,user->subq,user->yi_scatter[i],0,0);
    365:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
    366:       KSPSolve(user->solver,user->subq,user->suby);
    367:       KSPGetIterationNumber(user->solver,&its);
    368:       user->ksp_its+=its;
    369:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
    370:     }
    371:   }
    372:   return(0);
    373: }
    374: PetscErrorCode QMatMult(Mat J_shell, Vec X, Vec Y)
    375: {
    377:   AppCtx         *user;
    378:   PetscInt       i;

    381:   MatShellGetContext(J_shell,(void**)&user);
    382:   if (user->ns == 1) {
    383:     MatMult(user->Q,X,Y);
    384:   } else {
    385:     for (i=0;i<user->ns;i++) {
    386:       Scatter(X,user->subq,user->yi_scatter[i],0,0);
    387:       Scatter(Y,user->subd,user->di_scatter[i],0,0);
    388:       MatMult(user->Q,user->subq,user->subd);
    389:       Gather(Y,user->subd,user->di_scatter[i],0,0);
    390:     }
    391:   }
    392:   return(0);
    393: }

    395: PetscErrorCode QMatMultTranspose(Mat J_shell, Vec X, Vec Y)
    396: {
    398:   AppCtx         *user;
    399:   PetscInt       i;

    402:   MatShellGetContext(J_shell,(void**)&user);
    403:   if (user->ns == 1) {
    404:     MatMultTranspose(user->Q,X,Y);
    405:   } else {
    406:     for (i=0;i<user->ns;i++) {
    407:       Scatter(X,user->subd,user->di_scatter[i],0,0);
    408:       Scatter(Y,user->suby,user->yi_scatter[i],0,0);
    409:       MatMultTranspose(user->Q,user->subd,user->suby);
    410:       Gather(Y,user->suby,user->yi_scatter[i],0,0);
    411:     }
    412:   }
    413:   return(0);
    414: }

    416: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
    417: {
    419:   PetscInt       i;
    420:   AppCtx         *user;

    423:   MatShellGetContext(J_shell,(void**)&user);

    425:   /* sdiag(1./v) */
    426:   VecSet(user->uwork,0);
    427:   VecAXPY(user->uwork,-1.0,user->u);
    428:   VecExp(user->uwork);

    430:   /* sdiag(1./((Av*(1./v)).^2)) */
    431:   MatMult(user->Av,user->uwork,user->Swork);
    432:   VecPointwiseMult(user->Swork,user->Swork,user->Swork);
    433:   VecReciprocal(user->Swork);

    435:   /* (Av * (sdiag(1./v) * b)) */
    436:   VecPointwiseMult(user->uwork,user->uwork,X);
    437:   MatMult(user->Av,user->uwork,user->Twork);

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

    442:   if (user->ns == 1) {
    443:     /* (sdiag(Grad*y(:,i)) */
    444:     MatMult(user->Grad,user->y,user->Twork);

    446:     /* Div * (sdiag(Grad*y(:,i)) * (sdiag(1./((Av*(1./v)).^2)) * (Av * (sdiag(1./v) * b)))) */
    447:     VecPointwiseMult(user->Swork,user->Twork,user->Swork);
    448:     MatMultTranspose(user->Grad,user->Swork,Y);
    449:   } else {
    450:     for (i=0;i<user->ns;i++) {
    451:       Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
    452:       Scatter(Y,user->subq,user->yi_scatter[i],0,0);

    454:       MatMult(user->Grad,user->suby,user->Twork);
    455:       VecPointwiseMult(user->Twork,user->Twork,user->Swork);
    456:       MatMultTranspose(user->Grad,user->Twork,user->subq);
    457:       Gather(user->y,user->suby,user->yi_scatter[i],0,0);
    458:       Gather(Y,user->subq,user->yi_scatter[i],0,0);
    459:     }
    460:   }
    461:   return(0);
    462: }

    464: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
    465: {
    467:   PetscInt       i;
    468:   AppCtx         *user;

    471:   MatShellGetContext(J_shell,(void**)&user);
    472:   VecZeroEntries(Y);

    474:   /* Sdiag = 1./((Av*(1./v)).^2) */
    475:   VecSet(user->uwork,0);
    476:   VecAXPY(user->uwork,-1.0,user->u);
    477:   VecExp(user->uwork);
    478:   MatMult(user->Av,user->uwork,user->Swork);
    479:   VecPointwiseMult(user->Sdiag,user->Swork,user->Swork);
    480:   VecReciprocal(user->Sdiag);

    482:   for (i=0;i<user->ns;i++) {
    483:     Scatter(X,user->subq,user->yi_scatter[i],0,0);
    484:     Scatter(user->y,user->suby,user->yi_scatter[i],0,0);

    486:     /* Swork = (Div' * b(:,i)) */
    487:     MatMult(user->Grad,user->subq,user->Swork);

    489:     /* Twork = Grad*y(:,i) */
    490:     MatMult(user->Grad,user->suby,user->Twork);

    492:     /* Twork = sdiag(Twork) * Swork */
    493:     VecPointwiseMult(user->Twork,user->Swork,user->Twork);

    496:     /* Swork = pointwisemult(Sdiag,Twork) */
    497:     VecPointwiseMult(user->Swork,user->Twork,user->Sdiag);

    499:     /* Ywork = Av' * Swork */
    500:     MatMultTranspose(user->Av,user->Swork,user->Ywork);

    502:     /* Ywork = pointwisemult(uwork,Ywork) */
    503:     VecPointwiseMult(user->Ywork,user->uwork,user->Ywork);
    504:     VecAXPY(Y,1.0,user->Ywork);
    505:     Gather(user->y,user->suby,user->yi_scatter[i],0,0);
    506:   }
    507:   return(0);
    508: }

    510: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
    511: {
    512:    /* C=Ay - q      A = Div * Sigma * Grad + hx*hx*hx*ones(n,n) */
    514:    PetscReal      sum;
    515:    PetscInt       i;
    516:    AppCtx         *user = (AppCtx*)ptr;

    519:    Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
    520:    if (user->ns == 1) {
    521:      MatMult(user->Grad,user->y,user->Swork);
    522:      VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
    523:      MatMultTranspose(user->Grad,user->Swork,C);
    524:      VecSum(user->y,&sum);
    525:      sum /= user->ndesign;
    526:      VecShift(C,sum);
    527:    } else {
    528:      for (i=0;i<user->ns;i++) {
    529:       Scatter(user->y,user->suby,user->yi_scatter[i],0,0);
    530:       Scatter(C,user->subq,user->yi_scatter[i],0,0);
    531:       MatMult(user->Grad,user->suby,user->Swork);
    532:       VecPointwiseDivide(user->Swork,user->Swork,user->Av_u);
    533:       MatMultTranspose(user->Grad,user->Swork,user->subq);

    535:       VecSum(user->suby,&sum);
    536:       sum /= user->ndesign;
    537:       VecShift(user->subq,sum);

    539:       Gather(user->y,user->suby,user->yi_scatter[i],0,0);
    540:       Gather(C,user->subq,user->yi_scatter[i],0,0);
    541:      }
    542:    }
    543:    VecAXPY(C,-1.0,user->q);
    544:    return(0);
    545: }

    547: PetscErrorCode Scatter(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
    548: {

    552:   VecScatterBegin(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
    553:   VecScatterEnd(scat1,x,sub1,INSERT_VALUES,SCATTER_FORWARD);
    554:   if (sub2) {
    555:     VecScatterBegin(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
    556:     VecScatterEnd(scat2,x,sub2,INSERT_VALUES,SCATTER_FORWARD);
    557:   }
    558:   return(0);
    559: }

    561: PetscErrorCode Gather(Vec x, Vec sub1, VecScatter scat1, Vec sub2, VecScatter scat2)
    562: {

    566:   VecScatterBegin(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
    567:   VecScatterEnd(scat1,sub1,x,INSERT_VALUES,SCATTER_REVERSE);
    568:   if (sub2) {
    569:     VecScatterBegin(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
    570:     VecScatterEnd(scat2,sub2,x,INSERT_VALUES,SCATTER_REVERSE);
    571:   }
    572:   return(0);
    573: }

    575: PetscErrorCode EllipticInitialize(AppCtx *user)
    576: {
    578:   PetscInt       m,n,i,j,k,l,linear_index,is,js,ks,ls,istart,iend,iblock;
    579:   Vec            XX,YY,ZZ,XXwork,YYwork,ZZwork,UTwork;
    580:   PetscReal      *x,*y,*z;
    581:   PetscReal      h,meanut;
    582:   PetscScalar    hinv,neg_hinv,half = 0.5,sqrt_beta;
    583:   PetscInt       im,indx1,indx2,indy1,indy2,indz1,indz2,nx,ny,nz;
    584:   IS             is_alldesign,is_allstate;
    585:   IS             is_from_d;
    586:   IS             is_from_y;
    587:   PetscInt       lo,hi,hi2,lo2,ysubnlocal,dsubnlocal;
    588:   const PetscInt *ranges, *subranges;
    589:   PetscMPIInt    size;
    590:   PetscReal      xri,yri,zri,xim,yim,zim,dx1,dx2,dy1,dy2,dz1,dz2,Dx,Dy,Dz;
    591:   PetscScalar    v,vx,vy,vz;
    592:   PetscInt       offset,subindex,subvec,nrank,kk;

    594:   PetscScalar xr[64] = {0.4970,     0.8498,     0.7814,     0.6268,     0.7782,     0.6402,     0.3617,     0.3160,
    595:                         0.3610,     0.5298,     0.6987,     0.3331,     0.7962,     0.5596,     0.3866,     0.6774,
    596:                         0.5407,     0.4518,     0.6702,     0.6061,     0.7580,     0.8997,     0.5198,     0.8326,
    597:                         0.2138,     0.9198,     0.3000,     0.2833,     0.8288,     0.7076,     0.1820,     0.0728,
    598:                         0.8447,     0.2367,     0.3239,     0.6413,     0.3114,     0.4731,     0.1192,     0.9273,
    599:                         0.5724,     0.4331,     0.5136,     0.3547,     0.4413,     0.2602,     0.5698,     0.7278,
    600:                         0.5261,     0.6230,     0.2454,     0.3948,     0.7479,     0.6582,     0.4660,     0.5594,
    601:                         0.7574,     0.1143,     0.5900,     0.1065,     0.4260,     0.3294,     0.8276,     0.0756};

    603:   PetscScalar yr[64] = {0.7345,     0.9120,     0.9288,     0.7528,     0.4463,     0.4985,     0.2497,     0.6256,
    604:                         0.3425,     0.9026,     0.6983,     0.4230,     0.7140,     0.2970,     0.4474,     0.8792,
    605:                         0.6604,     0.2485,     0.7968,     0.6127,     0.1796,     0.2437,     0.5938,     0.6137,
    606:                         0.3867,     0.5658,     0.4575,     0.1009,     0.0863,     0.3361,     0.0738,     0.3985,
    607:                         0.6602,     0.1437,     0.0934,     0.5983,     0.5950,     0.0763,     0.0768,     0.2288,
    608:                         0.5761,     0.1129,     0.3841,     0.6150,     0.6904,     0.6686,     0.1361,     0.4601,
    609:                         0.4491,     0.3716,     0.1969,     0.6537,     0.6743,     0.6991,     0.4811,     0.5480,
    610:                         0.1684,     0.4569,     0.6889,     0.8437,     0.3015,     0.2854,     0.8199,     0.2658};

    612:   PetscScalar zr[64] = {0.7668,     0.8573,     0.2654,     0.2719,     0.1060,     0.1311,     0.6232,     0.2295,
    613:                         0.8009,     0.2147,     0.2119,     0.9325,     0.4473,     0.3600,     0.3374,     0.3819,
    614:                         0.4066,     0.5801,     0.1673,     0.0959,     0.4638,     0.8236,     0.8800,     0.2939,
    615:                         0.2028,     0.8262,     0.2706,     0.6276,     0.9085,     0.6443,     0.8241,     0.0712,
    616:                         0.1824,     0.7789,     0.4389,     0.8415,     0.7055,     0.6639,     0.3653,     0.2078,
    617:                         0.1987,     0.2297,     0.4321,     0.8115,     0.4915,     0.7764,     0.4657,     0.4627,
    618:                         0.4569,     0.4232,     0.8514,     0.0674,     0.3227,     0.1055,     0.6690,     0.6313,
    619:                         0.9226,     0.5461,     0.4126,     0.2364,     0.6096,     0.7042,     0.3914,     0.0711};

    622:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
    623:   PetscLogStageRegister("Elliptic Setup",&user->stages[0]);
    624:   PetscLogStagePush(user->stages[0]);

    626:   /* Create u,y,c,x */
    627:   VecCreate(PETSC_COMM_WORLD,&user->u);
    628:   VecCreate(PETSC_COMM_WORLD,&user->y);
    629:   VecCreate(PETSC_COMM_WORLD,&user->c);
    630:   VecSetSizes(user->u,PETSC_DECIDE,user->ndesign);
    631:   VecSetFromOptions(user->u);
    632:   VecGetLocalSize(user->u,&ysubnlocal);
    633:   VecSetSizes(user->y,ysubnlocal*user->ns,user->nstate);
    634:   VecSetSizes(user->c,ysubnlocal*user->ns,user->m);
    635:   VecSetFromOptions(user->y);
    636:   VecSetFromOptions(user->c);

    638:   /*
    639:      *******************************
    640:      Create scatters for x <-> y,u
    641:      *******************************

    643:      If the state vector y and design vector u are partitioned as
    644:      [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
    645:      then the solution vector x is organized as
    646:      [y_1; u_1; y_2; u_2; ...; y_np; u_np].
    647:      The index sets user->s_is and user->d_is correspond to the indices of the
    648:      state and design variables owned by the current processor.
    649:   */
    650:   VecCreate(PETSC_COMM_WORLD,&user->x);

    652:   VecGetOwnershipRange(user->y,&lo,&hi);
    653:   VecGetOwnershipRange(user->u,&lo2,&hi2);

    655:   ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_allstate);
    656:   ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+lo2,1,&user->s_is);
    657:   ISCreateStride(PETSC_COMM_SELF,hi2-lo2,lo2,1,&is_alldesign);
    658:   ISCreateStride(PETSC_COMM_SELF,hi2-lo2,hi+lo2,1,&user->d_is);

    660:   VecSetSizes(user->x,hi-lo+hi2-lo2,user->n);
    661:   VecSetFromOptions(user->x);

    663:   VecScatterCreate(user->x,user->s_is,user->y,is_allstate,&user->state_scatter);
    664:   VecScatterCreate(user->x,user->d_is,user->u,is_alldesign,&user->design_scatter);
    665:   ISDestroy(&is_alldesign);
    666:   ISDestroy(&is_allstate);
    667:   /*
    668:      *******************************
    669:      Create scatter from y to y_1,y_2,...,y_ns
    670:      *******************************
    671:   */
    672:   PetscMalloc1(user->ns,&user->yi_scatter);
    673:   VecDuplicate(user->u,&user->suby);
    674:   VecDuplicate(user->u,&user->subq);

    676:   VecGetOwnershipRange(user->y,&lo2,&hi2);
    677:   istart = 0;
    678:   for (i=0; i<user->ns; i++){
    679:     VecGetOwnershipRange(user->suby,&lo,&hi);
    680:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_y);
    681:     VecScatterCreate(user->y,is_from_y,user->suby,NULL,&user->yi_scatter[i]);
    682:     istart = istart + hi-lo;
    683:     ISDestroy(&is_from_y);
    684:   }
    685:   /*
    686:      *******************************
    687:      Create scatter from d to d_1,d_2,...,d_ns
    688:      *******************************
    689:   */
    690:   VecCreate(PETSC_COMM_WORLD,&user->subd);
    691:   VecSetSizes(user->subd,PETSC_DECIDE,user->ndata);
    692:   VecSetFromOptions(user->subd);
    693:   VecCreate(PETSC_COMM_WORLD,&user->d);
    694:   VecGetLocalSize(user->subd,&dsubnlocal);
    695:   VecSetSizes(user->d,dsubnlocal*user->ns,user->ndata*user->ns);
    696:   VecSetFromOptions(user->d);
    697:   PetscMalloc1(user->ns,&user->di_scatter);

    699:   VecGetOwnershipRange(user->d,&lo2,&hi2);
    700:   istart = 0;
    701:   for (i=0; i<user->ns; i++){
    702:     VecGetOwnershipRange(user->subd,&lo,&hi);
    703:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo2+istart,1,&is_from_d);
    704:     VecScatterCreate(user->d,is_from_d,user->subd,NULL,&user->di_scatter[i]);
    705:     istart = istart + hi-lo;
    706:     ISDestroy(&is_from_d);
    707:   }

    709:   PetscMalloc1(user->mx,&x);
    710:   PetscMalloc1(user->mx,&y);
    711:   PetscMalloc1(user->mx,&z);

    713:   user->ksp_its = 0;
    714:   user->ksp_its_initial = 0;

    716:   n = user->mx * user->mx * user->mx;
    717:   m = 3 * user->mx * user->mx * (user->mx-1);
    718:   sqrt_beta = PetscSqrtScalar(user->beta);

    720:   VecCreate(PETSC_COMM_WORLD,&XX);
    721:   VecCreate(PETSC_COMM_WORLD,&user->q);
    722:   VecSetSizes(XX,ysubnlocal,n);
    723:   VecSetSizes(user->q,ysubnlocal*user->ns,user->m);
    724:   VecSetFromOptions(XX);
    725:   VecSetFromOptions(user->q);

    727:   VecDuplicate(XX,&YY);
    728:   VecDuplicate(XX,&ZZ);
    729:   VecDuplicate(XX,&XXwork);
    730:   VecDuplicate(XX,&YYwork);
    731:   VecDuplicate(XX,&ZZwork);
    732:   VecDuplicate(XX,&UTwork);
    733:   VecDuplicate(XX,&user->utrue);

    735:   /* map for striding q */
    736:   VecGetOwnershipRanges(user->q,&ranges);
    737:   VecGetOwnershipRanges(user->u,&subranges);

    739:   VecGetOwnershipRange(user->q,&lo2,&hi2);
    740:   VecGetOwnershipRange(user->u,&lo,&hi);
    741:   /* Generate 3D grid, and collect ns (1<=ns<=8) right-hand-side vectors into user->q */
    742:   h = 1.0/user->mx;
    743:   hinv = user->mx;
    744:   neg_hinv = -hinv;

    746:   VecGetOwnershipRange(XX,&istart,&iend);
    747:   for (linear_index=istart; linear_index<iend; linear_index++){
    748:     i = linear_index % user->mx;
    749:     j = ((linear_index-i)/user->mx) % user->mx;
    750:     k = ((linear_index-i)/user->mx-j) / user->mx;
    751:     vx = h*(i+0.5);
    752:     vy = h*(j+0.5);
    753:     vz = h*(k+0.5);
    754:     VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
    755:     VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
    756:     VecSetValues(ZZ,1,&linear_index,&vz,INSERT_VALUES);
    757:     for (is=0; is<2; is++){
    758:       for (js=0; js<2; js++){
    759:         for (ks=0; ks<2; ks++){
    760:           ls = is*4 + js*2 + ks;
    761:           if (ls<user->ns){
    762:             l =ls*n + linear_index;
    763:             /* remap */
    764:             subindex = l%n;
    765:             subvec = l/n;
    766:             nrank=0;
    767:             while (subindex >= subranges[nrank+1]) nrank++;
    768:             offset = subindex - subranges[nrank];
    769:             istart=0;
    770:             for (kk=0;kk<nrank;kk++) istart+=user->ns*(subranges[kk+1]-subranges[kk]);
    771:             istart += (subranges[nrank+1]-subranges[nrank])*subvec;
    772:             l = istart+offset;
    773:             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));
    774:             VecSetValues(user->q,1,&l,&v,INSERT_VALUES);
    775:           }
    776:         }
    777:       }
    778:     }
    779:   }

    781:   VecAssemblyBegin(XX);
    782:   VecAssemblyEnd(XX);
    783:   VecAssemblyBegin(YY);
    784:   VecAssemblyEnd(YY);
    785:   VecAssemblyBegin(ZZ);
    786:   VecAssemblyEnd(ZZ);
    787:   VecAssemblyBegin(user->q);
    788:   VecAssemblyEnd(user->q);

    790:   /* Compute true parameter function
    791:      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) */
    792:   VecCopy(XX,XXwork);
    793:   VecCopy(YY,YYwork);
    794:   VecCopy(ZZ,ZZwork);

    796:   VecShift(XXwork,-0.25);
    797:   VecShift(YYwork,-0.25);
    798:   VecShift(ZZwork,-0.25);

    800:   VecPointwiseMult(XXwork,XXwork,XXwork);
    801:   VecPointwiseMult(YYwork,YYwork,YYwork);
    802:   VecPointwiseMult(ZZwork,ZZwork,ZZwork);

    804:   VecCopy(XXwork,UTwork);
    805:   VecAXPY(UTwork,1.0,YYwork);
    806:   VecAXPY(UTwork,1.0,ZZwork);
    807:   VecScale(UTwork,-20.0);
    808:   VecExp(UTwork);
    809:   VecCopy(UTwork,user->utrue);

    811:   VecCopy(XX,XXwork);
    812:   VecCopy(YY,YYwork);
    813:   VecCopy(ZZ,ZZwork);

    815:   VecShift(XXwork,-0.75);
    816:   VecShift(YYwork,-0.75);
    817:   VecShift(ZZwork,-0.75);

    819:   VecPointwiseMult(XXwork,XXwork,XXwork);
    820:   VecPointwiseMult(YYwork,YYwork,YYwork);
    821:   VecPointwiseMult(ZZwork,ZZwork,ZZwork);

    823:   VecCopy(XXwork,UTwork);
    824:   VecAXPY(UTwork,1.0,YYwork);
    825:   VecAXPY(UTwork,1.0,ZZwork);
    826:   VecScale(UTwork,-20.0);
    827:   VecExp(UTwork);

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

    831:   VecDestroy(&XX);
    832:   VecDestroy(&YY);
    833:   VecDestroy(&ZZ);
    834:   VecDestroy(&XXwork);
    835:   VecDestroy(&YYwork);
    836:   VecDestroy(&ZZwork);
    837:   VecDestroy(&UTwork);

    839:   /* Initial guess and reference model */
    840:   VecDuplicate(user->utrue,&user->ur);
    841:   VecSum(user->utrue,&meanut);
    842:   meanut = meanut / n;
    843:   VecSet(user->ur,meanut);
    844:   VecCopy(user->ur,user->u);

    846:   /* Generate Grad matrix */
    847:   MatCreate(PETSC_COMM_WORLD,&user->Grad);
    848:   MatSetSizes(user->Grad,PETSC_DECIDE,ysubnlocal,m,n);
    849:   MatSetFromOptions(user->Grad);
    850:   MatMPIAIJSetPreallocation(user->Grad,2,NULL,2,NULL);
    851:   MatSeqAIJSetPreallocation(user->Grad,2,NULL);
    852:   MatGetOwnershipRange(user->Grad,&istart,&iend);

    854:   for (i=istart; i<iend; i++){
    855:     if (i<m/3){
    856:       iblock = i / (user->mx-1);
    857:       j = iblock*user->mx + (i % (user->mx-1));
    858:       MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
    859:       j = j+1;
    860:       MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
    861:     }
    862:     if (i>=m/3 && i<2*m/3){
    863:       iblock = (i-m/3) / (user->mx*(user->mx-1));
    864:       j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
    865:       MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
    866:       j = j + user->mx;
    867:       MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
    868:     }
    869:     if (i>=2*m/3){
    870:       j = i-2*m/3;
    871:       MatSetValues(user->Grad,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
    872:       j = j + user->mx*user->mx;
    873:       MatSetValues(user->Grad,1,&i,1,&j,&hinv,INSERT_VALUES);
    874:     }
    875:   }

    877:   MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
    878:   MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);

    880:   /* Generate arithmetic averaging matrix Av */
    881:   MatCreate(PETSC_COMM_WORLD,&user->Av);
    882:   MatSetSizes(user->Av,PETSC_DECIDE,ysubnlocal,m,n);
    883:   MatSetFromOptions(user->Av);
    884:   MatMPIAIJSetPreallocation(user->Av,2,NULL,2,NULL);
    885:   MatSeqAIJSetPreallocation(user->Av,2,NULL);
    886:   MatGetOwnershipRange(user->Av,&istart,&iend);

    888:   for (i=istart; i<iend; i++){
    889:     if (i<m/3){
    890:       iblock = i / (user->mx-1);
    891:       j = iblock*user->mx + (i % (user->mx-1));
    892:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
    893:       j = j+1;
    894:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
    895:     }
    896:     if (i>=m/3 && i<2*m/3){
    897:       iblock = (i-m/3) / (user->mx*(user->mx-1));
    898:       j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
    899:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
    900:       j = j + user->mx;
    901:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
    902:     }
    903:     if (i>=2*m/3){
    904:       j = i-2*m/3;
    905:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
    906:       j = j + user->mx*user->mx;
    907:       MatSetValues(user->Av,1,&i,1,&j,&half,INSERT_VALUES);
    908:     }
    909:   }

    911:   MatAssemblyBegin(user->Av,MAT_FINAL_ASSEMBLY);
    912:   MatAssemblyEnd(user->Av,MAT_FINAL_ASSEMBLY);

    914:   MatCreate(PETSC_COMM_WORLD,&user->L);
    915:   MatSetSizes(user->L,PETSC_DECIDE,ysubnlocal,m+n,n);
    916:   MatSetFromOptions(user->L);
    917:   MatMPIAIJSetPreallocation(user->L,2,NULL,2,NULL);
    918:   MatSeqAIJSetPreallocation(user->L,2,NULL);
    919:   MatGetOwnershipRange(user->L,&istart,&iend);

    921:   for (i=istart; i<iend; i++){
    922:     if (i<m/3){
    923:       iblock = i / (user->mx-1);
    924:       j = iblock*user->mx + (i % (user->mx-1));
    925:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
    926:       j = j+1;
    927:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
    928:     }
    929:     if (i>=m/3 && i<2*m/3){
    930:       iblock = (i-m/3) / (user->mx*(user->mx-1));
    931:       j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
    932:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
    933:       j = j + user->mx;
    934:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
    935:     }
    936:     if (i>=2*m/3 && i<m){
    937:       j = i-2*m/3;
    938:       MatSetValues(user->L,1,&i,1,&j,&neg_hinv,INSERT_VALUES);
    939:       j = j + user->mx*user->mx;
    940:       MatSetValues(user->L,1,&i,1,&j,&hinv,INSERT_VALUES);
    941:     }
    942:     if (i>=m){
    943:       j = i - m;
    944:       MatSetValues(user->L,1,&i,1,&j,&sqrt_beta,INSERT_VALUES);
    945:     }
    946:   }
    947:   MatAssemblyBegin(user->L,MAT_FINAL_ASSEMBLY);
    948:   MatAssemblyEnd(user->L,MAT_FINAL_ASSEMBLY);
    949:   MatScale(user->L,PetscPowScalar(h,1.5));

    951:   /* Generate Div matrix */
    952:   if (!user->use_ptap) {
    953:     /* Generate Div matrix */
    954:     MatCreate(PETSC_COMM_WORLD,&user->Div);
    955:     MatSetSizes(user->Div,ysubnlocal,PETSC_DECIDE,n,m);
    956:     MatSetFromOptions(user->Div);
    957:     MatMPIAIJSetPreallocation(user->Div,4,NULL,4,NULL);
    958:     MatSeqAIJSetPreallocation(user->Div,6,NULL);
    959:     MatGetOwnershipRange(user->Grad,&istart,&iend);

    961:     for (i=istart; i<iend; i++){
    962:       if (i<m/3){
    963:         iblock = i / (user->mx-1);
    964:         j = iblock*user->mx + (i % (user->mx-1));
    965:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
    966:         j = j+1;
    967:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
    968:       }
    969:       if (i>=m/3 && i<2*m/3){
    970:         iblock = (i-m/3) / (user->mx*(user->mx-1));
    971:         j = iblock*user->mx*user->mx + ((i-m/3) % (user->mx*(user->mx-1)));
    972:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
    973:         j = j + user->mx;
    974:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
    975:       }
    976:       if (i>=2*m/3){
    977:         j = i-2*m/3;
    978:         MatSetValues(user->Div,1,&j,1,&i,&neg_hinv,INSERT_VALUES);
    979:         j = j + user->mx*user->mx;
    980:         MatSetValues(user->Div,1,&j,1,&i,&hinv,INSERT_VALUES);
    981:       }
    982:     }

    984:     MatAssemblyBegin(user->Div,MAT_FINAL_ASSEMBLY);
    985:     MatAssemblyEnd(user->Div,MAT_FINAL_ASSEMBLY);
    986:     MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
    987:   } else {
    988:     MatCreate(PETSC_COMM_WORLD,&user->Diag);
    989:     MatSetSizes(user->Diag,PETSC_DECIDE,PETSC_DECIDE,m,m);
    990:     MatSetFromOptions(user->Diag);
    991:     MatMPIAIJSetPreallocation(user->Diag,1,NULL,0,NULL);
    992:     MatSeqAIJSetPreallocation(user->Diag,1,NULL);
    993:   }

    995:   /* Build work vectors and matrices */
    996:   VecCreate(PETSC_COMM_WORLD,&user->S);
    997:   VecSetSizes(user->S, PETSC_DECIDE, m);
    998:   VecSetFromOptions(user->S);

    1000:   VecCreate(PETSC_COMM_WORLD,&user->lwork);
    1001:   VecSetSizes(user->lwork,PETSC_DECIDE,m+user->mx*user->mx*user->mx);
    1002:   VecSetFromOptions(user->lwork);

    1004:   MatDuplicate(user->Av,MAT_SHARE_NONZERO_PATTERN,&user->Avwork);

    1006:   VecDuplicate(user->S,&user->Swork);
    1007:   VecDuplicate(user->S,&user->Sdiag);
    1008:   VecDuplicate(user->S,&user->Av_u);
    1009:   VecDuplicate(user->S,&user->Twork);
    1010:   VecDuplicate(user->y,&user->ywork);
    1011:   VecDuplicate(user->u,&user->Ywork);
    1012:   VecDuplicate(user->u,&user->uwork);
    1013:   VecDuplicate(user->u,&user->js_diag);
    1014:   VecDuplicate(user->c,&user->cwork);
    1015:   VecDuplicate(user->d,&user->dwork);

    1017:   /* Create a matrix-free shell user->Jd for computing B*x */
    1018:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal,user->nstate,user->ndesign,user,&user->Jd);
    1019:   MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
    1020:   MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);

    1022:   /* Compute true state function ytrue given utrue */
    1023:   VecDuplicate(user->y,&user->ytrue);

    1025:   /* First compute Av_u = Av*exp(-u) */
    1026:   VecSet(user->uwork, 0);
    1027:   VecAXPY(user->uwork,-1.0,user->utrue); /* Note: user->utrue */
    1028:   VecExp(user->uwork);
    1029:   MatMult(user->Av,user->uwork,user->Av_u);

    1031:   /* Next form DSG = Div*S*Grad */
    1032:   VecCopy(user->Av_u,user->Swork);
    1033:   VecReciprocal(user->Swork);
    1034:   if (user->use_ptap) {
    1035:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
    1036:     MatPtAP(user->Diag,user->Grad,MAT_INITIAL_MATRIX,1.0,&user->DSG);
    1037:   } else {
    1038:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
    1039:     MatDiagonalScale(user->Divwork,NULL,user->Swork);

    1041:     MatMatMult(user->Divwork,user->Grad,MAT_INITIAL_MATRIX,1.0,&user->DSG);
    1042:   }

    1044:   MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
    1045:   MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

    1047:   if (user->use_lrc == PETSC_TRUE) {
    1048:     v=PetscSqrtReal(1.0 /user->ndesign);
    1049:     PetscMalloc1(user->ndesign,&user->ones);

    1051:     for (i=0;i<user->ndesign;i++) {
    1052:       user->ones[i]=v;
    1053:     }
    1054:     MatCreateDense(PETSC_COMM_WORLD,ysubnlocal,PETSC_DECIDE,user->ndesign,1,user->ones,&user->Ones);
    1055:     MatAssemblyBegin(user->Ones, MAT_FINAL_ASSEMBLY);
    1056:     MatAssemblyEnd(user->Ones, MAT_FINAL_ASSEMBLY);
    1057:     MatCreateLRC(user->DSG,user->Ones,NULL,user->Ones,&user->JsBlock);
    1058:     MatSetUp(user->JsBlock);
    1059:   } else {
    1060:     /* Create matrix-free shell user->Js for computing (A + h^3*e*e^T)*x */
    1061:     MatCreateShell(PETSC_COMM_WORLD,ysubnlocal,ysubnlocal,user->ndesign,user->ndesign,user,&user->JsBlock);
    1062:     MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateBlockMatMult);
    1063:     MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateBlockMatMult);
    1064:   }
    1065:   MatSetOption(user->JsBlock,MAT_SYMMETRIC,PETSC_TRUE);
    1066:   MatSetOption(user->JsBlock,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
    1067:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->Js);
    1068:   MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
    1069:   MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMult);
    1070:   MatSetOption(user->Js,MAT_SYMMETRIC,PETSC_TRUE);
    1071:   MatSetOption(user->Js,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

    1073:   MatCreateShell(PETSC_COMM_WORLD,ysubnlocal*user->ns,ysubnlocal*user->ns,user->nstate,user->nstate,user,&user->JsInv);
    1074:   MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateInvMatMult);
    1075:   MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateInvMatMult);
    1076:   MatSetOption(user->JsInv,MAT_SYMMETRIC,PETSC_TRUE);
    1077:   MatSetOption(user->JsInv,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);

    1079:   MatSetOption(user->DSG,MAT_SYMMETRIC,PETSC_TRUE);
    1080:   MatSetOption(user->DSG,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
    1081:   /* Now solve for ytrue */
    1082:   KSPCreate(PETSC_COMM_WORLD,&user->solver);
    1083:   KSPSetFromOptions(user->solver);

    1085:   KSPSetOperators(user->solver,user->JsBlock,user->DSG);

    1087:   MatMult(user->JsInv,user->q,user->ytrue);
    1088:   /* First compute Av_u = Av*exp(-u) */
    1089:   VecSet(user->uwork,0);
    1090:   VecAXPY(user->uwork,-1.0,user->u); /* Note: user->u */
    1091:   VecExp(user->uwork);
    1092:   MatMult(user->Av,user->uwork,user->Av_u);

    1094:   /* Next update DSG = Div*S*Grad  with user->u */
    1095:   VecCopy(user->Av_u,user->Swork);
    1096:   VecReciprocal(user->Swork);
    1097:   if (user->use_ptap) {
    1098:     MatDiagonalSet(user->Diag,user->Swork,INSERT_VALUES);
    1099:     MatPtAP(user->Diag,user->Grad,MAT_REUSE_MATRIX,1.0,&user->DSG);
    1100:   } else {
    1101:     MatCopy(user->Div,user->Divwork,SAME_NONZERO_PATTERN);
    1102:     MatDiagonalScale(user->Divwork,NULL,user->Av_u);
    1103:     MatProductNumeric(user->DSG);
    1104:   }

    1106:   /* Now solve for y */

    1108:   MatMult(user->JsInv,user->q,user->y);

    1110:   user->ksp_its_initial = user->ksp_its;
    1111:   user->ksp_its = 0;
    1112:   /* Construct projection matrix Q (blocks) */
    1113:   MatCreate(PETSC_COMM_WORLD,&user->Q);
    1114:   MatSetSizes(user->Q,dsubnlocal,ysubnlocal,user->ndata,user->ndesign);
    1115:   MatSetFromOptions(user->Q);
    1116:   MatMPIAIJSetPreallocation(user->Q,8,NULL,8,NULL);
    1117:   MatSeqAIJSetPreallocation(user->Q,8,NULL);

    1119:   for (i=0; i<user->mx; i++){
    1120:     x[i] = h*(i+0.5);
    1121:     y[i] = h*(i+0.5);
    1122:     z[i] = h*(i+0.5);
    1123:   }
    1124:   MatGetOwnershipRange(user->Q,&istart,&iend);

    1126:   nx = user->mx; ny = user->mx; nz = user->mx;
    1127:   for (i=istart; i<iend; i++){

    1129:     xri = xr[i];
    1130:     im = 0;
    1131:     xim = x[im];
    1132:     while (xri>xim && im<nx){
    1133:       im = im+1;
    1134:       xim = x[im];
    1135:     }
    1136:     indx1 = im-1;
    1137:     indx2 = im;
    1138:     dx1 = xri - x[indx1];
    1139:     dx2 = x[indx2] - xri;

    1141:     yri = yr[i];
    1142:     im = 0;
    1143:     yim = y[im];
    1144:     while (yri>yim && im<ny){
    1145:       im = im+1;
    1146:       yim = y[im];
    1147:     }
    1148:     indy1 = im-1;
    1149:     indy2 = im;
    1150:     dy1 = yri - y[indy1];
    1151:     dy2 = y[indy2] - yri;

    1153:     zri = zr[i];
    1154:     im = 0;
    1155:     zim = z[im];
    1156:     while (zri>zim && im<nz){
    1157:       im = im+1;
    1158:       zim = z[im];
    1159:     }
    1160:     indz1 = im-1;
    1161:     indz2 = im;
    1162:     dz1 = zri - z[indz1];
    1163:     dz2 = z[indz2] - zri;

    1165:     Dx = x[indx2] - x[indx1];
    1166:     Dy = y[indy2] - y[indy1];
    1167:     Dz = z[indz2] - z[indz1];

    1169:     j = indx1 + indy1*nx + indz1*nx*ny;
    1170:     v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
    1171:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

    1173:     j = indx1 + indy1*nx + indz2*nx*ny;
    1174:     v = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
    1175:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

    1177:     j = indx1 + indy2*nx + indz1*nx*ny;
    1178:     v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
    1179:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

    1181:     j = indx1 + indy2*nx + indz2*nx*ny;
    1182:     v = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
    1183:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

    1185:     j = indx2 + indy1*nx + indz1*nx*ny;
    1186:     v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);
    1187:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

    1189:     j = indx2 + indy1*nx + indz2*nx*ny;
    1190:     v = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);
    1191:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

    1193:     j = indx2 + indy2*nx + indz1*nx*ny;
    1194:     v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);
    1195:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);

    1197:     j = indx2 + indy2*nx + indz2*nx*ny;
    1198:     v = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);
    1199:     MatSetValues(user->Q,1,&i,1,&j,&v,INSERT_VALUES);
    1200:   }

    1202:   MatAssemblyBegin(user->Q,MAT_FINAL_ASSEMBLY);
    1203:   MatAssemblyEnd(user->Q,MAT_FINAL_ASSEMBLY);
    1204:   /* Create MQ (composed of blocks of Q */
    1205:   MatCreateShell(PETSC_COMM_WORLD,dsubnlocal*user->ns,PETSC_DECIDE,user->ndata*user->ns,user->nstate,user,&user->MQ);
    1206:   MatShellSetOperation(user->MQ,MATOP_MULT,(void(*)(void))QMatMult);
    1207:   MatShellSetOperation(user->MQ,MATOP_MULT_TRANSPOSE,(void(*)(void))QMatMultTranspose);

    1209:   /* Add noise to the measurement data */
    1210:   VecSet(user->ywork,1.0);
    1211:   VecAYPX(user->ywork,user->noise,user->ytrue);
    1212:   MatMult(user->MQ,user->ywork,user->d);

    1214:   /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
    1215:   PetscFree(x);
    1216:   PetscFree(y);
    1217:   PetscFree(z);
    1218:   PetscLogStagePop();
    1219:   return(0);
    1220: }

    1222: PetscErrorCode EllipticDestroy(AppCtx *user)
    1223: {
    1225:   PetscInt       i;

    1228:   MatDestroy(&user->DSG);
    1229:   KSPDestroy(&user->solver);
    1230:   MatDestroy(&user->Q);
    1231:   MatDestroy(&user->MQ);
    1232:   if (!user->use_ptap) {
    1233:     MatDestroy(&user->Div);
    1234:     MatDestroy(&user->Divwork);
    1235:   } else {
    1236:     MatDestroy(&user->Diag);
    1237:   }
    1238:   if (user->use_lrc) {
    1239:     MatDestroy(&user->Ones);
    1240:   }

    1242:   MatDestroy(&user->Grad);
    1243:   MatDestroy(&user->Av);
    1244:   MatDestroy(&user->Avwork);
    1245:   MatDestroy(&user->L);
    1246:   MatDestroy(&user->Js);
    1247:   MatDestroy(&user->Jd);
    1248:   MatDestroy(&user->JsBlock);
    1249:   MatDestroy(&user->JsInv);

    1251:   VecDestroy(&user->x);
    1252:   VecDestroy(&user->u);
    1253:   VecDestroy(&user->uwork);
    1254:   VecDestroy(&user->utrue);
    1255:   VecDestroy(&user->y);
    1256:   VecDestroy(&user->ywork);
    1257:   VecDestroy(&user->ytrue);
    1258:   VecDestroy(&user->c);
    1259:   VecDestroy(&user->cwork);
    1260:   VecDestroy(&user->ur);
    1261:   VecDestroy(&user->q);
    1262:   VecDestroy(&user->d);
    1263:   VecDestroy(&user->dwork);
    1264:   VecDestroy(&user->lwork);
    1265:   VecDestroy(&user->S);
    1266:   VecDestroy(&user->Swork);
    1267:   VecDestroy(&user->Sdiag);
    1268:   VecDestroy(&user->Ywork);
    1269:   VecDestroy(&user->Twork);
    1270:   VecDestroy(&user->Av_u);
    1271:   VecDestroy(&user->js_diag);
    1272:   ISDestroy(&user->s_is);
    1273:   ISDestroy(&user->d_is);
    1274:   VecDestroy(&user->suby);
    1275:   VecDestroy(&user->subd);
    1276:   VecDestroy(&user->subq);
    1277:   VecScatterDestroy(&user->state_scatter);
    1278:   VecScatterDestroy(&user->design_scatter);
    1279:   for (i=0;i<user->ns;i++) {
    1280:     VecScatterDestroy(&user->yi_scatter[i]);
    1281:     VecScatterDestroy(&user->di_scatter[i]);
    1282:   }
    1283:   PetscFree(user->yi_scatter);
    1284:   PetscFree(user->di_scatter);
    1285:   if (user->use_lrc) {
    1286:     PetscFree(user->ones);
    1287:     MatDestroy(&user->Ones);
    1288:   }
    1289:   return(0);
    1290: }

    1292: PetscErrorCode EllipticMonitor(Tao tao, void *ptr)
    1293: {
    1295:   Vec            X;
    1296:   PetscReal      unorm,ynorm;
    1297:   AppCtx         *user = (AppCtx*)ptr;

    1300:   TaoGetSolutionVector(tao,&X);
    1301:   Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
    1302:   VecAXPY(user->ywork,-1.0,user->ytrue);
    1303:   VecAXPY(user->uwork,-1.0,user->utrue);
    1304:   VecNorm(user->uwork,NORM_2,&unorm);
    1305:   VecNorm(user->ywork,NORM_2,&ynorm);
    1306:   PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
    1307:   return(0);
    1308: }

    1313: /*TEST

    1315:    build:
    1316:       requires: !complex

    1318:    test:
    1319:       args: -tao_cmonitor -ns 1 -tao_type lcl -tao_gatol 1.e-3 -tao_max_it 11
    1320:       requires: !single

    1322:    test:
    1323:       suffix: 2
    1324:       args: -tao_cmonitor -tao_type lcl -tao_max_it 11 -use_ptap -use_lrc -ns 1 -tao_gatol 1.e-3
    1325:       requires: !single

    1327: TEST*/