Actual source code: minsurf1.c

petsc-master 2018-01-17
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  1:  #include <petsctao.h>

  3: static char  help[] =
  4: "This example demonstrates use of the TAO package to\n\
  5: solve an unconstrained system of equations.  This example is based on a\n\
  6: problem from the MINPACK-2 test suite.  Given a rectangular 2-D domain and\n\
  7: boundary values along the edges of the domain, the objective is to find the\n\
  8: surface with the minimal area that satisfies the boundary conditions.\n\
  9: This application solves this problem using complimentarity -- We are actually\n\
 10: solving the system  (grad f)_i >= 0, if x_i == l_i \n\
 11:                     (grad f)_i = 0, if l_i < x_i < u_i \n\
 12:                     (grad f)_i <= 0, if x_i == u_i  \n\
 13: where f is the function to be minimized. \n\
 14: \n\
 15: The command line options are:\n\
 16:   -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
 17:   -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
 18:   -start <st>, where <st> =0 for zero vector, and an average of the boundary conditions otherwise \n\n";

 20: /*T
 21:    Concepts: TAO^Solving a complementarity problem
 22:    Routines: TaoCreate(); TaoDestroy();

 24:    Processors: 1
 25: T*/




 30: /*
 31:    User-defined application context - contains data needed by the
 32:    application-provided call-back routines, FormFunctionGradient(),
 33:    FormHessian().
 34: */
 35: typedef struct {
 36:   PetscInt  mx, my;
 37:   PetscReal *bottom, *top, *left, *right;
 38: } AppCtx;


 41: /* -------- User-defined Routines --------- */

 43: static PetscErrorCode MSA_BoundaryConditions(AppCtx *);
 44: static PetscErrorCode MSA_InitialPoint(AppCtx *, Vec);
 45: PetscErrorCode FormConstraints(Tao, Vec, Vec, void *);
 46: PetscErrorCode FormJacobian(Tao, Vec, Mat, Mat, void *);

 48: int main(int argc, char **argv)
 49: {
 51:   Vec            x;                 /* solution vector */
 52:   Vec            c;                 /* Constraints function vector */
 53:   Vec            xl,xu;             /* Bounds on the variables */
 54:   PetscBool      flg;               /* A return variable when checking for user options */
 55:   Tao            tao;               /* TAO solver context */
 56:   Mat            J;                 /* Jacobian matrix */
 57:   PetscInt       N;                 /* Number of elements in vector */
 58:   PetscScalar    lb =  PETSC_NINFINITY;      /* lower bound constant */
 59:   PetscScalar    ub =  PETSC_INFINITY;      /* upper bound constant */
 60:   AppCtx         user;                    /* user-defined work context */

 62:   /* Initialize PETSc, TAO */
 63:   PetscInitialize(&argc, &argv, (char *)0, help );

 65:   /* Specify default dimension of the problem */
 66:   user.mx = 4; user.my = 4;

 68:   /* Check for any command line arguments that override defaults */
 69:   PetscOptionsGetInt(NULL,NULL, "-mx", &user.mx, &flg);
 70:   PetscOptionsGetInt(NULL,NULL, "-my", &user.my, &flg);

 72:   /* Calculate any derived values from parameters */
 73:   N = user.mx*user.my;

 75:   PetscPrintf(PETSC_COMM_SELF,"\n---- Minimum Surface Area Problem -----\n");
 76:   PetscPrintf(PETSC_COMM_SELF,"mx:%D, my:%D\n", user.mx,user.my);

 78:   /* Create appropriate vectors and matrices */
 79:   VecCreateSeq(MPI_COMM_SELF, N, &x);
 80:   VecDuplicate(x, &c);
 81:   MatCreateSeqAIJ(MPI_COMM_SELF, N, N, 7, NULL, &J);

 83:   /* The TAO code begins here */

 85:   /* Create TAO solver and set desired solution method */
 86:   TaoCreate(PETSC_COMM_SELF,&tao);
 87:   TaoSetType(tao,TAOSSILS);

 89:   /* Set data structure */
 90:   TaoSetInitialVector(tao, x);

 92:   /*  Set routines for constraints function and Jacobian evaluation */
 93:   TaoSetConstraintsRoutine(tao, c, FormConstraints, (void *)&user);
 94:   TaoSetJacobianRoutine(tao, J, J, FormJacobian, (void *)&user);

 96:   /* Set the variable bounds */
 97:   MSA_BoundaryConditions(&user);

 99:   /* Set initial solution guess */
100:   MSA_InitialPoint(&user, x);

102:   /* Set Bounds on variables */
103:   VecDuplicate(x, &xl);
104:   VecDuplicate(x, &xu);
105:   VecSet(xl, lb);
106:   VecSet(xu, ub);
107:   TaoSetVariableBounds(tao,xl,xu);

109:   /* Check for any tao command line options */
110:   TaoSetFromOptions(tao);

112:   /* Solve the application */
113:   TaoSolve(tao);

115:   /* Free Tao data structures */
116:   TaoDestroy(&tao);

118:   /* Free PETSc data structures */
119:   VecDestroy(&x);
120:   VecDestroy(&xl);
121:   VecDestroy(&xu);
122:   VecDestroy(&c);
123:   MatDestroy(&J);

125:   /* Free user-created data structures */
126:   PetscFree(user.bottom);
127:   PetscFree(user.top);
128:   PetscFree(user.left);
129:   PetscFree(user.right);

131:   PetscFinalize();
132:   return ierr;
133: }

135: /* -------------------------------------------------------------------- */

137: /*  FormConstraints - Evaluates gradient of f.

139:     Input Parameters:
140: .   tao  - the TAO_APPLICATION context
141: .   X    - input vector
142: .   ptr  - optional user-defined context, as set by TaoSetConstraintsRoutine()

144:     Output Parameters:
145: .   G - vector containing the newly evaluated gradient
146: */
147: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec G, void *ptr)
148: {
149:   AppCtx         *user = (AppCtx *) ptr;
151:   PetscInt       i,j,row;
152:   PetscInt       mx=user->mx, my=user->my;
153:   PetscReal      hx=1.0/(mx+1),hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy;
154:   PetscReal      f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
155:   PetscReal      df1dxc,df2dxc,df3dxc,df4dxc,df5dxc,df6dxc;
156:   PetscScalar    zero=0.0;
157:   PetscScalar    *g, *x;

160:   /* Initialize vector to zero */
161:   VecSet(G, zero);

163:   /* Get pointers to vector data */
164:   VecGetArray(X, &x);
165:   VecGetArray(G, &g);

167:   /* Compute function over the locally owned part of the mesh */
168:   for (j=0; j<my; j++){
169:     for (i=0; i< mx; i++){
170:       row= j*mx + i;

172:       xc = x[row];
173:       xlt=xrb=xl=xr=xb=xt=xc;

175:       if (i==0){ /* left side */
176:         xl= user->left[j+1];
177:         xlt = user->left[j+2];
178:       } else {
179:         xl = x[row-1];
180:       }

182:       if (j==0){ /* bottom side */
183:         xb=user->bottom[i+1];
184:         xrb = user->bottom[i+2];
185:       } else {
186:         xb = x[row-mx];
187:       }

189:       if (i+1 == mx){ /* right side */
190:         xr=user->right[j+1];
191:         xrb = user->right[j];
192:       } else {
193:         xr = x[row+1];
194:       }

196:       if (j+1==0+my){ /* top side */
197:         xt=user->top[i+1];
198:         xlt = user->top[i];
199:       }else {
200:         xt = x[row+mx];
201:       }

203:       if (i>0 && j+1<my){
204:         xlt = x[row-1+mx];
205:       }
206:       if (j>0 && i+1<mx){
207:         xrb = x[row+1-mx];
208:       }

210:       d1 = (xc-xl);
211:       d2 = (xc-xr);
212:       d3 = (xc-xt);
213:       d4 = (xc-xb);
214:       d5 = (xr-xrb);
215:       d6 = (xrb-xb);
216:       d7 = (xlt-xl);
217:       d8 = (xt-xlt);

219:       df1dxc = d1*hydhx;
220:       df2dxc = ( d1*hydhx + d4*hxdhy );
221:       df3dxc = d3*hxdhy;
222:       df4dxc = ( d2*hydhx + d3*hxdhy );
223:       df5dxc = d2*hydhx;
224:       df6dxc = d4*hxdhy;

226:       d1 /= hx;
227:       d2 /= hx;
228:       d3 /= hy;
229:       d4 /= hy;
230:       d5 /= hy;
231:       d6 /= hx;
232:       d7 /= hy;
233:       d8 /= hx;

235:       f1 = PetscSqrtScalar( 1.0 + d1*d1 + d7*d7);
236:       f2 = PetscSqrtScalar( 1.0 + d1*d1 + d4*d4);
237:       f3 = PetscSqrtScalar( 1.0 + d3*d3 + d8*d8);
238:       f4 = PetscSqrtScalar( 1.0 + d3*d3 + d2*d2);
239:       f5 = PetscSqrtScalar( 1.0 + d2*d2 + d5*d5);
240:       f6 = PetscSqrtScalar( 1.0 + d4*d4 + d6*d6);

242:       df1dxc /= f1;
243:       df2dxc /= f2;
244:       df3dxc /= f3;
245:       df4dxc /= f4;
246:       df5dxc /= f5;
247:       df6dxc /= f6;

249:       g[row] = (df1dxc+df2dxc+df3dxc+df4dxc+df5dxc+df6dxc )/2.0;
250:     }
251:   }

253:   /* Restore vectors */
254:   VecRestoreArray(X, &x);
255:   VecRestoreArray(G, &g);
256:   PetscLogFlops(67*mx*my);
257:   return(0);
258: }

260: /* ------------------------------------------------------------------- */
261: /*
262:    FormJacobian - Evaluates Jacobian matrix.

264:    Input Parameters:
265: .  tao  - the TAO_APPLICATION context
266: .  X    - input vector
267: .  ptr  - optional user-defined context, as set by TaoSetJacobian()

269:    Output Parameters:
270: .  tH    - Jacobian matrix

272: */
273: PetscErrorCode FormJacobian(Tao tao, Vec X, Mat H, Mat tHPre, void *ptr)
274: {
275:   AppCtx            *user = (AppCtx *) ptr;
276:   PetscErrorCode    ierr;
277:   PetscInt          i,j,k,row;
278:   PetscInt          mx=user->mx, my=user->my;
279:   PetscInt          col[7];
280:   PetscReal         hx=1.0/(mx+1), hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy;
281:   PetscReal         f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
282:   PetscReal         hl,hr,ht,hb,hc,htl,hbr;
283:   const PetscScalar *x;
284:   PetscScalar       v[7];
285:   PetscBool         assembled;

287:   /* Set various matrix options */
288:   MatSetOption(H,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE);
289:   MatAssembled(H,&assembled);
290:   if (assembled){MatZeroEntries(H); }

292:   /* Get pointers to vector data */
293:   VecGetArrayRead(X, &x);

295:   /* Compute Jacobian over the locally owned part of the mesh */
296:   for (i=0; i< mx; i++){
297:     for (j=0; j<my; j++){
298:       row= j*mx + i;

300:       xc = x[row];
301:       xlt=xrb=xl=xr=xb=xt=xc;

303:       /* Left side */
304:       if (i==0){
305:         xl  = user->left[j+1];
306:         xlt = user->left[j+2];
307:       } else {
308:         xl = x[row-1];
309:       }

311:       if (j==0){
312:         xb  = user->bottom[i+1];
313:         xrb = user->bottom[i+2];
314:       } else {
315:         xb = x[row-mx];
316:       }

318:       if (i+1 == mx){
319:         xr  = user->right[j+1];
320:         xrb = user->right[j];
321:       } else {
322:         xr = x[row+1];
323:       }

325:       if (j+1==my){
326:         xt  = user->top[i+1];
327:         xlt = user->top[i];
328:       }else {
329:         xt = x[row+mx];
330:       }

332:       if (i>0 && j+1<my){
333:         xlt = x[row-1+mx];
334:       }
335:       if (j>0 && i+1<mx){
336:         xrb = x[row+1-mx];
337:       }


340:       d1 = (xc-xl)/hx;
341:       d2 = (xc-xr)/hx;
342:       d3 = (xc-xt)/hy;
343:       d4 = (xc-xb)/hy;
344:       d5 = (xrb-xr)/hy;
345:       d6 = (xrb-xb)/hx;
346:       d7 = (xlt-xl)/hy;
347:       d8 = (xlt-xt)/hx;

349:       f1 = PetscSqrtScalar( 1.0 + d1*d1 + d7*d7);
350:       f2 = PetscSqrtScalar( 1.0 + d1*d1 + d4*d4);
351:       f3 = PetscSqrtScalar( 1.0 + d3*d3 + d8*d8);
352:       f4 = PetscSqrtScalar( 1.0 + d3*d3 + d2*d2);
353:       f5 = PetscSqrtScalar( 1.0 + d2*d2 + d5*d5);
354:       f6 = PetscSqrtScalar( 1.0 + d4*d4 + d6*d6);


357:       hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+(-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2);
358:       hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+(-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4);
359:       ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+(-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4);
360:       hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+(-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2);

362:       hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6);
363:       htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3);

365:       hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) + hydhx*(1.0+d5*d5)/(f5*f5*f5) + hxdhy*(1.0+d6*d6)/(f6*f6*f6) +
366:            (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-2*d1*d4)/(f2*f2*f2) + (hxdhy*(1.0+d2*d2)+hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4);

368:       hl/=2.0; hr/=2.0; ht/=2.0; hb/=2.0; hbr/=2.0; htl/=2.0;  hc/=2.0;

370:       k=0;
371:       if (j>0){
372:         v[k]=hb; col[k]=row - mx; k++;
373:       }

375:       if (j>0 && i < mx -1){
376:         v[k]=hbr; col[k]=row - mx+1; k++;
377:       }

379:       if (i>0){
380:         v[k]= hl; col[k]=row - 1; k++;
381:       }

383:       v[k]= hc; col[k]=row; k++;

385:       if (i < mx-1 ){
386:         v[k]= hr; col[k]=row+1; k++;
387:       }

389:       if (i>0 && j < my-1 ){
390:         v[k]= htl; col[k] = row+mx-1; k++;
391:       }

393:       if (j < my-1 ){
394:         v[k]= ht; col[k] = row+mx; k++;
395:       }

397:       /*
398:          Set matrix values using local numbering, which was defined
399:          earlier, in the main routine.
400:       */
401:       MatSetValues(H,1,&row,k,col,v,INSERT_VALUES);
402:     }
403:   }

405:   /* Restore vectors */
406:   VecRestoreArrayRead(X,&x);

408:   /* Assemble the matrix */
409:   MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
410:   MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
411:   PetscLogFlops(199*mx*my);
412:   return(0);
413: }

415: /* ------------------------------------------------------------------- */
416: /*
417:    MSA_BoundaryConditions -  Calculates the boundary conditions for
418:    the region.

420:    Input Parameter:
421: .  user - user-defined application context

423:    Output Parameter:
424: .  user - user-defined application context
425: */
426: static PetscErrorCode MSA_BoundaryConditions(AppCtx * user)
427: {
428:   PetscErrorCode  ierr;
429:   PetscInt        i,j,k,limit=0,maxits=5;
430:   PetscInt        mx=user->mx,my=user->my;
431:   PetscInt        bsize=0, lsize=0, tsize=0, rsize=0;
432:   PetscReal       one=1.0, two=2.0, three=3.0, tol=1e-10;
433:   PetscReal       fnorm,det,hx,hy,xt=0,yt=0;
434:   PetscReal       u1,u2,nf1,nf2,njac11,njac12,njac21,njac22;
435:   PetscReal       b=-0.5, t=0.5, l=-0.5, r=0.5;
436:   PetscReal       *boundary;

439:   bsize=mx+2; lsize=my+2; rsize=my+2; tsize=mx+2;

441:   PetscMalloc1(bsize, &user->bottom);
442:   PetscMalloc1(tsize, &user->top);
443:   PetscMalloc1(lsize, &user->left);
444:   PetscMalloc1(rsize, &user->right);

446:   hx= (r-l)/(mx+1); hy=(t-b)/(my+1);

448:   for (j=0; j<4; j++){
449:     if (j==0){
450:       yt=b;
451:       xt=l;
452:       limit=bsize;
453:       boundary=user->bottom;
454:     } else if (j==1){
455:       yt=t;
456:       xt=l;
457:       limit=tsize;
458:       boundary=user->top;
459:     } else if (j==2){
460:       yt=b;
461:       xt=l;
462:       limit=lsize;
463:       boundary=user->left;
464:     } else { /* if  (j==3) */
465:       yt=b;
466:       xt=r;
467:       limit=rsize;
468:       boundary=user->right;
469:     }

471:     for (i=0; i<limit; i++){
472:       u1=xt;
473:       u2=-yt;
474:       for (k=0; k<maxits; k++){
475:         nf1=u1 + u1*u2*u2 - u1*u1*u1/three-xt;
476:         nf2=-u2 - u1*u1*u2 + u2*u2*u2/three-yt;
477:         fnorm=PetscSqrtScalar(nf1*nf1+nf2*nf2);
478:         if (fnorm <= tol) break;
479:         njac11=one+u2*u2-u1*u1;
480:         njac12=two*u1*u2;
481:         njac21=-two*u1*u2;
482:         njac22=-one - u1*u1 + u2*u2;
483:         det = njac11*njac22-njac21*njac12;
484:         u1 = u1-(njac22*nf1-njac12*nf2)/det;
485:         u2 = u2-(njac11*nf2-njac21*nf1)/det;
486:       }

488:       boundary[i]=u1*u1-u2*u2;
489:       if (j==0 || j==1) {
490:         xt=xt+hx;
491:       } else { /* if (j==2 || j==3) */
492:         yt=yt+hy;
493:       }
494:     }
495:   }
496:   return(0);
497: }

499: /* ------------------------------------------------------------------- */
500: /*
501:    MSA_InitialPoint - Calculates the initial guess in one of three ways.

503:    Input Parameters:
504: .  user - user-defined application context
505: .  X - vector for initial guess

507:    Output Parameters:
508: .  X - newly computed initial guess
509: */
510: static PetscErrorCode MSA_InitialPoint(AppCtx * user, Vec X)
511: {
513:   PetscInt       start=-1,i,j;
514:   PetscScalar    zero=0.0;
515:   PetscBool      flg;

518:   PetscOptionsGetInt(NULL,NULL,"-start",&start,&flg);

520:   if (flg && start==0){ /* The zero vector is reasonable */
521:     VecSet(X, zero);
522:   } else { /* Take an average of the boundary conditions */
523:     PetscInt    row;
524:     PetscInt    mx=user->mx,my=user->my;
525:     PetscScalar *x;

527:     /* Get pointers to vector data */
528:     VecGetArray(X,&x);

530:     /* Perform local computations */
531:     for (j=0; j<my; j++){
532:       for (i=0; i< mx; i++){
533:         row=(j)*mx + (i);
534:         x[row] = ( ((j+1)*user->bottom[i+1]+(my-j+1)*user->top[i+1])/(my+2)+ ((i+1)*user->left[j+1]+(mx-i+1)*user->right[j+1])/(mx+2))/2.0;
535:       }
536:     }

538:     /* Restore vectors */
539:     VecRestoreArray(X,&x);
540:   }
541:   return(0);
542: }


545: /*TEST

547:    build:
548:       requires: !complex

550:    test:
551:       args: -tao_monitor -tao_view -tao_type ssils
552:       requires: !single

554:    test:
555:       suffix: 2
556:       args: -tao_monitor -tao_view -tao_type ssfls

558: TEST*/