Actual source code: jbearing2.c

petsc-master 2017-02-28
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  1: /*
  2:   Include "petsctao.h" so we can use TAO solvers
  3:   Include "petscdmda.h" so that we can use distributed arrays (DMs) for managing
  4:   Include "petscksp.h" so we can set KSP type
  5:   the parallel mesh.
  6: */

  8:  #include <petsctao.h>
  9:  #include <petscdmda.h>

 11: static  char help[]=
 12: "This example demonstrates use of the TAO package to \n\
 13: solve a bound constrained minimization problem.  This example is based on \n\
 14: the problem DPJB from the MINPACK-2 test suite.  This pressure journal \n\
 15: bearing problem is an example of elliptic variational problem defined over \n\
 16: a two dimensional rectangle.  By discretizing the domain into triangular \n\
 17: elements, the pressure surrounding the journal bearing is defined as the \n\
 18: minimum of a quadratic function whose variables are bounded below by zero.\n\
 19: The command line options are:\n\
 20:   -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
 21:   -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
 22:  \n";

 24: /*T
 25:    Concepts: TAO^Solving a bound constrained minimization problem
 26:    Routines: TaoCreate();
 27:    Routines: TaoSetType(); TaoSetObjectiveAndGradientRoutine();
 28:    Routines: TaoSetHessianRoutine();
 29:    Routines: TaoSetVariableBounds();
 30:    Routines: TaoSetMonitor(); TaoSetConvergenceTest();
 31:    Routines: TaoSetInitialVector();
 32:    Routines: TaoSetFromOptions();
 33:    Routines: TaoSolve();
 34:    Routines: TaoDestroy();
 35:    Processors: n
 36: T*/

 38: /*
 39:    User-defined application context - contains data needed by the
 40:    application-provided call-back routines, FormFunctionGradient(),
 41:    FormHessian().
 42: */
 43: typedef struct {
 44:   /* problem parameters */
 45:   PetscReal      ecc;          /* test problem parameter */
 46:   PetscReal      b;            /* A dimension of journal bearing */
 47:   PetscInt       nx,ny;        /* discretization in x, y directions */

 49:   /* Working space */
 50:   DM          dm;           /* distributed array data structure */
 51:   Mat         A;            /* Quadratic Objective term */
 52:   Vec         B;            /* Linear Objective term */
 53: } AppCtx;

 55: /* User-defined routines */
 56: static PetscReal p(PetscReal xi, PetscReal ecc);
 57: static PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal *,Vec,void *);
 58: static PetscErrorCode FormHessian(Tao,Vec,Mat, Mat, void *);
 59: static PetscErrorCode ComputeB(AppCtx*);
 60: static PetscErrorCode Monitor(Tao, void*);
 61: static PetscErrorCode ConvergenceTest(Tao, void*);

 63: int main( int argc, char **argv )
 64: {
 65:   PetscErrorCode     ierr;               /* used to check for functions returning nonzeros */
 66:   PetscInt           Nx, Ny;             /* number of processors in x- and y- directions */
 67:   PetscInt           m;               /* number of local elements in vectors */
 68:   Vec                x;                  /* variables vector */
 69:   Vec                xl,xu;                  /* bounds vectors */
 70:   PetscReal          d1000 = 1000;
 71:   PetscBool          flg;              /* A return variable when checking for user options */
 72:   Tao                tao;                /* Tao solver context */
 73:   KSP                ksp;
 74:   AppCtx             user;               /* user-defined work context */
 75:   PetscReal          zero=0.0;           /* lower bound on all variables */

 77:   /* Initialize PETSC and TAO */
 78:   PetscInitialize( &argc, &argv,(char *)0,help );if (ierr) return ierr;

 80:   /* Set the default values for the problem parameters */
 81:   user.nx = 50; user.ny = 50; user.ecc = 0.1; user.b = 10.0;

 83:   /* Check for any command line arguments that override defaults */
 84:   PetscOptionsGetInt(NULL,NULL,"-mx",&user.nx,&flg);
 85:   PetscOptionsGetInt(NULL,NULL,"-my",&user.ny,&flg);
 86:   PetscOptionsGetReal(NULL,NULL,"-ecc",&user.ecc,&flg);
 87:   PetscOptionsGetReal(NULL,NULL,"-b",&user.b,&flg);


 90:   PetscPrintf(PETSC_COMM_WORLD,"\n---- Journal Bearing Problem SHB-----\n");
 91:   PetscPrintf(PETSC_COMM_WORLD,"mx: %D,  my: %D,  ecc: %g \n\n",user.nx,user.ny,(double)user.ecc);

 93:   /* Let Petsc determine the grid division */
 94:   Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;

 96:   /*
 97:      A two dimensional distributed array will help define this problem,
 98:      which derives from an elliptic PDE on two dimensional domain.  From
 99:      the distributed array, Create the vectors.
100:   */
101:   DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,user.nx,user.ny,Nx,Ny,1,1,NULL,NULL,&user.dm);
102:   DMSetFromOptions(user.dm);
103:   DMSetUp(user.dm);

105:   /*
106:      Extract global and local vectors from DM; the vector user.B is
107:      used solely as work space for the evaluation of the function,
108:      gradient, and Hessian.  Duplicate for remaining vectors that are
109:      the same types.
110:   */
111:   DMCreateGlobalVector(user.dm,&x); /* Solution */
112:   VecDuplicate(x,&user.B); /* Linear objective */


115:   /*  Create matrix user.A to store quadratic, Create a local ordering scheme. */
116:   VecGetLocalSize(x,&m);
117:   DMCreateMatrix(user.dm,&user.A);

119:   /* User defined function -- compute linear term of quadratic */
120:   ComputeB(&user);

122:   /* The TAO code begins here */

124:   /*
125:      Create the optimization solver
126:      Suitable methods: TAOGPCG, TAOBQPIP, TAOTRON, TAOBLMVM
127:   */
128:   TaoCreate(PETSC_COMM_WORLD,&tao);
129:   TaoSetType(tao,TAOBLMVM);


132:   /* Set the initial vector */
133:   VecSet(x, zero);
134:   TaoSetInitialVector(tao,x);

136:   /* Set the user function, gradient, hessian evaluation routines and data structures */
137:   TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void*) &user);

139:   TaoSetHessianRoutine(tao,user.A,user.A,FormHessian,(void*)&user);

141:   /* Set a routine that defines the bounds */
142:   VecDuplicate(x,&xl);
143:   VecDuplicate(x,&xu);
144:   VecSet(xl, zero);
145:   VecSet(xu, d1000);
146:   TaoSetVariableBounds(tao,xl,xu);

148:   TaoGetKSP(tao,&ksp);
149:   if (ksp) {
150:     KSPSetType(ksp,KSPCG);
151:   }

153:   PetscOptionsHasName(NULL,NULL,"-testmonitor",&flg);
154:   if (flg) {
155:     TaoSetMonitor(tao,Monitor,&user,NULL);
156:   }
157:   PetscOptionsHasName(NULL,NULL,"-testconvergence",&flg);
158:   if (flg) {
159:     TaoSetConvergenceTest(tao,ConvergenceTest,&user);
160:   }

162:   /* Check for any tao command line options */
163:   TaoSetFromOptions(tao);

165:   /* Solve the bound constrained problem */
166:   TaoSolve(tao);

168:   /* Free PETSc data structures */
169:   VecDestroy(&x);
170:   VecDestroy(&xl);
171:   VecDestroy(&xu);
172:   MatDestroy(&user.A);
173:   VecDestroy(&user.B);

175:   /* Free TAO data structures */
176:   TaoDestroy(&tao);
177:   DMDestroy(&user.dm);
178:   PetscFinalize();
179:   return ierr;
180: }


183: static PetscReal p(PetscReal xi, PetscReal ecc)
184: {
185:   PetscReal t=1.0+ecc*PetscCosScalar(xi);
186:   return (t*t*t);
187: }

189: PetscErrorCode ComputeB(AppCtx* user)
190: {
192:   PetscInt       i,j,k;
193:   PetscInt       nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
194:   PetscReal      two=2.0, pi=4.0*atan(1.0);
195:   PetscReal      hx,hy,ehxhy;
196:   PetscReal      temp,*b;
197:   PetscReal      ecc=user->ecc;

199:   nx=user->nx;
200:   ny=user->ny;
201:   hx=two*pi/(nx+1.0);
202:   hy=two*user->b/(ny+1.0);
203:   ehxhy = ecc*hx*hy;


206:   /*
207:      Get local grid boundaries
208:   */
209:   DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
210:   DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);

212:   /* Compute the linear term in the objective function */
213:   VecGetArray(user->B,&b);
214:   for (i=xs; i<xs+xm; i++){
215:     temp=PetscSinScalar((i+1)*hx);
216:     for (j=ys; j<ys+ym; j++){
217:       k=xm*(j-ys)+(i-xs);
218:       b[k]=  - ehxhy*temp;
219:     }
220:   }
221:   VecRestoreArray(user->B,&b);
222:   PetscLogFlops(5*xm*ym+3*xm);

224:   return 0;
225: }

227: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *fcn,Vec G,void *ptr)
228: {
229:   AppCtx*        user=(AppCtx*)ptr;
231:   PetscInt       i,j,k,kk;
232:   PetscInt       col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
233:   PetscReal      one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
234:   PetscReal      hx,hy,hxhy,hxhx,hyhy;
235:   PetscReal      xi,v[5];
236:   PetscReal      ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
237:   PetscReal      vmiddle, vup, vdown, vleft, vright;
238:   PetscReal      tt,f1,f2;
239:   PetscReal      *x,*g,zero=0.0;
240:   Vec            localX;

242:   nx=user->nx;
243:   ny=user->ny;
244:   hx=two*pi/(nx+1.0);
245:   hy=two*user->b/(ny+1.0);
246:   hxhy=hx*hy;
247:   hxhx=one/(hx*hx);
248:   hyhy=one/(hy*hy);

250:   DMGetLocalVector(user->dm,&localX);

252:   DMGlobalToLocalBegin(user->dm,X,INSERT_VALUES,localX);
253:   DMGlobalToLocalEnd(user->dm,X,INSERT_VALUES,localX);

255:   VecSet(G, zero);
256:   /*
257:     Get local grid boundaries
258:   */
259:   DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
260:   DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);

262:   VecGetArray(localX,&x);
263:   VecGetArray(G,&g);

265:   for (i=xs; i< xs+xm; i++){
266:     xi=(i+1)*hx;
267:     trule1=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc) ) / six; /* L(i,j) */
268:     trule2=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc) ) / six; /* U(i,j) */
269:     trule3=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc) ) / six; /* U(i+1,j) */
270:     trule4=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc) ) / six; /* L(i-1,j) */
271:     trule5=trule1; /* L(i,j-1) */
272:     trule6=trule2; /* U(i,j+1) */

274:     vdown=-(trule5+trule2)*hyhy;
275:     vleft=-hxhx*(trule2+trule4);
276:     vright= -hxhx*(trule1+trule3);
277:     vup=-hyhy*(trule1+trule6);
278:     vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);

280:     for (j=ys; j<ys+ym; j++){

282:       row=(j-gys)*gxm + (i-gxs);
283:        v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;

285:        k=0;
286:        if (j>gys){
287:          v[k]=vdown; col[k]=row - gxm; k++;
288:        }

290:        if (i>gxs){
291:          v[k]= vleft; col[k]=row - 1; k++;
292:        }

294:        v[k]= vmiddle; col[k]=row; k++;

296:        if (i+1 < gxs+gxm){
297:          v[k]= vright; col[k]=row+1; k++;
298:        }

300:        if (j+1 <gys+gym){
301:          v[k]= vup; col[k] = row+gxm; k++;
302:        }
303:        tt=0;
304:        for (kk=0;kk<k;kk++){
305:          tt+=v[kk]*x[col[kk]];
306:        }
307:        row=(j-ys)*xm + (i-xs);
308:        g[row]=tt;

310:      }

312:   }

314:   VecRestoreArray(localX,&x);
315:   VecRestoreArray(G,&g);

317:   DMRestoreLocalVector(user->dm,&localX);

319:   VecDot(X,G,&f1);
320:   VecDot(user->B,X,&f2);
321:   VecAXPY(G, one, user->B);
322:   *fcn = f1/2.0 + f2;


325:   PetscLogFlops((91 + 10*ym) * xm);
326:   return 0;

328: }


331: /*
332:    FormHessian computes the quadratic term in the quadratic objective function
333:    Notice that the objective function in this problem is quadratic (therefore a constant
334:    hessian).  If using a nonquadratic solver, then you might want to reconsider this function
335: */
336: PetscErrorCode FormHessian(Tao tao,Vec X,Mat hes, Mat Hpre, void *ptr)
337: {
338:   AppCtx*        user=(AppCtx*)ptr;
340:   PetscInt       i,j,k;
341:   PetscInt       col[5],row,nx,ny,xs,xm,gxs,gxm,ys,ym,gys,gym;
342:   PetscReal      one=1.0, two=2.0, six=6.0,pi=4.0*atan(1.0);
343:   PetscReal      hx,hy,hxhy,hxhx,hyhy;
344:   PetscReal      xi,v[5];
345:   PetscReal      ecc=user->ecc, trule1,trule2,trule3,trule4,trule5,trule6;
346:   PetscReal      vmiddle, vup, vdown, vleft, vright;
347:   PetscBool      assembled;

349:   nx=user->nx;
350:   ny=user->ny;
351:   hx=two*pi/(nx+1.0);
352:   hy=two*user->b/(ny+1.0);
353:   hxhy=hx*hy;
354:   hxhx=one/(hx*hx);
355:   hyhy=one/(hy*hy);

357:   /*
358:     Get local grid boundaries
359:   */
360:   DMDAGetCorners(user->dm,&xs,&ys,NULL,&xm,&ym,NULL);
361:   DMDAGetGhostCorners(user->dm,&gxs,&gys,NULL,&gxm,&gym,NULL);
362:   MatAssembled(hes,&assembled);
363:   if (assembled){MatZeroEntries(hes);}

365:   for (i=xs; i< xs+xm; i++){
366:     xi=(i+1)*hx;
367:     trule1=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi,ecc) ) / six; /* L(i,j) */
368:     trule2=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi,ecc) ) / six; /* U(i,j) */
369:     trule3=hxhy*( p(xi,ecc) + p(xi+hx,ecc) + p(xi+hx,ecc) ) / six; /* U(i+1,j) */
370:     trule4=hxhy*( p(xi,ecc) + p(xi-hx,ecc) + p(xi-hx,ecc) ) / six; /* L(i-1,j) */
371:     trule5=trule1; /* L(i,j-1) */
372:     trule6=trule2; /* U(i,j+1) */

374:     vdown=-(trule5+trule2)*hyhy;
375:     vleft=-hxhx*(trule2+trule4);
376:     vright= -hxhx*(trule1+trule3);
377:     vup=-hyhy*(trule1+trule6);
378:     vmiddle=(hxhx)*(trule1+trule2+trule3+trule4)+hyhy*(trule1+trule2+trule5+trule6);
379:     v[0]=0; v[1]=0; v[2]=0; v[3]=0; v[4]=0;

381:     for (j=ys; j<ys+ym; j++){
382:       row=(j-gys)*gxm + (i-gxs);

384:       k=0;
385:       if (j>gys){
386:         v[k]=vdown; col[k]=row - gxm; k++;
387:       }

389:       if (i>gxs){
390:         v[k]= vleft; col[k]=row - 1; k++;
391:       }

393:       v[k]= vmiddle; col[k]=row; k++;

395:       if (i+1 < gxs+gxm){
396:         v[k]= vright; col[k]=row+1; k++;
397:       }

399:       if (j+1 <gys+gym){
400:         v[k]= vup; col[k] = row+gxm; k++;
401:       }
402:       MatSetValuesLocal(hes,1,&row,k,col,v,INSERT_VALUES);

404:     }

406:   }

408:   /*
409:      Assemble matrix, using the 2-step process:
410:      MatAssemblyBegin(), MatAssemblyEnd().
411:      By placing code between these two statements, computations can be
412:      done while messages are in transition.
413:   */
414:   MatAssemblyBegin(hes,MAT_FINAL_ASSEMBLY);
415:   MatAssemblyEnd(hes,MAT_FINAL_ASSEMBLY);

417:   /*
418:     Tell the matrix we will never add a new nonzero location to the
419:     matrix. If we do it will generate an error.
420:   */
421:   MatSetOption(hes,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
422:   MatSetOption(hes,MAT_SYMMETRIC,PETSC_TRUE);

424:   PetscLogFlops(9*xm*ym+49*xm);
425:   MatNorm(hes,NORM_1,&hx);
426:   return 0;
427: }

429: PetscErrorCode Monitor(Tao tao, void *ctx)
430: {
431:   PetscErrorCode     ierr;
432:   PetscInt           its;
433:   PetscReal          f,gnorm,cnorm,xdiff;
434:   TaoConvergedReason reason;

437:   TaoGetSolutionStatus(tao, &its, &f, &gnorm, &cnorm, &xdiff, &reason);
438:   if (!(its%5)) {
439:     PetscPrintf(PETSC_COMM_WORLD,"iteration=%D\tf=%g\n",its,(double)f);
440:   }
441:   return(0);
442: }

444: PetscErrorCode ConvergenceTest(Tao tao, void *ctx)
445: {
446:   PetscErrorCode     ierr;
447:   PetscInt           its;
448:   PetscReal          f,gnorm,cnorm,xdiff;
449:   TaoConvergedReason reason;

452:   TaoGetSolutionStatus(tao, &its, &f, &gnorm, &cnorm, &xdiff, &reason);
453:   if (its == 100) {
454:     TaoSetConvergedReason(tao,TAO_DIVERGED_MAXITS);
455:   }
456:   return(0);

458: }