Actual source code: eptorsion2.c

  1: /*$Id$*/

  3: /* Program usage: mpirun -np <proc> eptorsion2 [-help] [all TAO options] */

  5: /* ----------------------------------------------------------------------

  7:   Elastic-plastic torsion problem.  

  9:   The elastic plastic torsion problem arises from the determination 
 10:   of the stress field on an infinitely long cylindrical bar, which is
 11:   equivalent to the solution of the following problem:

 13:   min{ .5 * integral(||gradient(v(x))||^2 dx) - C * integral(v(x) dx)}
 14:   
 15:   where C is the torsion angle per unit length.

 17:   The uniprocessor version of this code is eptorsion1.c; the Fortran 
 18:   version of this code is eptorsion2f.F.

 20:   This application solves the problem without calculating hessians 
 21: ---------------------------------------------------------------------- */

 23: /*
 24:   Include "tao.h" so that we can use TAO solvers.  Note that this 
 25:   file automatically includes files for lower-level support, such as those
 26:   provided by the PETSc library:
 27:      petsc.h       - base PETSc routines   petscvec.h - vectors
 28:      petscsys.h    - sysem routines        petscmat.h - matrices
 29:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 30:      petscviewer.h - viewers               petscpc.h  - preconditioners
 31:   Include "petscda.h" so that we can use distributed arrays (DAs) for managing
 32:   the parallel mesh.
 33: */

 35: #include "tao.h"
 36: #include "petscda.h"

 38: static  char help[] = 
 39: "Demonstrates use of the TAO package to solve \n\
 40: unconstrained minimization problems in parallel.  This example is based on \n\
 41: the Elastic-Plastic Torsion (dept) problem from the MINPACK-2 test suite.\n\
 42: The command line options are:\n\
 43:   -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
 44:   -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
 45:   -par <param>, where <param> = angle of twist per unit length\n\n";

 47: /*T
 48:    Concepts: TAO - Solving an unconstrained minimization problem
 49:    Routines: TaoInitialize(); TaoFinalize();              
 50:    Routines: TaoApplicationCreate(); TaoAppDestroy();
 51:    Routines: TaoCreate(); TaoDestroy(); 
 52:    Routines: TaoAppSetObjectiveAndGradientRoutine();
 53:    Routines: TaoAppSetHessianMat(); TaoAppSetHessianRoutine();
 54:    Routines: TaoSetOptions();
 55:    Routines: TaoAppSetInitialSolutionVec();
 56:    Routines: TaoSolve(); TaoView(); TaoAppGetKSP();
 57:    Routines: TaoGetSolutionStatus(); 
 58:    Processors: n
 59: T*/



 63: /* 
 64:    User-defined application context - contains data needed by the 
 65:    application-provided call-back routines, FormFunction() and
 66:    FormGradient().
 67: */
 68: typedef struct {
 69:   /* parameters */
 70:    int           mx, my;         /* global discretization in x- and y-directions */
 71:    PetscReal        param;          /* nonlinearity parameter */

 73:   /* work space */
 74:    Vec           localX;         /* local vectors */
 75:    DA            da;             /* distributed array data structure */
 76: } AppCtx;

 78: /* -------- User-defined Routines --------- */

 80: int FormInitialGuess(AppCtx*,Vec);
 81: int FormFunctionGradient(TAO_APPLICATION,Vec,double*,Vec,void*);
 82: int ComputeHessian(TAO_APPLICATION,Vec,Mat*,Mat*,MatStructure*,void*);

 86: int main(int argc,char **argv)
 87: {
 88:   int             info;                  /* used to check for functions returning nonzeros */
 89:   Vec             x;                     /* solution, gradient vectors */
 90:   Mat             H;                     /* Hessian matrix */
 91:   int             Nx, Ny;                /* number of processes in x- and y-directions */
 92:   TAO_SOLVER      tao;                   /* TAO_SOLVER solver context */
 93:   TAO_APPLICATION torsionapp;            /* TAO application context */
 94:   TaoTerminateReason reason;
 95:   PetscTruth      flg;
 96:   int             iter;                  /* iteration information */
 97:   double          ff,gnorm;
 98:   AppCtx          user;                  /* application context */
 99:   KSP             ksp;

101:   /* Initialize TAO, PETSc contexts */
102:   info = PetscInitialize(&argc,&argv,(char *)0,help);
103:   info = TaoInitialize(&argc,&argv,(char *)0,help);

105:   /* Specify default parameters */
106:   user.param = 5.0; user.mx = 10; user.my = 10;
107:   Nx = Ny = PETSC_DECIDE;

109:   /* Check for any command line arguments that override defaults */
110:   info = PetscOptionsGetReal(TAO_NULL,"-par",&user.param,&flg); CHKERRQ(info);
111:   info = PetscOptionsGetInt(TAO_NULL,"-my",&user.my,&flg); CHKERRQ(info);
112:   info = PetscOptionsGetInt(TAO_NULL,"-mx",&user.mx,&flg); CHKERRQ(info);

114:   PetscPrintf(PETSC_COMM_WORLD,"\n---- Elastic-Plastic Torsion Problem -----\n");
115:   PetscPrintf(PETSC_COMM_WORLD,"mx: %d     my: %d   \n\n",user.mx,user.my);  

117:   /* Set up distributed array */
118:   info = DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,
119:                     user.mx,user.my,Nx,Ny,1,1,TAO_NULL,TAO_NULL,
120:                     &user.da); CHKERRQ(info);

122:   /* Create vectors */
123:   info = DACreateGlobalVector(user.da,&x); CHKERRQ(info);

125:   info = DACreateLocalVector(user.da,&user.localX); CHKERRQ(info);

127:   /* Create Hessian */
128:   info = DAGetMatrix(user.da,MATAIJ,&H); CHKERRQ(info);
129:   info = MatSetOption(H,MAT_SYMMETRIC); CHKERRQ(info);

131:   /* The TAO code begins here */

133:   /* Create TAO solver and set desired solution method */
134:   info = TaoCreate(MPI_COMM_WORLD,"tao_cg",&tao); CHKERRQ(info);
135:   info = TaoApplicationCreate(PETSC_COMM_WORLD,&torsionapp); CHKERRQ(info);

137:   /* Set initial solution guess */
138:   info = FormInitialGuess(&user,x); CHKERRQ(info);
139:   info = TaoAppSetInitialSolutionVec(torsionapp,x); CHKERRQ(info);

141:   /* Set routine for function and gradient evaluation */
142:   info = TaoAppSetObjectiveAndGradientRoutine(torsionapp,FormFunctionGradient,(void *)&user); CHKERRQ(info);

144:   info = TaoAppSetHessianMat(torsionapp,H,H); CHKERRQ(info);
145:   info = TaoAppSetHessianRoutine(torsionapp,ComputeHessian,(void*)&user); CHKERRQ(info);

147:   info = TaoAppGetKSP(torsionapp,&ksp); CHKERRQ(info);
148:   if (ksp) {                                              /* Modify the PETSc KSP structure */
149:     info = KSPSetType(ksp,KSPCG); CHKERRQ(info);
150:   }

152:   /* Check for any TAO command line options */
153:   info = TaoSetOptions(torsionapp,tao); CHKERRQ(info);

155:   /* SOLVE THE APPLICATION */
156:   info = TaoSolveApplication(torsionapp,tao);  CHKERRQ(info);

158:   /* Get information on termination */
159:   info = TaoGetSolutionStatus(tao,&iter,&ff,&gnorm,0,0,&reason); CHKERRQ(info);
160:   if (reason <= 0){
161:     PetscPrintf(MPI_COMM_WORLD, "Try another method! Iterations: %d, f: %4.2e, residual: %4.2e\n",
162:                 iter,ff,gnorm); CHKERRQ(info); 
163:   }  

165:   /* 
166:      To View TAO solver information use
167:       info = TaoView(tao); CHKERRQ(info);
168:   */

170:   /* Free TAO data structures */
171:   info = TaoDestroy(tao); CHKERRQ(info);
172:   info = TaoAppDestroy(torsionapp);  CHKERRQ(info);

174:   /* Free PETSc data structures */
175:   info = VecDestroy(x); CHKERRQ(info);
176:   info = MatDestroy(H); CHKERRQ(info);

178:   info = VecDestroy(user.localX); CHKERRQ(info);
179:   info = DADestroy(user.da); CHKERRQ(info);


182:   /* Finalize TAO and PETSc*/
183:   TaoFinalize();
184:   PetscFinalize();

186:   return 0;
187: }


190: /* ------------------------------------------------------------------- */
193: /*
194:     FormInitialGuess - Computes an initial approximation to the solution.

196:     Input Parameters:
197: .   user - user-defined application context
198: .   X    - vector

200:     Output Parameters:
201:     X    - vector
202: */
203: int FormInitialGuess(AppCtx *user,Vec X)
204: {
205:   int    info, i, j, k, mx = user->mx, my = user->my;
206:   int    xs, ys, xm, ym, gxm, gym, gxs, gys, xe, ye;
207:   PetscReal hx = 1.0/(mx+1), hy = 1.0/(my+1), temp, val;

209:   /* Get local mesh boundaries */
210:   info = DAGetCorners(user->da,&xs,&ys,TAO_NULL,&xm,&ym,TAO_NULL); CHKERRQ(info);
211:   info = DAGetGhostCorners(user->da,&gxs,&gys,TAO_NULL,&gxm,&gym,TAO_NULL); CHKERRQ(info);

213:   /* Compute initial guess over locally owned part of mesh */
214:   xe = xs+xm;
215:   ye = ys+ym;
216:   for (j=ys; j<ye; j++) {  /*  for (j=0; j<my; j++) */
217:     temp = TaoMin(j+1,my-j)*hy;
218:     for (i=xs; i<xe; i++) {  /*  for (i=0; i<mx; i++) */
219:       k   = (j-gys)*gxm + i-gxs;
220:       val = TaoMin((TaoMin(i+1,mx-i))*hx,temp);
221:       info = VecSetValuesLocal(X,1,&k,&val,ADD_VALUES); CHKERRQ(info);
222:     }
223:   }

225:   return 0;
226: }


229: /* ------------------------------------------------------------------ */
232: /* 
233:    FormFunctionGradient - Evaluates the function and corresponding gradient.
234:     
235:    Input Parameters:
236:    taoapp - the TAO_APPLICATION context
237:    X   - the input vector 
238:    ptr - optional user-defined context, as set by TaoSetFunction()

240:    Output Parameters:
241:    f   - the newly evaluated function
242:    G   - the newly evaluated gradient
243: */
244: int FormFunctionGradient(TAO_APPLICATION taoapp,Vec X,double *f,Vec G,void *ptr){

246:   AppCtx *user = (AppCtx *)ptr;
247:   int    info,i,j,k,ind;
248:   int    xe,ye,xsm,ysm,xep,yep;
249:   int    xs, ys, xm, ym, gxm, gym, gxs, gys;
250:   int    mx = user->mx, my = user->my;
251:   PetscReal three = 3.0, zero = 0.0, *x, floc, cdiv3 = user->param/three;
252:   PetscReal p5 = 0.5, area, val, flin, fquad;
253:   PetscReal v,vb,vl,vr,vt,dvdx,dvdy;
254:   PetscReal hx = 1.0/(user->mx + 1); 
255:   PetscReal hy = 1.0/(user->my + 1);  
256:   Vec    localX = user->localX;


259:   /* Initialize */
260:   flin = fquad = zero;

262:   info = VecSet(G, zero); CHKERRQ(info);
263:   /*
264:      Scatter ghost points to local vector,using the 2-step process
265:         DAGlobalToLocalBegin(),DAGlobalToLocalEnd().
266:      By placing code between these two statements, computations can be
267:      done while messages are in transition.
268:   */
269:   info = DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
270:   info = DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);

272:   /* Get pointer to vector data */
273:   info = VecGetArray(localX,&x); CHKERRQ(info);

275:   /* Get local mesh boundaries */
276:   info = DAGetCorners(user->da,&xs,&ys,TAO_NULL,&xm,&ym,TAO_NULL); CHKERRQ(info);
277:   info = DAGetGhostCorners(user->da,&gxs,&gys,TAO_NULL,&gxm,&gym,TAO_NULL); CHKERRQ(info);

279:   /* Set local loop dimensions */
280:   xe = xs+xm;
281:   ye = ys+ym;
282:   if (xs == 0)  xsm = xs-1;
283:   else          xsm = xs;
284:   if (ys == 0)  ysm = ys-1;
285:   else          ysm = ys;
286:   if (xe == mx) xep = xe+1;
287:   else          xep = xe;
288:   if (ye == my) yep = ye+1;
289:   else          yep = ye;

291:   /* Compute local gradient contributions over the lower triangular elements */
292:   for (j=ysm; j<ye; j++) {  /*  for (j=-1; j<my; j++) */
293:     for (i=xsm; i<xe; i++) {  /*   for (i=-1; i<mx; i++) */
294:       k = (j-gys)*gxm + i-gxs;
295:       v = zero;
296:       vr = zero;
297:       vt = zero;
298:       if (i >= 0 && j >= 0) v = x[k];
299:       if (i < mx-1 && j > -1) vr = x[k+1];
300:       if (i > -1 && j < my-1) vt = x[k+gxm];
301:       dvdx = (vr-v)/hx;
302:       dvdy = (vt-v)/hy;
303:       if (i != -1 && j != -1) {
304:         ind = k; val = - dvdx/hx - dvdy/hy - cdiv3;
305:         info = VecSetValuesLocal(G,1,&k,&val,ADD_VALUES); CHKERRQ(info);
306:       }
307:       if (i != mx-1 && j != -1) {
308:         ind = k+1; val =  dvdx/hx - cdiv3;
309:         info = VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES); CHKERRQ(info);
310:       }
311:       if (i != -1 && j != my-1) {
312:         ind = k+gxm; val = dvdy/hy - cdiv3;
313:         info = VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES); CHKERRQ(info);
314:       }
315:       fquad += dvdx*dvdx + dvdy*dvdy;
316:       flin -= cdiv3 * (v + vr + vt);
317:     }
318:   }

320:   /* Compute local gradient contributions over the upper triangular elements */
321:   for (j=ys; j<yep; j++) { /*  for (j=0; j<=my; j++) */
322:     for (i=xs; i<xep; i++) {  /*   for (i=0; i<=mx; i++) */
323:       k = (j-gys)*gxm + i-gxs;
324:       vb = zero;
325:       vl = zero;
326:       v  = zero;
327:       if (i < mx && j > 0) vb = x[k-gxm];
328:       if (i > 0 && j < my) vl = x[k-1];
329:       if (i < mx && j < my) v = x[k];
330:       dvdx = (v-vl)/hx;
331:       dvdy = (v-vb)/hy;
332:       if (i != mx && j != 0) {
333:         ind = k-gxm; val = - dvdy/hy - cdiv3;
334:         info = VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES); CHKERRQ(info);
335:       }
336:       if (i != 0 && j != my) {
337:         ind = k-1; val =  - dvdx/hx - cdiv3;
338:         info = VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES); CHKERRQ(info);
339:       }
340:       if (i != mx && j != my) {
341:         ind = k; val =  dvdx/hx + dvdy/hy - cdiv3;
342:         info = VecSetValuesLocal(G,1,&ind,&val,ADD_VALUES); CHKERRQ(info);
343:       }
344:       fquad += dvdx*dvdx + dvdy*dvdy;
345:       flin -= cdiv3 * (vb + vl + v);
346:     }
347:   }


350:   /* Restore vector */
351:   info = VecRestoreArray(localX,&x); CHKERRQ(info);

353:   /* Assemble gradient vector */
354:   info = VecAssemblyBegin(G); CHKERRQ(info);
355:   info = VecAssemblyEnd(G); CHKERRQ(info);

357:   /* Scale the gradient */
358:   area = p5*hx*hy;
359:   floc = area * (p5 * fquad + flin);
360:   info = VecScale(G, area); CHKERRQ(info);

362:   /* Sum function contributions from all processes */
363:   MPI_Allreduce((void*)&floc,(void*)f,1,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD);

365:   info=PetscLogFlops((ye-ysm)*(xe-xsm)*20+(xep-xs)*(yep-ys)*16); CHKERRQ(info);
366:   
367:   return 0;
368: }



374: int ComputeHessian(TAO_APPLICATION taoapp, Vec X, Mat *H, Mat *Hpre, MatStructure *flag, void*ctx){

376:   AppCtx *user= (AppCtx*) ctx;
377:   int i,j,k,info;
378:   int col[5],row;
379:   int xs,xm,gxs,gxm,ys,ym,gys,gym;
380:   PetscReal v[5];
381:   PetscReal hx=1.0/(user->mx+1), hy=1.0/(user->my+1), hxhx=1.0/(hx*hx), hyhy=1.0/(hy*hy), area=0.5*hx*hy;
382:   Mat A=*H;

384:   /* Compute the quadratic term in the objective function */  

386:   /*
387:      Get local grid boundaries
388:   */

390:   info = DAGetCorners(user->da,&xs,&ys,TAO_NULL,&xm,&ym,TAO_NULL); CHKERRQ(info);
391:   info = DAGetGhostCorners(user->da,&gxs,&gys,TAO_NULL,&gxm,&gym,TAO_NULL); CHKERRQ(info);

393:   for (j=ys; j<ys+ym; j++){
394:     
395:     for (i=xs; i< xs+xm; i++){

397:       row=(j-gys)*gxm + (i-gxs);

399:       k=0;
400:       if (j>gys){ 
401:         v[k]=-2*hyhy; col[k]=row - gxm; k++;
402:       }

404:       if (i>gxs){
405:         v[k]= -2*hxhx; col[k]=row - 1; k++;
406:       }

408:       v[k]= 4.0*(hxhx+hyhy); col[k]=row; k++;

410:       if (i+1 < gxs+gxm){
411:         v[k]= -2.0*hxhx; col[k]=row+1; k++;
412:       }

414:       if (j+1 <gys+gym){
415:         v[k]= -2*hyhy; col[k] = row+gxm; k++;
416:       }

418:       info = MatSetValuesLocal(A,1,&row,k,col,v,INSERT_VALUES); CHKERRQ(info);

420:     }
421:   }
422:   /* 
423:      Assemble matrix, using the 2-step process:
424:      MatAssemblyBegin(), MatAssemblyEnd().
425:      By placing code between these two statements, computations can be
426:      done while messages are in transition.
427:   */
428:   info = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY); CHKERRQ(info);
429:   info = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY); CHKERRQ(info);
430:   /*
431:     Tell the matrix we will never add a new nonzero location to the
432:     matrix. If we do it will generate an error.
433:   */
434:   info = MatScale(A,area); CHKERRQ(info);
435:   info = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR); CHKERRQ(info);
436:   info = MatSetOption(A,MAT_SYMMETRIC); CHKERRQ(info);

438:   info = PetscLogFlops(9*xm*ym+49*xm); CHKERRQ(info);

440:   return 0;
441: }