Actual source code: eptorsion2.c

  1: /*$Id: eptorsion2.c 1.55 05/05/11 08:44:55-05:00 sarich@zorak.(none) $*/

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

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

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

124:   /* Create Hessian */
125:   info = DAGetMatrix(user.da,MATAIJ,&H); CHKERRQ(info);
126:   info = MatSetOption(H,MAT_SYMMETRIC); CHKERRQ(info);

128:   /* The TAO code begins here */

130:   /* Create TAO solver and set desired solution method */
131:   info = TaoCreate(MPI_COMM_WORLD,"tao_cg_fr",&tao); CHKERRQ(info);
132:   info = TaoApplicationCreate(PETSC_COMM_WORLD,&torsionapp); CHKERRQ(info);

134:   /* Set initial solution guess */
135:   info = FormInitialGuess(&user,x); CHKERRQ(info);
136:   info = TaoAppSetInitialSolutionVec(torsionapp,x); CHKERRQ(info);

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

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

144:   info = TaoGetKSP(tao,&ksp); CHKERRQ(info);
145:   if (ksp) {                                              /* Modify the PETSc KSP structure */
146:     info = KSPSetType(ksp,KSPCG); CHKERRQ(info);
147:   }

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

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

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

162:   /* 
163:      To View TAO solver information use
164:       info = TaoView(tao); CHKERRQ(info);
165:   */

167:   /* Free TAO data structures */
168:   info = TaoDestroy(tao); CHKERRQ(info);
169:   info = TaoAppDestroy(torsionapp);  CHKERRQ(info);

171:   /* Free PETSc data structures */
172:   info = VecDestroy(x); CHKERRQ(info);
173:   info = MatDestroy(H); CHKERRQ(info);

175:   info = VecDestroy(user.localX); CHKERRQ(info);
176:   info = DADestroy(user.da); CHKERRQ(info);


179:   /* Finalize TAO and PETSc*/
180:   TaoFinalize();
181:   PetscFinalize();

183:   return 0;
184: }


187: /* ------------------------------------------------------------------- */
190: /*
191:     FormInitialGuess - Computes an initial approximation to the solution.

193:     Input Parameters:
194: .   user - user-defined application context
195: .   X    - vector

197:     Output Parameters:
198:     X    - vector
199: */
200: int FormInitialGuess(AppCtx *user,Vec X)
201: {
202:   int    info, i, j, k, mx = user->mx, my = user->my;
203:   int    xs, ys, xm, ym, gxm, gym, gxs, gys, xe, ye;
204:   PetscReal hx = 1.0/(mx+1), hy = 1.0/(my+1), temp, val;

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

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

222:   return 0;
223: }


226: /* ------------------------------------------------------------------ */
229: /* 
230:    FormFunctionGradient - Evaluates the function and corresponding gradient.
231:     
232:    Input Parameters:
233:    taoapp - the TAO_APPLICATION context
234:    X   - the input vector 
235:    ptr - optional user-defined context, as set by TaoSetFunction()

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

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


256:   /* Initialize */
257:   flin = fquad = zero;

259:   info = VecSet(G, zero); CHKERRQ(info);
260:   /*
261:      Scatter ghost points to local vector,using the 2-step process
262:         DAGlobalToLocalBegin(),DAGlobalToLocalEnd().
263:      By placing code between these two statements, computations can be
264:      done while messages are in transition.
265:   */
266:   info = DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
267:   info = DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);

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

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

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

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

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


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

350:   /* Assemble gradient vector */
351:   info = VecAssemblyBegin(G); CHKERRQ(info);
352:   info = VecAssemblyEnd(G); CHKERRQ(info);

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

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

362:   info=PetscLogFlops((ye-ysm)*(xe-xsm)*20+(xep-xs)*(yep-ys)*16); CHKERRQ(info);
363: 
364:   return 0;
365: }



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

373:   AppCtx *user= (AppCtx*) ctx;
374:   int i,j,k,info;
375:   int col[5],row;
376:   int xs,xm,gxs,gxm,ys,ym,gys,gym;
377:   PetscReal v[5];
378:   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;
379:   Mat A=*H;

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

383:   /*
384:      Get local grid boundaries
385:   */

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

390:   for (j=ys; j<ys+ym; j++){
391: 
392:     for (i=xs; i< xs+xm; i++){

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

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

401:       if (i>gxs){
402:         v[k]= -2*hxhx; col[k]=row - 1; k++;
403:       }

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

407:       if (i+1 < gxs+gxm){
408:         v[k]= -2.0*hxhx; col[k]=row+1; k++;
409:       }

411:       if (j+1 <gys+gym){
412:         v[k]= -2*hyhy; col[k] = row+gxm; k++;
413:       }

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

417:     }
418:   }
419:   /* 
420:      Assemble matrix, using the 2-step process:
421:      MatAssemblyBegin(), MatAssemblyEnd().
422:      By placing code between these two statements, computations can be
423:      done while messages are in transition.
424:   */
425:   info = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY); CHKERRQ(info);
426:   info = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY); CHKERRQ(info);
427:   /*
428:     Tell the matrix we will never add a new nonzero location to the
429:     matrix. If we do it will generate an error.
430:   */
431:   info = MatScale(A,area); CHKERRQ(info);
432:   info = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR); CHKERRQ(info);
433:   info = MatSetOption(A,MAT_SYMMETRIC); CHKERRQ(info);

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

437:   return 0;
438: }