Actual source code: eptorsion2f.F

  1: ! "$Id: eptorsion2f.F 1.52 05/05/12 13:59:03-05:00 sarich@zorak.(none) $";
  2: !
  3: !  Program usage: mpirun -np <proc> eptorsion2f [all TAO options]
  4: !
  5: !  Description:  This example demonstrates use of the TAO package to solve
  6: !  unconstrained minimization problems in parallel.  This example is based
  7: !  on the Elastic-Plastic Torsion (dept) problem from the MINPACK-2 test suite.
  8: !  The command line options are:
  9: !    -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction
 10: !    -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction
 11: !    -par <param>, where <param> = angle of twist per unit length
 12: !
 13: !/*T
 14: !   Concepts: TAO - Solving an unconstrained minimization problem
 15: !   Routines: TaoInitialize(); TaoFinalize(); 
 16: !   Routines: TaoCreate(); TaoDestroy();
 17: !   Routines: TaoApplicationCreate(); TaoAppDestroy();
 18: !   Routines: TaoAppSetObjectiveAndGradientRoutine();
 19: !   Routines: TaoAppSetHessianMat(); TaoAppSetHessianRoutine();
 20: !   Routines: TaoSetApplication(); TaoSetOptions();
 21: !   Routines: TaoAppSetInitialSolutionVec(); TaoSolveApplication(); TaoDestroy();
 22: !   Routines: TaoGetSolutionStatus();
 23: !   Processors: n
 24: !T*/
 25: !
 26: ! ----------------------------------------------------------------------
 27: !
 28: !  Elastic-plastic torsion problem.
 29: !
 30: !  The elastic plastic torsion problem arises from the determination
 31: !  of the stress field on an infinitely long cylindrical bar, which is
 32: !  equivalent to the solution of the following problem:
 33: !     min{ .5 * integral(||gradient(v(x))||^2 dx) - C * integral(v(x) dx)}
 34: !  where C is the torsion angle per unit length.
 35: !
 36: !  The C version of this code is eptorsion2.c
 37: !
 38: ! ----------------------------------------------------------------------

 40:       implicit none
 41: #include "eptorsion2f.h"

 43: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 44: !                   Variable declarations
 45: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 46: !
 47: !  See additional variable declarations in the file eptorsion2f.h
 48: !
 49:       integer          info           ! used to check for functions returning nonzeros
 50:       Vec              x              ! solution vector
 51:       Mat              H              ! hessian matrix
 52:       integer          Nx, Ny         ! number of processes in x- and y- directions
 53:       TAO_SOLVER       tao            ! TAO_SOLVER solver context
 54:       TAO_APPLICATION  torsionapp     ! TAO application context (PETSc)
 55:       TaoTerminateReason reason
 56:       PetscTruth       flg
 57:       integer          iter           ! iteration information
 58:       PetscScalar      ff,gnorm,cnorm,xdiff
 59: 

 61: !  Note: Any user-defined Fortran routines (such as FormGradient)
 62: !  MUST be declared as external.

 64:       external FormInitialGuess,FormFunctionGradient,ComputeHessian

 66: !     Initialize TAO, PETSc  contexts
 67:       call PetscInitialize(PETSC_NULL_CHARACTER,info)
 68:       call TaoInitialize(PETSC_NULL_CHARACTER,info)

 70: !     Specify default parameters
 71:       param = 5.0d0
 72:       mx = 10
 73:       my = 10
 74:       Nx = PETSC_DECIDE
 75:       Ny = PETSC_DECIDE

 77: !     Check for any command line arguments that might override defaults
 78:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,"-mx",mx,flg,info)
 79:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,"-my",my,flg,info)
 80:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,"-par",              &
 81:      &                         param,flg,info)

 83: 
 84: !     Set up distributed array and vectors
 85:       call DACreate2d(MPI_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX,      &
 86:      &     mx,my,Nx,Ny,1,1,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,        &
 87:      &     da,info)

 89: !     Create vectors
 90:       call DACreateGlobalVector(da,x,info)
 91:       call DACreateLocalVector(da,localX,info)

 93: !     Create Hessian
 94:       call DAGetMatrix(da,MATAIJ,H,info)
 95:       call MatSetOption(H,MAT_SYMMETRIC,info)

 97: !     The TAO code begins here

 99: !     Create TAO solver
100:       call TaoCreate(MPI_COMM_WORLD,'tao_cg_fr',tao,info)
101:       call TaoApplicationCreate(MPI_COMM_WORLD,torsionapp,info)

103: !     Set routines for function and gradient evaluation

105: !     TaoAppSetObjectiveAndGradientRoutine is shortened to 31 chars to comply with some compilers
106:       call TaoAppSetObjectiveAndGradientRo(torsionapp,                       &
107:      &     FormFunctionGradient,TAO_NULL_OBJECT,info)
108:       call TaoAppSetHessianMat(torsionapp,H,H,info)
109:       call TaoAppSetHessianRoutine(torsionapp,ComputeHessian,                &
110:      &    TAO_NULL_OBJECT,info)

112: !     Set initial guess
113:       call FormInitialGuess(x,info)
114:       call TaoAppSetInitialSolutionVec(torsionapp,x,info)

116: !     Check for any TAO command line options
117:       call TaoSetOptions(torsionapp, tao,info)

119: !     Now that the PETSc application is all set, attach to tao context
120:       call TaoSetApplication(tao,torsionapp,info)


123: !     SOLVE THE APPLICATION
124:       call TaoSolveApplication(torsionapp,tao,info)

126: !     Get information on termination
127:       call TaoGetSolutionStatus(tao,iter,ff,gnorm,cnorm,xdiff,           &
128:      &                          reason,info)
129:       if (reason .lt. 0) then
130:          print *,'TAO did not terminate successfully'
131:          call TaoView(tao,info)
132:       endif
133: 
134: !     Free TAO data structures
135:       call TaoDestroy(tao,info)
136:       call TaoAppDestroy(torsionapp,info);

138: 
139: !     Free PETSc data structures
140:       call VecDestroy(x,info)
141:       call VecDestroy(localX,info)
142:       call MatDestroy(H,info)
143:       call DADestroy(da,info)


146: !     Finalize TAO and PETSc
147:       call PetscFinalize(info)
148:       call TaoFinalize(info)

150:       end


153: ! ---------------------------------------------------------------------
154: !
155: !   FormInitialGuess - Computes an initial approximation to the solution.
156: !
157: !   Input Parameters:
158: !   X    - vector
159: !
160: !   Output Parameters:
161: !   X    - vector
162: !   info - error code
163: !
164:       subroutine FormInitialGuess(X,info)
165:       implicit none

167: ! mx, my are defined in eptorsion2f.h
168: #include "eptorsion2f.h"

170: !  Input/output variables:
171:       Vec              X
172:       integer          info

174: !  Local variables:
175:       integer          i, j, k, xe, ye
176:       PetscScalar      temp, val, hx, hy
177:       integer          xs, ys, xm, ym, gxm, gym, gxs, gys

179:       hx = 1.0d0/(mx + 1)
180:       hy = 1.0d0/(my + 1)

182: !  Get corner information
183:       call DAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
184:      &                  PETSC_NULL_INTEGER,info)
185:       call DAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,              &
186:      &                   gxm,gym,PETSC_NULL_INTEGER,info)



190: !  Compute initial guess over locally owned part of mesh
191:       xe = xs+xm
192:       ye = ys+ym
193:       do j=ys,ye-1
194:          temp = min(j+1,my-j)*hy
195:          do i=xs,xe-1
196:             k   = (j-gys)*gxm + i-gxs
197:             val = min((min(i+1,mx-i))*hx,temp)
198:             call VecSetValuesLocal(X,1,k,val,ADD_VALUES,info)
199:          end do
200:       end do

202:       return
203:       end


206: ! ---------------------------------------------------------------------
207: !
208: !  FormFunctionGradient - Evaluates gradient G(X).
209: !
210: !  Input Parameters:
211: !  tao   - the TAO_SOLVER context
212: !  X     - input vector
213: !  dummy - optional user-defined context (not used here)
214: !
215: !  Output Parameters:
216: !  f     - the function value at X
217: !  G     - vector containing the newly evaluated gradient
218: !  info  - error code
219: !
220: !  Notes:
221: !  This routine serves as a wrapper for the lower-level routine
222: !  "ApplicationGradient", where the actual computations are
223: !  done using the standard Fortran style of treating the local
224: !  input vector data as an array over the local mesh.
225: !
226:       subroutine FormFunctionGradient(taoapp,X,f,G,dummy,info)
227:       implicit none

229: ! da, mx, my, param, localX declared in eptorsion2f.h
230: #include "eptorsion2f.h"

232: !  Input/output variables:
233:       TAO_APPLICATION  taoapp
234:       Vec              X, G
235:       PetscScalar      f
236:       integer          dummy, info

238: !  Declarations for use with local array:


241: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
242: ! Calling VecGetArray((Vec) X, (PetscScalar) x_array(0:1), (PetscOffset) x_index, info)
243: ! will return an array of doubles referenced by x_array offset by x_index.
244: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
245: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
246:       PetscScalar      lx_v(0:1)
247:       PetscOffset      lx_i

249: !  Local variables:
250:       PetscScalar      zero, p5, area, cdiv3, val, flin, fquad,floc
251:       PetscScalar      v, vb, vl, vr, vt, dvdx, dvdy, hx, hy
252:       integer          xe, ye, xsm, ysm, xep, yep, i, j, k, ind
253:       integer          xs, ys, xm, ym, gxs, gys, gxm, gym

255:       info  = 0
256:       cdiv3 = param/3.0d0
257:       zero = 0.0d0
258:       p5   = 0.5d0
259:       hx = 1.0d0/(mx + 1)
260:       hy = 1.0d0/(my + 1)
261:       fquad = zero
262:       flin = zero

264: !  Initialize gradient to zero
265:       call VecSet(G,zero,info)

267: !  Scatter ghost points to local vector
268:       call DAGlobalToLocalBegin(da,X,INSERT_VALUES,localX,info)
269:       call DAGlobalToLocalEnd(da,X,INSERT_VALUES,localX,info)


272: !  Get corner information
273:       call DAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
274:      &                  PETSC_NULL_INTEGER,info)
275:       call DAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,              &
276:      &                   gxm,gym,PETSC_NULL_INTEGER,info)

278: !  Get pointer to vector data.
279:       call VecGetArray(localX,lx_v,lx_i,info)


282: !  Set local loop dimensions
283:       xe = xs+xm
284:       ye = ys+ym
285:       if (xs .eq. 0) then
286:          xsm = xs-1
287:       else
288:          xsm = xs
289:       endif
290:       if (ys .eq. 0) then
291:          ysm = ys-1
292:       else
293:          ysm = ys
294:       endif
295:       if (xe .eq. mx) then
296:          xep = xe+1
297:       else
298:          xep = xe
299:       endif
300:       if (ye .eq. my) then
301:          yep = ye+1
302:       else
303:          yep = ye
304:       endif

306: !     Compute local gradient contributions over the lower triangular elements
307: 
308:       do j = ysm, ye-1
309:          do i = xsm, xe-1
310:             k  = (j-gys)*gxm + i-gxs
311:             v  = zero
312:             vr = zero
313:             vt = zero
314:             if (i .ge. 0 .and. j .ge. 0)      v = lx_v(lx_i+k)
315:             if (i .lt. mx-1 .and. j .gt. -1) vr = lx_v(lx_i+k+1)
316:             if (i .gt. -1 .and. j .lt. my-1) vt = lx_v(lx_i+k+gxm)
317:             dvdx = (vr-v)/hx
318:             dvdy = (vt-v)/hy
319:             if (i .ne. -1 .and. j .ne. -1) then
320:                ind = k
321:                val = - dvdx/hx - dvdy/hy - cdiv3
322:                call VecSetValuesLocal(G,1,k,val,ADD_VALUES,info)
323:             endif
324:             if (i .ne. mx-1 .and. j .ne. -1) then
325:                ind = k+1
326:                val =  dvdx/hx - cdiv3
327:                call VecSetValuesLocal(G,1,ind,val,ADD_VALUES,info)
328:             endif
329:             if (i .ne. -1 .and. j .ne. my-1) then
330:               ind = k+gxm
331:               val = dvdy/hy - cdiv3
332:               call VecSetValuesLocal(G,1,ind,val,ADD_VALUES,info)
333:             endif
334:             fquad = fquad + dvdx*dvdx + dvdy*dvdy
335:             flin = flin - cdiv3 * (v+vr+vt)
336:          end do
337:       end do

339: !     Compute local gradient contributions over the upper triangular elements

341:       do j = ys, yep-1
342:          do i = xs, xep-1
343:             k  = (j-gys)*gxm + i-gxs
344:             vb = zero
345:             vl = zero
346:             v  = zero
347:             if (i .lt. mx .and. j .gt. 0) vb = lx_v(lx_i+k-gxm)
348:             if (i .gt. 0 .and. j .lt. my) vl = lx_v(lx_i+k-1)
349:             if (i .lt. mx .and. j .lt. my) v = lx_v(lx_i+k)
350:             dvdx = (v-vl)/hx
351:             dvdy = (v-vb)/hy
352:             if (i .ne. mx .and. j .ne. 0) then
353:                ind = k-gxm
354:                val = - dvdy/hy - cdiv3
355:                call VecSetValuesLocal(G,1,ind,val,ADD_VALUES,info)
356:             endif
357:             if (i .ne. 0 .and. j .ne. my) then
358:                ind = k-1
359:                val =  - dvdx/hx - cdiv3
360:                call VecSetValuesLocal(G,1,ind,val,ADD_VALUES,info)
361:             endif
362:             if (i .ne. mx .and. j .ne. my) then
363:                ind = k
364:                val =  dvdx/hx + dvdy/hy - cdiv3
365:                call VecSetValuesLocal(G,1,ind,val,ADD_VALUES,info)
366:             endif
367:             fquad = fquad + dvdx*dvdx + dvdy*dvdy
368:             flin = flin - cdiv3*(vb + vl + v)
369:          end do
370:       end do

372: !  Restore vector
373:       call VecRestoreArray(localX,lx_v,lx_i,info)

375: !  Assemble gradient vector
376:       call VecAssemblyBegin(G,info)
377:       call VecAssemblyEnd(G,info)

379: ! Scale the gradient
380:       area = p5*hx*hy
381:       floc = area *(p5*fquad+flin)
382:       call VecScale(G,area,info)


385: !  Sum function contributions from all processes
386:       call MPI_Allreduce(floc,f,1,MPI_DOUBLE_PRECISION,MPI_SUM,           &
387:      &                   MPI_COMM_WORLD,info)

389:       call PetscLogFlops((ye-ysm)*(xe-xsm)*20+(xep-xs)*(yep-ys)*16,       &
390:      &                    info)


393:       return
394:       end




399:       subroutine ComputeHessian(taoapp, X, H, Hpre, flag, dummy, info)
400:       implicit none
401: #include "eptorsion2f.h"      
402:       TAO_APPLICATION taoapp
403:       Vec             X
404:       Mat             H,Hpre
405:       MatStructure    flag
406:       integer         dummy,info

408: 
409:       integer i,j,k
410:       integer col(0:4),row
411:       integer xs,xm,gxs,gxm,ys,ym,gys,gym
412:       PetscScalar v(0:4)

414: !     Get local grid boundaries
415:       call DAGetCorners(da,xs,ys,TAO_NULL_INTEGER,xm,ym,                &
416:      &                TAO_NULL_INTEGER,info)
417:       call DAGetGhostCorners(da,gxs,gys,TAO_NULL_INTEGER,gxm,gym,        &
418:      &                TAO_NULL_INTEGER,info)

420:       do j=ys,ys+ym-1
421:          do i=xs,xs+xm-1
422:             row = (j-gys)*gxm + (i-gxs)

424:             k = 0
425:             if (j .gt. gys) then
426:                v(k) = -1.0d0
427:                col(k) = row-gxm
428:                k = k + 1
429:             endif

431:             if (i .gt. gxs) then
432:                v(k) = -1.0d0
433:                col(k) = row - 1
434:                k = k +1
435:             endif

437:             v(k) = 4.0d0
438:             col(k) = row
439:             k = k + 1

441:             if (i+1 .lt. gxs + gxm) then
442:                v(k) = -1.0d0
443:                col(k) = row + 1
444:                k = k + 1
445:             endif

447:             if (j+1 .lt. gys + gym) then
448:                v(k) = -1.0d0
449:                col(k) = row + gxm
450:                k = k + 1
451:             endif

453:             call MatSetValuesLocal(H,1,row,k,col,v,INSERT_VALUES,info)
454:          enddo
455:       enddo

457: 
458: !     Assemble matrix
459:       call MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY,info)
460:       call MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY,info)


463: !     Tell the matrix we will never add a new nonzero location to the
464: !     matrix.  If we do it will generate an error.

466:       call MatSetOption(H,MAT_NEW_NONZERO_LOCATION_ERR,info)
467:       call MatSetOption(H,MAT_SYMMETRIC,info)


470:       call PetscLogFlops(9*xm*ym + 49*xm,info)

472:       info = 0
473:       return
474:       end
475: 
476: 
477: