Actual source code: eptorsion2f.F

petsc-master 2016-12-08
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  1: !  Program usage: mpiexec -n <proc> eptorsion2f [all TAO options]
  2: !
  3: !  Description:  This example demonstrates use of the TAO package to solve
  4: !  unconstrained minimization problems in parallel.  This example is based
  5: !  on the Elastic-Plastic Torsion (dept) problem from the MINPACK-2 test suite.
  6: !  The command line options are:
  7: !    -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction
  8: !    -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction
  9: !    -par <param>, where <param> = angle of twist per unit length
 10: !
 11: !/*T
 12: !   Concepts: TAO^Solving an unconstrained minimization problem
 13: !   Routines: TaoCreate(); TaoSetType();
 14: !   Routines: TaoSetInitialVector();
 15: !   Routines: TaoSetObjectiveAndGradientRoutine();
 16: !   Routines: TaoSetHessianRoutine(); TaoSetFromOptions();
 17: !   Routines: TaoSetMonitor(); TaoSetConvergenceTest()
 18: !   Routines: TaoSolve(); TaoGetSolutionStatus()
 19: !   Routines: TaoDestroy();

 21: !   Processors: n
 22: !T*/
 23: !
 24: ! ----------------------------------------------------------------------
 25: !
 26: !  Elastic-plastic torsion problem.
 27: !
 28: !  The elastic plastic torsion problem arises from the deconverged
 29: !  of the stress field on an infinitely long cylindrical bar, which is
 30: !  equivalent to the solution of the following problem:
 31: !     min{ .5 * integral(||gradient(v(x))||^2 dx) - C * integral(v(x) dx)}
 32: !  where C is the torsion angle per unit length.
 33: !
 34: !  The C version of this code is eptorsion2.c
 35: !
 36: ! ----------------------------------------------------------------------

 38: #include "eptorsion2f.h"
 39: #if defined(PETSC_USING_F90) && !defined(PETSC_USE_FORTRANKIND)
 40:       external PETSC_NULL_FUNCTION
 41: #endif
 42: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 43: !                   Variable declarations
 44: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 45: !
 46: !  See additional variable declarations in the file eptorsion2f.h
 47: !
 48:       PetscErrorCode   ierr           ! used to check for functions returning nonzeros
 49:       Vec              x              ! solution vector
 50:       Mat              H              ! hessian matrix
 51:       PetscInt         Nx, Ny         ! number of processes in x- and y- directions
 52:       Tao        tao            ! Tao solver context
 53:       PetscBool        flg
 54:       PetscInt         i1
 55:       PetscInt         dummy


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

 61:       external FormInitialGuess,FormFunctionGradient,ComputeHessian
 62:       external Monitor,ConvergenceTest

 64:       i1 = 1

 66: !     Initialize TAO, PETSc  contexts
 67:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
 68:       if (ierr .ne. 0) then
 69:          print*,'Unable to initialize PETSc'
 70:          stop
 71:       endif

 73: !     Specify default parameters
 74:       param = 5.0
 75:       mx = 10
 76:       my = 10
 77:       Nx = PETSC_DECIDE
 78:       Ny = PETSC_DECIDE

 80: !     Check for any command line arguments that might override defaults
 81:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,    &
 82:      &                        '-mx',mx,flg,ierr)
 83:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,    &
 84:      &                        '-my',my,flg,ierr)
 85:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,   &
 86:      &                         '-par',param,flg,ierr)


 89: !     Set up distributed array and vectors
 90:       call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,               &
 91:      &     DM_BOUNDARY_NONE,                                             &
 92:      &     DMDA_STENCIL_BOX,mx,my,Nx,Ny,i1,i1,PETSC_NULL_INTEGER,        &
 93:      &     PETSC_NULL_INTEGER,dm,ierr)
 94:       call DMSetFromOptions(dm,ierr)
 95:       call DMSetUp(dm,ierr)

 97: !     Create vectors
 98:       call DMCreateGlobalVector(dm,x,ierr)
 99:       call DMCreateLocalVector(dm,localX,ierr)

101: !     Create Hessian
102:       call DMCreateMatrix(dm,H,ierr)
103:       call MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE,ierr)

105: !     The TAO code begins here

107: !     Create TAO solver
108:       call TaoCreate(PETSC_COMM_WORLD,tao,ierr)
109:       call TaoSetType(tao,TAOCG,ierr)

111: !     Set routines for function and gradient evaluation

113:       call TaoSetObjectiveAndGradientRoutine(tao,                       &
114:      &     FormFunctionGradient,0,ierr)
115:       call TaoSetHessianRoutine(tao,H,H,ComputeHessian,                 &
116:      &     0,ierr)

118: !     Set initial guess
119:       call FormInitialGuess(x,ierr)
120:       call TaoSetInitialVector(tao,x,ierr)

122:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,   &
123:      &                         '-testmonitor',flg,ierr)
124:       if (flg) then
125:          call TaoSetMonitor(tao,Monitor,dummy,PETSC_NULL_FUNCTION,      &
126:      &        ierr)
127:       endif

129:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,  &
130:      &                         '-testconvergence',flg, ierr)
131:       if (flg) then
132:          call TaoSetConvergenceTest(tao,ConvergenceTest,dummy,          &
133:      &        ierr)
134:       endif

136: !     Check for any TAO command line options
137:       call TaoSetFromOptions(tao,ierr)


140: !     SOLVE THE APPLICATION
141:       call TaoSolve(tao,ierr)

143: !     Free TAO data structures
144:       call TaoDestroy(tao,ierr)


147: !     Free PETSc data structures
148:       call VecDestroy(x,ierr)
149:       call VecDestroy(localX,ierr)
150:       call MatDestroy(H,ierr)
151:       call DMDestroy(dm,ierr)


154: !     Finalize TAO and PETSc
155:       call PetscFinalize(ierr)
156:       end


159: ! ---------------------------------------------------------------------
160: !
161: !   FormInitialGuess - Computes an initial approximation to the solution.
162: !
163: !   Input Parameters:
164: !   X    - vector
165: !
166: !   Output Parameters:
167: !   X    - vector
168: !   ierr - error code
169: !
170:       subroutine FormInitialGuess(X,ierr)
171: #include "eptorsion2f.h"

173: !  Input/output variables:
174:       Vec              X
175:       PetscErrorCode   ierr

177: !  Local variables:
178:       PetscInt         i, j, k, xe, ye
179:       PetscReal      temp, val, hx, hy
180:       PetscInt         xs, ys, xm, ym
181:       PetscInt         gxm, gym, gxs, gys
182:       PetscInt         i1

184:       i1 = 1
185:       hx = 1.0/(mx + 1)
186:       hy = 1.0/(my + 1)

188: !  Get corner information
189:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
190:      &                  PETSC_NULL_INTEGER,ierr)
191:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,              &
192:      &                   gxm,gym,PETSC_NULL_INTEGER,ierr)



196: !  Compute initial guess over locally owned part of mesh
197:       xe = xs+xm
198:       ye = ys+ym
199:       do j=ys,ye-1
200:          temp = min(j+1,my-j)*hy
201:          do i=xs,xe-1
202:             k   = (j-gys)*gxm + i-gxs
203:             val = min((min(i+1,mx-i))*hx,temp)
204:             call VecSetValuesLocal(X,i1,k,val,ADD_VALUES,ierr)
205:          end do
206:       end do
207:       call VecAssemblyBegin(X,ierr)
208:       call VecAssemblyEnd(X,ierr)
209:       return
210:       end


213: ! ---------------------------------------------------------------------
214: !
215: !  FormFunctionGradient - Evaluates gradient G(X).
216: !
217: !  Input Parameters:
218: !  tao   - the Tao context
219: !  X     - input vector
220: !  dummy - optional user-defined context (not used here)
221: !
222: !  Output Parameters:
223: !  f     - the function value at X
224: !  G     - vector containing the newly evaluated gradient
225: !  ierr  - error code
226: !
227: !  Notes:
228: !  This routine serves as a wrapper for the lower-level routine
229: !  "ApplicationGradient", where the actual computations are
230: !  done using the standard Fortran style of treating the local
231: !  input vector data as an array over the local mesh.
232: !
233:       subroutine FormFunctionGradient(tao,X,f,G,dummy,ierr)
234: #include "eptorsion2f.h"

236: !  Input/output variables:
237:       Tao        tao
238:       Vec              X, G
239:       PetscReal      f
240:       PetscErrorCode   ierr
241:       PetscInt         dummy

243: !  Declarations for use with local array:


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

254: !  Local variables:
255:       PetscReal      zero, p5, area, cdiv3
256:       PetscReal      val, flin, fquad,floc
257:       PetscReal      v, vb, vl, vr, vt, dvdx
258:       PetscReal      dvdy, hx, hy
259:       PetscInt         xe, ye, xsm, ysm
260:       PetscInt         xep, yep, i, j, k, ind
261:       PetscInt         xs, ys, xm, ym
262:       PetscInt         gxs, gys, gxm, gym
263:       PetscInt         i1

265:       i1 = 1
266:       0
267:       cdiv3 = param/3.0
268:       zero = 0.0
269:       p5   = 0.5
270:       hx = 1.0/(mx + 1)
271:       hy = 1.0/(my + 1)
272:       fquad = zero
273:       flin = zero

275: !  Initialize gradient to zero
276:       call VecSet(G,zero,ierr)

278: !  Scatter ghost points to local vector
279:       call DMGlobalToLocalBegin(dm,X,INSERT_VALUES,localX,ierr)
280:       call DMGlobalToLocalEnd(dm,X,INSERT_VALUES,localX,ierr)


283: !  Get corner information
284:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
285:      &                  PETSC_NULL_INTEGER,ierr)
286:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,              &
287:      &                   gxm,gym,PETSC_NULL_INTEGER,ierr)

289: !  Get pointer to vector data.
290:       call VecGetArray(localX,lx_v,lx_i,ierr)


293: !  Set local loop dimensions
294:       xe = xs+xm
295:       ye = ys+ym
296:       if (xs .eq. 0) then
297:          xsm = xs-1
298:       else
299:          xsm = xs
300:       endif
301:       if (ys .eq. 0) then
302:          ysm = ys-1
303:       else
304:          ysm = ys
305:       endif
306:       if (xe .eq. mx) then
307:          xep = xe+1
308:       else
309:          xep = xe
310:       endif
311:       if (ye .eq. my) then
312:          yep = ye+1
313:       else
314:          yep = ye
315:       endif

317: !     Compute local gradient contributions over the lower triangular elements

319:       do j = ysm, ye-1
320:          do i = xsm, xe-1
321:             k  = (j-gys)*gxm + i-gxs
322:             v  = zero
323:             vr = zero
324:             vt = zero
325:             if (i .ge. 0 .and. j .ge. 0)      v = lx_v(lx_i+k)
326:             if (i .lt. mx-1 .and. j .gt. -1) vr = lx_v(lx_i+k+1)
327:             if (i .gt. -1 .and. j .lt. my-1) vt = lx_v(lx_i+k+gxm)
328:             dvdx = (vr-v)/hx
329:             dvdy = (vt-v)/hy
330:             if (i .ne. -1 .and. j .ne. -1) then
331:                ind = k
332:                val = - dvdx/hx - dvdy/hy - cdiv3
333:                call VecSetValuesLocal(G,i1,k,val,ADD_VALUES,ierr)
334:             endif
335:             if (i .ne. mx-1 .and. j .ne. -1) then
336:                ind = k+1
337:                val =  dvdx/hx - cdiv3
338:                call VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr)
339:             endif
340:             if (i .ne. -1 .and. j .ne. my-1) then
341:               ind = k+gxm
342:               val = dvdy/hy - cdiv3
343:               call VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr)
344:             endif
345:             fquad = fquad + dvdx*dvdx + dvdy*dvdy
346:             flin = flin - cdiv3 * (v+vr+vt)
347:          end do
348:       end do

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

352:       do j = ys, yep-1
353:          do i = xs, xep-1
354:             k  = (j-gys)*gxm + i-gxs
355:             vb = zero
356:             vl = zero
357:             v  = zero
358:             if (i .lt. mx .and. j .gt. 0) vb = lx_v(lx_i+k-gxm)
359:             if (i .gt. 0 .and. j .lt. my) vl = lx_v(lx_i+k-1)
360:             if (i .lt. mx .and. j .lt. my) v = lx_v(lx_i+k)
361:             dvdx = (v-vl)/hx
362:             dvdy = (v-vb)/hy
363:             if (i .ne. mx .and. j .ne. 0) then
364:                ind = k-gxm
365:                val = - dvdy/hy - cdiv3
366:                call VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr)
367:             endif
368:             if (i .ne. 0 .and. j .ne. my) then
369:                ind = k-1
370:                val =  - dvdx/hx - cdiv3
371:                call VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr)
372:             endif
373:             if (i .ne. mx .and. j .ne. my) then
374:                ind = k
375:                val =  dvdx/hx + dvdy/hy - cdiv3
376:                call VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr)
377:             endif
378:             fquad = fquad + dvdx*dvdx + dvdy*dvdy
379:             flin = flin - cdiv3*(vb + vl + v)
380:          end do
381:       end do

383: !  Restore vector
384:       call VecRestoreArray(localX,lx_v,lx_i,ierr)

386: !  Assemble gradient vector
387:       call VecAssemblyBegin(G,ierr)
388:       call VecAssemblyEnd(G,ierr)

390: ! Scale the gradient
391:       area = p5*hx*hy
392:       floc = area *(p5*fquad+flin)
393:       call VecScale(G,area,ierr)


396: !  Sum function contributions from all processes
397:       call MPI_Allreduce(floc,f,1,MPIU_SCALAR,MPIU_SUM,                   &
398:      &                   PETSC_COMM_WORLD,ierr)
399:       call PetscLogFlops(20.0d0*(ye-ysm)*(xe-xsm)+                        &
400:      &                   16.0d0*(xep-xs)*(yep-ys),ierr)
401:       return
402:       end

404:       subroutine ComputeHessian(tao, X, H, Hpre, dummy, ierr)
405: #include "eptorsion2f.h"

407:       Tao       tao
408:       Vec             X
409:       Mat             H,Hpre
410:       PetscErrorCode  ierr
411:       PetscInt        dummy


414:       PetscInt i,j,k
415:       PetscInt col(0:4),row
416:       PetscInt xs,xm,gxs,gxm
417:       PetscInt ys,ym,gys,gym
418:       PetscReal v(0:4)
419:       PetscInt i1

421:       i1 = 1

423: !     Get local grid boundaries
424:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
425:      &                PETSC_NULL_INTEGER,ierr)
426:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,      &
427:      &                PETSC_NULL_INTEGER,ierr)

429:       do j=ys,ys+ym-1
430:          do i=xs,xs+xm-1
431:             row = (j-gys)*gxm + (i-gxs)

433:             k = 0
434:             if (j .gt. gys) then
435:                v(k) = -1.0
436:                col(k) = row-gxm
437:                k = k + 1
438:             endif

440:             if (i .gt. gxs) then
441:                v(k) = -1.0
442:                col(k) = row - 1
443:                k = k +1
444:             endif

446:             v(k) = 4.0
447:             col(k) = row
448:             k = k + 1

450:             if (i+1 .lt. gxs + gxm) then
451:                v(k) = -1.0
452:                col(k) = row + 1
453:                k = k + 1
454:             endif

456:             if (j+1 .lt. gys + gym) then
457:                v(k) = -1.0
458:                col(k) = row + gxm
459:                k = k + 1
460:             endif

462:             call MatSetValuesLocal(H,i1,row,k,col,v,INSERT_VALUES,ierr)
463:          enddo
464:       enddo


467: !     Assemble matrix
468:       call MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY,ierr)
469:       call MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY,ierr)


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

475:       call MatSetOption(H,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,ierr)
476:       call MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE,ierr)


479:       call PetscLogFlops(9.0d0*xm*ym + 49.0d0*xm,ierr)

481:       0
482:       return
483:       end



487:       subroutine Monitor(tao, dummy, ierr)
488: #include "eptorsion2f.h"

490:       Tao tao
491:       PetscInt dummy
492:       PetscErrorCode ierr

494:       PetscInt its
495:       PetscReal f,gnorm,cnorm,xdiff
496:       TaoConvergedReason reason

498:       call TaoGetSolutionStatus(tao,its,f,gnorm,cnorm,xdiff,             &
499:      &     reason,ierr)
500:       if (mod(its,5) .ne. 0) then
501:          call PetscPrintf(PETSC_COMM_WORLD,'iteration multiple of 5\n',  &
502:      &        ierr)
503:       endif

505:       0

507:       return
508:       end

510:       subroutine ConvergenceTest(tao, dummy, ierr)
511: #include "eptorsion2f.h"

513:       Tao tao
514:       PetscInt dummy
515:       PetscErrorCode ierr

517:       PetscInt its
518:       PetscReal f,gnorm,cnorm,xdiff
519:       TaoConvergedReason reason

521:       call TaoGetSolutionStatus(tao,its,f,gnorm,cnorm,xdiff,            &
522:      &     reason,ierr)
523:       if (its .eq. 7) then
524:        call TaoSetConvergedReason(tao,TAO_DIVERGED_MAXITS,ierr)
525:       endif

527:       0

529:       return
530:       end