Actual source code: eptorsion2f.F

petsc-master 2020-06-03
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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();
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:       module mymodule
39: #include "petsc/finclude/petsctao.h"
40:       use petscdmda
41:       use petsctao
42:       implicit none

44:       Vec              localX
45:       DM               dm
46:       PetscReal      param
47:       PetscInt         mx, my
48:       end module

50:       use mymodule
51:       implicit none
52: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
53: !                   Variable declarations
54: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
55: !
56: !  See additional variable declarations in the file eptorsion2f.h
57: !
58:       PetscErrorCode   ierr           ! used to check for functions returning nonzeros
59:       Vec              x              ! solution vector
60:       Mat              H              ! hessian matrix
61:       PetscInt         Nx, Ny         ! number of processes in x- and y- directions
62:       Tao        tao            ! Tao solver context
63:       PetscBool        flg
64:       PetscInt         i1
65:       PetscInt         dummy

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

72:       external Monitor,ConvergenceTest

74:       i1 = 1

76: !     Initialize TAO, PETSc  contexts
77:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
78:       if (ierr .ne. 0) then
79:          print*,'Unable to initialize PETSc'
80:          stop
81:       endif

83: !     Specify default parameters
84:       param = 5.0
85:       mx = 10
86:       my = 10
87:       Nx = PETSC_DECIDE
88:       Ny = PETSC_DECIDE

90: !     Check for any command line arguments that might override defaults
91:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,    &
92:      &                        '-mx',mx,flg,ierr)
93:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,    &
94:      &                        '-my',my,flg,ierr)
95:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,   &
96:      &                         '-par',param,flg,ierr)

99: !     Set up distributed array and vectors
100:       call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,               &
101:      &     DM_BOUNDARY_NONE,                                             &
102:      &     DMDA_STENCIL_BOX,mx,my,Nx,Ny,i1,i1,PETSC_NULL_INTEGER,        &
103:      &     PETSC_NULL_INTEGER,dm,ierr)
104:       call DMSetFromOptions(dm,ierr)
105:       call DMSetUp(dm,ierr)

107: !     Create vectors
108:       call DMCreateGlobalVector(dm,x,ierr)
109:       call DMCreateLocalVector(dm,localX,ierr)

111: !     Create Hessian
112:       call DMCreateMatrix(dm,H,ierr)
113:       call MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE,ierr)

115: !     The TAO code begins here

117: !     Create TAO solver
118:       call TaoCreate(PETSC_COMM_WORLD,tao,ierr)
119:       call TaoSetType(tao,TAOCG,ierr)

121: !     Set routines for function and gradient evaluation

125:       call TaoSetHessianRoutine(tao,H,H,ComputeHessian,                 &
126:      &     0,ierr)

128: !     Set initial guess
129:       call FormInitialGuess(x,ierr)
130:       call TaoSetInitialVector(tao,x,ierr)

132:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,   &
133:      &                         '-testmonitor',flg,ierr)
134:       if (flg) then
135:          call TaoSetMonitor(tao,Monitor,dummy,PETSC_NULL_FUNCTION,      &
136:      &        ierr)
137:       endif

139:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,  &
140:      &                         '-testconvergence',flg, ierr)
141:       if (flg) then
142:          call TaoSetConvergenceTest(tao,ConvergenceTest,dummy,          &
143:      &        ierr)
144:       endif

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

150: !     SOLVE THE APPLICATION
151:       call TaoSolve(tao,ierr)

153: !     Free TAO data structures
154:       call TaoDestroy(tao,ierr)

157: !     Free PETSc data structures
158:       call VecDestroy(x,ierr)
159:       call VecDestroy(localX,ierr)
160:       call MatDestroy(H,ierr)
161:       call DMDestroy(dm,ierr)

164: !     Finalize TAO and PETSc
165:       call PetscFinalize(ierr)
166:       end

169: ! ---------------------------------------------------------------------
170: !
171: !   FormInitialGuess - Computes an initial approximation to the solution.
172: !
173: !   Input Parameters:
174: !   X    - vector
175: !
176: !   Output Parameters:
177: !   X    - vector
178: !   ierr - error code
179: !
180:       subroutine FormInitialGuess(X,ierr)
181:       use mymodule
182:       implicit none

184: !  Input/output variables:
185:       Vec              X
186:       PetscErrorCode   ierr

188: !  Local variables:
189:       PetscInt         i, j, k, xe, ye
190:       PetscReal      temp, val, hx, hy
191:       PetscInt         xs, ys, xm, ym
192:       PetscInt         gxm, gym, gxs, gys
193:       PetscInt         i1

195:       i1 = 1
196:       hx = 1.0/real(mx + 1)
197:       hy = 1.0/real(my + 1)

199: !  Get corner information
200:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
201:      &                  PETSC_NULL_INTEGER,ierr)
202:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,              &
203:      &                   gxm,gym,PETSC_NULL_INTEGER,ierr)

207: !  Compute initial guess over locally owned part of mesh
208:       xe = xs+xm
209:       ye = ys+ym
210:       do j=ys,ye-1
211:          temp = min(j+1,my-j)*hy
212:          do i=xs,xe-1
213:             k   = (j-gys)*gxm + i-gxs
214:             val = min((min(i+1,mx-i))*hx,temp)
216:          end do
217:       end do
218:       call VecAssemblyBegin(X,ierr)
219:       call VecAssemblyEnd(X,ierr)
220:       return
221:       end

224: ! ---------------------------------------------------------------------
225: !
227: !
228: !  Input Parameters:
229: !  tao   - the Tao context
230: !  X     - input vector
231: !  dummy - optional user-defined context (not used here)
232: !
233: !  Output Parameters:
234: !  f     - the function value at X
235: !  G     - vector containing the newly evaluated gradient
236: !  ierr  - error code
237: !
238: !  Notes:
239: !  This routine serves as a wrapper for the lower-level routine
240: !  "ApplicationGradient", where the actual computations are
241: !  done using the standard Fortran style of treating the local
242: !  input vector data as an array over the local mesh.
243: !
245:       use mymodule
246:       implicit none

248: !  Input/output variables:
249:       Tao        tao
250:       Vec              X, G
251:       PetscReal      f
252:       PetscErrorCode   ierr
253:       PetscInt         dummy

255: !  Declarations for use with local array:

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

266: !  Local variables:
267:       PetscReal      zero, p5, area, cdiv3
269:       PetscReal      v, vb, vl, vr, vt, dvdx
270:       PetscReal      dvdy, hx, hy
271:       PetscInt         xe, ye, xsm, ysm
272:       PetscInt         xep, yep, i, j, k, ind
273:       PetscInt         xs, ys, xm, ym
274:       PetscInt         gxs, gys, gxm, gym
275:       PetscInt         i1

277:       i1 = 1
278:       0
279:       cdiv3 = param/3.0
280:       zero = 0.0
281:       p5   = 0.5
282:       hx = 1.0/real(mx + 1)
283:       hy = 1.0/real(my + 1)
285:       flin = zero

287: !  Initialize gradient to zero
288:       call VecSet(G,zero,ierr)

290: !  Scatter ghost points to local vector
291:       call DMGlobalToLocalBegin(dm,X,INSERT_VALUES,localX,ierr)
292:       call DMGlobalToLocalEnd(dm,X,INSERT_VALUES,localX,ierr)

295: !  Get corner information
296:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
297:      &                  PETSC_NULL_INTEGER,ierr)
298:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,              &
299:      &                   gxm,gym,PETSC_NULL_INTEGER,ierr)

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

305: !  Set local loop dimensions
306:       xe = xs+xm
307:       ye = ys+ym
308:       if (xs .eq. 0) then
309:          xsm = xs-1
310:       else
311:          xsm = xs
312:       endif
313:       if (ys .eq. 0) then
314:          ysm = ys-1
315:       else
316:          ysm = ys
317:       endif
318:       if (xe .eq. mx) then
319:          xep = xe+1
320:       else
321:          xep = xe
322:       endif
323:       if (ye .eq. my) then
324:          yep = ye+1
325:       else
326:          yep = ye
327:       endif

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

331:       do j = ysm, ye-1
332:          do i = xsm, xe-1
333:             k  = (j-gys)*gxm + i-gxs
334:             v  = zero
335:             vr = zero
336:             vt = zero
337:             if (i .ge. 0 .and. j .ge. 0)      v = lx_v(lx_i+k)
338:             if (i .lt. mx-1 .and. j .gt. -1) vr = lx_v(lx_i+k+1)
339:             if (i .gt. -1 .and. j .lt. my-1) vt = lx_v(lx_i+k+gxm)
340:             dvdx = (vr-v)/hx
341:             dvdy = (vt-v)/hy
342:             if (i .ne. -1 .and. j .ne. -1) then
343:                ind = k
344:                val = - dvdx/hx - dvdy/hy - cdiv3
346:             endif
347:             if (i .ne. mx-1 .and. j .ne. -1) then
348:                ind = k+1
349:                val =  dvdx/hx - cdiv3
351:             endif
352:             if (i .ne. -1 .and. j .ne. my-1) then
353:               ind = k+gxm
354:               val = dvdy/hy - cdiv3
356:             endif
358:             flin = flin - cdiv3 * (v+vr+vt)
359:          end do
360:       end do

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

364:       do j = ys, yep-1
365:          do i = xs, xep-1
366:             k  = (j-gys)*gxm + i-gxs
367:             vb = zero
368:             vl = zero
369:             v  = zero
370:             if (i .lt. mx .and. j .gt. 0) vb = lx_v(lx_i+k-gxm)
371:             if (i .gt. 0 .and. j .lt. my) vl = lx_v(lx_i+k-1)
372:             if (i .lt. mx .and. j .lt. my) v = lx_v(lx_i+k)
373:             dvdx = (v-vl)/hx
374:             dvdy = (v-vb)/hy
375:             if (i .ne. mx .and. j .ne. 0) then
376:                ind = k-gxm
377:                val = - dvdy/hy - cdiv3
379:             endif
380:             if (i .ne. 0 .and. j .ne. my) then
381:                ind = k-1
382:                val =  - dvdx/hx - cdiv3
384:             endif
385:             if (i .ne. mx .and. j .ne. my) then
386:                ind = k
387:                val =  dvdx/hx + dvdy/hy - cdiv3
389:             endif
391:             flin = flin - cdiv3*(vb + vl + v)
392:          end do
393:       end do

395: !  Restore vector
396:       call VecRestoreArray(localX,lx_v,lx_i,ierr)

399:       call VecAssemblyBegin(G,ierr)
400:       call VecAssemblyEnd(G,ierr)

403:       area = p5*hx*hy
405:       call VecScale(G,area,ierr)

408: !  Sum function contributions from all processes
409:       call MPI_Allreduce(floc,f,1,MPIU_SCALAR,MPIU_SUM,                   &
410:      &                   PETSC_COMM_WORLD,ierr)
411:       call PetscLogFlops(20.0d0*(ye-ysm)*(xe-xsm)+                        &
412:      &                   16.0d0*(xep-xs)*(yep-ys),ierr)
413:       return
414:       end

416:       subroutine ComputeHessian(tao, X, H, Hpre, dummy, ierr)
417:       use mymodule
418:       implicit none

420:       Tao       tao
421:       Vec             X
422:       Mat             H,Hpre
423:       PetscErrorCode  ierr
424:       PetscInt        dummy

427:       PetscInt i,j,k
428:       PetscInt col(0:4),row
429:       PetscInt xs,xm,gxs,gxm
430:       PetscInt ys,ym,gys,gym
431:       PetscReal v(0:4)
432:       PetscInt i1

434:       i1 = 1

436: !     Get local grid boundaries
437:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
438:      &                PETSC_NULL_INTEGER,ierr)
439:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,      &
440:      &                PETSC_NULL_INTEGER,ierr)

442:       do j=ys,ys+ym-1
443:          do i=xs,xs+xm-1
444:             row = (j-gys)*gxm + (i-gxs)

446:             k = 0
447:             if (j .gt. gys) then
448:                v(k) = -1.0
449:                col(k) = row-gxm
450:                k = k + 1
451:             endif

453:             if (i .gt. gxs) then
454:                v(k) = -1.0
455:                col(k) = row - 1
456:                k = k +1
457:             endif

459:             v(k) = 4.0
460:             col(k) = row
461:             k = k + 1

463:             if (i+1 .lt. gxs + gxm) then
464:                v(k) = -1.0
465:                col(k) = row + 1
466:                k = k + 1
467:             endif

469:             if (j+1 .lt. gys + gym) then
470:                v(k) = -1.0
471:                col(k) = row + gxm
472:                k = k + 1
473:             endif

475:             call MatSetValuesLocal(H,i1,row,k,col,v,INSERT_VALUES,ierr)
476:          enddo
477:       enddo

480: !     Assemble matrix
481:       call MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY,ierr)
482:       call MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY,ierr)

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

488:       call MatSetOption(H,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,ierr)
489:       call MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE,ierr)

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

494:       0
495:       return
496:       end

500:       subroutine Monitor(tao, dummy, ierr)
501:       use mymodule
502:       implicit none

504:       Tao tao
505:       PetscInt dummy
506:       PetscErrorCode ierr

508:       PetscInt its
509:       PetscReal f,gnorm,cnorm,xdiff
510:       TaoConvergedReason reason

512:       call TaoGetSolutionStatus(tao,its,f,gnorm,cnorm,xdiff,             &
513:      &     reason,ierr)
514:       if (mod(its,5) .ne. 0) then
515:          call PetscPrintf(PETSC_COMM_WORLD,'iteration multiple of 5\n',  &
516:      &        ierr)
517:       endif

519:       0

521:       return
522:       end

524:       subroutine ConvergenceTest(tao, dummy, ierr)
525:       use mymodule
526:       implicit none

528:       Tao tao
529:       PetscInt dummy
530:       PetscErrorCode ierr

532:       PetscInt its
533:       PetscReal f,gnorm,cnorm,xdiff
534:       TaoConvergedReason reason

536:       call TaoGetSolutionStatus(tao,its,f,gnorm,cnorm,xdiff,            &
537:      &     reason,ierr)
538:       if (its .eq. 7) then
539:        call TaoSetConvergedReason(tao,TAO_DIVERGED_MAXITS,ierr)
540:       endif

542:       0

544:       return
545:       end

547: !/*TEST
548: !
549: !   build:
550: !      requires: !complex
551: !
552: !   test:
553: !      args: -tao_smonitor -tao_type nls -tao_gttol 1.e-2
554: !
555: !   test:
556: !      suffix: 2
557: !      nsize: 2
558: !      args: -tao_smonitor -tao_type lmvm -tao_gttol 1.e-2
559: !
560: !   test:
561: !      suffix: 3
562: !      args: -testmonitor -tao_type lmvm -tao_gttol 1.e-2
563: !TEST*/
```