Actual source code: plate2f.F90

petsc-3.11.3 2019-06-26
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```  1: !  Program usage: mpiexec -n <proc> plate2f [all TAO options]
2: !
3: !  This example demonstrates use of the TAO package to solve a bound constrained
4: !  minimization problem.  This example is based on a problem from the
5: !  MINPACK-2 test suite.  Given a rectangular 2-D domain and boundary values
6: !  along the edges of the domain, the objective is to find the surface
7: !  with the minimal area that satisfies the boundary conditions.
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: !    -bmx <bxg>, where <bxg> = number of grid points under plate in 1st direction
12: !    -bmy <byg>, where <byg> = number of grid points under plate in 2nd direction
13: !    -bheight <ht>, where <ht> = height of the plate
14: !
15: !!/*T
16: !   Concepts: TAO^Solving a bound constrained minimization problem
17: !   Routines: TaoCreate();
19: !   Routines: TaoSetHessianRoutine();
20: !   Routines: TaoSetVariableBoundsRoutine();
21: !   Routines: TaoSetInitialVector();
22: !   Routines: TaoSetFromOptions();
23: !   Routines: TaoSolve();
24: !   Routines: TaoDestroy();
25: !   Processors: n
26: !T*/

28:       module mymodule
29: #include "petsc/finclude/petscdmda.h"
30: #include "petsc/finclude/petsctao.h"
31:       use petscdmda
32:       use petsctao

34:       Vec              localX, localV
35:       Vec              Top, Left
36:       Vec              Right, Bottom
37:       DM               dm
38:       PetscReal      bheight
39:       PetscInt         bmx, bmy
40:       PetscInt         mx, my, Nx, Ny, N
41:       end module

44: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
45: !                   Variable declarations
46: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
47: !
48: !  Variables:
49: !    (common from plate2f.h):
50: !    Nx, Ny           number of processors in x- and y- directions
51: !    mx, my           number of grid points in x,y directions
52: !    N    global dimension of vector
53:       use mymodule
54:       implicit none

56:       PetscErrorCode   ierr          ! used to check for functions returning nonzeros
57:       Vec              x             ! solution vector
58:       PetscInt         m             ! number of local elements in vector
59:       Tao              tao           ! Tao solver context
60:       Mat              H             ! Hessian matrix
61:       ISLocalToGlobalMapping isltog  ! local to global mapping object
62:       PetscBool        flg
63:       PetscInt         i1,i3,i7

67:       external FormHessian
68:       external MSA_BoundaryConditions
69:       external MSA_Plate
70:       external MSA_InitialPoint
71: ! Initialize Tao

73:       i1=1
74:       i3=3
75:       i7=7

78:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
79:       if (ierr .ne. 0) then
80:         print*,'Unable to initialize PETSc'
81:         stop
82:       endif

84: ! Specify default dimensions of the problem
85:       mx = 10
86:       my = 10
87:       bheight = 0.1

89: ! Check for any command line arguments that override defaults

91:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,     &
92:      &                        '-mx',mx,flg,ierr)
93:       CHKERRA(ierr)
94:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,     &
95:      &                        '-my',my,flg,ierr)
96:       CHKERRA(ierr)

98:       bmx = mx/2
99:       bmy = my/2

101:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,     &
102:      &                        '-bmx',bmx,flg,ierr)
103:       CHKERRA(ierr)
104:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,     &
105:      &                        '-bmy',bmy,flg,ierr)
106:       CHKERRA(ierr)
107:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,    &
108:      &                         '-bheight',bheight,flg,ierr)
109:       CHKERRA(ierr)

112: ! Calculate any derived values from parameters
113:       N = mx*my

115: ! Let Petsc determine the dimensions of the local vectors
116:       Nx = PETSC_DECIDE
117:       NY = PETSC_DECIDE

119: ! A two dimensional distributed array will help define this problem, which
120: ! derives from an elliptic PDE on a two-dimensional domain.  From the
121: ! distributed array, create the vectors

123:       call DMDACreate2d(MPI_COMM_WORLD,DM_BOUNDARY_NONE,                    &
124:      &     DM_BOUNDARY_NONE, DMDA_STENCIL_BOX,                              &
125:      &     mx,my,Nx,Ny,i1,i1,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,           &
126:      &     dm,ierr)
127:       CHKERRA(ierr)
128:       call DMSetFromOptions(dm,ierr)
129:       call DMSetUp(dm,ierr)

131: ! Extract global and local vectors from DM; The local vectors are
132: ! used solely as work space for the evaluation of the function,
133: ! gradient, and Hessian.  Duplicate for remaining vectors that are
134: ! the same types.

136:       call DMCreateGlobalVector(dm,x,ierr)
137:       CHKERRA(ierr)
138:       call DMCreateLocalVector(dm,localX,ierr)
139:       CHKERRA(ierr)
140:       call VecDuplicate(localX,localV,ierr)
141:       CHKERRA(ierr)

143: ! Create a matrix data structure to store the Hessian.
144: ! Here we (optionally) also associate the local numbering scheme
145: ! with the matrix so that later we can use local indices for matrix
146: ! assembly

148:       call VecGetLocalSize(x,m,ierr)
149:       CHKERRA(ierr)
150:       call MatCreateAIJ(MPI_COMM_WORLD,m,m,N,N,i7,PETSC_NULL_INTEGER,   &
151:      &     i3,PETSC_NULL_INTEGER,H,ierr)
152:       CHKERRA(ierr)

154:       call MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE,ierr)
155:       CHKERRA(ierr)
156:       call DMGetLocalToGlobalMapping(dm,isltog,ierr)
157:       CHKERRA(ierr)
158:       call MatSetLocalToGlobalMapping(H,isltog,isltog,ierr)
159:       CHKERRA(ierr)

162: ! The Tao code begins here
163: ! Create TAO solver and set desired solution method.
164: ! This problems uses bounded variables, so the
165: ! method must either be 'tao_tron' or 'tao_blmvm'

167:       call TaoCreate(PETSC_COMM_WORLD,tao,ierr)
168:       CHKERRA(ierr)
169:       call TaoSetType(tao,TAOBLMVM,ierr)
170:       CHKERRA(ierr)

172: !     Set minimization function and gradient, hessian evaluation functions

176:       CHKERRA(ierr)

178:       call TaoSetHessianRoutine(tao,H,H,FormHessian,                    &
179:      &     0, ierr)
180:       CHKERRA(ierr)

182: ! Set Variable bounds
183:       call MSA_BoundaryConditions(ierr)
184:       CHKERRA(ierr)
185:       call TaoSetVariableBoundsRoutine(tao,MSA_Plate,                   &
186:      &     0,ierr)
187:       CHKERRA(ierr)

189: ! Set the initial solution guess
190:       call MSA_InitialPoint(x, ierr)
191:       CHKERRA(ierr)
192:       call TaoSetInitialVector(tao,x,ierr)
193:       CHKERRA(ierr)

195: ! Check for any tao command line options
196:       call TaoSetFromOptions(tao,ierr)
197:       CHKERRA(ierr)

199: ! Solve the application
200:       call TaoSolve(tao,ierr)
201:       CHKERRA(ierr)

203: ! Free TAO data structures
204:       call TaoDestroy(tao,ierr)
205:       CHKERRA(ierr)

207: ! Free PETSc data structures
208:       call VecDestroy(x,ierr)
209:       call VecDestroy(Top,ierr)
210:       call VecDestroy(Bottom,ierr)
211:       call VecDestroy(Left,ierr)
212:       call VecDestroy(Right,ierr)
213:       call MatDestroy(H,ierr)
214:       call VecDestroy(localX,ierr)
215:       call VecDestroy(localV,ierr)
216:       call DMDestroy(dm,ierr)

218: ! Finalize TAO

220:       call PetscFinalize(ierr)

222:       end

224: ! ---------------------------------------------------------------------
225: !
226: !  FormFunctionGradient - Evaluates function f(X).
227: !
228: !  Input Parameters:
229: !  tao   - the Tao context
230: !  X     - the input vector
231: !  dummy - optional user-defined context, as set by TaoSetFunction()
232: !          (not used here)
233: !
234: !  Output Parameters:
235: !  fcn     - the newly evaluated function
236: !  G       - the gradient vector
237: !  info  - error code
238: !

242:       use mymodule
243:       implicit none
244:
245: ! Input/output variables

247:       Tao        tao
248:       PetscReal      fcn
249:       Vec              X, G
250:       PetscErrorCode   ierr
251:       PetscInt         dummy

253:       PetscInt         i,j,row
254:       PetscInt         xs, xm
255:       PetscInt         gxs, gxm
256:       PetscInt         ys, ym
257:       PetscInt         gys, gym
258:       PetscReal      ft,zero,hx,hy,hydhx,hxdhy
259:       PetscReal      area,rhx,rhy
260:       PetscReal      f1,f2,f3,f4,f5,f6,d1,d2,d3
261:       PetscReal      d4,d5,d6,d7,d8
262:       PetscReal      df1dxc,df2dxc,df3dxc,df4dxc
263:       PetscReal      df5dxc,df6dxc
264:       PetscReal      xc,xl,xr,xt,xb,xlt,xrb

267: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
268: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (PetscOffset) x_index, ierr)
269: ! will return an array of doubles referenced by x_array offset by x_index.
270: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
271: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
272:       PetscReal      g_v(0:1),x_v(0:1)
273:       PetscReal      top_v(0:1),left_v(0:1)
274:       PetscReal      right_v(0:1),bottom_v(0:1)
275:       PetscOffset      g_i,left_i,right_i
276:       PetscOffset      bottom_i,top_i,x_i

278:       ft = 0.0
279:       zero = 0.0
280:       hx = 1.0/real(mx + 1)
281:       hy = 1.0/real(my + 1)
282:       hydhx = hy/hx
283:       hxdhy = hx/hy
284:       area = 0.5 * hx * hy
285:       rhx = real(mx) + 1.0
286:       rhy = real(my) + 1.0

289: ! Get local mesh boundaries
290:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,              &
291:      &                  PETSC_NULL_INTEGER,ierr)
292:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,             &
293:      &                       gxm,gym,PETSC_NULL_INTEGER,ierr)

295: ! Scatter ghost points to local vector
296:       call DMGlobalToLocalBegin(dm,X,INSERT_VALUES,localX,ierr)
297:       call DMGlobalToLocalEnd(dm,X,INSERT_VALUES,localX,ierr)

299: ! Initialize the vector to zero
300:       call VecSet(localV,zero,ierr)

302: ! Get arrays to vector data (See note above about using VecGetArray in Fortran)
303:       call VecGetArray(localX,x_v,x_i,ierr)
304:       call VecGetArray(localV,g_v,g_i,ierr)
305:       call VecGetArray(Top,top_v,top_i,ierr)
306:       call VecGetArray(Bottom,bottom_v,bottom_i,ierr)
307:       call VecGetArray(Left,left_v,left_i,ierr)
308:       call VecGetArray(Right,right_v,right_i,ierr)

310: ! Compute function over the locally owned part of the mesh
311:       do j = ys,ys+ym-1
312:          do i = xs,xs+xm-1
313:             row = (j-gys)*gxm + (i-gxs)
314:             xc = x_v(row+x_i)
315:             xt = xc
316:             xb = xc
317:             xr = xc
318:             xl = xc
319:             xrb = xc
320:             xlt = xc

322:             if (i .eq. 0) then !left side
323:                xl = left_v(j - ys + 1 + left_i)
324:                xlt = left_v(j - ys + 2 + left_i)
325:             else
326:                xl = x_v(row - 1 + x_i)
327:             endif

329:             if (j .eq. 0) then !bottom side
330:                xb = bottom_v(i - xs + 1 + bottom_i)
331:                xrb = bottom_v(i - xs + 2 + bottom_i)
332:             else
333:                xb = x_v(row - gxm + x_i)
334:             endif

336:             if (i + 1 .eq. gxs + gxm) then !right side
337:                xr = right_v(j - ys + 1 + right_i)
338:                xrb = right_v(j - ys + right_i)
339:             else
340:                xr = x_v(row + 1 + x_i)
341:             endif

343:             if (j + 1 .eq. gys + gym) then !top side
344:                xt = top_v(i - xs + 1 + top_i)
345:                xlt = top_v(i - xs + top_i)
346:             else
347:                xt = x_v(row + gxm + x_i)
348:             endif

350:             if ((i .gt. gxs ) .and. (j + 1 .lt. gys + gym)) then
351:                xlt = x_v(row - 1 + gxm + x_i)
352:             endif

354:             if ((j .gt. gys) .and. (i + 1 .lt. gxs + gxm)) then
355:                xrb = x_v(row + 1 - gxm + x_i)
356:             endif

358:             d1 = xc-xl
359:             d2 = xc-xr
360:             d3 = xc-xt
361:             d4 = xc-xb
362:             d5 = xr-xrb
363:             d6 = xrb-xb
364:             d7 = xlt-xl
365:             d8 = xt-xlt

367:             df1dxc = d1 * hydhx
368:             df2dxc = d1 * hydhx + d4 * hxdhy
369:             df3dxc = d3 * hxdhy
370:             df4dxc = d2 * hydhx + d3 * hxdhy
371:             df5dxc = d2 * hydhx
372:             df6dxc = d4 * hxdhy

374:             d1 = d1 * rhx
375:             d2 = d2 * rhx
376:             d3 = d3 * rhy
377:             d4 = d4 * rhy
378:             d5 = d5 * rhy
379:             d6 = d6 * rhx
380:             d7 = d7 * rhy
381:             d8 = d8 * rhx

383:             f1 = sqrt(1.0 + d1*d1 + d7*d7)
384:             f2 = sqrt(1.0 + d1*d1 + d4*d4)
385:             f3 = sqrt(1.0 + d3*d3 + d8*d8)
386:             f4 = sqrt(1.0 + d3*d3 + d2*d2)
387:             f5 = sqrt(1.0 + d2*d2 + d5*d5)
388:             f6 = sqrt(1.0 + d4*d4 + d6*d6)

390:             ft = ft + f2 + f4

392:             df1dxc = df1dxc / f1
393:             df2dxc = df2dxc / f2
394:             df3dxc = df3dxc / f3
395:             df4dxc = df4dxc / f4
396:             df5dxc = df5dxc / f5
397:             df6dxc = df6dxc / f6

399:             g_v(row + g_i) = 0.5 * (df1dxc + df2dxc + df3dxc + df4dxc +  &
400:      &                              df5dxc + df6dxc)
401:          enddo
402:       enddo

404: ! Compute triangular areas along the border of the domain.
405:       if (xs .eq. 0) then  ! left side
406:          do j=ys,ys+ym-1
407:             d3 = (left_v(j-ys+1+left_i) - left_v(j-ys+2+left_i))         &
408:      &                 * rhy
409:             d2 = (left_v(j-ys+1+left_i) - x_v((j-gys)*gxm + x_i))        &
410:      &                 * rhx
411:             ft = ft + sqrt(1.0 + d3*d3 + d2*d2)
412:          enddo
413:       endif

416:       if (ys .eq. 0) then !bottom side
417:          do i=xs,xs+xm-1
418:             d2 = (bottom_v(i+1-xs+bottom_i)-bottom_v(i-xs+2+bottom_i))    &
419:      &                    * rhx
420:             d3 = (bottom_v(i-xs+1+bottom_i)-x_v(i-gxs+x_i))*rhy
421:             ft = ft + sqrt(1.0 + d3*d3 + d2*d2)
422:          enddo
423:       endif

426:       if (xs + xm .eq. mx) then ! right side
427:          do j=ys,ys+ym-1
428:             d1 = (x_v((j+1-gys)*gxm-1+x_i)-right_v(j-ys+1+right_i))*rhx
429:             d4 = (right_v(j-ys+right_i) - right_v(j-ys+1+right_i))*rhy
430:             ft = ft + sqrt(1.0 + d1*d1 + d4*d4)
431:          enddo
432:       endif

435:       if (ys + ym .eq. my) then
436:          do i=xs,xs+xm-1
437:             d1 = (x_v((gym-1)*gxm+i-gxs+x_i) - top_v(i-xs+1+top_i))*rhy
438:             d4 = (top_v(i-xs+1+top_i) - top_v(i-xs+top_i))*rhx
439:             ft = ft + sqrt(1.0 + d1*d1 + d4*d4)
440:          enddo
441:       endif

444:       if ((ys .eq. 0) .and. (xs .eq. 0)) then
445:          d1 = (left_v(0 + left_i) - left_v(1 + left_i)) * rhy
446:          d2 = (bottom_v(0+bottom_i)-bottom_v(1+bottom_i))*rhx
447:          ft = ft + sqrt(1.0 + d1*d1 + d2*d2)
448:       endif

450:       if ((ys + ym .eq. my) .and. (xs + xm .eq. mx)) then
451:          d1 = (right_v(ym+1+right_i) - right_v(ym+right_i))*rhy
452:          d2 = (top_v(xm+1+top_i) - top_v(xm + top_i))*rhx
453:          ft = ft + sqrt(1.0 + d1*d1 + d2*d2)
454:       endif

456:       ft = ft * area
457:       call MPI_Allreduce(ft,fcn,1,MPIU_SCALAR,                            &
458:      &             MPIU_SUM,MPI_COMM_WORLD,ierr)

461: ! Restore vectors
462:       call VecRestoreArray(localX,x_v,x_i,ierr)
463:       call VecRestoreArray(localV,g_v,g_i,ierr)
464:       call VecRestoreArray(Left,left_v,left_i,ierr)
465:       call VecRestoreArray(Top,top_v,top_i,ierr)
466:       call VecRestoreArray(Bottom,bottom_v,bottom_i,ierr)
467:       call VecRestoreArray(Right,right_v,right_i,ierr)

469: ! Scatter values to global vector
470:       call DMLocalToGlobalBegin(dm,localV,INSERT_VALUES,G,ierr)
471:       call DMLocalToGlobalEnd(dm,localV,INSERT_VALUES,G,ierr)

473:       call PetscLogFlops(70.0d0*xm*ym,ierr)

475:       return

482: ! ----------------------------------------------------------------------------
483: !
484: !
485: !   FormHessian - Evaluates Hessian matrix.
486: !
487: !   Input Parameters:
488: !.  tao  - the Tao context
489: !.  X    - input vector
490: !.  dummy  - not used
491: !
492: !   Output Parameters:
493: !.  Hessian    - Hessian matrix
494: !.  Hpc    - optionally different preconditioning matrix
495: !.  flag - flag indicating matrix structure
496: !
497: !   Notes:
498: !   Due to mesh point reordering with DMs, we must always work
499: !   with the local mesh points, and then transform them to the new
500: !   global numbering with the local-to-global mapping.  We cannot work
501: !   directly with the global numbers for the original uniprocessor mesh!
502: !
503: !      MatSetValuesLocal(), using the local ordering (including
504: !         ghost points!)
505: !         - Then set matrix entries using the local ordering
506: !           by calling MatSetValuesLocal()

508:       subroutine FormHessian(tao, X, Hessian, Hpc, dummy, ierr)
509:       use mymodule
510:       implicit none

512:       Tao     tao
513:       Vec            X
514:       Mat            Hessian,Hpc
515:       PetscInt       dummy
516:       PetscErrorCode ierr

518:       PetscInt       i,j,k,row
519:       PetscInt       xs,xm,gxs,gxm
520:       PetscInt       ys,ym,gys,gym
521:       PetscInt       col(0:6)
522:       PetscReal    hx,hy,hydhx,hxdhy,rhx,rhy
523:       PetscReal    f1,f2,f3,f4,f5,f6,d1,d2,d3
524:       PetscReal    d4,d5,d6,d7,d8
525:       PetscReal    xc,xl,xr,xt,xb,xlt,xrb
526:       PetscReal    hl,hr,ht,hb,hc,htl,hbr

528: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
529: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (PetscOffset) x_index, ierr)
530: ! will return an array of doubles referenced by x_array offset by x_index.
531: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
532: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
533:       PetscReal   right_v(0:1),left_v(0:1)
534:       PetscReal   bottom_v(0:1),top_v(0:1)
535:       PetscReal   x_v(0:1)
536:       PetscOffset   x_i,right_i,left_i
537:       PetscOffset   bottom_i,top_i
538:       PetscReal   v(0:6)
539:       PetscBool     assembled
540:       PetscInt      i1

542:       i1=1

544: ! Set various matrix options
545:       call MatSetOption(Hessian,MAT_IGNORE_OFF_PROC_ENTRIES,              &
546:      &                  PETSC_TRUE,ierr)

548: ! Get local mesh boundaries
549:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,              &
550:      &                  PETSC_NULL_INTEGER,ierr)
551:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,     &
552:      &                       PETSC_NULL_INTEGER,ierr)

554: ! Scatter ghost points to local vectors
555:       call DMGlobalToLocalBegin(dm,X,INSERT_VALUES,localX,ierr)
556:       call DMGlobalToLocalEnd(dm,X,INSERT_VALUES,localX,ierr)

558: ! Get pointers to vector data (see note on Fortran arrays above)
559:       call VecGetArray(localX,x_v,x_i,ierr)
560:       call VecGetArray(Top,top_v,top_i,ierr)
561:       call VecGetArray(Bottom,bottom_v,bottom_i,ierr)
562:       call VecGetArray(Left,left_v,left_i,ierr)
563:       call VecGetArray(Right,right_v,right_i,ierr)

565: ! Initialize matrix entries to zero
566:       call MatAssembled(Hessian,assembled,ierr)
567:       if (assembled .eqv. PETSC_TRUE) call MatZeroEntries(Hessian,ierr)

570:       rhx = real(mx) + 1.0
571:       rhy = real(my) + 1.0
572:       hx = 1.0/rhx
573:       hy = 1.0/rhy
574:       hydhx = hy/hx
575:       hxdhy = hx/hy
576: ! compute Hessian over the locally owned part of the mesh

578:       do  i=xs,xs+xm-1
579:          do  j=ys,ys+ym-1
580:             row = (j-gys)*gxm + (i-gxs)

582:             xc = x_v(row + x_i)
583:             xt = xc
584:             xb = xc
585:             xr = xc
586:             xl = xc
587:             xrb = xc
588:             xlt = xc

590:             if (i .eq. gxs) then   ! Left side
591:                xl = left_v(left_i + j - ys + 1)
592:                xlt = left_v(left_i + j - ys + 2)
593:             else
594:                xl = x_v(x_i + row -1 )
595:             endif

597:             if (j .eq. gys) then ! bottom side
598:                xb = bottom_v(bottom_i + i - xs + 1)
599:                xrb = bottom_v(bottom_i + i - xs + 2)
600:             else
601:                xb = x_v(x_i + row - gxm)
602:             endif

604:             if (i+1 .eq. gxs + gxm) then !right side
605:                xr = right_v(right_i + j - ys + 1)
606:                xrb = right_v(right_i + j - ys)
607:             else
608:                xr = x_v(x_i + row + 1)
609:             endif

611:             if (j+1 .eq. gym+gys) then !top side
612:                xt = top_v(top_i +i - xs + 1)
613:                xlt = top_v(top_i + i - xs)
614:             else
615:                xt = x_v(x_i + row + gxm)
616:             endif

618:             if ((i .gt. gxs) .and. (j+1 .lt. gys+gym)) then
619:                xlt = x_v(x_i + row - 1 + gxm)
620:             endif

622:             if ((i+1 .lt. gxs+gxm) .and. (j .gt. gys)) then
623:                xrb = x_v(x_i + row + 1 - gxm)
624:             endif

626:             d1 = (xc-xl)*rhx
627:             d2 = (xc-xr)*rhx
628:             d3 = (xc-xt)*rhy
629:             d4 = (xc-xb)*rhy
630:             d5 = (xrb-xr)*rhy
631:             d6 = (xrb-xb)*rhx
632:             d7 = (xlt-xl)*rhy
633:             d8 = (xlt-xt)*rhx

635:             f1 = sqrt( 1.0 + d1*d1 + d7*d7)
636:             f2 = sqrt( 1.0 + d1*d1 + d4*d4)
637:             f3 = sqrt( 1.0 + d3*d3 + d8*d8)
638:             f4 = sqrt( 1.0 + d3*d3 + d2*d2)
639:             f5 = sqrt( 1.0 + d2*d2 + d5*d5)
640:             f6 = sqrt( 1.0 + d4*d4 + d6*d6)

643:             hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+                 &
644:      &              (-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2)

646:             hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+                 &
647:      &            (-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4)

649:             ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+                 &
650:      &                (-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4)

652:             hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+                 &
653:      &              (-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2)

655:             hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6)
656:             htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3)

658:             hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) +                         &
659:      &              hxdhy*(1.0+d8*d8)/(f3*f3*f3) +                      &
660:      &              hydhx*(1.0+d5*d5)/(f5*f5*f5) +                      &
661:      &              hxdhy*(1.0+d6*d6)/(f6*f6*f6) +                      &
662:      &              (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-               &
663:      &              2*d1*d4)/(f2*f2*f2) +  (hxdhy*(1.0+d2*d2)+          &
664:      &              hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4)

666:             hl = hl * 0.5
667:             hr = hr * 0.5
668:             ht = ht * 0.5
669:             hb = hb * 0.5
670:             hbr = hbr * 0.5
671:             htl = htl * 0.5
672:             hc = hc * 0.5

674:             k = 0

676:             if (j .gt. 0) then
677:                v(k) = hb
678:                col(k) = row - gxm
679:                k=k+1
680:             endif

682:             if ((j .gt. 0) .and. (i .lt. mx-1)) then
683:                v(k) = hbr
684:                col(k) = row-gxm+1
685:                k=k+1
686:             endif

688:             if (i .gt. 0) then
689:                v(k) = hl
690:                col(k) = row - 1
691:                k = k+1
692:             endif

694:             v(k) = hc
695:             col(k) = row
696:             k=k+1

698:             if (i .lt. mx-1) then
699:                v(k) = hr
700:                col(k) = row + 1
701:                k=k+1
702:             endif

704:             if ((i .gt. 0) .and. (j .lt. my-1)) then
705:                v(k) = htl
706:                col(k) = row + gxm - 1
707:                k=k+1
708:             endif

710:             if (j .lt. my-1) then
711:                v(k) = ht
712:                col(k) = row + gxm
713:                k=k+1
714:             endif

716: ! Set matrix values using local numbering, defined earlier in main routine
717:             call MatSetValuesLocal(Hessian,i1,row,k,col,v,INSERT_VALUES,      &
718:      &                              ierr)

722:          enddo
723:       enddo

725: ! restore vectors
726:       call VecRestoreArray(localX,x_v,x_i,ierr)
727:       call VecRestoreArray(Left,left_v,left_i,ierr)
728:       call VecRestoreArray(Right,right_v,right_i,ierr)
729:       call VecRestoreArray(Top,top_v,top_i,ierr)
730:       call VecRestoreArray(Bottom,bottom_v,bottom_i,ierr)

733: ! Assemble the matrix
734:       call MatAssemblyBegin(Hessian,MAT_FINAL_ASSEMBLY,ierr)
735:       call MatAssemblyEnd(Hessian,MAT_FINAL_ASSEMBLY,ierr)

737:       call PetscLogFlops(199.0d0*xm*ym,ierr)

739:       return
740:       end

746: ! Top,Left,Right,Bottom,bheight,mx,my,bmx,bmy,H, defined in plate2f.h

748: ! ----------------------------------------------------------------------------
749: !
750: !/*
751: !     MSA_BoundaryConditions - calculates the boundary conditions for the region
752: !
753: !
754: !*/

756:       subroutine MSA_BoundaryConditions(ierr)
757:       use mymodule
758:       implicit none

760:       PetscErrorCode   ierr
761:       PetscInt         i,j,k,limit,maxits
762:       PetscInt         xs, xm, gxs, gxm
763:       PetscInt         ys, ym, gys, gym
764:       PetscInt         bsize, lsize
765:       PetscInt         tsize, rsize
766:       PetscReal      one,two,three,tol
767:       PetscReal      scl,fnorm,det,xt
768:       PetscReal      yt,hx,hy,u1,u2,nf1,nf2
769:       PetscReal      njac11,njac12,njac21,njac22
770:       PetscReal      b, t, l, r
771:       PetscReal      boundary_v(0:1)
772:       PetscOffset      boundary_i
773:       logical exitloop
774:       PetscBool flg

776:       limit=0
777:       maxits = 5
778:       tol=1e-10
779:       b=-0.5
780:       t= 0.5
781:       l=-0.5
782:       r= 0.5
783:       xt=0
784:       yt=0
785:       one=1.0
786:       two=2.0
787:       three=3.0

790:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
791:      &                  PETSC_NULL_INTEGER,ierr)
792:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,              &
793:      &                       gxm,gym,PETSC_NULL_INTEGER,ierr)

795:       bsize = xm + 2
796:       lsize = ym + 2
797:       rsize = ym + 2
798:       tsize = xm + 2

801:       call VecCreateMPI(MPI_COMM_WORLD,bsize,PETSC_DECIDE,Bottom,ierr)
802:       call VecCreateMPI(MPI_COMM_WORLD,tsize,PETSC_DECIDE,Top,ierr)
803:       call VecCreateMPI(MPI_COMM_WORLD,lsize,PETSC_DECIDE,Left,ierr)
804:       call VecCreateMPI(MPI_COMM_WORLD,rsize,PETSC_DECIDE,Right,ierr)

806:       hx= (r-l)/(mx+1)
807:       hy= (t-b)/(my+1)

809:       do j=0,3

811:          if (j.eq.0) then
812:             yt=b
813:             xt=l+hx*xs
814:             limit=bsize
815:             call VecGetArray(Bottom,boundary_v,boundary_i,ierr)

818:          elseif (j.eq.1) then
819:             yt=t
820:             xt=l+hx*xs
821:             limit=tsize
822:             call VecGetArray(Top,boundary_v,boundary_i,ierr)

824:          elseif (j.eq.2) then
825:             yt=b+hy*ys
826:             xt=l
827:             limit=lsize
828:             call VecGetArray(Left,boundary_v,boundary_i,ierr)

830:          elseif (j.eq.3) then
831:             yt=b+hy*ys
832:             xt=r
833:             limit=rsize
834:             call VecGetArray(Right,boundary_v,boundary_i,ierr)
835:          endif

838:          do i=0,limit-1

840:             u1=xt
841:             u2=-yt
842:             k = 0
843:             exitloop = .false.
844:             do while (k .lt. maxits .and. (.not. exitloop) )

846:                nf1=u1 + u1*u2*u2 - u1*u1*u1/three-xt
847:                nf2=-u2 - u1*u1*u2 + u2*u2*u2/three-yt
848:                fnorm=sqrt(nf1*nf1+nf2*nf2)
849:                if (fnorm .gt. tol) then
850:                   njac11=one+u2*u2-u1*u1
851:                   njac12=two*u1*u2
852:                   njac21=-two*u1*u2
853:                   njac22=-one - u1*u1 + u2*u2
854:                   det = njac11*njac22-njac21*njac12
855:                   u1 = u1-(njac22*nf1-njac12*nf2)/det
856:                   u2 = u2-(njac11*nf2-njac21*nf1)/det
857:                else
858:                   exitloop = .true.
859:                endif
860:                k=k+1
861:             enddo

863:             boundary_v(i + boundary_i) = u1*u1-u2*u2
864:             if ((j .eq. 0) .or. (j .eq. 1)) then
865:                xt = xt + hx
866:             else
867:                yt = yt + hy
868:             endif

870:          enddo

873:          if (j.eq.0) then
874:             call VecRestoreArray(Bottom,boundary_v,boundary_i,ierr)
875:          elseif (j.eq.1) then
876:             call VecRestoreArray(Top,boundary_v,boundary_i,ierr)
877:          elseif (j.eq.2) then
878:             call VecRestoreArray(Left,boundary_v,boundary_i,ierr)
879:          elseif (j.eq.3) then
880:             call VecRestoreArray(Right,boundary_v,boundary_i,ierr)
881:          endif

883:       enddo

886: ! Scale the boundary if desired
887:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,          &
888:      &                         '-bottom',scl,flg,ierr)
889:       if (flg .eqv. PETSC_TRUE) then
890:          call VecScale(Bottom,scl,ierr)
891:       endif

893:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,          &
894:      &                         '-top',scl,flg,ierr)
895:       if (flg .eqv. PETSC_TRUE) then
896:          call VecScale(Top,scl,ierr)
897:       endif

899:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,          &
900:      &                         '-right',scl,flg,ierr)
901:       if (flg .eqv. PETSC_TRUE) then
902:          call VecScale(Right,scl,ierr)
903:       endif

905:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,          &
906:      &                         '-left',scl,flg,ierr)
907:       if (flg .eqv. PETSC_TRUE) then
908:          call VecScale(Left,scl,ierr)
909:       endif

912:       return
913:       end

915: ! ----------------------------------------------------------------------------
916: !
917: !/*
918: !     MSA_Plate - Calculates an obstacle for surface to stretch over
919: !
920: !     Output Parameter:
921: !.    xl - lower bound vector
922: !.    xu - upper bound vector
923: !
924: !*/

926:       subroutine MSA_Plate(tao,xl,xu,dummy,ierr)
927:       use mymodule
928:       implicit none

930:       Tao        tao
931:       Vec              xl,xu
932:       PetscErrorCode   ierr
933:       PetscInt         i,j,row
934:       PetscInt         xs, xm, ys, ym
935:       PetscReal      lb,ub
936:       PetscInt         dummy

938: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
939: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (PetscOffset) x_index, ierr)
940: ! will return an array of doubles referenced by x_array offset by x_index.
941: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
942: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
943:       PetscReal      xl_v(0:1)
944:       PetscOffset      xl_i

946:       print *,'msa_plate'

948:       lb = PETSC_NINFINITY
949:       ub = PETSC_INFINITY

951:       if (bmy .lt. 0) bmy = 0
952:       if (bmy .gt. my) bmy = my
953:       if (bmx .lt. 0) bmx = 0
954:       if (bmx .gt. mx) bmx = mx

957:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
958:      &             PETSC_NULL_INTEGER,ierr)

960:       call VecSet(xl,lb,ierr)
961:       call VecSet(xu,ub,ierr)

963:       call VecGetArray(xl,xl_v,xl_i,ierr)

966:       do i=xs,xs+xm-1

968:          do j=ys,ys+ym-1

970:             row=(j-ys)*xm + (i-xs)

972:             if (i.ge.((mx-bmx)/2) .and. i.lt.(mx-(mx-bmx)/2) .and.           &
973:      &          j.ge.((my-bmy)/2) .and. j.lt.(my-(my-bmy)/2)) then
974:                xl_v(xl_i+row) = bheight

976:             endif

978:          enddo
979:       enddo

982:       call VecRestoreArray(xl,xl_v,xl_i,ierr)

984:       return
985:       end

991: ! ----------------------------------------------------------------------------
992: !
993: !/*
994: !     MSA_InitialPoint - Calculates an obstacle for surface to stretch over
995: !
996: !     Output Parameter:
997: !.    X - vector for initial guess
998: !
999: !*/

1001:       subroutine MSA_InitialPoint(X, ierr)
1002:       use mymodule
1003:       implicit none

1005:       Vec               X
1006:       PetscErrorCode    ierr
1007:       PetscInt          start,i,j
1008:       PetscInt          row
1009:       PetscInt          xs,xm,gxs,gxm
1010:       PetscInt          ys,ym,gys,gym
1011:       PetscReal       zero, np5

1013: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
1014: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (integer) x_index, ierr)
1015: ! will return an array of doubles referenced by x_array offset by x_index.
1016: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
1017: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
1018:       PetscReal   left_v(0:1),right_v(0:1)
1019:       PetscReal   bottom_v(0:1),top_v(0:1)
1020:       PetscReal   x_v(0:1)
1021:       PetscOffset   left_i, right_i, top_i
1022:       PetscOffset   bottom_i,x_i
1023:       PetscBool     flg
1024:       PetscRandom   rctx

1026:       zero = 0.0
1027:       np5 = -0.5

1029:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,        &
1030:      &                        '-start', start,flg,ierr)

1032:       if ((flg .eqv. PETSC_TRUE) .and. (start .eq. 0)) then  ! the zero vector is reasonable
1033:          call VecSet(X,zero,ierr)

1035:       elseif ((flg .eqv. PETSC_TRUE) .and. (start .gt. 0)) then  ! random start -0.5 < xi < 0.5
1036:          call PetscRandomCreate(MPI_COMM_WORLD,rctx,ierr)
1037:          do i=0,start-1
1038:             call VecSetRandom(X,rctx,ierr)
1039:          enddo

1041:          call PetscRandomDestroy(rctx,ierr)
1042:          call VecShift(X,np5,ierr)

1044:       else   ! average of boundary conditions

1046: !        Get Local mesh boundaries
1047:          call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,             &
1048:      &                     PETSC_NULL_INTEGER,ierr)
1049:          call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,    &
1050:      &                     PETSC_NULL_INTEGER,ierr)

1054: !        Get pointers to vector data
1055:          call VecGetArray(Top,top_v,top_i,ierr)
1056:          call VecGetArray(Bottom,bottom_v,bottom_i,ierr)
1057:          call VecGetArray(Left,left_v,left_i,ierr)
1058:          call VecGetArray(Right,right_v,right_i,ierr)

1060:          call VecGetArray(localX,x_v,x_i,ierr)

1062: !        Perform local computations
1063:          do  j=ys,ys+ym-1
1064:             do i=xs,xs+xm-1
1065:                row = (j-gys)*gxm  + (i-gxs)
1066:                x_v(x_i + row) = ((j+1)*bottom_v(bottom_i +i-xs+1)/my        &
1067:      &             + (my-j+1)*top_v(top_i+i-xs+1)/(my+2) +                  &
1068:      &              (i+1)*left_v(left_i+j-ys+1)/mx       +                  &
1069:      &              (mx-i+1)*right_v(right_i+j-ys+1)/(mx+2))*0.5
1070:             enddo
1071:          enddo

1073: !        Restore vectors
1074:          call VecRestoreArray(localX,x_v,x_i,ierr)

1076:          call VecRestoreArray(Left,left_v,left_i,ierr)
1077:          call VecRestoreArray(Top,top_v,top_i,ierr)
1078:          call VecRestoreArray(Bottom,bottom_v,bottom_i,ierr)
1079:          call VecRestoreArray(Right,right_v,right_i,ierr)

1081:          call DMLocalToGlobalBegin(dm,localX,INSERT_VALUES,X,ierr)
1082:          call DMLocalToGlobalEnd(dm,localX,INSERT_VALUES,X,ierr)

1084:       endif

1086:       return
1087:       end

1089: !
1090: !/*TEST
1091: !
1092: !   build:
1093: !      requires: !complex
1094: !
1095: !   test:
1096: !      args: -tao_smonitor -mx 8 -my 6 -bmx 3 -bmy 3 -bheight 0.2 -tao_type bqnls -tao_gatol 1.e-4
1097: !      filter: sort -b
1098: !      filter_output: sort -b
1099: !      requires: !single
1100: !
1101: !   test:
1102: !      suffix: 2
1103: !      nsize: 2
1104: !      args: -tao_smonitor -mx 8 -my 6 -bmx 3 -bmy 3 -bheight 0.2 -tao_type bqnls -tao_gatol 1.e-4
1105: !      filter: sort -b
1106: !      filter_output: sort -b
1107: !      requires: !single
1108: !
1109: !TEST*/
```