Actual source code: plate2f.F

petsc-dev 2014-07-21
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  1: !  Program usage: mpirun -np <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();
 18: !   Routines: TaoSetType(); TaoSetObjectiveAndGradientRoutine();
 19: !   Routines: TaoSetHessianRoutine();
 20: !   Routines: TaoSetVariableBoundsRoutine();
 21: !   Routines: TaoSetInitialVector();
 22: !   Routines: TaoSetFromOptions();
 23: !   Routines: TaoSolve();
 24: !   Routines: TaoDestroy();
 25: !   Processors: n
 26: !T*/



 30:       implicit none

 32: #include "plate2f.h"

 34: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 35: !                   Variable declarations
 36: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 37: !
 38: !  Variables:
 39: !    (common from plate2f.h):
 40: !    Nx, Ny           number of processors in x- and y- directions
 41: !    mx, my           number of grid points in x,y directions
 42: !    N    global dimension of vector

 44:       PetscErrorCode   ierr          ! used to check for functions returning nonzeros
 45:       Vec              x             ! solution vector
 46:       Vec              xl, xu        ! lower and upper bounds vectorsp
 47:       PetscInt         m             ! number of local elements in vector
 48:       Tao              tao           ! Tao solver context
 49:       Mat              H             ! Hessian matrix
 50:       ISLocalToGlobalMapping isltog  ! local to global mapping object
 51:       PetscBool        flg
 52:       PetscInt         i1,i3,i7


 55:       external FormFunctionGradient
 56:       external FormHessian
 57:       external MSA_BoundaryConditions
 58:       external MSA_Plate
 59:       external MSA_InitialPoint
 60: ! Initialize Tao

 62:       i1=1
 63:       i3=3
 64:       i7=7


 67:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)

 69: ! Specify default dimensions of the problem
 70:       mx = 10
 71:       my = 10
 72:       bheight = 0.1

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

 76:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,"-mx",mx,flg,ierr)
 77:       CHKERRQ(ierr)
 78:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,"-my",my,flg,ierr)
 79:       CHKERRQ(ierr)

 81:       bmx = mx/2
 82:       bmy = my/2

 84:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,"-bmx",bmx,flg,ierr)
 85:       CHKERRQ(ierr)
 86:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,"-bmy",bmy,flg,ierr)
 87:       CHKERRQ(ierr)
 88:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,"-bheight",bheight,   &
 89:      &      flg,ierr)
 90:       CHKERRQ(ierr)


 93: ! Calculate any derived values from parameters
 94:       N = mx*my

 96: ! Let Petsc determine the dimensions of the local vectors
 97:       Nx = PETSC_DECIDE
 98:       NY = PETSC_DECIDE

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

104:       call DMDACreate2d(MPI_COMM_WORLD,DM_BOUNDARY_NONE,                    &
105:      &     DM_BOUNDARY_NONE, DMDA_STENCIL_BOX,                              &
106:      &     mx,my,Nx,Ny,i1,i1,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,           &
107:      &     dm,ierr)
108:       CHKERRQ(ierr)


111: ! Extract global and local vectors from DM; The local vectors are
112: ! used solely as work space for the evaluation of the function,
113: ! gradient, and Hessian.  Duplicate for remaining vectors that are
114: ! the same types.

116:       call DMCreateGlobalVector(dm,x,ierr)
117:       CHKERRQ(ierr)
118:       call DMCreateLocalVector(dm,localX,ierr)
119:       CHKERRQ(ierr)
120:       call VecDuplicate(localX,localV,ierr)
121:       CHKERRQ(ierr)

123: ! Create a matrix data structure to store the Hessian.
124: ! Here we (optionally) also associate the local numbering scheme
125: ! with the matrix so that later we can use local indices for matrix
126: ! assembly

128:       call VecGetLocalSize(x,m,ierr)
129:       CHKERRQ(ierr)
130:       call MatCreateAIJ(MPI_COMM_WORLD,m,m,N,N,i7,PETSC_NULL_INTEGER,   &
131:      &     i3,PETSC_NULL_INTEGER,H,ierr)
132:       CHKERRQ(ierr)

134:       call MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE,ierr)
135:       CHKERRQ(ierr)
136:       call DMGetLocalToGlobalMapping(dm,isltog,ierr)
137:       CHKERRQ(ierr)
138:       call MatSetLocalToGlobalMapping(H,isltog,isltog,ierr)
139:       CHKERRQ(ierr)


142: ! The Tao code begins here
143: ! Create TAO solver and set desired solution method.
144: ! This problems uses bounded variables, so the
145: ! method must either be 'tao_tron' or 'tao_blmvm'

147:       call TaoCreate(PETSC_COMM_WORLD,tao,ierr)
148:       CHKERRQ(ierr)
149:       call TaoSetType(tao,TAOBLMVM,ierr)
150:       CHKERRQ(ierr)

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

154:       call TaoSetObjectiveAndGradientRoutine(tao,                       &
155:      &     FormFunctionGradient,PETSC_NULL_OBJECT,ierr)
156:       CHKERRQ(ierr)

158:       call TaoSetHessianRoutine(tao,H,H,FormHessian,                    &
159:      &     PETSC_NULL_OBJECT, ierr)
160:       CHKERRQ(ierr)

162: ! Set Variable bounds
163:       call MSA_BoundaryConditions(ierr)
164:       CHKERRQ(ierr)
165:       call TaoSetVariableBoundsRoutine(tao,MSA_Plate,                   &
166:      &     PETSC_NULL_OBJECT,ierr)
167:       CHKERRQ(ierr)

169: ! Set the initial solution guess
170:       call MSA_InitialPoint(x, ierr)
171:       CHKERRQ(ierr)
172:       call TaoSetInitialVector(tao,x,ierr)
173:       CHKERRQ(ierr)

175: ! Check for any tao command line options
176:       call TaoSetFromOptions(tao,ierr)
177:       CHKERRQ(ierr)

179: ! Solve the application
180:       call TaoSolve(tao,ierr)
181:       CHKERRQ(ierr)

183: ! Free TAO data structures
184:       call TaoDestroy(tao,ierr)
185:       CHKERRQ(ierr)

187: ! Free PETSc data structures
188:       call VecDestroy(x,ierr)
189:       call VecDestroy(Top,ierr)
190:       call VecDestroy(Bottom,ierr)
191:       call VecDestroy(Left,ierr)
192:       call VecDestroy(Right,ierr)
193:       call MatDestroy(H,ierr)
194:       call VecDestroy(localX,ierr)
195:       call VecDestroy(localV,ierr)
196:       call DMDestroy(dm,ierr)

198: ! Finalize TAO

200:       call PetscFinalize(ierr)

202:       end

204: ! ---------------------------------------------------------------------
205: !
206: !  FormFunctionGradient - Evaluates function f(X).
207: !
208: !  Input Parameters:
209: !  tao   - the Tao context
210: !  X     - the input vector
211: !  dummy - optional user-defined context, as set by TaoSetFunction()
212: !          (not used here)
213: !
214: !  Output Parameters:
215: !  fcn     - the newly evaluated function
216: !  G       - the gradient vector
217: !  info  - error code
218: !


221:       subroutine FormFunctionGradient(tao,X,fcn,G,dummy,ierr)
222:       implicit none

224: ! dm, localX, localG, Top, Bottom, Left, Right defined in plate2f.h
225: #include "plate2f.h"

227: ! Input/output variables

229:       Tao        tao
230:       PetscReal      fcn
231:       Vec              X, G
232:       PetscErrorCode   ierr
233:       PetscInt         dummy

235:       PetscInt         i,j,row
236:       PetscInt         xs, xm
237:       PetscInt         gxs, gxm
238:       PetscInt         ys, ym
239:       PetscInt         gys, gym
240:       PetscReal      ft,zero,hx,hy,hydhx,hxdhy
241:       PetscReal      area,rhx,rhy
242:       PetscReal      f1,f2,f3,f4,f5,f6,d1,d2,d3
243:       PetscReal      d4,d5,d6,d7,d8
244:       PetscReal      df1dxc,df2dxc,df3dxc,df4dxc
245:       PetscReal      df5dxc,df6dxc
246:       PetscReal      xc,xl,xr,xt,xb,xlt,xrb


249: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
250: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (PetscOffset) x_index, ierr)
251: ! will return an array of doubles referenced by x_array offset by x_index.
252: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
253: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
254:       PetscReal      g_v(0:1),x_v(0:1)
255:       PetscReal      top_v(0:1),left_v(0:1)
256:       PetscReal      right_v(0:1),bottom_v(0:1)
257:       PetscOffset      g_i,left_i,right_i
258:       PetscOffset      bottom_i,top_i,x_i

260:       ft = 0.0d0
261:       zero = 0.0d0
262:       hx = 1.0d0/(mx + 1)
263:       hy = 1.0d0/(my + 1)
264:       hydhx = hy/hx
265:       hxdhy = hx/hy
266:       area = 0.5d0 * hx * hy
267:       rhx = mx + 1.0d0
268:       rhy = my + 1.0d0


271: ! Get local mesh boundaries
272:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,              &
273:      &                  PETSC_NULL_INTEGER,ierr)
274:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,             &
275:      &                       gxm,gym,PETSC_NULL_INTEGER,ierr)

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

281: ! Initialize the vector to zero
282:       call VecSet(localV,zero,ierr)

284: ! Get arrays to vector data (See note above about using VecGetArray in Fortran)
285:       call VecGetArray(localX,x_v,x_i,ierr)
286:       call VecGetArray(localV,g_v,g_i,ierr)
287:       call VecGetArray(Top,top_v,top_i,ierr)
288:       call VecGetArray(Bottom,bottom_v,bottom_i,ierr)
289:       call VecGetArray(Left,left_v,left_i,ierr)
290:       call VecGetArray(Right,right_v,right_i,ierr)

292: ! Compute function over the locally owned part of the mesh
293:       do j = ys,ys+ym-1
294:          do i = xs,xs+xm-1
295:             row = (j-gys)*gxm + (i-gxs)
296:             xc = x_v(row+x_i)
297:             xt = xc
298:             xb = xc
299:             xr = xc
300:             xl = xc
301:             xrb = xc
302:             xlt = xc

304:             if (i .eq. 0) then !left side
305:                xl = left_v(j - ys + 1 + left_i)
306:                xlt = left_v(j - ys + 2 + left_i)
307:             else
308:                xl = x_v(row - 1 + x_i)
309:             endif

311:             if (j .eq. 0) then !bottom side
312:                xb = bottom_v(i - xs + 1 + bottom_i)
313:                xrb = bottom_v(i - xs + 2 + bottom_i)
314:             else
315:                xb = x_v(row - gxm + x_i)
316:             endif

318:             if (i + 1 .eq. gxs + gxm) then !right side
319:                xr = right_v(j - ys + 1 + right_i)
320:                xrb = right_v(j - ys + right_i)
321:             else
322:                xr = x_v(row + 1 + x_i)
323:             endif

325:             if (j + 1 .eq. gys + gym) then !top side
326:                xt = top_v(i - xs + 1 + top_i)
327:                xlt = top_v(i - xs + top_i)
328:             else
329:                xt = x_v(row + gxm + x_i)
330:             endif

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

336:             if ((j .gt. gys) .and. (i + 1 .lt. gxs + gxm)) then
337:                xrb = x_v(row + 1 - gxm + x_i)
338:             endif

340:             d1 = xc-xl
341:             d2 = xc-xr
342:             d3 = xc-xt
343:             d4 = xc-xb
344:             d5 = xr-xrb
345:             d6 = xrb-xb
346:             d7 = xlt-xl
347:             d8 = xt-xlt

349:             df1dxc = d1 * hydhx
350:             df2dxc = d1 * hydhx + d4 * hxdhy
351:             df3dxc = d3 * hxdhy
352:             df4dxc = d2 * hydhx + d3 * hxdhy
353:             df5dxc = d2 * hydhx
354:             df6dxc = d4 * hxdhy

356:             d1 = d1 * rhx
357:             d2 = d2 * rhx
358:             d3 = d3 * rhy
359:             d4 = d4 * rhy
360:             d5 = d5 * rhy
361:             d6 = d6 * rhx
362:             d7 = d7 * rhy
363:             d8 = d8 * rhx

365:             f1 = sqrt(1.0d0 + d1*d1 + d7*d7)
366:             f2 = sqrt(1.0d0 + d1*d1 + d4*d4)
367:             f3 = sqrt(1.0d0 + d3*d3 + d8*d8)
368:             f4 = sqrt(1.0d0 + d3*d3 + d2*d2)
369:             f5 = sqrt(1.0d0 + d2*d2 + d5*d5)
370:             f6 = sqrt(1.0d0 + d4*d4 + d6*d6)

372:             ft = ft + f2 + f4

374:             df1dxc = df1dxc / f1
375:             df2dxc = df2dxc / f2
376:             df3dxc = df3dxc / f3
377:             df4dxc = df4dxc / f4
378:             df5dxc = df5dxc / f5
379:             df6dxc = df6dxc / f6

381:             g_v(row + g_i) = 0.5 * (df1dxc + df2dxc + df3dxc + df4dxc +  &
382:      &                              df5dxc + df6dxc)
383:          enddo
384:       enddo

386: ! Compute triangular areas along the border of the domain.
387:       if (xs .eq. 0) then  ! left side
388:          do j=ys,ys+ym-1
389:             d3 = (left_v(j-ys+1+left_i) - left_v(j-ys+2+left_i))         &
390:      &                 * rhy
391:             d2 = (left_v(j-ys+1+left_i) - x_v((j-gys)*gxm + x_i))        &
392:      &                 * rhx
393:             ft = ft + sqrt(1.0d0 + d3*d3 + d2*d2)
394:          enddo
395:       endif


398:       if (ys .eq. 0) then !bottom side
399:          do i=xs,xs+xm-1
400:             d2 = (bottom_v(i+1-xs+bottom_i)-bottom_v(i-xs+2+bottom_i))    &
401:      &                    * rhx
402:             d3 = (bottom_v(i-xs+1+bottom_i)-x_v(i-gxs+x_i))*rhy
403:             ft = ft + sqrt(1.0 + d3*d3 + d2*d2)
404:          enddo
405:       endif


408:       if (xs + xm .eq. mx) then ! right side
409:          do j=ys,ys+ym-1
410:             d1 = (x_v((j+1-gys)*gxm-1+x_i)-right_v(j-ys+1+right_i))*rhx
411:             d4 = (right_v(j-ys+right_i) - right_v(j-ys+1+right_i))*rhy
412:             ft = ft + sqrt(1.0d0 + d1*d1 + d4*d4)
413:          enddo
414:       endif


417:       if (ys + ym .eq. my) then
418:          do i=xs,xs+xm-1
419:             d1 = (x_v((gym-1)*gxm+i-gxs+x_i) - top_v(i-xs+1+top_i))*rhy
420:             d4 = (top_v(i-xs+1+top_i) - top_v(i-xs+top_i))*rhx
421:             ft = ft + sqrt(1.0d0 + d1*d1 + d4*d4)
422:          enddo
423:       endif


426:       if ((ys .eq. 0) .and. (xs .eq. 0)) then
427:          d1 = (left_v(0 + left_i) - left_v(1 + left_i)) * rhy
428:          d2 = (bottom_v(0+bottom_i)-bottom_v(1+bottom_i))*rhx
429:          ft = ft + sqrt(1.0d0 + d1*d1 + d2*d2)
430:       endif

432:       if ((ys + ym .eq. my) .and. (xs + xm .eq. mx)) then
433:          d1 = (right_v(ym+1+right_i) - right_v(ym+right_i))*rhy
434:          d2 = (top_v(xm+1+top_i) - top_v(xm + top_i))*rhx
435:          ft = ft + sqrt(1.0d0 + d1*d1 + d2*d2)
436:       endif

438:       ft = ft * area
439:       call MPI_Allreduce(ft,fcn,1,MPIU_SCALAR,                            &
440:      &             MPIU_SUM,MPI_COMM_WORLD,ierr)


443: ! Restore vectors
444:       call VecRestoreArray(localX,x_v,x_i,ierr)
445:       call VecRestoreArray(localV,g_v,g_i,ierr)
446:       call VecRestoreArray(Left,left_v,left_i,ierr)
447:       call VecRestoreArray(Top,top_v,top_i,ierr)
448:       call VecRestoreArray(Bottom,bottom_v,bottom_i,ierr)
449:       call VecRestoreArray(Right,right_v,right_i,ierr)

451: ! Scatter values to global vector
452:       call DMLocalToGlobalBegin(dm,localV,INSERT_VALUES,G,ierr)
453:       call DMLocalToGlobalEnd(dm,localV,INSERT_VALUES,G,ierr)

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

457:       return
458:       end  !FormFunctionGradient





464: ! ----------------------------------------------------------------------------
465: !
466: !
467: !   FormHessian - Evaluates Hessian matrix.
468: !
469: !   Input Parameters:
470: !.  tao  - the Tao context
471: !.  X    - input vector
472: !.  dummy  - not used
473: !
474: !   Output Parameters:
475: !.  Hessian    - Hessian matrix
476: !.  Hpc    - optionally different preconditioning matrix
477: !.  flag - flag indicating matrix structure
478: !
479: !   Notes:
480: !   Due to mesh point reordering with DMs, we must always work
481: !   with the local mesh points, and then transform them to the new
482: !   global numbering with the local-to-global mapping.  We cannot work
483: !   directly with the global numbers for the original uniprocessor mesh!
484: !
485: !      MatSetValuesLocal(), using the local ordering (including
486: !         ghost points!)
487: !         - Then set matrix entries using the local ordering
488: !           by calling MatSetValuesLocal()

490:       subroutine FormHessian(tao, X, Hessian, Hpc, dummy, ierr)
491:       implicit none

493: ! dm,Top,Left,Right,Bottom,mx,my,localX defined in plate2f.h
494: #include "plate2f.h"

496:       Tao     tao
497:       Vec            X
498:       Mat            Hessian,Hpc
499:       PetscInt       dummy
500:       PetscErrorCode ierr

502:       PetscInt       i,j,k,row
503:       PetscInt       xs,xm,gxs,gxm
504:       PetscInt       ys,ym,gys,gym
505:       PetscInt       col(0:6)
506:       PetscReal    hx,hy,hydhx,hxdhy,rhx,rhy
507:       PetscReal    f1,f2,f3,f4,f5,f6,d1,d2,d3
508:       PetscReal    d4,d5,d6,d7,d8
509:       PetscReal    xc,xl,xr,xt,xb,xlt,xrb
510:       PetscReal    hl,hr,ht,hb,hc,htl,hbr

512: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
513: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (PetscOffset) x_index, ierr)
514: ! will return an array of doubles referenced by x_array offset by x_index.
515: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
516: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
517:       PetscReal   right_v(0:1),left_v(0:1)
518:       PetscReal   bottom_v(0:1),top_v(0:1)
519:       PetscReal   x_v(0:1)
520:       PetscOffset   x_i,right_i,left_i
521:       PetscOffset   bottom_i,top_i
522:       PetscReal   v(0:6)
523:       PetscBool     assembled
524:       PetscInt      i1

526:       i1=1

528: ! Set various matrix options
529:       call MatSetOption(Hessian,MAT_IGNORE_OFF_PROC_ENTRIES,              &
530:      &                  PETSC_TRUE,ierr)

532: ! Get local mesh boundaries
533:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,              &
534:      &                  PETSC_NULL_INTEGER,ierr)
535:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,     &
536:      &                       PETSC_NULL_INTEGER,ierr)

538: ! Scatter ghost points to local vectors
539:       call DMGlobalToLocalBegin(dm,X,INSERT_VALUES,localX,ierr)
540:       call DMGlobalToLocalEnd(dm,X,INSERT_VALUES,localX,ierr)

542: ! Get pointers to vector data (see note on Fortran arrays above)
543:       call VecGetArray(localX,x_v,x_i,ierr)
544:       call VecGetArray(Top,top_v,top_i,ierr)
545:       call VecGetArray(Bottom,bottom_v,bottom_i,ierr)
546:       call VecGetArray(Left,left_v,left_i,ierr)
547:       call VecGetArray(Right,right_v,right_i,ierr)

549: ! Initialize matrix entries to zero
550:       call MatAssembled(Hessian,assembled,ierr)
551:       if (assembled .eqv. PETSC_TRUE) call MatZeroEntries(Hessian,ierr)


554:       rhx = mx + 1.0
555:       rhy = my + 1.0
556:       hx = 1.0/rhx
557:       hy = 1.0/rhy
558:       hydhx = hy/hx
559:       hxdhy = hx/hy
560: ! compute Hessian over the locally owned part of the mesh

562:       do  i=xs,xs+xm-1
563:          do  j=ys,ys+ym-1
564:             row = (j-gys)*gxm + (i-gxs)

566:             xc = x_v(row + x_i)
567:             xt = xc
568:             xb = xc
569:             xr = xc
570:             xl = xc
571:             xrb = xc
572:             xlt = xc

574:             if (i .eq. gxs) then   ! Left side
575:                xl = left_v(left_i + j - ys + 1)
576:                xlt = left_v(left_i + j - ys + 2)
577:             else
578:                xl = x_v(x_i + row -1 )
579:             endif

581:             if (j .eq. gys) then ! bottom side
582:                xb = bottom_v(bottom_i + i - xs + 1)
583:                xrb = bottom_v(bottom_i + i - xs + 2)
584:             else
585:                xb = x_v(x_i + row - gxm)
586:             endif

588:             if (i+1 .eq. gxs + gxm) then !right side
589:                xr = right_v(right_i + j - ys + 1)
590:                xrb = right_v(right_i + j - ys)
591:             else
592:                xr = x_v(x_i + row + 1)
593:             endif

595:             if (j+1 .eq. gym+gys) then !top side
596:                xt = top_v(top_i +i - xs + 1)
597:                xlt = top_v(top_i + i - xs)
598:             else
599:                xt = x_v(x_i + row + gxm)
600:             endif

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

606:             if ((i+1 .lt. gxs+gxm) .and. (j .gt. gys)) then
607:                xrb = x_v(x_i + row + 1 - gxm)
608:             endif

610:             d1 = (xc-xl)*rhx
611:             d2 = (xc-xr)*rhx
612:             d3 = (xc-xt)*rhy
613:             d4 = (xc-xb)*rhy
614:             d5 = (xrb-xr)*rhy
615:             d6 = (xrb-xb)*rhx
616:             d7 = (xlt-xl)*rhy
617:             d8 = (xlt-xt)*rhx

619:             f1 = sqrt( 1.0d0 + d1*d1 + d7*d7)
620:             f2 = sqrt( 1.0d0 + d1*d1 + d4*d4)
621:             f3 = sqrt( 1.0d0 + d3*d3 + d8*d8)
622:             f4 = sqrt( 1.0d0 + d3*d3 + d2*d2)
623:             f5 = sqrt( 1.0d0 + d2*d2 + d5*d5)
624:             f6 = sqrt( 1.0d0 + d4*d4 + d6*d6)


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

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

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

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

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

642:             hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) +                         &
643:      &              hxdhy*(1.0+d8*d8)/(f3*f3*f3) +                      &
644:      &              hydhx*(1.0+d5*d5)/(f5*f5*f5) +                      &
645:      &              hxdhy*(1.0+d6*d6)/(f6*f6*f6) +                      &
646:      &              (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-               &
647:      &              2*d1*d4)/(f2*f2*f2) +  (hxdhy*(1.0+d2*d2)+          &
648:      &              hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4)

650:             hl = hl * 0.5
651:             hr = hr * 0.5
652:             ht = ht * 0.5
653:             hb = hb * 0.5
654:             hbr = hbr * 0.5
655:             htl = htl * 0.5
656:             hc = hc * 0.5

658:             k = 0

660:             if (j .gt. 0) then
661:                v(k) = hb
662:                col(k) = row - gxm
663:                k=k+1
664:             endif

666:             if ((j .gt. 0) .and. (i .lt. mx-1)) then
667:                v(k) = hbr
668:                col(k) = row-gxm+1
669:                k=k+1
670:             endif

672:             if (i .gt. 0) then
673:                v(k) = hl
674:                col(k) = row - 1
675:                k = k+1
676:             endif

678:             v(k) = hc
679:             col(k) = row
680:             k=k+1

682:             if (i .lt. mx-1) then
683:                v(k) = hr
684:                col(k) = row + 1
685:                k=k+1
686:             endif

688:             if ((i .gt. 0) .and. (j .lt. my-1)) then
689:                v(k) = htl
690:                col(k) = row + gxm - 1
691:                k=k+1
692:             endif

694:             if (j .lt. my-1) then
695:                v(k) = ht
696:                col(k) = row + gxm
697:                k=k+1
698:             endif

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



706:          enddo
707:       enddo

709: ! restore vectors
710:       call VecRestoreArray(localX,x_v,x_i,ierr)
711:       call VecRestoreArray(Left,left_v,left_i,ierr)
712:       call VecRestoreArray(Right,right_v,right_i,ierr)
713:       call VecRestoreArray(Top,top_v,top_i,ierr)
714:       call VecRestoreArray(Bottom,bottom_v,bottom_i,ierr)


717: ! Assemble the matrix
718:       call MatAssemblyBegin(Hessian,MAT_FINAL_ASSEMBLY,ierr)
719:       call MatAssemblyEnd(Hessian,MAT_FINAL_ASSEMBLY,ierr)

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

723:       return
724:       end





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

732: ! ----------------------------------------------------------------------------
733: !
734: !/*
735: !     MSA_BoundaryConditions - calculates the boundary conditions for the region
736: !
737: !
738: !*/

740:       subroutine MSA_BoundaryConditions(ierr)
741:       implicit none

743: ! Top,Left,Right,Bottom,bheight,mx,my,bmx,bmy defined in plate2f.h
744: #include "plate2f.h"

746:       PetscErrorCode   ierr
747:       PetscInt         i,j,k,limit,maxits
748:       PetscInt         xs, xm, gxs, gxm
749:       PetscInt         ys, ym, gys, gym
750:       PetscInt         bsize, lsize
751:       PetscInt         tsize, rsize
752:       PetscReal      one,two,three,tol
753:       PetscReal      scl,fnorm,det,xt
754:       PetscReal      yt,hx,hy,u1,u2,nf1,nf2
755:       PetscReal      njac11,njac12,njac21,njac22
756:       PetscReal      b, t, l, r
757:       PetscReal      boundary_v(0:1)
758:       PetscOffset      boundary_i
759:       logical exitloop
760:       PetscBool flg

762:       limit=0
763:       maxits = 5
764:       tol=1e-10
765:       b=-0.5d0
766:       t= 0.5d0
767:       l=-0.5d0
768:       r= 0.5d0
769:       xt=0
770:       yt=0
771:       one=1.0d0
772:       two=2.0d0
773:       three=3.0d0


776:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
777:      &                  PETSC_NULL_INTEGER,ierr)
778:       call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,              &
779:      &                       gxm,gym,PETSC_NULL_INTEGER,ierr)

781:       bsize = xm + 2
782:       lsize = ym + 2
783:       rsize = ym + 2
784:       tsize = xm + 2


787:       call VecCreateMPI(MPI_COMM_WORLD,bsize,PETSC_DECIDE,Bottom,ierr)
788:       call VecCreateMPI(MPI_COMM_WORLD,tsize,PETSC_DECIDE,Top,ierr)
789:       call VecCreateMPI(MPI_COMM_WORLD,lsize,PETSC_DECIDE,Left,ierr)
790:       call VecCreateMPI(MPI_COMM_WORLD,rsize,PETSC_DECIDE,Right,ierr)

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

795:       do j=0,3

797:          if (j.eq.0) then
798:             yt=b
799:             xt=l+hx*xs
800:             limit=bsize
801:             call VecGetArray(Bottom,boundary_v,boundary_i,ierr)


804:          elseif (j.eq.1) then
805:             yt=t
806:             xt=l+hx*xs
807:             limit=tsize
808:             call VecGetArray(Top,boundary_v,boundary_i,ierr)

810:          elseif (j.eq.2) then
811:             yt=b+hy*ys
812:             xt=l
813:             limit=lsize
814:             call VecGetArray(Left,boundary_v,boundary_i,ierr)

816:          elseif (j.eq.3) then
817:             yt=b+hy*ys
818:             xt=r
819:             limit=rsize
820:             call VecGetArray(Right,boundary_v,boundary_i,ierr)
821:          endif


824:          do i=0,limit-1

826:             u1=xt
827:             u2=-yt
828:             k = 0
829:             exitloop = .false.
830:             do while (k .lt. maxits .and. (.not. exitloop) )

832:                nf1=u1 + u1*u2*u2 - u1*u1*u1/three-xt
833:                nf2=-u2 - u1*u1*u2 + u2*u2*u2/three-yt
834:                fnorm=sqrt(nf1*nf1+nf2*nf2)
835:                if (fnorm .gt. tol) then
836:                   njac11=one+u2*u2-u1*u1
837:                   njac12=two*u1*u2
838:                   njac21=-two*u1*u2
839:                   njac22=-one - u1*u1 + u2*u2
840:                   det = njac11*njac22-njac21*njac12
841:                   u1 = u1-(njac22*nf1-njac12*nf2)/det
842:                   u2 = u2-(njac11*nf2-njac21*nf1)/det
843:                else
844:                   exitloop = .true.
845:                endif
846:                k=k+1
847:             enddo

849:             boundary_v(i + boundary_i) = u1*u1-u2*u2
850:             if ((j .eq. 0) .or. (j .eq. 1)) then
851:                xt = xt + hx
852:             else
853:                yt = yt + hy
854:             endif

856:          enddo


859:          if (j.eq.0) then
860:             call VecRestoreArray(Bottom,boundary_v,boundary_i,ierr)
861:          elseif (j.eq.1) then
862:             call VecRestoreArray(Top,boundary_v,boundary_i,ierr)
863:          elseif (j.eq.2) then
864:             call VecRestoreArray(Left,boundary_v,boundary_i,ierr)
865:          elseif (j.eq.3) then
866:             call VecRestoreArray(Right,boundary_v,boundary_i,ierr)
867:          endif

869:       enddo


872: ! Scale the boundary if desired
873:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,"-bottom",            &
874:      &                         scl,flg,ierr)
875:       if (flg .eqv. PETSC_TRUE) then
876:          call VecScale(scl,Bottom,ierr)
877:       endif

879:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,"-top",               &
880:      &                         scl,flg,ierr)
881:       if (flg .eqv. PETSC_TRUE) then
882:          call VecScale(scl,Top,ierr)
883:       endif

885:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,"-right",             &
886:      &                         scl,flg,ierr)
887:       if (flg .eqv. PETSC_TRUE) then
888:          call VecScale(scl,Right,ierr)
889:       endif

891:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,"-left",              &
892:      &                         scl,flg,ierr)
893:       if (flg .eqv. PETSC_TRUE) then
894:          call VecScale(scl,Left,ierr)
895:       endif


898:       return
899:       end

901: ! ----------------------------------------------------------------------------
902: !
903: !/*
904: !     MSA_Plate - Calculates an obstacle for surface to stretch over
905: !
906: !     Output Parameter:
907: !.    xl - lower bound vector
908: !.    xu - upper bound vector
909: !
910: !*/

912:       subroutine MSA_Plate(tao,xl,xu,dummy,ierr)
913:       implicit none
914: ! mx,my,bmx,bmy,dm,bheight defined in plate2f.h
915: #include "plate2f.h"
916:       Tao        tao
917:       Vec              xl,xu
918:       PetscErrorCode   ierr
919:       PetscInt         i,j,row
920:       PetscInt         xs, xm, ys, ym
921:       PetscReal      lb,ub
922:       PetscInt         dummy

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

932:       print *,'msa_plate'

934:       lb = -1.0d300
935:       ub = 1.0d300

937:       if (bmy .lt. 0) bmy = 0
938:       if (bmy .gt. my) bmy = my
939:       if (bmx .lt. 0) bmx = 0
940:       if (bmx .gt. mx) bmx = mx


943:       call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
944:      &             PETSC_NULL_INTEGER,ierr)

946:       call VecSet(xl,lb,ierr)
947:       call VecSet(xu,ub,ierr)

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


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

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

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

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

962:             endif

964:          enddo
965:       enddo


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

970:       return
971:       end





977: ! ----------------------------------------------------------------------------
978: !
979: !/*
980: !     MSA_InitialPoint - Calculates an obstacle for surface to stretch over
981: !
982: !     Output Parameter:
983: !.    X - vector for initial guess
984: !
985: !*/

987:       subroutine MSA_InitialPoint(X, ierr)
988:       implicit none

990: ! mx,my,localX,dm,Top,Left,Bottom,Right defined in plate2f.h
991: #include "plate2f.h"
992:       Vec               X
993:       PetscErrorCode    ierr
994:       PetscInt          start,i,j
995:       PetscInt          row
996:       PetscInt          xs,xm,gxs,gxm
997:       PetscInt          ys,ym,gys,gym
998:       PetscReal       zero, np5

1000: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
1001: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (integer) x_index, ierr)
1002: ! will return an array of doubles referenced by x_array offset by x_index.
1003: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
1004: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
1005:       PetscReal   left_v(0:1),right_v(0:1)
1006:       PetscReal   bottom_v(0:1),top_v(0:1)
1007:       PetscReal   x_v(0:1)
1008:       PetscOffset   left_i, right_i, top_i
1009:       PetscOffset   bottom_i,x_i
1010:       PetscBool     flg
1011:       PetscRandom   rctx

1013:       zero = 0.0d0
1014:       np5 = -0.5d0

1016:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,"-start",            &
1017:      &                        start,flg,ierr)

1019:       if ((flg .eqv. PETSC_TRUE) .and. (start .eq. 0)) then  ! the zero vector is reasonable
1020:          call VecSet(X,zero,ierr)

1022:       elseif ((flg .eqv. PETSC_TRUE) .and. (start .gt. 0)) then  ! random start -0.5 < xi < 0.5
1023:          call PetscRandomCreate(MPI_COMM_WORLD,rctx,ierr)
1024:          do i=0,start-1
1025:             call VecSetRandom(X,rctx,ierr)
1026:          enddo

1028:          call PetscRandomDestroy(rctx,ierr)
1029:          call VecShift(X,np5,ierr)

1031:       else   ! average of boundary conditions

1033: !        Get Local mesh boundaries
1034:          call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,             &
1035:      &                     PETSC_NULL_INTEGER,ierr)
1036:          call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,    &
1037:      &                     PETSC_NULL_INTEGER,ierr)



1041: !        Get pointers to vector data
1042:          call VecGetArray(Top,top_v,top_i,ierr)
1043:          call VecGetArray(Bottom,bottom_v,bottom_i,ierr)
1044:          call VecGetArray(Left,left_v,left_i,ierr)
1045:          call VecGetArray(Right,right_v,right_i,ierr)

1047:          call VecGetArray(localX,x_v,x_i,ierr)

1049: !        Perform local computations
1050:          do  j=ys,ys+ym-1
1051:             do i=xs,xs+xm-1
1052:                row = (j-gys)*gxm  + (i-gxs)
1053:                x_v(x_i + row) = ((j+1)*bottom_v(bottom_i +i-xs+1)/my        &
1054:      &             + (my-j+1)*top_v(top_i+i-xs+1)/(my+2) +                  &
1055:      &              (i+1)*left_v(left_i+j-ys+1)/mx       +                  &
1056:      &              (mx-i+1)*right_v(right_i+j-ys+1)/(mx+2))*0.5
1057:             enddo
1058:          enddo

1060: !        Restore vectors
1061:          call VecRestoreArray(localX,x_v,x_i,ierr)

1063:          call VecRestoreArray(Left,left_v,left_i,ierr)
1064:          call VecRestoreArray(Top,top_v,top_i,ierr)
1065:          call VecRestoreArray(Bottom,bottom_v,bottom_i,ierr)
1066:          call VecRestoreArray(Right,right_v,right_i,ierr)

1068:          call DMLocalToGlobalBegin(dm,localX,INSERT_VALUES,X,ierr)
1069:          call DMLocalToGlobalEnd(dm,localX,INSERT_VALUES,X,ierr)

1071:       endif

1073:       return
1074:       end