Actual source code: plate2f.F

  1: ! "$Id: plate2f.F 1.47 05/05/12 13:59:03-05:00 sarich@zorak.(none) $";
  2: !
  3: !  Program usage: mpirun -np <proc> plate2f [all TAO options]
  4: !
  5: !  This example demonstrates use of the TAO package to solve a bound constrained
  6: !  minimization problem.  This example is based on a problem from the
  7: !  MINPACK-2 test suite.  Given a rectangular 2-D domain and boundary values
  8: !  along the edges of the domain, the objective is to find the surface
  9: !  with the minimal area that satisfies the boundary conditions.
 10: !  The command line options are:
 11: !    -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction
 12: !    -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction
 13: !    -bmx <bxg>, where <bxg> = number of grid points under plate in 1st direction
 14: !    -bmy <byg>, where <byg> = number of grid points under plate in 2nd direction
 15: !    -bheight <ht>, where <ht> = height of the plate
 16: !
 17: !/*T
 18: !   Concepts: TAO - Solving a bound constrained minimization problem
 19: !   Routines: TaoInitialize(); TaoFinalize();
 20: !   Routines: TaoCreate(); TaoDestroy();
 21: !   Routines: TaoAppSetObjectiveAndGradientRoutine(); 
 22: !   Routines: TaoAppSetHessianMat(); TaoAppSetHessianRoutine();
 23: !   Routines: TaoAppSetInitialSolutionVec(); TaoAppSetVariableBounds();
 24: !   Routines: TaoSetApplication(); TaoSetOptions();
 25: !   Routines: TaoApplicationCreate(); TaoSolve();
 26: !   Routines: TaoView(); TaoAppDestroy();
 27: !   Processors: n
 28: !T*/



 32:       implicit none

 34: #include "plate2f.h"

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

 46:       integer          info          ! used to check for functions returning nonzeros
 47:       Vec              x             ! solution vector
 48:       Vec              xl, xu        ! lower and upper bounds vectorsp
 49:       integer          m             ! number of local elements in vector
 50:       TAO_SOLVER       tao           ! TAO_SOLVER solver context
 51:       TAO_APPLICATION  plateapp      ! PETSc application
 52:       Mat              H             ! Hessian matrix
 53:       ISLocalToGlobalMapping isltog  ! local to global mapping object
 54:       PetscTruth       flg


 57:       external FormFunctionGradient
 58:       external FormHessian
 59:       external MSA_BoundaryConditions
 60:       external MSA_Plate
 61:       external MSA_InitialPoint
 62: ! Initialize Tao
 63:       call PetscInitialize(PETSC_NULL_CHARACTER,info)
 64:       call TaoInitialize(PETSC_NULL_CHARACTER,info)
 65: 

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

 72: ! Check for any command line arguments that override defaults
 73: 
 74:       call PetscOptionsGetInt(TAO_NULL_CHARACTER,"-mx",mx,flg,info)
 75:       call PetscOptionsGetInt(TAO_NULL_CHARACTER,"-my",my,flg,info)
 76: 
 77:       bmx = mx/2
 78:       bmy = my/2

 80:       call PetscOptionsGetInt(TAO_NULL_CHARACTER,"-bmx",bmx,flg,info)
 81:       call PetscOptionsGetInt(TAO_NULL_CHARACTER,"-bmy",bmy,flg,info)
 82:       call PetscOptionsGetReal(TAO_NULL_CHARACTER,"-bheight",bheight,   &
 83:      &      flg,info)
 84: 

 86: ! Calculate any derived values from parameters
 87:       N = mx*my

 89: ! Let Petsc determine the dimensions of the local vectors
 90:       Nx = PETSC_DECIDE
 91:       NY = PETSC_DECIDE

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

 97:       call DACreate2d(MPI_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX,         &
 98:      &     mx,my,Nx,Ny,1,1,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,           &
 99:      &     da,info)
100: 

102: ! Extract global and local vectors from DA; The local vectors are
103: ! used solely as work space for the evaluation of the function,
104: ! gradient, and Hessian.  Duplicate for remaining vectors that are
105: ! the same types.

107:       call DACreateGlobalVector(da,x,info)
108:       call DACreateLocalVector(da,localX,info)
109:       call VecDuplicate(localX,localV,info)

111: ! Create a matrix data structure to store the Hessian.
112: ! Here we (optionally) also associate the local numbering scheme
113: ! with the matrix so that later we can use local indices for matrix
114: ! assembly

116:       call VecGetLocalSize(x,m,info)
117:       call MatCreateMPIAIJ(MPI_COMM_WORLD,m,m,N,N,7,PETSC_NULL_INTEGER,  &
118:      &     3,PETSC_NULL_INTEGER,H,info)

120:       call MatSetOption(H,MAT_SYMMETRIC,info)
121:       call DAGetISLocalToGlobalMapping(da,isltog,info)
122:       call MatSetLocalToGlobalMapping(H,isltog,info)
123: 

125: ! The Tao code begins here
126: ! Create TAO solver and set desired solution method.
127: ! This problems uses bounded variables, so the
128: ! method must either be 'tao_tron' or 'tao_blmvm'

130:       call TaoCreate(MPI_COMM_WORLD,'tao_blmvm',tao,info)
131:       call TaoApplicationCreate(MPI_COMM_WORLD,plateapp,info)
132: 

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

136: !     TaoAppSetObjectiveAndGradientRoutine is shortened to 31 chars to comply with some compilers
137:       call TaoAppSetObjectiveAndGradientRo(plateapp,                    &
138:      &     FormFunctionGradient,PETSC_NULL_OBJECT,info)

140:       call TaoAppSetHessianMat(plateapp,H,H,info)
141:       call TaoAppSetHessianRoutine(plateapp,FormHessian,                 &
142:      &     PETSC_NULL_OBJECT, info)
143: 

145: ! Set Variable bounds
146:       call MSA_BoundaryConditions(info)
147:       call VecDuplicate(x,xl,info)
148:       call VecDuplicate(x,xu,info)
149:       call MSA_Plate(xl,xu,info)
150:       call TaoAppSetVariableBounds(plateapp,xl,xu,info)

152: ! Set the initial solution guess
153:       call MSA_InitialPoint(x, info)
154:       call TaoAppSetInitialSolutionVec(plateapp,x,info)

156: ! Now that the PETSc application is all set, attach to tao context
157:       call TaoSetApplication(tao,plateapp,info)

159: ! Check for any tao command line options
160:       call TaoSetOptions(plateapp,tao,info)

162: ! Solve the application
163:       call TaoSolveApplication(plateapp,tao,info)

165: !     View TAO solver information
166: !      call TaoView(tao,info)

168: ! Free TAO data structures
169:       call TaoDestroy(tao,info)
170:       call TaoAppDestroy(plateapp,info)

172: ! Free PETSc data structures
173:       call VecDestroy(x,info)
174:       call VecDestroy(xl,info)
175:       call VecDestroy(xu,info)
176:       call VecDestroy(Top,info)
177:       call VecDestroy(Bottom,info)
178:       call VecDestroy(Left,info)
179:       call VecDestroy(Right,info)
180:       call MatDestroy(H,info)
181:       call VecDestroy(localX,info)
182:       call VecDestroy(localV,info)
183:       call DADestroy(da,info)

185: ! Finalize TAO

187:       call TaoFinalize(info)
188:       call PetscFinalize(info)

190:       end

192: ! ---------------------------------------------------------------------
193: !
194: !  FormFunctionGradient - Evaluates function f(X).
195: !
196: !  Input Parameters:
197: !  tao   - the TAO_SOLVER context
198: !  X     - the input vector
199: !  dummy - optional user-defined context, as set by TaoSetFunction()
200: !          (not used here)
201: !
202: !  Output Parameters:
203: !  fcn     - the newly evaluated function
204: !  G       - the gradient vector
205: !  info  - error code
206: !


209:       subroutine FormFunctionGradient(tao,X,fcn,G,dummy,info)
210:       implicit none

212: ! da, localX, localG, Top, Bottom, Left, Right defined in plate2f.h
213: #include "plate2f.h"
214: 
215: ! Input/output variables

217:       TAO_SOLVER       tao
218:       PetscScalar fcn
219:       Vec              X, G
220:       integer          dummy, info
221: 
222:       integer          i,j,row
223:       integer          xs, xm, gxs, gxm, ys, ym, gys, gym
224:       PetscScalar      ft,zero,hx,hy,hydhx,hxdhy,area,rhx,rhy
225:       PetscScalar      f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8
226:       PetscScalar      df1dxc,df2dxc,df3dxc,df4dxc,df5dxc,df6dxc
227:       PetscScalar      xc,xl,xr,xt,xb,xlt,xrb


230: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
231: ! Calling VecGetArray((Vec) X, (PetscScalar) x_array(0:1), (PetscOffset) x_index, info)
232: ! will return an array of doubles referenced by x_array offset by x_index.
233: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
234: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
235:       PetscScalar          g_v(0:1),x_v(0:1), top_v(0:1)
236:       PetscScalar          left_v(0:1), right_v(0:1),bottom_v(0:1)
237:       PetscOffset          g_i,left_i,right_i,bottom_i,top_i
238:       PetscOffset          x_i

240:       ft = 0.0d0
241:       zero = 0.0d0
242:       hx = 1.0d0/(mx + 1)
243:       hy = 1.0d0/(my + 1)
244:       hydhx = hy/hx
245:       hxdhy = hx/hy
246:       area = 0.5d0 * hx * hy
247:       rhx = mx + 1.0d0
248:       rhy = my + 1.0d0


251: ! Get local mesh boundaries
252:       call DAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,              &
253:      &                  PETSC_NULL_INTEGER,info)
254:       call DAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,             &
255:      &                       gxm,gym,PETSC_NULL_INTEGER,info)

257: ! Scatter ghost points to local vector
258:       call DAGlobalToLocalBegin(da,X,INSERT_VALUES,localX,info)
259:       call DAGlobalToLocalEnd(da,X,INSERT_VALUES,localX,info)

261: ! Initialize the vector to zero
262:       call VecSet(localV,zero,info)

264: ! Get arrays to vector data (See note above about using VecGetArray in Fortran)
265:       call VecGetArray(localX,x_v,x_i,info)
266:       call VecGetArray(localV,g_v,g_i,info)
267:       call VecGetArray(Top,top_v,top_i,info)
268:       call VecGetArray(Bottom,bottom_v,bottom_i,info)
269:       call VecGetArray(Left,left_v,left_i,info)
270:       call VecGetArray(Right,right_v,right_i,info)

272: ! Compute function over the locally owned part of the mesh
273:       do j = ys,ys+ym-1
274:          do i = xs,xs+xm-1
275:             row = (j-gys)*gxm + (i-gxs)
276:             xc = x_v(row+x_i)
277:             xt = xc
278:             xb = xc
279:             xr = xc
280:             xl = xc
281:             xrb = xc
282:             xlt = xc

284:             if (i .eq. 0) then !left side
285:                xl = left_v(j - ys + 1 + left_i)
286:                xlt = left_v(j - ys + 2 + left_i)
287:             else
288:                xl = x_v(row - 1 + x_i)
289:             endif

291:             if (j .eq. 0) then !bottom side
292:                xb = bottom_v(i - xs + 1 + bottom_i)
293:                xrb = bottom_v(i - xs + 2 + bottom_i)
294:             else
295:                xb = x_v(row - gxm + x_i)
296:             endif

298:             if (i + 1 .eq. gxs + gxm) then !right side
299:                xr = right_v(j - ys + 1 + right_i)
300:                xrb = right_v(j - ys + right_i)
301:             else
302:                xr = x_v(row + 1 + x_i)
303:             endif

305:             if (j + 1 .eq. gys + gym) then !top side
306:                xt = top_v(i - xs + 1 + top_i)
307:                xlt = top_v(i - xs + top_i)
308:             else
309:                xt = x_v(row + gxm + x_i)
310:             endif

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

316:             if ((j .gt. gys) .and. (i + 1 .lt. gxs + gxm)) then
317:                xrb = x_v(row + 1 - gxm + x_i)
318:             endif

320:             d1 = xc-xl
321:             d2 = xc-xr
322:             d3 = xc-xt
323:             d4 = xc-xb
324:             d5 = xr-xrb
325:             d6 = xrb-xb
326:             d7 = xlt-xl
327:             d8 = xt-xlt

329:             df1dxc = d1 * hydhx
330:             df2dxc = d1 * hydhx + d4 * hxdhy
331:             df3dxc = d3 * hxdhy
332:             df4dxc = d2 * hydhx + d3 * hxdhy
333:             df5dxc = d2 * hydhx
334:             df6dxc = d4 * hxdhy

336:             d1 = d1 * rhx
337:             d2 = d2 * rhx
338:             d3 = d3 * rhy
339:             d4 = d4 * rhy
340:             d5 = d5 * rhy
341:             d6 = d6 * rhx
342:             d7 = d7 * rhy
343:             d8 = d8 * rhx

345:             f1 = sqrt(1.0d0 + d1*d1 + d7*d7)
346:             f2 = sqrt(1.0d0 + d1*d1 + d4*d4)
347:             f3 = sqrt(1.0d0 + d3*d3 + d8*d8)
348:             f4 = sqrt(1.0d0 + d3*d3 + d2*d2)
349:             f5 = sqrt(1.0d0 + d2*d2 + d5*d5)
350:             f6 = sqrt(1.0d0 + d4*d4 + d6*d6)

352:             ft = ft + f2 + f4

354:             df1dxc = df1dxc / f1
355:             df2dxc = df2dxc / f2
356:             df3dxc = df3dxc / f3
357:             df4dxc = df4dxc / f4
358:             df5dxc = df5dxc / f5
359:             df6dxc = df6dxc / f6

361:             g_v(row + g_i) = 0.5 * (df1dxc + df2dxc + df3dxc + df4dxc +  &
362:      &                              df5dxc + df6dxc)
363:          enddo
364:       enddo

366: ! Compute triangular areas along the border of the domain.
367:       if (xs .eq. 0) then  ! left side
368:          do j=ys,ys+ym-1
369:             d3 = (left_v(j-ys+1+left_i) - left_v(j-ys+2+left_i))         &
370:      &                 * rhy
371:             d2 = (left_v(j-ys+1+left_i) - x_v((j-gys)*gxm + x_i))        &
372:      &                 * rhx
373:             ft = ft + sqrt(1.0d0 + d3*d3 + d2*d2)
374:          enddo
375:       endif

377: 
378:       if (ys .eq. 0) then !bottom side
379:          do i=xs,xs+xm-1
380:             d2 = (bottom_v(i+1-xs+bottom_i)-bottom_v(i-xs+2+bottom_i))    &
381:      &                    * rhx
382:             d3 = (bottom_v(i-xs+1+bottom_i)-x_v(i-gxs+x_i))*rhy
383:             ft = ft + sqrt(1.0 + d3*d3 + d2*d2)
384:          enddo
385:       endif

387: 
388:       if (xs + xm .eq. mx) then ! right side
389:          do j=ys,ys+ym-1
390:             d1 = (x_v((j+1-gys)*gxm-1+x_i)-right_v(j-ys+1+right_i))*rhx
391:             d4 = (right_v(j-ys+right_i) - right_v(j-ys+1+right_i))*rhy
392:             ft = ft + sqrt(1.0d0 + d1*d1 + d4*d4)
393:          enddo
394:       endif

396: 
397:       if (ys + ym .eq. my) then
398:          do i=xs,xs+xm-1
399:             d1 = (x_v((gym-1)*gxm+i-gxs+x_i) - top_v(i-xs+1+top_i))*rhy
400:             d4 = (top_v(i-xs+1+top_i) - top_v(i-xs+top_i))*rhx
401:             ft = ft + sqrt(1.0d0 + d1*d1 + d4*d4)
402:          enddo
403:       endif

405: 
406:       if ((ys .eq. 0) .and. (xs .eq. 0)) then
407:          d1 = (left_v(0 + left_i) - left_v(1 + left_i)) * rhy
408:          d2 = (bottom_v(0+bottom_i)-bottom_v(1+bottom_i))*rhx
409:          ft = ft + sqrt(1.0d0 + d1*d1 + d2*d2)
410:       endif

412:       if ((ys + ym .eq. my) .and. (xs + xm .eq. mx)) then
413:          d1 = (right_v(ym+1+right_i) - right_v(ym+right_i))*rhy
414:          d2 = (top_v(xm+1+top_i) - top_v(xm + top_i))*rhx
415:          ft = ft + sqrt(1.0d0 + d1*d1 + d2*d2)
416:       endif

418:       ft = ft * area
419:       call MPI_Allreduce(ft,fcn,1,MPI_DOUBLE_PRECISION,                  &
420:      &             MPI_SUM,MPI_COMM_WORLD,info)



424: ! Restore vectors
425:       call VecRestoreArray(localX,x_v,x_i,info)
426:       call VecRestoreArray(localV,g_v,g_i,info)
427:       call VecRestoreArray(Left,left_v,left_i,info)
428:       call VecRestoreArray(Top,top_v,top_i,info)
429:       call VecRestoreArray(Bottom,bottom_v,bottom_i,info)
430:       call VecRestoreArray(Right,right_v,right_i,info)

432: ! Scatter values to global vector
433:       call DALocalToGlobal(da,localV,INSERT_VALUES,G,info)

435:       call PetscLogFlops(70*xm*ym,info)

437:       return
438:       end  !FormFunctionGradient
439: 




444: ! ----------------------------------------------------------------------------
445: !
446: !/*
447: !   FormHessian - Evaluates Hessian matrix.
448: !
449: !   Input Parameters:
450: !.  tao  - the TAO_SOLVER context
451: !.  X    - input vector
452: !.  dummy  - not used 
453: !
454: !   Output Parameters:
455: !.  Hessian    - Hessian matrix
456: !.  Hpc    - optionally different preconditioning matrix
457: !.  flag - flag indicating matrix structure
458: !
459: !   Notes:
460: !   Due to mesh point reordering with DAs, we must always work
461: !   with the local mesh points, and then transform them to the new
462: !   global numbering with the local-to-global mapping.  We cannot work
463: !   directly with the global numbers for the original uniprocessor mesh!  
464: !
465: !   Two methods are available for imposing this transformation
466: !   when setting matrix entries:
467: !     (A) MatSetValuesLocal(), using the local ordering (including
468: !         ghost points!)
469: !         - Do the following two steps once, before calling TaoSolve()
470: !           - Use DAGetISLocalToGlobalMapping() to extract the
471: !             local-to-global map from the DA
472: !           - Associate this map with the matrix by calling
473: !             MatSetLocalToGlobalMapping() 
474: !         - Then set matrix entries using the local ordering
475: !           by calling MatSetValuesLocal()
476: !     (B) MatSetValues(), using the global ordering 
477: !         - Use DAGetGlobalIndices() to extract the local-to-global map
478: !         - Then apply this map explicitly yourself
479: !         - Set matrix entries using the global ordering by calling
480: !           MatSetValues()
481: !   Option (A) seems cleaner/easier in many cases, and is the procedure
482: !   used in this example.
483: */
484:       subroutine FormHessian(tao, X, Hessian, Hpc, flg, dummy, info)
485:       implicit none

487: ! da,Top,Left,Right,Bottom,mx,my,localX defined in plate2f.h
488: #include "plate2f.h"
489: 
490:       TAO_SOLVER       tao
491:       Vec              X
492:       Mat              Hessian,Hpc
493:       MatStructure     flg
494:       integer          dummy,info

496:       integer          i,j,k,row
497:       integer          xs,xm,gxs,gxm,ys,ym,gys,gym,col(0:6)
498:       PetscScalar      hx,hy,hydhx,hxdhy,rhx,rhy
499:       PetscScalar      f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8
500:       PetscScalar      xc,xl,xr,xt,xb,xlt,xrb
501:       PetscScalar      hl,hr,ht,hb,hc,htl,hbr

503: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
504: ! Calling VecGetArray((Vec) X, (PetscScalar) x_array(0:1), (PetscOffset) x_index, info)
505: ! will return an array of doubles referenced by x_array offset by x_index.
506: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
507: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
508:       PetscScalar      right_v(0:1),left_v(0:1),bottom_v(0:1),top_v(0:1)
509:       PetscScalar      x_v(0:1)
510:       PetscOffset      x_i,right_i,left_i,bottom_i,top_i
511:       PetscScalar      v(0:6)
512:       PetscTruth       assembled
513: 
514: ! Set various matrix options
515:       call MatSetOption(Hessian,MAT_IGNORE_OFF_PROC_ENTRIES,info)
516:       call MatSetOption(Hessian,MAT_COLUMNS_SORTED,info)
517:       call MatSetOption(Hessian,MAT_ROWS_SORTED,info)

519: ! Get local mesh boundaries
520:       call DAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,              &
521:      &                  PETSC_NULL_INTEGER,info)
522:       call DAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,     &
523:      &                       PETSC_NULL_INTEGER,info)

525: ! Scatter ghost points to local vectors
526:       call DAGlobalToLocalBegin(da,X,INSERT_VALUES,localX,info)
527:       call DAGlobalToLocalEnd(da,X,INSERT_VALUES,localX,info)

529: ! Get pointers to vector data (see note on Fortran arrays above)
530:       call VecGetArray(localX,x_v,x_i,info)
531:       call VecGetArray(Top,top_v,top_i,info)
532:       call VecGetArray(Bottom,bottom_v,bottom_i,info)
533:       call VecGetArray(Left,left_v,left_i,info)
534:       call VecGetArray(Right,right_v,right_i,info)

536: ! Initialize matrix entries to zero
537:       call MatAssembled(Hessian,assembled,info)
538:       if (assembled .eq. PETSC_TRUE) call MatZeroEntries(Hessian,info)


541:       rhx = mx + 1.0
542:       rhy = my + 1.0
543:       hx = 1.0/rhx
544:       hy = 1.0/rhy
545:       hydhx = hy/hx
546:       hxdhy = hx/hy
547: ! compute Hessian over the locally owned part of the mesh

549:       do  i=xs,xs+xm-1
550:          do  j=ys,ys+ym-1
551:             row = (j-gys)*gxm + (i-gxs)
552: 
553:             xc = x_v(row + x_i)
554:             xt = xc
555:             xb = xc
556:             xr = xc
557:             xl = xc
558:             xrb = xc
559:             xlt = xc

561:             if (i .eq. gxs) then   ! Left side
562:                xl = left_v(left_i + j - ys + 1)
563:                xlt = left_v(left_i + j - ys + 2)
564:             else
565:                xl = x_v(x_i + row -1 )
566:             endif

568:             if (j .eq. gys) then ! bottom side
569:                xb = bottom_v(bottom_i + i - xs + 1)
570:                xrb = bottom_v(bottom_i + i - xs + 2)
571:             else
572:                xb = x_v(x_i + row - gxm)
573:             endif

575:             if (i+1 .eq. gxs + gxm) then !right side
576:                xr = right_v(right_i + j - ys + 1)
577:                xrb = right_v(right_i + j - ys)
578:             else
579:                xr = x_v(x_i + row + 1)
580:             endif

582:             if (j+1 .eq. gym+gys) then !top side
583:                xt = top_v(top_i +i - xs + 1)
584:                xlt = top_v(top_i + i - xs)
585:             else
586:                xt = x_v(x_i + row + gxm)
587:             endif

589:             if ((i .gt. gxs) .and. (j+1 .lt. gys+gym)) then
590:                xlt = x_v(x_i + row - 1 + gxm)
591:             endif
592: 
593:             if ((i+1 .lt. gxs+gxm) .and. (j .gt. gys)) then
594:                xrb = x_v(x_i + row + 1 - gxm)
595:             endif

597:             d1 = (xc-xl)*rhx
598:             d2 = (xc-xr)*rhx
599:             d3 = (xc-xt)*rhy
600:             d4 = (xc-xb)*rhy
601:             d5 = (xrb-xr)*rhy
602:             d6 = (xrb-xb)*rhx
603:             d7 = (xlt-xl)*rhy
604:             d8 = (xlt-xt)*rhx
605: 
606:             f1 = sqrt( 1.0d0 + d1*d1 + d7*d7)
607:             f2 = sqrt( 1.0d0 + d1*d1 + d4*d4)
608:             f3 = sqrt( 1.0d0 + d3*d3 + d8*d8)
609:             f4 = sqrt( 1.0d0 + d3*d3 + d2*d2)
610:             f5 = sqrt( 1.0d0 + d2*d2 + d5*d5)
611:             f6 = sqrt( 1.0d0 + d4*d4 + d6*d6)
612: 
613: 
614:             hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+                 &
615:      &              (-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2)

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

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

623:             hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+                 &
624:      &              (-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2)
625: 
626:             hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6)
627:             htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3)
628: 
629:             hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) +                         &
630:      &              hxdhy*(1.0+d8*d8)/(f3*f3*f3) +                      &
631:      &              hydhx*(1.0+d5*d5)/(f5*f5*f5) +                      &
632:      &              hxdhy*(1.0+d6*d6)/(f6*f6*f6) +                      &
633:      &              (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-               &
634:      &              2*d1*d4)/(f2*f2*f2) +  (hxdhy*(1.0+d2*d2)+          &
635:      &              hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4)
636: 
637:             hl = hl * 0.5
638:             hr = hr * 0.5
639:             ht = ht * 0.5
640:             hb = hb * 0.5
641:             hbr = hbr * 0.5
642:             htl = htl * 0.5
643:             hc = hc * 0.5

645:             k = 0

647:             if (j .gt. 0) then
648:                v(k) = hb
649:                col(k) = row - gxm
650:                k=k+1
651:             endif

653:             if ((j .gt. 0) .and. (i .lt. mx-1)) then
654:                v(k) = hbr
655:                col(k) = row-gxm+1
656:                k=k+1
657:             endif

659:             if (i .gt. 0) then
660:                v(k) = hl
661:                col(k) = row - 1
662:                k = k+1
663:             endif

665:             v(k) = hc
666:             col(k) = row
667:             k=k+1

669:             if (i .lt. mx-1) then
670:                v(k) = hr
671:                col(k) = row + 1
672:                k=k+1
673:             endif

675:             if ((i .gt. 0) .and. (j .lt. my-1)) then
676:                v(k) = htl
677:                col(k) = row + gxm - 1
678:                k=k+1
679:             endif

681:             if (j .lt. my-1) then
682:                v(k) = ht
683:                col(k) = row + gxm
684:                k=k+1
685:             endif

687: ! Set matrix values using local numbering, defined earlier in main routine
688:             call MatSetValuesLocal(Hessian,1,row,k,col,v,INSERT_VALUES,       &
689:      &                              info)

691: 

693:          enddo
694:       enddo
695: 
696: ! restore vectors
697:       call VecRestoreArray(localX,x_v,x_i,info)
698:       call VecRestoreArray(Left,left_v,left_i,info)
699:       call VecRestoreArray(Right,right_v,right_i,info)
700:       call VecRestoreArray(Top,top_v,top_i,info)
701:       call VecRestoreArray(Bottom,bottom_v,bottom_i,info)


704: ! Assemble the matrix
705:       call MatAssemblyBegin(Hessian,MAT_FINAL_ASSEMBLY,info)
706:       call MatAssemblyEnd(Hessian,MAT_FINAL_ASSEMBLY,info)

708:       call PetscLogFlops(199*xm*ym,info)

710:       return
711:       end
712: 
713: 



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

719: ! ----------------------------------------------------------------------------
720: !
721: !/*
722: !     MSA_BoundaryConditions - calculates the boundary conditions for the region
723: !
724: !
725: !*/

727:       subroutine MSA_BoundaryConditions(info)
728:       implicit none

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

733:       integer i,j,k,limit,info,maxits
734:       integer          xs, xm, gxs, gxm, ys, ym, gys, gym
735:       integer bsize, lsize, tsize, rsize
736:       PetscScalar           one, two, three, tol
737:       PetscScalar           scl,fnorm,det,xt,yt,hx,hy
738:       PetscScalar           u1,u2,nf1,nf2,njac11,njac12,njac21,njac22
739:       PetscScalar           b, t, l, r
740:       PetscScalar           boundary_v(0:1)
741:       PetscOffset           boundary_i
742:       logical exitloop
743:       TaoTruth flg

745:       limit=0
746:       maxits = 5
747:       tol=1e-10
748:       b=-0.5d0
749:       t= 0.5d0
750:       l=-0.5d0
751:       r= 0.5d0
752:       xt=0
753:       yt=0
754:       one=1.0d0
755:       two=2.0d0
756:       three=3.0d0


759:       call DAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
760:      &                  PETSC_NULL_INTEGER,info)
761:       call DAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,              &
762:      &                       gxm,gym,PETSC_NULL_INTEGER,info)

764:       bsize = xm + 2
765:       lsize = ym + 2
766:       rsize = ym + 2
767:       tsize = xm + 2
768: 

770:       call VecCreateMPI(MPI_COMM_WORLD,bsize,PETSC_DECIDE,Bottom,info)
771:       call VecCreateMPI(MPI_COMM_WORLD,tsize,PETSC_DECIDE,Top,info)
772:       call VecCreateMPI(MPI_COMM_WORLD,lsize,PETSC_DECIDE,Left,info)
773:       call VecCreateMPI(MPI_COMM_WORLD,rsize,PETSC_DECIDE,Right,info)

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

778:       do j=0,3
779: 
780:          if (j.eq.0) then
781:             yt=b
782:             xt=l+hx*xs
783:             limit=bsize
784:             call VecGetArray(Bottom,boundary_v,boundary_i,info)
785: 

787:          elseif (j.eq.1) then
788:             yt=t
789:             xt=l+hx*xs
790:             limit=tsize
791:             call VecGetArray(Top,boundary_v,boundary_i,info)

793:          elseif (j.eq.2) then
794:             yt=b+hy*ys
795:             xt=l
796:             limit=lsize
797:             call VecGetArray(Left,boundary_v,boundary_i,info)

799:          elseif (j.eq.3) then
800:             yt=b+hy*ys
801:             xt=r
802:             limit=rsize
803:             call VecGetArray(Right,boundary_v,boundary_i,info)
804:          endif
805: 

807:          do i=0,limit-1
808: 
809:             u1=xt
810:             u2=-yt
811:             k = 0
812:             exitloop = .false.
813:             do while (k .lt. maxits .and. (.not. exitloop) )

815:                nf1=u1 + u1*u2*u2 - u1*u1*u1/three-xt
816:                nf2=-u2 - u1*u1*u2 + u2*u2*u2/three-yt
817:                fnorm=sqrt(nf1*nf1+nf2*nf2)
818:                if (fnorm .gt. tol) then
819:                   njac11=one+u2*u2-u1*u1
820:                   njac12=two*u1*u2
821:                   njac21=-two*u1*u2
822:                   njac22=-one - u1*u1 + u2*u2
823:                   det = njac11*njac22-njac21*njac12
824:                   u1 = u1-(njac22*nf1-njac12*nf2)/det
825:                   u2 = u2-(njac11*nf2-njac21*nf1)/det
826:                else
827:                   exitloop = .true.
828:                endif
829:                k=k+1
830:             enddo

832:             boundary_v(i + boundary_i) = u1*u1-u2*u2
833:             if ((j .eq. 0) .or. (j .eq. 1)) then
834:                xt = xt + hx
835:             else
836:                yt = yt + hy
837:             endif

839:          enddo
840: 

842:          if (j.eq.0) then
843:             call VecRestoreArray(Bottom,boundary_v,boundary_i,info)
844:          elseif (j.eq.1) then
845:             call VecRestoreArray(Top,boundary_v,boundary_i,info)
846:          elseif (j.eq.2) then
847:             call VecRestoreArray(Left,boundary_v,boundary_i,info)
848:          elseif (j.eq.3) then
849:             call VecRestoreArray(Right,boundary_v,boundary_i,info)
850:          endif
851: 
852:       enddo


855: ! Scale the boundary if desired
856:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,"-bottom",            &
857:      &                         scl,flg,info)
858:       if (flg .eq. PETSC_TRUE) then
859:          call VecScale(scl,Bottom,info)
860:       endif

862:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,"-top",               &
863:      &                         scl,flg,info)
864:       if (flg .eq. PETSC_TRUE) then
865:          call VecScale(scl,Top,info)
866:       endif

868:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,"-right",             &
869:      &                         scl,flg,info)
870:       if (flg .eq. PETSC_TRUE) then
871:          call VecScale(scl,Right,info)
872:       endif

874:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,"-left",              &
875:      &                         scl,flg,info)
876:       if (flg .eq. PETSC_TRUE) then
877:          call VecScale(scl,Left,info)
878:       endif
879: 
880: 
881:       return
882:       end

884: ! ----------------------------------------------------------------------------
885: !
886: !/*
887: !     MSA_Plate - Calculates an obstacle for surface to stretch over
888: !
889: !     Output Parameter:
890: !.    xl - lower bound vector
891: !.    xu - upper bound vector
892: !
893: !*/

895:       subroutine MSA_Plate(xl,xu,info)
896:       implicit none

898: ! mx,my,bmx,bmy,da,bheight defined in plate2f.h
899: #include "plate2f.h"
900:       Vec              xl,xu
901:       integer          i,j,row,info
902:       integer          xs, xm, ys, ym
903:       PetscScalar      lb,ub

905: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
906: ! Calling VecGetArray((Vec) X, (PetscScalar) x_array(0:1), (PetscOffset) x_index, info)
907: ! will return an array of doubles referenced by x_array offset by x_index.
908: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
909: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
910:       PetscScalar      xl_v(0:1)
911:       PetscOffset      xl_i


914:       lb = -1.0d300
915:       ub = 1.0d300

917:       if (bmy .lt. 0) bmy = 0
918:       if (bmy .gt. my) bmy = my
919:       if (bmx .lt. 0) bmx = 0
920:       if (bmx .gt. mx) bmx = mx
921: 

923:       call DAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,               &
924:      &             PETSC_NULL_INTEGER,info)

926:       call VecSet(xl,lb,info)
927:       call VecSet(xu,ub,info)

929:       call VecGetArray(xl,xl_v,xl_i,info)
930: 

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

934:          do j=ys,ys+ym-1
935: 
936:             row=(j-ys)*xm + (i-xs)

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

942:             endif

944:          enddo
945:       enddo


948:       call VecRestoreArray(xl,xl_v,xl_i,info)
949: 
950:       return
951:       end



955: 
956: 
957: ! ----------------------------------------------------------------------------
958: !
959: !/*
960: !     MSA_InitialPoint - Calculates an obstacle for surface to stretch over
961: !
962: !     Output Parameter:
963: !.    X - vector for initial guess
964: !
965: !*/

967:       subroutine MSA_InitialPoint(X, info)
968:       implicit none

970: ! mx,my,localX,da,Top,Left,Bottom,Right defined in plate2f.h
971: #include "plate2f.h"
972:       Vec               X

974:       integer           start,i,j,info
975:       integer           row,xs,xm,gxs,gxm,ys,ym,gys,gym
976:       PetscScalar       zero, np5

978: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
979: ! Calling VecGetArray((Vec) X, (PetscScalar) x_array(0:1), (integer) x_index, info)
980: ! will return an array of doubles referenced by x_array offset by x_index.
981: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
982: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
983:       PetscScalar       left_v(0:1), right_v(0:1), top_v(0:1)
984:       PetscScalar       x_v(0:1), bottom_v(0:1)
985:       PetscOffset       left_i, right_i, top_i, bottom_i, x_i
986:       PetscTruth        flg
987:       PetscRandom       rctx
988: 
989:       zero = 0.0d0
990:       np5 = -0.5d0

992:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,"-start",            &
993:      &                        start,flg,info)

995:       if ((flg .eq. PETSC_TRUE) .and. (start .eq. 0)) then  ! the zero vector is reasonable
996:          call VecSet(X,zero,info)

998:       elseif ((flg .eq. PETSC_TRUE) .and. (start .gt. 0)) then  ! random start -0.5 < xi < 0.5
999:          call PetscRandomCreate(MPI_COMM_WORLD,RANDOM_DEFAULT,rctx,info)
1000:          do i=0,start-1
1001:             call VecSetRandom(X,rctx,info)
1002:          enddo

1004:          call PetscRandomDestroy(rctx,info)
1005:          call VecShift(X,np5,info)

1007:       else   ! average of boundary conditions
1008: 
1009: !        Get Local mesh boundaries
1010:          call DAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,             &
1011:      &                     PETSC_NULL_INTEGER,info)
1012:          call DAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,    &
1013:      &                     PETSC_NULL_INTEGER,info)



1017: !        Get pointers to vector data
1018:          call VecGetArray(Top,top_v,top_i,info)
1019:          call VecGetArray(Bottom,bottom_v,bottom_i,info)
1020:          call VecGetArray(Left,left_v,left_i,info)
1021:          call VecGetArray(Right,right_v,right_i,info)
1022: 
1023:          call VecGetArray(localX,x_v,x_i,info)
1024: 
1025: !        Perform local computations
1026:          do  j=ys,ys+ym-1
1027:             do i=xs,xs+xm-1
1028:                row = (j-gys)*gxm  + (i-gxs)
1029:                x_v(x_i + row) = ((j+1)*bottom_v(bottom_i +i-xs+1)/my        &
1030:      &             + (my-j+1)*top_v(top_i+i-xs+1)/(my+2) +                  &
1031:      &              (i+1)*left_v(left_i+j-ys+1)/mx       +                  &
1032:      &              (mx-i+1)*right_v(right_i+j-ys+1)/(mx+2))*0.5
1033:             enddo
1034:          enddo

1036: !        Restore vectors
1037:          call VecRestoreArray(localX,x_v,x_i,info)

1039:          call VecRestoreArray(Left,left_v,left_i,info)
1040:          call VecRestoreArray(Top,top_v,top_i,info)
1041:          call VecRestoreArray(Bottom,bottom_v,bottom_i,info)
1042:          call VecRestoreArray(Right,right_v,right_i,info)

1044:          call DALocalToGlobal(da,localX,INSERT_VALUES,X,info)

1046:       endif

1048:       return
1049:       end