Actual source code: ex21f.F

  1: !
  2: !    "$Id: ex21f.F,v 1.9 2001/08/07 03:04:00 balay Exp $";
  3: !
  4: !   Solves a linear system in parallel with SLES.  Also indicates
  5: !   use of a user-provided preconditioner.  Input parameters include:
  6: !
  7: !  Program usage: mpirun ex21f [-help] [all PETSc options]
  8: !
  9: !/*T
 10: !   Concepts: SLES^basic parallel example
 11: !   Concepts: PC^setting a user-defined shell preconditioner
 12: !   Processors: n
 13: !T*/
 14: !
 15: !  -------------------------------------------------------------------------

 17:       program main
 18:       implicit none

 20: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 21: !                    Include files
 22: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 23: !
 24: !     petsc.h  - base PETSc routines      petscvec.h - vectors
 25: !     petscsys.h    - system routines          petscmat.h - matrices
 26: !     petscksp.h    - Krylov subspace methods  petscpc.h  - preconditioners
 27: !     petscsles.h   - SLES interface

 29:  #include include/finclude/petsc.h
 30:  #include include/finclude/petscvec.h
 31:  #include include/finclude/petscmat.h
 32:  #include include/finclude/petscpc.h
 33:  #include include/finclude/petscksp.h
 34:  #include include/finclude/petscsles.h

 36: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 37: !                   Variable declarations
 38: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 39: !
 40: !  Variables:
 41: !     sles     - linear solver context
 42: !     ksp      - Krylov subspace method context
 43: !     pc       - preconditioner context
 44: !     x, b, u  - approx solution, right-hand-side, exact solution vectors
 45: !     A        - matrix that defines linear system
 46: !     its      - iterations for convergence
 47: !     norm     - norm of solution error

 49:       Vec              x,b,u
 50:       Mat              A
 51:       SLES             sles
 52:       PC               pc
 53:       KSP              ksp
 54:       PetscScalar      v,one,neg_one
 55:       double precision norm,tol
 56:       integer          i,j,II,JJ,Istart,Iend,ierr,m,n
 57:       integer          its,flg,rank

 59: !  Note: Any user-defined Fortran routines MUST be declared as external.

 61:       external SampleShellPCSetUp,SampleShellPCApply

 63: !  Common block to store data for user-provided preconditioner
 64:       common /mypcs/ jacobi,sor,work
 65:       PC jacobi,sor
 66:       Vec work

 68: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 69: !                 Beginning of program
 70: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 72:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
 73:       one     = 1.0
 74:       neg_one = -1.0
 75:       m       = 8
 76:       n       = 7
 77:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-m',m,flg,ierr)
 78:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
 79:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)

 81: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 82: !      Compute the matrix and right-hand-side vector that define
 83: !      the linear system, Ax = b.
 84: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 86: !  Create parallel matrix, specifying only its global dimensions.
 87: !  When using MatCreate(), the matrix format can be specified at
 88: !  runtime. Also, the parallel partitioning of the matrix is
 89: !  determined by PETSc at runtime.

 91:       call MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,m*n,    &
 92:      &               m*n,A,ierr)

 94:       call MatSetFromOptions(A,ierr)

 96: !  Currently, all PETSc parallel matrix formats are partitioned by
 97: !  contiguous chunks of rows across the processors.  Determine which
 98: !  rows of the matrix are locally owned.

100:       call MatGetOwnershipRange(A,Istart,Iend,ierr)

102: !  Set matrix elements for the 2-D, five-point stencil in parallel.
103: !   - Each processor needs to insert only elements that it owns
104: !     locally (but any non-local elements will be sent to the
105: !     appropriate processor during matrix assembly).
106: !   - Always specify global row and columns of matrix entries.
107: !   - Note that MatSetValues() uses 0-based row and column numbers
108: !     in Fortran as well as in C.

110:       do 10, II=Istart,Iend-1
111:         v = -1.0
112:         i = II/n
113:         j = II - i*n
114:         if (i.gt.0) then
115:           JJ = II - n
116:           call MatSetValues(A,1,II,1,JJ,v,ADD_VALUES,ierr)
117:         endif
118:         if (i.lt.m-1) then
119:           JJ = II + n
120:           call MatSetValues(A,1,II,1,JJ,v,ADD_VALUES,ierr)
121:         endif
122:         if (j.gt.0) then
123:           JJ = II - 1
124:           call MatSetValues(A,1,II,1,JJ,v,ADD_VALUES,ierr)
125:         endif
126:         if (j.lt.n-1) then
127:           JJ = II + 1
128:           call MatSetValues(A,1,II,1,JJ,v,ADD_VALUES,ierr)
129:         endif
130:         v = 4.0
131:         call  MatSetValues(A,1,II,1,II,v,ADD_VALUES,ierr)
132:  10   continue

134: !  Assemble matrix, using the 2-step process:
135: !       MatAssemblyBegin(), MatAssemblyEnd()
136: !  Computations can be done while messages are in transition,
137: !  by placing code between these two statements.

139:       call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
140:       call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)

142: !  Create parallel vectors.
143: !   - Here, the parallel partitioning of the vector is determined by
144: !     PETSc at runtime.  We could also specify the local dimensions
145: !     if desired -- or use the more general routine VecCreate().
146: !   - When solving a linear system, the vectors and matrices MUST
147: !     be partitioned accordingly.  PETSc automatically generates
148: !     appropriately partitioned matrices and vectors when MatCreate()
149: !     and VecCreate() are used with the same communicator.
150: !   - Note: We form 1 vector from scratch and then duplicate as needed.

152:       call VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,m*n,u,ierr)
153:       call VecDuplicate(u,b,ierr)
154:       call VecDuplicate(b,x,ierr)

156: !  Set exact solution; then compute right-hand-side vector.

158:       call VecSet(one,u,ierr)
159:       call MatMult(A,u,b,ierr)

161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162: !         Create the linear solver and set various options
163: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

165: !  Create linear solver context

167:       call SLESCreate(PETSC_COMM_WORLD,sles,ierr)

169: !  Set operators. Here the matrix that defines the linear system
170: !  also serves as the preconditioning matrix.

172:       call SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN,ierr)

174: !  Set linear solver defaults for this problem (optional).
175: !   - By extracting the KSP and PC contexts from the SLES context,
176: !     we can then directly directly call any KSP and PC routines
177: !     to set various options.

179:       call SLESGetKSP(sles,ksp,ierr)
180:       call SLESGetPC(sles,pc,ierr)
181:       tol = 1.e-7
182:       call KSPSetTolerances(ksp,tol,PETSC_DEFAULT_DOUBLE_PRECISION,     &
183:      &     PETSC_DEFAULT_DOUBLE_PRECISION,PETSC_DEFAULT_INTEGER,ierr)

185: !
186: !  Set a user-defined shell preconditioner
187: !

189: !  (Required) Indicate to PETSc that we are using a shell preconditioner
190:       call PCSetType(pc,PCSHELL,ierr)

192: !  (Required) Set the user-defined routine for applying the preconditioner
193:       call PCShellSetApply(pc,SampleShellPCApply,PETSC_NULL_OBJECT,     &
194:      &        ierr)

196: !  (Optional) Do any setup required for the preconditioner
197:       call SampleShellPCSetUp(A,x,ierr)


200: !  Set runtime options, e.g.,
201: !      -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
202: !  These options will override those specified above as long as
203: !  SLESSetFromOptions() is called _after_ any other customization
204: !  routines.

206:       call SLESSetFromOptions(sles,ierr)

208: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209: !                      Solve the linear system
210: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

212:       call SLESSolve(sles,b,x,its,ierr)

214: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
215: !                     Check solution and clean up
216: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

218: !  Check the error

220:       call VecAXPY(neg_one,u,x,ierr)
221:       call VecNorm(x,NORM_2,norm,ierr)
222:       if (rank .eq. 0) then
223:         if (norm .gt. 1.e-12) then
224:            write(6,100) norm,its
225:         else
226:            write(6,110) its
227:         endif
228:       endif
229:   100 format('Norm of error ',1pe10.4,' iterations ',i5)
230:   110 format('Norm of error < 1.e-12,iterations ',i5)


233: !  Free work space.  All PETSc objects should be destroyed when they
234: !  are no longer needed.

236:       call SLESDestroy(sles,ierr)
237:       call VecDestroy(u,ierr)
238:       call VecDestroy(x,ierr)
239:       call VecDestroy(b,ierr)
240:       call MatDestroy(A,ierr)

242: ! Free up PCShell data
243:       call PCDestroy(sor,ierr)
244:       call PCDestroy(jacobi,ierr)
245:       call VecDestroy(work,ierr)


248: !  Always call PetscFinalize() before exiting a program.

250:       call PetscFinalize(ierr)
251:       end

253: !/***********************************************************************/
254: !/*          Routines for a user-defined shell preconditioner           */
255: !/***********************************************************************/

257: !
258: !   SampleShellPCSetUp - This routine sets up a user-defined
259: !   preconditioner context.
260: !
261: !   Input Parameters:
262: !   pmat  - preconditioner matrix
263: !   x     - vector
264: !
265: !   Output Parameter:
266: !   ierr  - error code (nonzero if error has been detected)
267: !
268: !   Notes:
269: !   In this example, we define the shell preconditioner to be Jacobi
270: !   method.  Thus, here we create a work vector for storing the reciprocal
271: !   of the diagonal of the preconditioner matrix; this vector is then
272: !   used within the routine SampleShellPCApply().
273: !
274:       subroutine SampleShellPCSetUp(pmat,x,ierr)

276:       implicit none

278:  #include include/finclude/petsc.h
279:  #include include/finclude/petscvec.h
280:  #include include/finclude/petscmat.h

282:       Vec     x
283:       Mat     pmat
284:       integer ierr

286: !  Common block to store data for user-provided preconditioner
287:       common /mypcs/ jacobi,sor,work
288:       PC jacobi,sor
289:       Vec work

291:       call PCCreate(PETSC_COMM_WORLD,jacobi,ierr)
292:       call PCSetType(jacobi,PCJACOBI,ierr)
293:       call PCSetVector(jacobi,x,ierr)
294:       call PCSetOperators(jacobi,pmat,pmat,DIFFERENT_NONZERO_PATTERN,    &
295:      &                     ierr)
296:       call PCSetUp(jacobi,ierr)

298:       call PCCreate(PETSC_COMM_WORLD,sor,ierr)
299:       call PCSetType(sor,PCSOR,ierr)
300:       call PCSetVector(sor,x,ierr)
301:       call PCSetOperators(sor,pmat,pmat,DIFFERENT_NONZERO_PATTERN,       &
302:      &                     ierr)
303: !      call PCSORSetSymmetric(sor,SOR_LOCAL_SYMMETRIC_SWEEP,ierr)
304:       call PCSetUp(sor,ierr)

306:       call VecDuplicate(x,work,ierr)

308:       end

310: ! -------------------------------------------------------------------
311: !
312: !   SampleShellPCApply - This routine demonstrates the use of a
313: !   user-provided preconditioner.
314: !
315: !   Input Parameters:
316: !   dummy - optional user-defined context, not used here
317: !   x - input vector
318: !
319: !   Output Parameters:
320: !   y - preconditioned vector
321: !   ierr  - error code (nonzero if error has been detected)
322: !
323: !   Notes:
324: !   This code implements the Jacobi preconditioner plus the
325: !   SOR preconditioner
326: !
327: ! YOU CAN GET THE EXACT SAME EFFECT WITH THE PCCOMPOSITE preconditioner using
328: ! mpirun -np 1 ex21f -ksp_monitor -pc_type composite -pc_composite_pcs jacobi,sor -pc_composite_type additive
329: !
330:       subroutine SampleShellPCApply(dummy,x,y,ierr)

332:       implicit none

334:  #include include/finclude/petsc.h
335:  #include include/finclude/petscvec.h

337:       Vec     x,y
338:       integer dummy,ierr
339:       PetscScalar  one
340: 
341: !  Common block to store data for user-provided preconditioner
342:       common /mypcs/ jacobi,sor,work
343:       PC  jacobi,sor
344:       Vec work

346:       one = 1.0
347:       call PCApply(jacobi,x,y,ierr)
348:       call PCApply(sor,x,work,ierr)
349:       call VecAXPY(one,work,y,ierr)

351:       end