Actual source code: ex15f.F

petsc-master 2016-08-29
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  1: !
  2: !   Solves a linear system in parallel with KSP.  Also indicates
  3: !   use of a user-provided preconditioner.  Input parameters include:
  4: !      -user_defined_pc : Activate a user-defined preconditioner
  5: !
  6: !
  7: !/*T
  8: !   Concepts: KSP^basic parallel example
  9: !   Concepts: PC^setting a user-defined shell preconditioner
 10: !   Processors: n
 11: !T*/
 12: !
 13: !  -------------------------------------------------------------------------

 15:       program main
 16:       implicit none

 18: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 19: !                    Include files
 20: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 21: !
 22: !     petscsys.h  - base PETSc routines      petscvec.h - vectors
 23: !     petscmat.h - matrices
 24: !     petscksp.h    - Krylov subspace methods  petscpc.h  - preconditioners

 26:  #include <petsc/finclude/petscsys.h>
 27:  #include <petsc/finclude/petscvec.h>
 28:  #include <petsc/finclude/petscmat.h>
 29:  #include <petsc/finclude/petscpc.h>
 30:  #include <petsc/finclude/petscksp.h>

 32: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 33: !                   Variable declarations
 34: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 35: !
 36: !  Variables:
 37: !     ksp     - linear solver context
 38: !     ksp      - Krylov subspace method context
 39: !     pc       - preconditioner context
 40: !     x, b, u  - approx solution, right-hand-side, exact solution vectors
 41: !     A        - matrix that defines linear system
 42: !     its      - iterations for convergence
 43: !     norm     - norm of solution error

 45:       Vec              x,b,u
 46:       Mat              A
 47:       PC               pc
 48:       KSP              ksp
 49:       PetscScalar      v,one,neg_one
 50:       PetscReal norm,tol
 51:       PetscErrorCode ierr
 52:       PetscInt   i,j,II,JJ,Istart
 53:       PetscInt   Iend,m,n,i1,its,five
 54:       PetscMPIInt rank
 55:       PetscBool  user_defined_pc,flg

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

 59:       external SampleShellPCSetUp, SampleShellPCApply
 60:       external  SampleShellPCDestroy

 62: !  Common block to store data for user-provided preconditioner
 63:       common /myshellpc/ diag
 64:       Vec    diag

 66: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 67: !                 Beginning of program
 68: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 70:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
 71:       one     = 1.0
 72:       neg_one = -1.0
 73:       i1 = 1
 74:       m       = 8
 75:       n       = 7
 76:       five    = 5
 77:       call PetscOptionsGetInt(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER,     &
 78:      &                        '-m',m,flg,ierr)
 79:       call PetscOptionsGetInt(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER,     &
 80:      &                        '-n',n,flg,ierr)
 81:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)

 83: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 84: !      Compute the matrix and right-hand-side vector that define
 85: !      the linear system, Ax = b.
 86: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

 93:       call MatCreate(PETSC_COMM_WORLD,A,ierr)
 94:       call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr)
 95:       call MatSetType(A, MATAIJ,ierr)
 96:       call MatSetFromOptions(A,ierr)
 97:       call MatMPIAIJSetPreallocation(A,five,PETSC_NULL_INTEGER,five,            &
 98:      &                     PETSC_NULL_INTEGER,ierr)
 99:       call MatSeqAIJSetPreallocation(A,five,PETSC_NULL_INTEGER,ierr)

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

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

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

115:       do 10, II=Istart,Iend-1
116:         v = -1.0
117:         i = II/n
118:         j = II - i*n
119:         if (i.gt.0) then
120:           JJ = II - n
121:           call MatSetValues(A,i1,II,i1,JJ,v,ADD_VALUES,ierr)
122:         endif
123:         if (i.lt.m-1) then
124:           JJ = II + n
125:           call MatSetValues(A,i1,II,i1,JJ,v,ADD_VALUES,ierr)
126:         endif
127:         if (j.gt.0) then
128:           JJ = II - 1
129:           call MatSetValues(A,i1,II,i1,JJ,v,ADD_VALUES,ierr)
130:         endif
131:         if (j.lt.n-1) then
132:           JJ = II + 1
133:           call MatSetValues(A,i1,II,i1,JJ,v,ADD_VALUES,ierr)
134:         endif
135:         v = 4.0
136:         call  MatSetValues(A,i1,II,i1,II,v,ADD_VALUES,ierr)
137:  10   continue

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

144:       call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
145:       call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)

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

157:       call VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,m*n,u,ierr)
158:       call VecDuplicate(u,b,ierr)
159:       call VecDuplicate(b,x,ierr)

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

163:       call VecSet(u,one,ierr)
164:       call MatMult(A,u,b,ierr)

166: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167: !         Create the linear solver and set various options
168: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

170: !  Create linear solver context

172:       call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)

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

177:       call KSPSetOperators(ksp,A,A,ierr)

179: !  Set linear solver defaults for this problem (optional).
180: !   - By extracting the KSP and PC contexts from the KSP context,
181: !     we can then directly directly call any KSP and PC routines
182: !     to set various options.

184:       call KSPGetPC(ksp,pc,ierr)
185:       tol = 1.e-7
186:       call KSPSetTolerances(ksp,tol,PETSC_DEFAULT_REAL,                       &
187:      &     PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr)

189: !
190: !  Set a user-defined shell preconditioner if desired
191: !
192:       call PetscOptionsHasName(PETSC_NULL_OBJECT,PETSC_NULL_CHARACTER,        &
193:      &                         '-user_defined_pc',user_defined_pc,ierr)

195:       if (user_defined_pc) then

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

200: !  (Required) Set the user-defined routine for applying the preconditioner
201:          call PCShellSetApply(pc,SampleShellPCApply,ierr)

203: !  (Optional) Do any setup required for the preconditioner
204:          call PCShellSetSetUp(pc,SampleShellPCSetUp,ierr)

206: !  (Optional) Frees any objects we created for the preconditioner
207:          call PCShellSetDestroy(pc,SampleShellPCDestroy,ierr)

209:       else
210:          call PCSetType(pc,PCJACOBI,ierr)
211:       endif

213: !  Set runtime options, e.g.,
214: !      -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
215: !  These options will override those specified above as long as
216: !  KSPSetFromOptions() is called _after_ any other customization
217: !  routines.

219:       call KSPSetFromOptions(ksp,ierr)

221: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
222: !                      Solve the linear system
223: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

225:       call KSPSolve(ksp,b,x,ierr)

227: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
228: !                     Check solution and clean up
229: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

231: !  Check the error

233:       call VecAXPY(x,neg_one,u,ierr)
234:       call VecNorm(x,NORM_2,norm,ierr)
235:       call KSPGetIterationNumber(ksp,its,ierr)

237:       if (rank .eq. 0) then
238:         if (norm .gt. 1.e-12) then
239:            write(6,100) norm,its
240:         else
241:            write(6,110) its
242:         endif
243:       endif
244:   100 format('Norm of error ',1pe11.4,' iterations ',i5)
245:   110 format('Norm of error < 1.e-12,iterations ',i5)

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

250:       call KSPDestroy(ksp,ierr)
251:       call VecDestroy(u,ierr)
252:       call VecDestroy(x,ierr)
253:       call VecDestroy(b,ierr)
254:       call MatDestroy(A,ierr)

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

258:       call PetscFinalize(ierr)
259:       end

261: !/***********************************************************************/
262: !/*          Routines for a user-defined shell preconditioner           */
263: !/***********************************************************************/

265: !
266: !   SampleShellPCSetUp - This routine sets up a user-defined
267: !   preconditioner context.
268: !
269: !   Input Parameters:
270: !   pc - preconditioner object
271: !
272: !   Output Parameter:
273: !   ierr  - error code (nonzero if error has been detected)
274: !
275: !   Notes:
276: !   In this example, we define the shell preconditioner to be Jacobi
277: !   method.  Thus, here we create a work vector for storing the reciprocal
278: !   of the diagonal of the preconditioner matrix; this vector is then
279: !   used within the routine SampleShellPCApply().
280: !
281:       subroutine SampleShellPCSetUp(pc,ierr)

283:       implicit none

285:  #include <petsc/finclude/petscsys.h>
286:  #include <petsc/finclude/petscvec.h>
287:  #include <petsc/finclude/petscmat.h>
288:       PC      pc

290:       Mat     pmat
291:       integer ierr

293: !  Common block to store data for user-provided preconditioner
294: !  Normally we would recommend storing all the work data (like diag) in
295: !  the context set with PCShellSetContext()

297:       common /myshellpc/ diag
298:       Vec    diag

300:       call PCGetOperators(pc,PETSC_NULL_OBJECT,pmat,ierr)
301:       call MatCreateVecs(pmat,diag,PETSC_NULL_OBJECT,ierr)
302:       call MatGetDiagonal(pmat,diag,ierr)
303:       call VecReciprocal(diag,ierr)

305:       end

307: ! -------------------------------------------------------------------
308: !
309: !   SampleShellPCApply - This routine demonstrates the use of a
310: !   user-provided preconditioner.
311: !
312: !   Input Parameters:
313: !   pc - preconditioner object
314: !   x - input vector
315: !
316: !   Output Parameters:
317: !   y - preconditioned vector
318: !   ierr  - error code (nonzero if error has been detected)
319: !
320: !   Notes:
321: !   This code implements the Jacobi preconditioner, merely as an
322: !   example of working with a PCSHELL.  Note that the Jacobi method
323: !   is already provided within PETSc.
324: !
325:       subroutine SampleShellPCApply(pc,x,y,ierr)

327:       implicit none

329:  #include <petsc/finclude/petscsys.h>
330:  #include <petsc/finclude/petscvec.h>

332:       PC      pc
333:       Vec     x,y
334:       integer ierr

336: !  Common block to store data for user-provided preconditioner
337:       common /myshellpc/ diag
338:       Vec    diag

340:       call VecPointwiseMult(y,x,diag,ierr)

342:       end

344: !/***********************************************************************/
345: !/*          Routines for a user-defined shell preconditioner           */
346: !/***********************************************************************/

348: !
349: !   SampleShellPCDestroy - This routine destroys (frees the memory of) any
350: !      objects we made for the preconditioner
351: !
352: !   Input Parameters:
353: !   pc - for this example we use the actual PC as our shell context
354: !
355: !   Output Parameter:
356: !   ierr  - error code (nonzero if error has been detected)
357: !

359:       subroutine SampleShellPCDestroy(pc,ierr)

361:       implicit none

363:  #include <petsc/finclude/petscsys.h>
364:  #include <petsc/finclude/petscvec.h>
365:  #include <petsc/finclude/petscmat.h>
366:       PC      pc
367:       PetscErrorCode ierr

369: !  Common block to store data for user-provided preconditioner
370: !  Normally we would recommend storing all the work data (like diag) in
371: !  the context set with PCShellSetContext()

373:       common /myshellpc/ diag
374:       Vec    diag

376:       call VecDestroy(diag,ierr)

378:       end