Actual source code: ex2f.F

petsc-3.5.1 2014-07-24
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  1: !
  2: !  Description: Solves a linear system in parallel with KSP (Fortran code).
  3: !               Also shows how to set a user-defined monitoring routine.
  4: !
  5: !
  6: !/*T
  7: !  Concepts: KSP^basic parallel example
  8: !  Concepts: KSP^setting a user-defined monitoring routine
  9: !  Processors: n
 10: !T*/
 11: !
 12: ! -----------------------------------------------------------------------

 14:       program main
 15:       implicit none

 17: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 18: !                    Include files
 19: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 20: !
 21: !  This program uses CPP for preprocessing, as indicated by the use of
 22: !  PETSc include files in the directory petsc/include/finclude.  This
 23: !  convention enables use of the CPP preprocessor, which allows the use
 24: !  of the #include statements that define PETSc objects and variables.
 25: !
 26: !  Use of the conventional Fortran include statements is also supported
 27: !  In this case, the PETsc include files are located in the directory
 28: !  petsc/include/foldinclude.
 29: !
 30: !  Since one must be very careful to include each file no more than once
 31: !  in a Fortran routine, application programmers must exlicitly list
 32: !  each file needed for the various PETSc components within their
 33: !  program (unlike the C/C++ interface).
 34: !
 35: !  See the Fortran section of the PETSc users manual for details.
 36: !
 37: !  The following include statements are required for KSP Fortran programs:
 38: !     petscsys.h       - base PETSc routines
 39: !     petscvec.h    - vectors
 40: !     petscmat.h    - matrices
 41: !     petscpc.h     - preconditioners
 42: !     petscksp.h    - Krylov subspace methods
 43: !  Additional include statements may be needed if using additional
 44: !  PETSc routines in a Fortran program, e.g.,
 45: !     petscviewer.h - viewers
 46: !     petscis.h     - index sets
 47: !
 48: #include <finclude/petscsys.h>
 49: #include <finclude/petscvec.h>
 50: #include <finclude/petscmat.h>
 51: #include <finclude/petscpc.h>
 52: #include <finclude/petscksp.h>
 53: !
 54: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 55: !                   Variable declarations
 56: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 57: !
 58: !  Variables:
 59: !     ksp     - linear solver context
 60: !     ksp      - Krylov subspace method context
 61: !     pc       - preconditioner context
 62: !     x, b, u  - approx solution, right-hand-side, exact solution vectors
 63: !     A        - matrix that defines linear system
 64: !     its      - iterations for convergence
 65: !     norm     - norm of error in solution
 66: !     rctx     - random number generator context
 67: !
 68: !  Note that vectors are declared as PETSc "Vec" objects.  These vectors
 69: !  are mathematical objects that contain more than just an array of
 70: !  double precision numbers. I.e., vectors in PETSc are not just
 71: !        double precision x(*).
 72: !  However, local vector data can be easily accessed via VecGetArray().
 73: !  See the Fortran section of the PETSc users manual for details.
 74: !
 75:       PetscReal  norm
 76:       PetscInt  i,j,II,JJ,m,n,its
 77:       PetscInt  Istart,Iend,ione
 78:       PetscErrorCode ierr
 79:       PetscMPIInt     rank,size
 80:       PetscBool   flg
 81:       PetscScalar v,one,neg_one
 82:       Vec         x,b,u
 83:       Mat         A
 84:       KSP         ksp
 85:       PetscRandom rctx

 87: !  These variables are not currently used.
 88: !      PC          pc
 89: !      PCType      ptype
 90: !      PetscReal tol


 93: !  Note: Any user-defined Fortran routines (such as MyKSPMonitor)
 94: !  MUST be declared as external.

 96:       external MyKSPMonitor,MyKSPConverged

 98: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 99: !                 Beginning of program
100: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

102:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
103:       m = 3
104:       n = 3
105:       one  = 1.0
106:       neg_one = -1.0
107:       ione    = 1
108:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-m',m,flg,ierr)
109:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
110:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
111:       call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)

113: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114: !      Compute the matrix and right-hand-side vector that define
115: !      the linear system, Ax = b.
116: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

118: !  Create parallel matrix, specifying only its global dimensions.
119: !  When using MatCreate(), the matrix format can be specified at
120: !  runtime. Also, the parallel partitioning of the matrix is
121: !  determined by PETSc at runtime.

123:       call MatCreate(PETSC_COMM_WORLD,A,ierr)
124:       call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr)
125:       call MatSetFromOptions(A,ierr)
126:       call MatSetUp(A,ierr)

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

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

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

142: !     Note: this uses the less common natural ordering that orders first
143: !     all the unknowns for x = h then for x = 2h etc; Hence you see JH = II +- n
144: !     instead of JJ = II +- m as you might expect. The more standard ordering
145: !     would first do all variables for y = h, then y = 2h etc.

147:       do 10, II=Istart,Iend-1
148:         v = -1.0
149:         i = II/n
150:         j = II - i*n
151:         if (i.gt.0) then
152:           JJ = II - n
153:           call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
154:         endif
155:         if (i.lt.m-1) then
156:           JJ = II + n
157:           call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
158:         endif
159:         if (j.gt.0) then
160:           JJ = II - 1
161:           call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
162:         endif
163:         if (j.lt.n-1) then
164:           JJ = II + 1
165:           call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
166:         endif
167:         v = 4.0
168:         call  MatSetValues(A,ione,II,ione,II,v,INSERT_VALUES,ierr)
169:  10   continue

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

176:       call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
177:       call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)

179: !  Create parallel vectors.
180: !   - Here, the parallel partitioning of the vector is determined by
181: !     PETSc at runtime.  We could also specify the local dimensions
182: !     if desired -- or use the more general routine VecCreate().
183: !   - When solving a linear system, the vectors and matrices MUST
184: !     be partitioned accordingly.  PETSc automatically generates
185: !     appropriately partitioned matrices and vectors when MatCreate()
186: !     and VecCreate() are used with the same communicator.
187: !   - Note: We form 1 vector from scratch and then duplicate as needed.

189:       call VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,m*n,u,ierr)
190:       call VecSetFromOptions(u,ierr)
191:       call VecDuplicate(u,b,ierr)
192:       call VecDuplicate(b,x,ierr)

194: !  Set exact solution; then compute right-hand-side vector.
195: !  By default we use an exact solution of a vector with all
196: !  elements of 1.0;  Alternatively, using the runtime option
197: !  -random_sol forms a solution vector with random components.

199:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,                    &
200:      &             "-random_exact_sol",flg,ierr)
201:       if (flg) then
202:          call PetscRandomCreate(PETSC_COMM_WORLD,rctx,ierr)
203:          call PetscRandomSetFromOptions(rctx,ierr)
204:          call VecSetRandom(u,rctx,ierr)
205:          call PetscRandomDestroy(rctx,ierr)
206:       else
207:          call VecSet(u,one,ierr)
208:       endif
209:       call MatMult(A,u,b,ierr)

211: !  View the exact solution vector if desired

213:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,                    &
214:      &             "-view_exact_sol",flg,ierr)
215:       if (flg) then
216:          call VecView(u,PETSC_VIEWER_STDOUT_WORLD,ierr)
217:       endif

219: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
220: !         Create the linear solver and set various options
221: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

223: !  Create linear solver context

225:       call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)

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

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

232: !  Set linear solver defaults for this problem (optional).
233: !   - By extracting the KSP and PC contexts from the KSP context,
234: !     we can then directly directly call any KSP and PC routines
235: !     to set various options.
236: !   - The following four statements are optional; all of these
237: !     parameters could alternatively be specified at runtime via
238: !     KSPSetFromOptions(). All of these defaults can be
239: !     overridden at runtime, as indicated below.

241: !     We comment out this section of code since the Jacobi
242: !     preconditioner is not a good general default.

244: !      call KSPGetPC(ksp,pc,ierr)
245: !      ptype = PCJACOBI
246: !      call PCSetType(pc,ptype,ierr)
247: !      tol = 1.e-7
248: !      call KSPSetTolerances(ksp,tol,PETSC_DEFAULT_REAL,
249: !     &     PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr)

251: !  Set user-defined monitoring routine if desired

253:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-my_ksp_monitor',  &
254:      &                    flg,ierr)
255:       if (flg) then
256:         call KSPMonitorSet(ksp,MyKSPMonitor,PETSC_NULL_OBJECT,          &
257:      &                     PETSC_NULL_FUNCTION,ierr)
258:       endif


261: !  Set runtime options, e.g.,
262: !      -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
263: !  These options will override those specified above as long as
264: !  KSPSetFromOptions() is called _after_ any other customization
265: !  routines.

267:       call KSPSetFromOptions(ksp,ierr)

269: !  Set convergence test routine if desired

271:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,                    &
272:      &     '-my_ksp_convergence',flg,ierr)
273:       if (flg) then
274:         call KSPSetConvergenceTest(ksp,MyKSPConverged,                  &
275:      &          PETSC_NULL_OBJECT,PETSC_NULL_FUNCTION,ierr)
276:       endif
277: !
278: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
279: !                      Solve the linear system
280: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

284: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
285: !                     Check solution and clean up
286: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

288: !  Check the error
289:       call VecAXPY(x,neg_one,u,ierr)
290:       call VecNorm(x,NORM_2,norm,ierr)
291:       call KSPGetIterationNumber(ksp,its,ierr)
292:       if (rank .eq. 0) then
293:         if (norm .gt. 1.e-12) then
294:            write(6,100) norm,its
295:         else
296:            write(6,110) its
297:         endif
298:       endif
299:   100 format('Norm of error ',e11.4,' iterations ',i5)
300:   110 format('Norm of error < 1.e-12,iterations ',i5)

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

305:       call KSPDestroy(ksp,ierr)
306:       call VecDestroy(u,ierr)
307:       call VecDestroy(x,ierr)
308:       call VecDestroy(b,ierr)
309:       call MatDestroy(A,ierr)

311: !  Always call PetscFinalize() before exiting a program.  This routine
312: !    - finalizes the PETSc libraries as well as MPI
313: !    - provides summary and diagnostic information if certain runtime
314: !      options are chosen (e.g., -log_summary).  See PetscFinalize()
315: !      manpage for more information.

317:       call PetscFinalize(ierr)
318:       end

320: ! --------------------------------------------------------------
321: !
322: !  MyKSPMonitor - This is a user-defined routine for monitoring
323: !  the KSP iterative solvers.
324: !
325: !  Input Parameters:
326: !    ksp   - iterative context
327: !    n     - iteration number
328: !    rnorm - 2-norm (preconditioned) residual value (may be estimated)
329: !    dummy - optional user-defined monitor context (unused here)
330: !
331:       subroutine MyKSPMonitor(ksp,n,rnorm,dummy,ierr)

333:       implicit none

335: #include <finclude/petscsys.h>
336: #include <finclude/petscvec.h>
337: #include <finclude/petscksp.h>

339:       KSP              ksp
340:       Vec              x
341:       PetscErrorCode ierr
342:       PetscInt n,dummy
343:       PetscMPIInt rank
344:       PetscReal rnorm

346: !  Build the solution vector

348:       call KSPBuildSolution(ksp,PETSC_NULL_OBJECT,x,ierr)

350: !  Write the solution vector and residual norm to stdout
351: !   - Note that the parallel viewer PETSC_VIEWER_STDOUT_WORLD
352: !     handles data from multiple processors so that the
353: !     output is not jumbled.

355:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
356:       if (rank .eq. 0) write(6,100) n
357:       call VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr)
358:       if (rank .eq. 0) write(6,200) n,rnorm

360:  100  format('iteration ',i5,' solution vector:')
361:  200  format('iteration ',i5,' residual norm ',e11.4)
362:       0
363:       end

365: ! --------------------------------------------------------------
366: !
367: !  MyKSPConverged - This is a user-defined routine for testing
368: !  convergence of the KSP iterative solvers.
369: !
370: !  Input Parameters:
371: !    ksp   - iterative context
372: !    n     - iteration number
373: !    rnorm - 2-norm (preconditioned) residual value (may be estimated)
374: !    dummy - optional user-defined monitor context (unused here)
375: !
376:       subroutine MyKSPConverged(ksp,n,rnorm,flag,dummy,ierr)

378:       implicit none

380: #include <finclude/petscsys.h>
381: #include <finclude/petscvec.h>
382: #include <finclude/petscksp.h>

384:       KSP              ksp
385:       PetscErrorCode ierr
386:       PetscInt n,dummy
387:       KSPConvergedReason flag
388:       PetscReal rnorm

390:       if (rnorm .le. .05) then
391:         flag = 1
392:       else
393:         flag = 0
394:       endif
395:       0

397:       end