Actual source code: ex2f.F90

petsc-master 2020-12-02
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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: #include <petsc/finclude/petscksp.h>
 16:       use petscksp
 17:       implicit none
 18: !
 19: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 20: !                   Variable declarations
 21: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 22: !
 23: !  Variables:
 24: !     ksp     - linear solver context
 25: !     ksp      - Krylov subspace method context
 26: !     pc       - preconditioner context
 27: !     x, b, u  - approx solution, right-hand-side, exact solution vectors
 28: !     A        - matrix that defines linear system
 29: !     its      - iterations for convergence
 30: !     norm     - norm of error in solution
 31: !     rctx     - random number generator context
 32: !
 33: !  Note that vectors are declared as PETSc "Vec" objects.  These vectors
 34: !  are mathematical objects that contain more than just an array of
 35: !  double precision numbers. I.e., vectors in PETSc are not just
 36: !        double precision x(*).
 37: !  However, local vector data can be easily accessed via VecGetArray().
 38: !  See the Fortran section of the PETSc users manual for details.
 39: !
 40:       PetscReal  norm
 41:       PetscInt  i,j,II,JJ,m,n,its
 42:       PetscInt  Istart,Iend,ione
 43:       PetscErrorCode ierr
 44:       PetscMPIInt     rank,size
 45:       PetscBool   flg
 46:       PetscScalar v,one,neg_one
 47:       Vec         x,b,u
 48:       Mat         A
 49:       KSP         ksp
 50:       PetscRandom rctx
 51:       PetscViewerAndFormat vf,vzero

 53: !  These variables are not currently used.
 54: !      PC          pc
 55: !      PCType      ptype
 56: !      PetscReal tol


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

 62:       external MyKSPMonitor,MyKSPConverged

 64: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 65: !                 Beginning of program
 66: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 68:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
 69:       if (ierr .ne. 0) then
 70:         print*,'Unable to initialize PETSc'
 71:         stop
 72:       endif
 73:       m = 3
 74:       n = 3
 75:       one  = 1.0
 76:       neg_one = -1.0
 77:       ione    = 1
 78:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-m',m,flg,ierr)
 79:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
 80:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
 81:       call MPI_Comm_size(PETSC_COMM_WORLD,size,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 MatSetFromOptions(A,ierr)
 96:       call MatSetUp(A,ierr)

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

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

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

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

117:       do 10, II=Istart,Iend-1
118:         v = -1.0
119:         i = II/n
120:         j = II - i*n
121:         if (i.gt.0) then
122:           JJ = II - n
123:           call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
124:         endif
125:         if (i.lt.m-1) then
126:           JJ = II + n
127:           call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
128:         endif
129:         if (j.gt.0) then
130:           JJ = II - 1
131:           call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
132:         endif
133:         if (j.lt.n-1) then
134:           JJ = II + 1
135:           call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
136:         endif
137:         v = 4.0
138:         call  MatSetValues(A,ione,II,ione,II,v,INSERT_VALUES,ierr)
139:  10   continue

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

146:       call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
147:       call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)

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

159:       call VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,m*n,u,ierr)
160:       call VecSetFromOptions(u,ierr)
161:       call VecDuplicate(u,b,ierr)
162:       call VecDuplicate(b,x,ierr)

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

169:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-random_exact_sol',flg,ierr)
170:       if (flg) then
171:          call PetscRandomCreate(PETSC_COMM_WORLD,rctx,ierr)
172:          call PetscRandomSetFromOptions(rctx,ierr)
173:          call VecSetRandom(u,rctx,ierr)
174:          call PetscRandomDestroy(rctx,ierr)
175:       else
176:          call VecSet(u,one,ierr)
177:       endif
178:       call MatMult(A,u,b,ierr)

180: !  View the exact solution vector if desired

182:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-view_exact_sol',flg,ierr)
183:       if (flg) then
184:          call VecView(u,PETSC_VIEWER_STDOUT_WORLD,ierr)
185:       endif

187: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
188: !         Create the linear solver and set various options
189: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

191: !  Create linear solver context

193:       call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)

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

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

200: !  Set linear solver defaults for this problem (optional).
201: !   - By extracting the KSP and PC contexts from the KSP context,
202: !     we can then directly directly call any KSP and PC routines
203: !     to set various options.
204: !   - The following four statements are optional; all of these
205: !     parameters could alternatively be specified at runtime via
206: !     KSPSetFromOptions(). All of these defaults can be
207: !     overridden at runtime, as indicated below.

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

212: !      call KSPGetPC(ksp,pc,ierr)
213: !      ptype = PCJACOBI
214: !      call PCSetType(pc,ptype,ierr)
215: !      tol = 1.e-7
216: !      call KSPSetTolerances(ksp,tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr)

218: !  Set user-defined monitoring routine if desired

220:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_ksp_monitor',flg,ierr)
221:       if (flg) then
222:         vzero = 0
223:         call KSPMonitorSet(ksp,MyKSPMonitor,vzero,PETSC_NULL_FUNCTION,ierr)
224: !
225: !     Also use the default KSP monitor routine showing how it may be used from Fortran
226: !
227:         call PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,vf,ierr)
228:         call KSPMonitorSet(ksp,KSPMonitorDefault,vf,PetscViewerAndFormatDestroy,ierr)
229:       endif


232: !  Set runtime options, e.g.,
233: !      -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
234: !  These options will override those specified above as long as
235: !  KSPSetFromOptions() is called _after_ any other customization
236: !  routines.

238:       call KSPSetFromOptions(ksp,ierr)

240: !  Set convergence test routine if desired

242:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_ksp_convergence',flg,ierr)
243:       if (flg) then
244:         call KSPSetConvergenceTest(ksp,MyKSPConverged,0,PETSC_NULL_FUNCTION,ierr)
245:       endif
246: !
247: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
248: !                      Solve the linear system
249: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

253: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
254: !                     Check solution and clean up
255: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

257: !  Check the error
258:       call VecAXPY(x,neg_one,u,ierr)
259:       call VecNorm(x,NORM_2,norm,ierr)
260:       call KSPGetIterationNumber(ksp,its,ierr)
261:       if (rank .eq. 0) then
262:         if (norm .gt. 1.e-12) then
263:            write(6,100) norm,its
264:         else
265:            write(6,110) its
266:         endif
267:       endif
268:   100 format('Norm of error ',e11.4,' iterations ',i5)
269:   110 format('Norm of error < 1.e-12 iterations ',i5)

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

274:       call KSPDestroy(ksp,ierr)
275:       call VecDestroy(u,ierr)
276:       call VecDestroy(x,ierr)
277:       call VecDestroy(b,ierr)
278:       call MatDestroy(A,ierr)

280: !  Always call PetscFinalize() before exiting a program.  This routine
281: !    - finalizes the PETSc libraries as well as MPI
282: !    - provides summary and diagnostic information if certain runtime
283: !      options are chosen (e.g., -log_view).  See PetscFinalize()
284: !      manpage for more information.

286:       call PetscFinalize(ierr)
287:       end

289: ! --------------------------------------------------------------
290: !
291: !  MyKSPMonitor - This is a user-defined routine for monitoring
292: !  the KSP iterative solvers.
293: !
294: !  Input Parameters:
295: !    ksp   - iterative context
296: !    n     - iteration number
297: !    rnorm - 2-norm (preconditioned) residual value (may be estimated)
298: !    dummy - optional user-defined monitor context (unused here)
299: !
300:       subroutine MyKSPMonitor(ksp,n,rnorm,dummy,ierr)
301:       use petscksp
302:       implicit none

304:       KSP              ksp
305:       Vec              x
306:       PetscErrorCode ierr
307:       PetscInt n,dummy
308:       PetscMPIInt rank
309:       PetscReal rnorm

311: !  Build the solution vector
312:       call KSPBuildSolution(ksp,PETSC_NULL_VEC,x,ierr)

314: !  Write the solution vector and residual norm to stdout
315: !   - Note that the parallel viewer PETSC_VIEWER_STDOUT_WORLD
316: !     handles data from multiple processors so that the
317: !     output is not jumbled.

319:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
320:       if (rank .eq. 0) write(6,100) n
321:       call VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr)
322:       if (rank .eq. 0) write(6,200) n,rnorm

324:  100  format('iteration ',i5,' solution vector:')
325:  200  format('iteration ',i5,' residual norm ',e11.4)
326:       0
327:       end

329: ! --------------------------------------------------------------
330: !
331: !  MyKSPConverged - This is a user-defined routine for testing
332: !  convergence of the KSP iterative solvers.
333: !
334: !  Input Parameters:
335: !    ksp   - iterative context
336: !    n     - iteration number
337: !    rnorm - 2-norm (preconditioned) residual value (may be estimated)
338: !    dummy - optional user-defined monitor context (unused here)
339: !
340:       subroutine MyKSPConverged(ksp,n,rnorm,flag,dummy,ierr)
341:       use petscksp
342:       implicit none

344:       KSP              ksp
345:       PetscErrorCode ierr
346:       PetscInt n,dummy
347:       KSPConvergedReason flag
348:       PetscReal rnorm

350:       if (rnorm .le. .05) then
351:         flag = 1
352:       else
353:         flag = 0
354:       endif
355:       0

357:       end

359: !/*TEST
360: !
361: !   test:
362: !      nsize: 2
363: !      args: -pc_type jacobi -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
364: !
365: !   test:
366: !      suffix: 2
367: !      nsize: 2
368: !      args: -pc_type jacobi -my_ksp_monitor -ksp_gmres_cgs_refinement_type refine_always
369: !
370: !TEST*/