Actual source code: ex15f.F90

  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: !
  8: !     Module contains diag needed by shell preconditioner
  9: !
 10:       module ex15fmodule
 11: #include <petsc/finclude/petscksp.h>
 12:       use petscksp
 13:       Vec    diag
 14:       end module

 16:       program main
 17:       use ex15fmodule
 18:       implicit none

 20: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 21: !                   Variable declarations
 22: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 23: !
 24: !  Variables:
 25: !     ksp     - linear solver context
 26: !     ksp      - Krylov subspace method context
 27: !     pc       - preconditioner context
 28: !     x, b, u  - approx solution, right-hand side, exact solution vectors
 29: !     A        - matrix that defines linear system
 30: !     its      - iterations for convergence
 31: !     norm     - norm of solution error

 33:       Vec              x,b,u
 34:       Mat              A
 35:       PC               pc
 36:       KSP              ksp
 37:       PetscScalar      v,one,neg_one
 38:       PetscReal norm,tol
 39:       PetscErrorCode ierr
 40:       PetscInt   i,j,II,JJ,Istart
 41:       PetscInt   Iend,m,n,i1,its,five
 42:       PetscMPIInt rank
 43:       PetscBool  user_defined_pc,flg

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

 47:       external SampleShellPCSetUp, SampleShellPCApply
 48:       external  SampleShellPCDestroy

 50: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 51: !                 Beginning of program
 52: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 54:       PetscCallA(PetscInitialize(ierr))
 55:       one     = 1.0
 56:       neg_one = -1.0
 57:       i1 = 1
 58:       m       = 8
 59:       n       = 7
 60:       five    = 5
 61:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-m',m,flg,ierr))
 62:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n',n,flg,ierr))
 63:       PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr))

 65: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 66: !      Compute the matrix and right-hand-side vector that define
 67: !      the linear system, Ax = b.
 68: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 70: !  Create parallel matrix, specifying only its global dimensions.
 71: !  When using MatCreate(), the matrix format can be specified at
 72: !  runtime. Also, the parallel partitioning of the matrix is
 73: !  determined by PETSc at runtime.

 75:       PetscCallA(MatCreate(PETSC_COMM_WORLD,A,ierr))
 76:       PetscCallA(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr))
 77:       PetscCallA(MatSetType(A, MATAIJ,ierr))
 78:       PetscCallA(MatSetFromOptions(A,ierr))
 79:       PetscCallA(MatMPIAIJSetPreallocation(A,five,PETSC_NULL_INTEGER_ARRAY,five,PETSC_NULL_INTEGER_ARRAY,ierr))
 80:       PetscCallA(MatSeqAIJSetPreallocation(A,five,PETSC_NULL_INTEGER_ARRAY,ierr))

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

 86:       PetscCallA(MatGetOwnershipRange(A,Istart,Iend,ierr))

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

 96:       do 10, II=Istart,Iend-1
 97:         v = -1.0
 98:         i = II/n
 99:         j = II - i*n
100:         if (i.gt.0) then
101:           JJ = II - n
102:           PetscCallA(MatSetValues(A,i1,[II],i1,[JJ],[v],ADD_VALUES,ierr))
103:         endif
104:         if (i.lt.m-1) then
105:           JJ = II + n
106:           PetscCallA(MatSetValues(A,i1,[II],i1,[JJ],[v],ADD_VALUES,ierr))
107:         endif
108:         if (j.gt.0) then
109:           JJ = II - 1
110:           PetscCallA(MatSetValues(A,i1,[II],i1,[JJ],[v],ADD_VALUES,ierr))
111:         endif
112:         if (j.lt.n-1) then
113:           JJ = II + 1
114:           PetscCallA(MatSetValues(A,i1,[II],i1,[JJ],[v],ADD_VALUES,ierr))
115:         endif
116:         v = 4.0
117:         PetscCallA( MatSetValues(A,i1,[II],i1,[II],[v],ADD_VALUES,ierr))
118:  10   continue

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

125:       PetscCallA(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr))
126:       PetscCallA(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr))

128: !  Create parallel vectors.
129: !   - Here, the parallel partitioning of the vector is determined by
130: !     PETSc at runtime.  We could also specify the local dimensions
131: !     if desired -- or use the more general routine VecCreate().
132: !   - When solving a linear system, the vectors and matrices MUST
133: !     be partitioned accordingly.  PETSc automatically generates
134: !     appropriately partitioned matrices and vectors when MatCreate()
135: !     and VecCreate() are used with the same communicator.
136: !   - Note: We form 1 vector from scratch and then duplicate as needed.

138:       PetscCallA(VecCreateFromOptions(PETSC_COMM_WORLD,PETSC_NULL_CHARACTER,i1,PETSC_DECIDE,m*n,u,ierr))
139:       PetscCallA(VecDuplicate(u,b,ierr))
140:       PetscCallA(VecDuplicate(b,x,ierr))

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

144:       PetscCallA(VecSet(u,one,ierr))
145:       PetscCallA(MatMult(A,u,b,ierr))

147: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: !         Create the linear solver and set various options
149: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

151: !  Create linear solver context

153:       PetscCallA(KSPCreate(PETSC_COMM_WORLD,ksp,ierr))

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

158:       PetscCallA(KSPSetOperators(ksp,A,A,ierr))

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

165:       PetscCallA(KSPGetPC(ksp,pc,ierr))
166:       tol = 1.e-7
167:       PetscCallA(KSPSetTolerances(ksp,tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr))

169: !
170: !  Set a user-defined shell preconditioner if desired
171: !
172:       PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-user_defined_pc',user_defined_pc,ierr))

174:       if (user_defined_pc) then

176: !  (Required) Indicate to PETSc that we are using a shell preconditioner
177:          PetscCallA(PCSetType(pc,PCSHELL,ierr))

179: !  (Required) Set the user-defined routine for applying the preconditioner
180:          PetscCallA(PCShellSetApply(pc,SampleShellPCApply,ierr))

182: !  (Optional) Do any setup required for the preconditioner
183:          PetscCallA(PCShellSetSetUp(pc,SampleShellPCSetUp,ierr))

185: !  (Optional) Frees any objects we created for the preconditioner
186:          PetscCallA(PCShellSetDestroy(pc,SampleShellPCDestroy,ierr))

188:       else
189:          PetscCallA(PCSetType(pc,PCJACOBI,ierr))
190:       endif

192: !  Set runtime options, e.g.,
193: !      -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
194: !  These options will override those specified above as long as
195: !  KSPSetFromOptions() is called _after_ any other customization
196: !  routines.

198:       PetscCallA(KSPSetFromOptions(ksp,ierr))

200: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
201: !                      Solve the linear system
202: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

204:       PetscCallA(KSPSolve(ksp,b,x,ierr))

206: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
207: !                     Check solution and clean up
208: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

210: !  Check the error

212:       PetscCallA(VecAXPY(x,neg_one,u,ierr))
213:       PetscCallA(VecNorm(x,NORM_2,norm,ierr))
214:       PetscCallA(KSPGetIterationNumber(ksp,its,ierr))

216:       if (rank .eq. 0) then
217:         if (norm .gt. 1.e-12) then
218:            write(6,100) norm,its
219:         else
220:            write(6,110) its
221:         endif
222:       endif
223:   100 format('Norm of error ',1pe11.4,' iterations ',i5)
224:   110 format('Norm of error < 1.e-12,iterations ',i5)

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

229:       PetscCallA(KSPDestroy(ksp,ierr))
230:       PetscCallA(VecDestroy(u,ierr))
231:       PetscCallA(VecDestroy(x,ierr))
232:       PetscCallA(VecDestroy(b,ierr))
233:       PetscCallA(MatDestroy(A,ierr))

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

237:       PetscCallA(PetscFinalize(ierr))
238:       end

240: !/***********************************************************************/
241: !/*          Routines for a user-defined shell preconditioner           */
242: !/***********************************************************************/

244: !
245: !   SampleShellPCSetUp - This routine sets up a user-defined
246: !   preconditioner context.
247: !
248: !   Input Parameters:
249: !   pc - preconditioner object
250: !
251: !   Output Parameter:
252: !   ierr  - error code (nonzero if error has been detected)
253: !
254: !   Notes:
255: !   In this example, we define the shell preconditioner to be Jacobi
256: !   method.  Thus, here we create a work vector for storing the reciprocal
257: !   of the diagonal of the preconditioner matrix; this vector is then
258: !   used within the routine SampleShellPCApply().
259: !
260:       subroutine SampleShellPCSetUp(pc,ierr)
261:       use ex15fmodule
262:       implicit none

264:       PC      pc
265:       Mat     pmat
266:       PetscErrorCode ierr

268:       PetscCallA(PCGetOperators(pc,PETSC_NULL_MAT,pmat,ierr))
269:       PetscCallA(MatCreateVecs(pmat,diag,PETSC_NULL_VEC,ierr))
270:       PetscCallA(MatGetDiagonal(pmat,diag,ierr))
271:       PetscCallA(VecReciprocal(diag,ierr))

273:       end

275: ! -------------------------------------------------------------------
276: !
277: !   SampleShellPCApply - This routine demonstrates the use of a
278: !   user-provided preconditioner.
279: !
280: !   Input Parameters:
281: !   pc - preconditioner object
282: !   x - input vector
283: !
284: !   Output Parameters:
285: !   y - preconditioned vector
286: !   ierr  - error code (nonzero if error has been detected)
287: !
288: !   Notes:
289: !   This code implements the Jacobi preconditioner, merely as an
290: !   example of working with a PCSHELL.  Note that the Jacobi method
291: !   is already provided within PETSc.
292: !
293:       subroutine SampleShellPCApply(pc,x,y,ierr)
294:       use ex15fmodule
295:       implicit none

297:       PC      pc
298:       Vec     x,y
299:       PetscErrorCode ierr

301:       PetscCallA(VecPointwiseMult(y,x,diag,ierr))

303:       end

305: !/***********************************************************************/
306: !/*          Routines for a user-defined shell preconditioner           */
307: !/***********************************************************************/

309: !
310: !   SampleShellPCDestroy - This routine destroys (frees the memory of) any
311: !      objects we made for the preconditioner
312: !
313: !   Input Parameters:
314: !   pc - for this example we use the actual PC as our shell context
315: !
316: !   Output Parameter:
317: !   ierr  - error code (nonzero if error has been detected)
318: !

320:       subroutine SampleShellPCDestroy(pc,ierr)
321:       use ex15fmodule
322:       implicit none

324:       PC      pc
325:       PetscErrorCode ierr

327: !  Normally we would recommend storing all the work data (like diag) in
328: !  the context set with PCShellSetContext()

330:       PetscCallA(VecDestroy(diag,ierr))

332:       end

334: !
335: !/*TEST
336: !
337: !   test:
338: !      nsize: 2
339: !      args: -ksp_view -user_defined_pc -ksp_gmres_cgs_refinement_type refine_always
340: !
341: !TEST*/