Actual source code: ex62f.F90

  1: !
  2: !   Solves a linear system in parallel with KSP.  Also indicates
  3: !   use of a user-provided preconditioner.  Input parameters include:
  4: !
  5: !

  7: !
  8: !  -------------------------------------------------------------------------
  9:       module ex62fmodule
 10: #include <petsc/finclude/petscksp.h>
 11:       use petscksp
 12:       PC jacobi,sor
 13:       Vec work
 14:       end module

 16:       program main
 17:       use ex62fmodule
 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:       PetscInt i,j,II,JJ,Istart
 40:       PetscInt Iend,m,n,its,ione
 41:       PetscMPIInt rank
 42:       PetscBool  flg
 43:       PetscErrorCode ierr

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

 47:       external SampleShellPCSetUp,SampleShellPCApply

 49: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 50: !                 Beginning of program
 51: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

 63: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 64: !      Compute the matrix and right-hand-side vector that define
 65: !      the linear system, Ax = b.
 66: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

 73:       PetscCallA(MatCreate(PETSC_COMM_WORLD,A,ierr))
 74:       PetscCallA(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr))
 75:       PetscCallA(MatSetFromOptions(A,ierr))
 76:       PetscCallA(MatSetUp(A,ierr))

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

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

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

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

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

121:       PetscCallA(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr))
122:       PetscCallA(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr))

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

134:       PetscCallA(VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,m*n,u,ierr))
135:       PetscCallA(VecDuplicate(u,b,ierr))
136:       PetscCallA(VecDuplicate(b,x,ierr))

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

140:       PetscCallA(VecSet(u,one,ierr))
141:       PetscCallA(MatMult(A,u,b,ierr))

143: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144: !         Create the linear solver and set various options
145: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

147: !  Create linear solver context

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

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

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

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

161:       PetscCallA(KSPGetPC(ksp,pc,ierr))
162:       tol = 1.e-7
163:       PetscCallA(KSPSetTolerances(ksp,tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr))

165: !
166: !  Set a user-defined shell preconditioner
167: !

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

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

175: !  (Optional) Do any setup required for the preconditioner
176: !     Note: if you use PCShellSetSetUp, this will be done for your
177:       PetscCallA(SampleShellPCSetUp(pc,x,ierr))

179: !  Set runtime options, e.g.,
180: !      -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
181: !  These options will override those specified above as long as
182: !  KSPSetFromOptions() is called _after_ any other customization
183: !  routines.

185:       PetscCallA(KSPSetFromOptions(ksp,ierr))

187: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
188: !                      Solve the linear system
189: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

193: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194: !                     Check solution and clean up
195: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

197: !  Check the error

199:       PetscCallA(VecAXPY(x,neg_one,u,ierr))
200:       PetscCallA(VecNorm(x,NORM_2,norm,ierr))
201:       PetscCallA(KSPGetIterationNumber(ksp,its,ierr))

203:       if (rank .eq. 0) then
204:         if (norm .gt. 1.e-12) then
205:            write(6,100) norm,its
206:         else
207:            write(6,110) its
208:         endif
209:       endif
210:   100 format('Norm of error ',1pe11.4,' iterations ',i5)
211:   110 format('Norm of error < 1.e-12,iterations ',i5)

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

216:       PetscCallA(KSPDestroy(ksp,ierr))
217:       PetscCallA(VecDestroy(u,ierr))
218:       PetscCallA(VecDestroy(x,ierr))
219:       PetscCallA(VecDestroy(b,ierr))
220:       PetscCallA(MatDestroy(A,ierr))

222: ! Free up PCShell data
223:       PetscCallA(PCDestroy(sor,ierr))
224:       PetscCallA(PCDestroy(jacobi,ierr))
225:       PetscCallA(VecDestroy(work,ierr))

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

229:       PetscCallA(PetscFinalize(ierr))
230:       end

232: !/***********************************************************************/
233: !/*          Routines for a user-defined shell preconditioner           */
234: !/***********************************************************************/

236: !
237: !   SampleShellPCSetUp - This routine sets up a user-defined
238: !   preconditioner context.
239: !
240: !   Input Parameters:
241: !   pc    - preconditioner object
242: !   x     - vector
243: !
244: !   Output Parameter:
245: !   ierr  - error code (nonzero if error has been detected)
246: !
247: !   Notes:
248: !   In this example, we define the shell preconditioner to be Jacobi
249: !   method.  Thus, here we create a work vector for storing the reciprocal
250: !   of the diagonal of the preconditioner matrix; this vector is then
251: !   used within the routine SampleShellPCApply().
252: !
253:       subroutine SampleShellPCSetUp(pc,x,ierr)
254:       use ex62fmodule
255:       implicit none

257:       PC      pc
258:       Vec     x
259:       Mat     pmat
260:       PetscErrorCode ierr

262:       PetscCallA(PCGetOperators(pc,PETSC_NULL_MAT,pmat,ierr))
263:       PetscCallA(PCCreate(PETSC_COMM_WORLD,jacobi,ierr))
264:       PetscCallA(PCSetType(jacobi,PCJACOBI,ierr))
265:       PetscCallA(PCSetOperators(jacobi,pmat,pmat,ierr))
266:       PetscCallA(PCSetUp(jacobi,ierr))

268:       PetscCallA(PCCreate(PETSC_COMM_WORLD,sor,ierr))
269:       PetscCallA(PCSetType(sor,PCSOR,ierr))
270:       PetscCallA(PCSetOperators(sor,pmat,pmat,ierr))
271: !      PetscCallA(PCSORSetSymmetric(sor,SOR_LOCAL_SYMMETRIC_SWEEP,ierr))
272:       PetscCallA(PCSetUp(sor,ierr))

274:       PetscCallA(VecDuplicate(x,work,ierr))

276:       end

278: ! -------------------------------------------------------------------
279: !
280: !   SampleShellPCApply - This routine demonstrates the use of a
281: !   user-provided preconditioner.
282: !
283: !   Input Parameters:
284: !   pc - preconditioner object
285: !   x - input vector
286: !
287: !   Output Parameters:
288: !   y - preconditioned vector
289: !   ierr  - error code (nonzero if error has been detected)
290: !
291: !   Notes:
292: !   This code implements the Jacobi preconditioner plus the
293: !   SOR preconditioner
294: !
295: ! YOU CAN GET THE EXACT SAME EFFECT WITH THE PCCOMPOSITE preconditioner using
296: ! mpiexec -n 1 ex21f -ksp_monitor -pc_type composite -pc_composite_pcs jacobi,sor -pc_composite_type additive
297: !
298:       subroutine SampleShellPCApply(pc,x,y,ierr)
299:       use ex62fmodule
300:       implicit none

302:       PC      pc
303:       Vec     x,y
304:       PetscErrorCode ierr
305:       PetscScalar  one

307:       one = 1.0
308:       PetscCallA(PCApply(jacobi,x,y,ierr))
309:       PetscCallA(PCApply(sor,x,work,ierr))
310:       PetscCallA(VecAXPY(y,one,work,ierr))

312:       end

314: !/*TEST
315: !
316: !   test:
317: !     requires: !single
318: !
319: !TEST*/