Actual source code: ex57f.F90

  1: !
  2: !  Description: Modified from ex2f.F and ex52.c to illustrate how use external packages MUMPS
  3: !               Solves a linear system in parallel with KSP (Fortran code).
  4: !               Also shows how to set a user-defined monitoring routine.
  5: !
  6: ! -----------------------------------------------------------------------

  8:       program main
  9: #include <petsc/finclude/petscksp.h>
 10:       use petscksp
 11:       implicit none

 13: !
 14: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 15: !                   Variable declarations
 16: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 17: !
 18: !  Variables:
 19: !     ksp     - linear solver context
 20: !     ksp      - Krylov subspace method context
 21: !     pc       - preconditioner context
 22: !     x, b, u  - approx solution, right-hand-side, exact solution vectors
 23: !     A        - matrix that defines linear system
 24: !     its      - iterations for convergence
 25: !     norm     - norm of error in solution
 26: !     rctx     - random number generator context
 27: !
 28: !  Note that vectors are declared as PETSc "Vec" objects.  These vectors
 29: !  are mathematical objects that contain more than just an array of
 30: !  double precision numbers. I.e., vectors in PETSc are not just
 31: !        double precision x(*).
 32: !  However, local vector data can be easily accessed via VecGetArray().
 33: !  See the Fortran section of the PETSc users manual for details.
 34: !
 35: #ifdef PETSC_HAVE_MUMPS
 36:       PetscInt        icntl,ival
 37:       Mat             F
 38: #endif
 39:       PC              pc
 40:       PetscReal       norm,zero
 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

 52: !  These variables are not currently used.
 53: !      PC          pc
 54: !      PCType      ptype
 55: !      double precision tol

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

 60:       external MyKSPMonitor,MyKSPConverged

 62: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 63: !                 Beginning of program
 64: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 66:       PetscCallA(PetscInitialize(ierr))
 67:       m = 3
 68:       n = 3
 69:       one  = 1.0
 70:       neg_one = -1.0
 71:       ione    = 1
 72:       zero    = 0.0
 73:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-m',m,flg,ierr))
 74:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n',n,flg,ierr))
 75:       PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr))
 76:       PetscCallMPIA(MPI_Comm_size(PETSC_COMM_WORLD,size,ierr))

 78: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 79: !      Compute the matrix and right-hand-side vector that define
 80: !      the linear system, Ax = b.
 81: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 83: !  Create parallel matrix, specifying only its global dimensions.
 84: !  When using MatCreate(), the matrix format can be specified at
 85: !  runtime. Also, the parallel partitioning of the matrix is
 86: !  determined by PETSc at runtime.

 88:       PetscCallA(MatCreate(PETSC_COMM_WORLD,A,ierr))
 89:       PetscCallA(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr))
 90:       PetscCallA(MatSetFromOptions(A,ierr))
 91:       PetscCallA(MatSetUp(A,ierr))

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

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

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

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

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

138: !   Check if A is symmetric
139:       if (size == 1) then
140:         PetscCallA(MatIsSymmetric(A,zero,flg,ierr))
141:         if (flg .eqv. PETSC_FALSE) then
142:           write(6,120)
143:         endif
144:       endif

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

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

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

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

177: !  View the exact solution vector if desired

179:       PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-view_exact_sol',flg,ierr))
180:       if (flg) then
181:          PetscCallA(VecView(u,PETSC_VIEWER_STDOUT_WORLD,ierr))
182:       endif

184: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185: !         Create the linear solver and set various options
186: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

188: !  Create linear solver context

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

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

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

197:       PetscCallA(KSPSetType(ksp,KSPPREONLY,ierr))
198:       PetscCallA(KSPGetPC(ksp,pc,ierr))
199:       PetscCallA(PCSetType(pc,PCCHOLESKY,ierr))
200: #ifdef PETSC_HAVE_MUMPS
201:       PetscCallA(PCFactorSetMatSolverType(pc,MATSOLVERMUMPS,ierr))
202:       PetscCallA(PCFactorSetUpMatSolverType(pc,ierr))
203:       PetscCallA(PCFactorGetMatrix(pc,F,ierr))
204:       PetscCallA(KSPSetFromOptions(ksp,ierr))
205:       icntl = 7; ival = 2;
206:       PetscCallA(MatMumpsSetIcntl(F,icntl,ival,ierr))
207: #endif

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

215:       PetscCallA(KSPSetFromOptions(ksp,ierr))

217: !  Set convergence test routine if desired

219:       PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_ksp_convergence',flg,ierr))
220:       if (flg) then
221:         PetscCallA(KSPSetConvergenceTest(ksp,MyKSPConverged,0,PETSC_NULL_FUNCTION,ierr))
222:       endif
223: !
224: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
225: !                      Solve the linear system
226: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

230: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
231: !                     Check solution and clean up
232: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

234: !  Check the error
235:       PetscCallA(VecAXPY(x,neg_one,u,ierr))
236:       PetscCallA(VecNorm(x,NORM_2,norm,ierr))
237:       PetscCallA(KSPGetIterationNumber(ksp,its,ierr))
238:       if (rank .eq. 0) then
239:          write(6,100) norm,its
240:       endif
241:   100 format('Norm of error ',e11.4,' iterations ',i5)
242:   120 format('Matrix A is non-symmetric ')

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

247:       PetscCallA(KSPDestroy(ksp,ierr))
248:       PetscCallA(VecDestroy(u,ierr))
249:       PetscCallA(VecDestroy(x,ierr))
250:       PetscCallA(VecDestroy(b,ierr))
251:       PetscCallA(MatDestroy(A,ierr))

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

259:       PetscCallA(PetscFinalize(ierr))
260:       end

262: ! --------------------------------------------------------------
263: !
264: !  MyKSPMonitor - This is a user-defined routine for monitoring
265: !  the KSP iterative solvers.
266: !
267: !  Input Parameters:
268: !    ksp   - iterative context
269: !    n     - iteration number
270: !    rnorm - 2-norm (preconditioned) residual value (may be estimated)
271: !    dummy - optional user-defined monitor context (unused here)
272: !
273:       subroutine MyKSPMonitor(ksp,n,rnorm,dummy,ierr)
274:       use petscksp
275:       implicit none

277:       KSP              ksp
278:       Vec              x
279:       PetscErrorCode ierr
280:       PetscInt n,dummy
281:       PetscMPIInt rank
282:       PetscReal rnorm

284: !  Build the solution vector

286:       PetscCallA(KSPBuildSolution(ksp,PETSC_NULL_VEC,x,ierr))

288: !  Write the solution vector and residual norm to stdout
289: !   - Note that the parallel viewer PETSC_VIEWER_STDOUT_WORLD
290: !     handles data from multiple processors so that the
291: !     output is not jumbled.

293:       PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr))
294:       if (rank .eq. 0) write(6,100) n
295:       PetscCallA(VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr))
296:       if (rank .eq. 0) write(6,200) n,rnorm

298:  100  format('iteration ',i5,' solution vector:')
299:  200  format('iteration ',i5,' residual norm ',e11.4)
300:       0
301:       end

303: ! --------------------------------------------------------------
304: !
305: !  MyKSPConverged - This is a user-defined routine for testing
306: !  convergence of the KSP iterative solvers.
307: !
308: !  Input Parameters:
309: !    ksp   - iterative context
310: !    n     - iteration number
311: !    rnorm - 2-norm (preconditioned) residual value (may be estimated)
312: !    dummy - optional user-defined monitor context (unused here)
313: !
314:       subroutine MyKSPConverged(ksp,n,rnorm,flag,dummy,ierr)
315:       use petscksp
316:       implicit none

318:       KSP              ksp
319:       PetscErrorCode ierr
320:       PetscInt n,dummy
321:       KSPConvergedReason flag
322:       PetscReal rnorm

324:       if (rnorm .le. .05) then
325:         flag = 1
326:       else
327:         flag = 0
328:       endif
329:       0

331:       end

333: !/*TEST
334: !
335: !     test:
336: !
337: !TEST*/