Actual source code: ex15f.F
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: ! Program usage: mpirun ex15f [-help] [all PETSc options]
7: !
8: !/*T
9: ! Concepts: KSP^basic parallel example
10: ! Concepts: PC^setting a user-defined shell preconditioner
11: ! Processors: n
12: !T*/
13: !
14: ! -------------------------------------------------------------------------
16: program main
17: implicit none
19: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
20: ! Include files
21: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
22: !
23: ! petsc.h - base PETSc routines petscvec.h - vectors
24: ! petscsys.h - system routines petscmat.h - matrices
25: ! petscksp.h - Krylov subspace methods petscpc.h - preconditioners
27: #include include/finclude/petsc.h
28: #include include/finclude/petscvec.h
29: #include include/finclude/petscmat.h
30: #include include/finclude/petscpc.h
31: #include include/finclude/petscksp.h
33: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
34: ! Variable declarations
35: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
36: !
37: ! Variables:
38: ! ksp - linear solver context
39: ! ksp - Krylov subspace method context
40: ! pc - preconditioner context
41: ! x, b, u - approx solution, right-hand-side, exact solution vectors
42: ! A - matrix that defines linear system
43: ! its - iterations for convergence
44: ! norm - norm of solution error
46: Vec x,b,u
47: Mat A
48: PC pc
49: KSP ksp
50: PetscScalar v,one,neg_one
51: double precision norm,tol
52: PetscErrorCode ierr
53: PetscInt i,j,II,JJ,Istart,Iend,m,n,i1
54: PetscInt its
55: PetscMPIInt rank
56: PetscTruth user_defined_pc,flg
58: ! Note: Any user-defined Fortran routines MUST be declared as external.
60: external SampleShellPCSetUp, SampleShellPCApply
62: ! Common block to store data for user-provided preconditioner
63: common /myshellpc/ diag
64: Vec diag
66: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
67: ! Beginning of program
68: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
70: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
71: one = 1.0
72: neg_one = -1.0
73: i1 = 1
74: m = 8
75: n = 7
76: call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-m',m,flg,ierr)
77: call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
78: call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
80: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
81: ! Compute the matrix and right-hand-side vector that define
82: ! the linear system, Ax = b.
83: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
85: ! Create parallel matrix, specifying only its global dimensions.
86: ! When using MatCreate(), the matrix format can be specified at
87: ! runtime. Also, the parallel partitioning of the matrix is
88: ! determined by PETSc at runtime.
90: call MatCreate(PETSC_COMM_WORLD,A,ierr)
91: call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr)
92: call MatSetFromOptions(A,ierr)
94: ! Currently, all PETSc parallel matrix formats are partitioned by
95: ! contiguous chunks of rows across the processors. Determine which
96: ! rows of the matrix are locally owned.
98: call MatGetOwnershipRange(A,Istart,Iend,ierr)
100: ! Set matrix elements for the 2-D, five-point stencil in parallel.
101: ! - Each processor needs to insert only elements that it owns
102: ! locally (but any non-local elements will be sent to the
103: ! appropriate processor during matrix assembly).
104: ! - Always specify global row and columns of matrix entries.
105: ! - Note that MatSetValues() uses 0-based row and column numbers
106: ! in Fortran as well as in C.
108: do 10, II=Istart,Iend-1
109: v = -1.0
110: i = II/n
111: j = II - i*n
112: if (i.gt.0) then
113: JJ = II - n
114: call MatSetValues(A,i1,II,i1,JJ,v,ADD_VALUES,ierr)
115: endif
116: if (i.lt.m-1) then
117: JJ = II + n
118: call MatSetValues(A,i1,II,i1,JJ,v,ADD_VALUES,ierr)
119: endif
120: if (j.gt.0) then
121: JJ = II - 1
122: call MatSetValues(A,i1,II,i1,JJ,v,ADD_VALUES,ierr)
123: endif
124: if (j.lt.n-1) then
125: JJ = II + 1
126: call MatSetValues(A,i1,II,i1,JJ,v,ADD_VALUES,ierr)
127: endif
128: v = 4.0
129: call MatSetValues(A,i1,II,i1,II,v,ADD_VALUES,ierr)
130: 10 continue
132: ! Assemble matrix, using the 2-step process:
133: ! MatAssemblyBegin(), MatAssemblyEnd()
134: ! Computations can be done while messages are in transition,
135: ! by placing code between these two statements.
137: call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
138: call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
140: ! Create parallel vectors.
141: ! - Here, the parallel partitioning of the vector is determined by
142: ! PETSc at runtime. We could also specify the local dimensions
143: ! if desired -- or use the more general routine VecCreate().
144: ! - When solving a linear system, the vectors and matrices MUST
145: ! be partitioned accordingly. PETSc automatically generates
146: ! appropriately partitioned matrices and vectors when MatCreate()
147: ! and VecCreate() are used with the same communicator.
148: ! - Note: We form 1 vector from scratch and then duplicate as needed.
150: call VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,m*n,u,ierr)
151: call VecDuplicate(u,b,ierr)
152: call VecDuplicate(b,x,ierr)
154: ! Set exact solution; then compute right-hand-side vector.
156: call VecSet(u,one,ierr)
157: call MatMult(A,u,b,ierr)
159: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: ! Create the linear solver and set various options
161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163: ! Create linear solver context
165: call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)
167: ! Set operators. Here the matrix that defines the linear system
168: ! also serves as the preconditioning matrix.
170: call KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN,ierr)
172: ! Set linear solver defaults for this problem (optional).
173: ! - By extracting the KSP and PC contexts from the KSP context,
174: ! we can then directly directly call any KSP and PC routines
175: ! to set various options.
177: call KSPGetPC(ksp,pc,ierr)
178: tol = 1.e-7
179: call KSPSetTolerances(ksp,tol,PETSC_DEFAULT_DOUBLE_PRECISION, &
180: & PETSC_DEFAULT_DOUBLE_PRECISION,PETSC_DEFAULT_INTEGER,ierr)
182: !
183: ! Set a user-defined shell preconditioner if desired
184: !
185: call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-user_defined_pc', &
186: & user_defined_pc,ierr)
188: if (user_defined_pc .eq. 1) then
190: ! (Required) Indicate to PETSc that we are using a shell preconditioner
191: call PCSetType(pc,PCSHELL,ierr)
193: ! (Required) Set the user-defined routine for applying the preconditioner
194: call PCShellSetApply(pc,SampleShellPCApply,ierr)
196: ! (Optional) Do any setup required for the preconditioner
197: call SampleShellPCSetUp(A,x,ierr)
199: else
200: call PCSetType(pc,PCJACOBI,ierr)
201: endif
203: ! Set runtime options, e.g.,
204: ! -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
205: ! These options will override those specified above as long as
206: ! KSPSetFromOptions() is called _after_ any other customization
207: ! routines.
209: call KSPSetFromOptions(ksp,ierr)
211: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
212: ! Solve the linear system
213: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
215: call KSPSolve(ksp,b,x,ierr)
217: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
218: ! Check solution and clean up
219: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
221: ! Check the error
223: call VecAXPY(x,neg_one,u,ierr)
224: call VecNorm(x,NORM_2,norm,ierr)
225: call KSPGetIterationNumber(ksp,its,ierr)
227: if (rank .eq. 0) then
228: if (norm .gt. 1.e-12) then
229: write(6,100) norm,its
230: else
231: write(6,110) its
232: endif
233: endif
234: 100 format('Norm of error ',1pe10.4,' iterations ',i5)
235: 110 format('Norm of error < 1.e-12,iterations ',i5)
237: ! Free work space. All PETSc objects should be destroyed when they
238: ! are no longer needed.
240: call KSPDestroy(ksp,ierr)
241: call VecDestroy(u,ierr)
242: call VecDestroy(x,ierr)
243: call VecDestroy(b,ierr)
244: call MatDestroy(A,ierr)
245: if (user_defined_pc .eq. 1) then
246: call VecDestroy(diag,ierr)
247: endif
250: ! Always call PetscFinalize() before exiting a program.
252: call PetscFinalize(ierr)
253: end
255: !/***********************************************************************/
256: !/* Routines for a user-defined shell preconditioner */
257: !/***********************************************************************/
259: !
260: ! SampleShellPCSetUp - This routine sets up a user-defined
261: ! preconditioner context.
262: !
263: ! Input Parameters:
264: ! pmat - preconditioner matrix
265: ! x - vector
266: !
267: ! Output Parameter:
268: ! ierr - error code (nonzero if error has been detected)
269: !
270: ! Notes:
271: ! In this example, we define the shell preconditioner to be Jacobi
272: ! method. Thus, here we create a work vector for storing the reciprocal
273: ! of the diagonal of the preconditioner matrix; this vector is then
274: ! used within the routine SampleShellPCApply().
275: !
276: subroutine SampleShellPCSetUp(pmat,x,ierr)
278: implicit none
280: #include include/finclude/petsc.h
281: #include include/finclude/petscvec.h
282: #include include/finclude/petscmat.h
284: Vec x
285: Mat pmat
286: integer ierr
288: ! Common block to store data for user-provided preconditioner
289: common /myshellpc/ diag
290: Vec diag
292: call VecDuplicate(x,diag,ierr)
293: call MatGetDiagonal(pmat,diag,ierr)
294: call VecReciprocal(diag,ierr)
296: end
298: ! -------------------------------------------------------------------
299: !
300: ! SampleShellPCApply - This routine demonstrates the use of a
301: ! user-provided preconditioner.
302: !
303: ! Input Parameters:
304: ! dummy - optional user-defined context, not used here
305: ! x - input vector
306: !
307: ! Output Parameters:
308: ! y - preconditioned vector
309: ! ierr - error code (nonzero if error has been detected)
310: !
311: ! Notes:
312: ! This code implements the Jacobi preconditioner, merely as an
313: ! example of working with a PCSHELL. Note that the Jacobi method
314: ! is already provided within PETSc.
315: !
316: subroutine SampleShellPCApply(dummy,x,y,ierr)
318: implicit none
320: #include include/finclude/petsc.h
321: #include include/finclude/petscvec.h
323: Vec x,y
324: integer dummy,ierr
326: ! Common block to store data for user-provided preconditioner
327: common /myshellpc/ diag
328: Vec diag
330: call VecPointwiseMult(y,x,diag,ierr)
332: end