Actual source code: ex2f.F
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: ! Program usage: mpirun -np <procs> ex2f [-help] [all PETSc options]
6: !
7: !/*T
8: ! Concepts: KSP^basic parallel example
9: ! Concepts: KSP^setting a user-defined monitoring routine
10: ! Processors: n
11: !T*/
12: !
13: ! -----------------------------------------------------------------------
15: program main
16: implicit none
18: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
19: ! Include files
20: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
21: !
22: ! This program uses CPP for preprocessing, as indicated by the use of
23: ! PETSc include files in the directory petsc/include/finclude. This
24: ! convention enables use of the CPP preprocessor, which allows the use
25: ! of the #include statements that define PETSc objects and variables.
26: !
27: ! Use of the conventional Fortran include statements is also supported
28: ! In this case, the PETsc include files are located in the directory
29: ! petsc/include/foldinclude.
30: !
31: ! Since one must be very careful to include each file no more than once
32: ! in a Fortran routine, application programmers must exlicitly list
33: ! each file needed for the various PETSc components within their
34: ! program (unlike the C/C++ interface).
35: !
36: ! See the Fortran section of the PETSc users manual for details.
37: !
38: ! The following include statements are required for KSP Fortran programs:
39: ! petsc.h - base PETSc routines
40: ! petscvec.h - vectors
41: ! petscmat.h - matrices
42: ! petscpc.h - preconditioners
43: ! petscksp.h - Krylov subspace methods
44: ! Include the following to use PETSc random numbers:
45: ! petscsys.h - system routines
46: ! Additional include statements may be needed if using additional
47: ! PETSc routines in a Fortran program, e.g.,
48: ! petscviewer.h - viewers
49: ! petscis.h - index sets
50: !
51: #include include/finclude/petsc.h
52: #include include/finclude/petscvec.h
53: #include include/finclude/petscmat.h
54: #include include/finclude/petscpc.h
55: #include include/finclude/petscksp.h
56: #include include/finclude/petscsys.h
57: !
58: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
59: ! Variable declarations
60: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
61: !
62: ! Variables:
63: ! ksp - linear solver context
64: ! ksp - Krylov subspace method context
65: ! pc - preconditioner context
66: ! x, b, u - approx solution, right-hand-side, exact solution vectors
67: ! A - matrix that defines linear system
68: ! its - iterations for convergence
69: ! norm - norm of error in solution
70: ! rctx - random number generator context
71: !
72: ! Note that vectors are declared as PETSc "Vec" objects. These vectors
73: ! are mathematical objects that contain more than just an array of
74: ! double precision numbers. I.e., vectors in PETSc are not just
75: ! double precision x(*).
76: ! However, local vector data can be easily accessed via VecGetArray().
77: ! See the Fortran section of the PETSc users manual for details.
78: !
79: double precision norm
80: PetscInt i,j,II,JJ,m,n,its,Istart,Iend,ione
81: PetscErrorCode ierr
82: PetscMPIInt rank,size
83: PetscTruth flg
84: PetscScalar v,one,neg_one
85: Vec x,b,u
86: Mat A
87: KSP ksp
88: PetscRandom rctx
90: ! These variables are not currently used.
91: ! PC pc
92: ! PCType ptype
93: ! double precision tol
96: ! Note: Any user-defined Fortran routines (such as MyKSPMonitor)
97: ! MUST be declared as external.
99: external MyKSPMonitor,MyKSPConverged
101: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102: ! Beginning of program
103: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
105: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
106: m = 3
107: n = 3
108: one = 1.0
109: neg_one = -1.0
110: ione = 1
111: call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-m',m,flg,ierr)
112: call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
113: call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
114: call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
116: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
117: ! Compute the matrix and right-hand-side vector that define
118: ! the linear system, Ax = b.
119: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
121: ! Create parallel matrix, specifying only its global dimensions.
122: ! When using MatCreate(), the matrix format can be specified at
123: ! runtime. Also, the parallel partitioning of the matrix is
124: ! determined by PETSc at runtime.
126: call MatCreate(PETSC_COMM_WORLD,A,ierr)
127: call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr)
128: call MatSetFromOptions(A,ierr)
130: ! Currently, all PETSc parallel matrix formats are partitioned by
131: ! contiguous chunks of rows across the processors. Determine which
132: ! rows of the matrix are locally owned.
134: call MatGetOwnershipRange(A,Istart,Iend,ierr)
136: ! Set matrix elements for the 2-D, five-point stencil in parallel.
137: ! - Each processor needs to insert only elements that it owns
138: ! locally (but any non-local elements will be sent to the
139: ! appropriate processor during matrix assembly).
140: ! - Always specify global row and columns of matrix entries.
141: ! - Note that MatSetValues() uses 0-based row and column numbers
142: ! in Fortran as well as in C.
144: ! Note: this uses the less common natural ordering that orders first
145: ! all the unknowns for x = h then for x = 2h etc; Hence you see JH = II +- n
146: ! instead of JJ = II +- m as you might expect. The more standard ordering
147: ! would first do all variables for y = h, then y = 2h etc.
149: do 10, II=Istart,Iend-1
150: v = -1.0
151: i = II/n
152: j = II - i*n
153: if (i.gt.0) then
154: JJ = II - n
155: call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
156: endif
157: if (i.lt.m-1) then
158: JJ = II + n
159: call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
160: endif
161: if (j.gt.0) then
162: JJ = II - 1
163: call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
164: endif
165: if (j.lt.n-1) then
166: JJ = II + 1
167: call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
168: endif
169: v = 4.0
170: call MatSetValues(A,ione,II,ione,II,v,INSERT_VALUES,ierr)
171: 10 continue
173: ! Assemble matrix, using the 2-step process:
174: ! MatAssemblyBegin(), MatAssemblyEnd()
175: ! Computations can be done while messages are in transition,
176: ! by placing code between these two statements.
178: call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
179: call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
181: ! Create parallel vectors.
182: ! - Here, the parallel partitioning of the vector is determined by
183: ! PETSc at runtime. We could also specify the local dimensions
184: ! if desired -- or use the more general routine VecCreate().
185: ! - When solving a linear system, the vectors and matrices MUST
186: ! be partitioned accordingly. PETSc automatically generates
187: ! appropriately partitioned matrices and vectors when MatCreate()
188: ! and VecCreate() are used with the same communicator.
189: ! - Note: We form 1 vector from scratch and then duplicate as needed.
191: call VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,m*n,u,ierr)
192: call VecSetFromOptions(u,ierr)
193: call VecDuplicate(u,b,ierr)
194: call VecDuplicate(b,x,ierr)
196: ! Set exact solution; then compute right-hand-side vector.
197: ! By default we use an exact solution of a vector with all
198: ! elements of 1.0; Alternatively, using the runtime option
199: ! -random_sol forms a solution vector with random components.
201: call PetscOptionsHasName(PETSC_NULL_CHARACTER, &
202: & "-random_exact_sol",flg,ierr)
203: if (flg .eq. 1) then
204: call PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT, &
205: & rctx,ierr)
206: call VecSetRandom(rctx,u,ierr)
207: call PetscRandomDestroy(rctx,ierr)
208: else
209: call VecSet(u,one,ierr)
210: endif
211: call MatMult(A,u,b,ierr)
213: ! View the exact solution vector if desired
215: call PetscOptionsHasName(PETSC_NULL_CHARACTER, &
216: & "-view_exact_sol",flg,ierr)
217: if (flg .eq. 1) then
218: call VecView(u,PETSC_VIEWER_STDOUT_WORLD,ierr)
219: endif
221: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
222: ! Create the linear solver and set various options
223: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
225: ! Create linear solver context
227: call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)
229: ! Set operators. Here the matrix that defines the linear system
230: ! also serves as the preconditioning matrix.
232: call KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN,ierr)
234: ! Set linear solver defaults for this problem (optional).
235: ! - By extracting the KSP and PC contexts from the KSP context,
236: ! we can then directly directly call any KSP and PC routines
237: ! to set various options.
238: ! - The following four statements are optional; all of these
239: ! parameters could alternatively be specified at runtime via
240: ! KSPSetFromOptions(). All of these defaults can be
241: ! overridden at runtime, as indicated below.
243: ! We comment out this section of code since the Jacobi
244: ! preconditioner is not a good general default.
246: ! call KSPGetPC(ksp,pc,ierr)
247: ! ptype = PCJACOBI
248: ! call PCSetType(pc,ptype,ierr)
249: ! tol = 1.e-7
250: ! call KSPSetTolerances(ksp,tol,PETSC_DEFAULT_DOUBLE_PRECISION,
251: ! & PETSC_DEFAULT_DOUBLE_PRECISION,PETSC_DEFAULT_INTEGER,ierr)
253: ! Set user-defined monitoring routine if desired
255: call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-my_ksp_monitor', &
256: & flg,ierr)
257: if (flg .eq. 1) then
258: call KSPSetMonitor(ksp,MyKSPMonitor,PETSC_NULL_OBJECT, &
259: & PETSC_NULL_FUNCTION,ierr)
260: endif
263: ! Set runtime options, e.g.,
264: ! -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
265: ! These options will override those specified above as long as
266: ! KSPSetFromOptions() is called _after_ any other customization
267: ! routines.
269: call KSPSetFromOptions(ksp,ierr)
271: ! Set convergence test routine if desired
273: call PetscOptionsHasName(PETSC_NULL_CHARACTER, &
274: & '-my_ksp_convergence',flg,ierr)
275: if (flg .eq. 1) then
276: call KSPSetConvergenceTest(ksp,MyKSPConverged, &
277: & PETSC_NULL_OBJECT,ierr)
278: endif
279: !
280: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
281: ! Solve the linear system
282: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
284: call KSPSolve(ksp,b,x,ierr)
286: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
287: ! Check solution and clean up
288: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
290: ! Check the error
292: call VecAXPY(x,neg_one,u,ierr)
293: call VecNorm(x,NORM_2,norm,ierr)
294: call KSPGetIterationNumber(ksp,its,ierr)
295: if (rank .eq. 0) then
296: if (norm .gt. 1.e-12) then
297: write(6,100) norm,its
298: else
299: write(6,110) its
300: endif
301: endif
302: 100 format('Norm of error ',e10.4,' iterations ',i5)
303: 110 format('Norm of error < 1.e-12,iterations ',i5)
305: ! Free work space. All PETSc objects should be destroyed when they
306: ! are no longer needed.
308: call KSPDestroy(ksp,ierr)
309: call VecDestroy(u,ierr)
310: call VecDestroy(x,ierr)
311: call VecDestroy(b,ierr)
312: call MatDestroy(A,ierr)
314: ! Always call PetscFinalize() before exiting a program. This routine
315: ! - finalizes the PETSc libraries as well as MPI
316: ! - provides summary and diagnostic information if certain runtime
317: ! options are chosen (e.g., -log_summary). See PetscFinalize()
318: ! manpage for more information.
320: call PetscFinalize(ierr)
321: end
323: ! --------------------------------------------------------------
324: !
325: ! MyKSPMonitor - This is a user-defined routine for monitoring
326: ! the KSP iterative solvers.
327: !
328: ! Input Parameters:
329: ! ksp - iterative context
330: ! n - iteration number
331: ! rnorm - 2-norm (preconditioned) residual value (may be estimated)
332: ! dummy - optional user-defined monitor context (unused here)
333: !
334: subroutine MyKSPMonitor(ksp,n,rnorm,dummy,ierr)
336: implicit none
338: #include include/finclude/petsc.h
339: #include include/finclude/petscvec.h
340: #include include/finclude/petscksp.h
342: KSP ksp
343: Vec x
344: PetscErrorCode ierr
345: PetscInt n,dummy
346: PetscMPIInt rank
347: double precision rnorm
349: ! Build the solution vector
351: call KSPBuildSolution(ksp,PETSC_NULL_OBJECT,x,ierr)
353: ! Write the solution vector and residual norm to stdout
354: ! - Note that the parallel viewer PETSC_VIEWER_STDOUT_WORLD
355: ! handles data from multiple processors so that the
356: ! output is not jumbled.
358: call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
359: if (rank .eq. 0) write(6,100) n
360: call VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr)
361: if (rank .eq. 0) write(6,200) n,rnorm
363: 100 format('iteration ',i5,' solution vector:')
364: 200 format('iteration ',i5,' residual norm ',e10.4)
365: 0
366: end
368: ! --------------------------------------------------------------
369: !
370: ! MyKSPConverged - This is a user-defined routine for testing
371: ! convergence of the KSP iterative solvers.
372: !
373: ! Input Parameters:
374: ! ksp - iterative context
375: ! n - iteration number
376: ! rnorm - 2-norm (preconditioned) residual value (may be estimated)
377: ! dummy - optional user-defined monitor context (unused here)
378: !
379: subroutine MyKSPConverged(ksp,n,rnorm,flag,dummy,ierr)
381: implicit none
383: #include include/finclude/petsc.h
384: #include include/finclude/petscvec.h
385: #include include/finclude/petscksp.h
387: KSP ksp
388: PetscErrorCode ierr
389: PetscInt n,dummy
390: KSPConvergedReason flag
391: double precision rnorm
393: if (rnorm .le. .05) then
394: flag = 1
395: else
396: flag = 0
397: endif
398: 0
400: end