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: !
6: !/*T
7: ! Concepts: KSP^basic parallel example
8: ! Concepts: KSP^setting a user-defined monitoring routine
9: ! Processors: n
10: !T*/
11: !
12: ! -----------------------------------------------------------------------
14: program main
15: #include <petsc/finclude/petscksp.h> 16: use petscksp
17: implicit none
18: #if defined(PETSC_USING_F90) && !defined(PETSC_USE_FORTRANKIND)
19: external PETSC_NULL_FUNCTION
20: external KSPMONITORDEFAULT
21: external PETSCVIEWERANDFORMATDESTROY
22: #endif
23: !
24: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
25: ! Variable declarations
26: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
27: !
28: ! Variables:
29: ! ksp - linear solver context
30: ! ksp - Krylov subspace method context
31: ! pc - preconditioner context
32: ! x, b, u - approx solution, right-hand-side, exact solution vectors
33: ! A - matrix that defines linear system
34: ! its - iterations for convergence
35: ! norm - norm of error in solution
36: ! rctx - random number generator context
37: !
38: ! Note that vectors are declared as PETSc "Vec" objects. These vectors
39: ! are mathematical objects that contain more than just an array of
40: ! double precision numbers. I.e., vectors in PETSc are not just
41: ! double precision x(*).
42: ! However, local vector data can be easily accessed via VecGetArray().
43: ! See the Fortran section of the PETSc users manual for details.
44: !
45: PetscReal norm
46: PetscInt i,j,II,JJ,m,n,its
47: PetscInt Istart,Iend,ione
48: PetscErrorCode ierr
49: PetscMPIInt rank,size
50: PetscBool flg
51: PetscScalar v,one,neg_one
52: Vec x,b,u
53: Mat A
54: KSP ksp
55: PetscRandom rctx
56: PetscViewerAndFormat vf;
58: ! These variables are not currently used.
59: ! PC pc
60: ! PCType ptype
61: ! PetscReal tol
64: ! Note: Any user-defined Fortran routines (such as MyKSPMonitor)
65: ! MUST be declared as external.
67: external MyKSPMonitor,MyKSPConverged
69: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
70: ! Beginning of program
71: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
73: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
74: if (ierr .ne. 0) then
75: print*,'Unable to initialize PETSc'
76: stop
77: endif
78: m = 3
79: n = 3
80: one = 1.0
81: neg_one = -1.0
82: ione = 1
83: call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-m',m,flg,ierr)
84: call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
85: call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
86: call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
88: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
89: ! Compute the matrix and right-hand-side vector that define
90: ! the linear system, Ax = b.
91: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
93: ! Create parallel matrix, specifying only its global dimensions.
94: ! When using MatCreate(), the matrix format can be specified at
95: ! runtime. Also, the parallel partitioning of the matrix is
96: ! determined by PETSc at runtime.
98: call MatCreate(PETSC_COMM_WORLD,A,ierr)
99: call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr)
100: call MatSetFromOptions(A,ierr)
101: call MatSetUp(A,ierr)
103: ! Currently, all PETSc parallel matrix formats are partitioned by
104: ! contiguous chunks of rows across the processors. Determine which
105: ! rows of the matrix are locally owned.
107: call MatGetOwnershipRange(A,Istart,Iend,ierr)
109: ! Set matrix elements for the 2-D, five-point stencil in parallel.
110: ! - Each processor needs to insert only elements that it owns
111: ! locally (but any non-local elements will be sent to the
112: ! appropriate processor during matrix assembly).
113: ! - Always specify global row and columns of matrix entries.
114: ! - Note that MatSetValues() uses 0-based row and column numbers
115: ! in Fortran as well as in C.
117: ! Note: this uses the less common natural ordering that orders first
118: ! all the unknowns for x = h then for x = 2h etc; Hence you see JH = II +- n
119: ! instead of JJ = II +- m as you might expect. The more standard ordering
120: ! would first do all variables for y = h, then y = 2h etc.
122: do 10, II=Istart,Iend-1
123: v = -1.0
124: i = II/n
125: j = II - i*n
126: if (i.gt.0) then
127: JJ = II - n
128: call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
129: endif
130: if (i.lt.m-1) then
131: JJ = II + n
132: call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
133: endif
134: if (j.gt.0) then
135: JJ = II - 1
136: call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
137: endif
138: if (j.lt.n-1) then
139: JJ = II + 1
140: call MatSetValues(A,ione,II,ione,JJ,v,INSERT_VALUES,ierr)
141: endif
142: v = 4.0
143: call MatSetValues(A,ione,II,ione,II,v,INSERT_VALUES,ierr)
144: 10 continue
146: ! Assemble matrix, using the 2-step process:
147: ! MatAssemblyBegin(), MatAssemblyEnd()
148: ! Computations can be done while messages are in transition,
149: ! by placing code between these two statements.
151: call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
152: call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
154: ! Create parallel vectors.
155: ! - Here, the parallel partitioning of the vector is determined by
156: ! PETSc at runtime. We could also specify the local dimensions
157: ! if desired -- or use the more general routine VecCreate().
158: ! - When solving a linear system, the vectors and matrices MUST
159: ! be partitioned accordingly. PETSc automatically generates
160: ! appropriately partitioned matrices and vectors when MatCreate()
161: ! and VecCreate() are used with the same communicator.
162: ! - Note: We form 1 vector from scratch and then duplicate as needed.
164: call VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,m*n,u,ierr)
165: call VecSetFromOptions(u,ierr)
166: call VecDuplicate(u,b,ierr)
167: call VecDuplicate(b,x,ierr)
169: ! Set exact solution; then compute right-hand-side vector.
170: ! By default we use an exact solution of a vector with all
171: ! elements of 1.0; Alternatively, using the runtime option
172: ! -random_sol forms a solution vector with random components.
174: call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-random_exact_sol',flg,ierr)
175: if (flg) then
176: call PetscRandomCreate(PETSC_COMM_WORLD,rctx,ierr)
177: call PetscRandomSetFromOptions(rctx,ierr)
178: call VecSetRandom(u,rctx,ierr)
179: call PetscRandomDestroy(rctx,ierr)
180: else
181: call VecSet(u,one,ierr)
182: endif
183: call MatMult(A,u,b,ierr)
185: ! View the exact solution vector if desired
187: call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-view_exact_sol',flg,ierr)
188: if (flg) then
189: call VecView(u,PETSC_VIEWER_STDOUT_WORLD,ierr)
190: endif
192: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193: ! Create the linear solver and set various options
194: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196: ! Create linear solver context
198: call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)
200: ! Set operators. Here the matrix that defines the linear system
201: ! also serves as the preconditioning matrix.
203: call KSPSetOperators(ksp,A,A,ierr)
205: ! Set linear solver defaults for this problem (optional).
206: ! - By extracting the KSP and PC contexts from the KSP context,
207: ! we can then directly directly call any KSP and PC routines
208: ! to set various options.
209: ! - The following four statements are optional; all of these
210: ! parameters could alternatively be specified at runtime via
211: ! KSPSetFromOptions(). All of these defaults can be
212: ! overridden at runtime, as indicated below.
214: ! We comment out this section of code since the Jacobi
215: ! preconditioner is not a good general default.
217: ! call KSPGetPC(ksp,pc,ierr)
218: ! ptype = PCJACOBI219: ! call PCSetType(pc,ptype,ierr)
220: ! tol = 1.e-7
221: ! call KSPSetTolerances(ksp,tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr)
223: ! Set user-defined monitoring routine if desired
225: call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_ksp_monitor',flg,ierr)
226: if (flg) then
227: call KSPMonitorSet(ksp,MyKSPMonitor,0,PETSC_NULL_FUNCTION,ierr)
228: !
229: ! Also use the default KSP monitor routine showing how it may be used from Fortran
230: !
231: call PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_DEFAULT,vf,ierr)
232: call KSPMonitorSet(ksp,KSPMonitorDefault,vf,PetscViewerAndFormatDestroy,ierr)
233: endif
236: ! Set runtime options, e.g.,
237: ! -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
238: ! These options will override those specified above as long as
239: ! KSPSetFromOptions() is called _after_ any other customization
240: ! routines.
242: call KSPSetFromOptions(ksp,ierr)
244: ! Set convergence test routine if desired
246: call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_ksp_convergence',flg,ierr)
247: if (flg) then
248: call KSPSetConvergenceTest(ksp,MyKSPConverged,0,PETSC_NULL_FUNCTION,ierr)
249: endif
250: !
251: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
252: ! Solve the linear system
253: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
255: call KSPSolve(ksp,b,x,ierr)
257: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
258: ! Check solution and clean up
259: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
261: ! Check the error
262: call VecAXPY(x,neg_one,u,ierr)
263: call VecNorm(x,NORM_2,norm,ierr)
264: call KSPGetIterationNumber(ksp,its,ierr)
265: if (rank .eq. 0) then
266: if (norm .gt. 1.e-12) then
267: write(6,100) norm,its
268: else
269: write(6,110) its
270: endif
271: endif
272: 100 format('Norm of error ',e11.4,' iterations ',i5)
273: 110 format('Norm of error < 1.e-12 iterations ',i5)
275: ! Free work space. All PETSc objects should be destroyed when they
276: ! are no longer needed.
278: call KSPDestroy(ksp,ierr)
279: call VecDestroy(u,ierr)
280: call VecDestroy(x,ierr)
281: call VecDestroy(b,ierr)
282: call MatDestroy(A,ierr)
284: ! Always call PetscFinalize() before exiting a program. This routine
285: ! - finalizes the PETSc libraries as well as MPI
286: ! - provides summary and diagnostic information if certain runtime
287: ! options are chosen (e.g., -log_view). See PetscFinalize()
288: ! manpage for more information.
290: call PetscFinalize(ierr)
291: end
293: ! --------------------------------------------------------------
294: !
295: ! MyKSPMonitor - This is a user-defined routine for monitoring
296: ! the KSP iterative solvers.
297: !
298: ! Input Parameters:
299: ! ksp - iterative context
300: ! n - iteration number
301: ! rnorm - 2-norm (preconditioned) residual value (may be estimated)
302: ! dummy - optional user-defined monitor context (unused here)
303: !
304: subroutine MyKSPMonitor(ksp,n,rnorm,dummy,ierr)
305: use petscksp
306: implicit none
308: KSP ksp
309: Vec x
310: PetscErrorCode ierr
311: PetscInt n,dummy
312: PetscMPIInt rank
313: PetscReal rnorm
315: ! Build the solution vector
316: call KSPBuildSolution(ksp,PETSC_NULL_VEC,x,ierr)
318: ! Write the solution vector and residual norm to stdout
319: ! - Note that the parallel viewer PETSC_VIEWER_STDOUT_WORLD320: ! handles data from multiple processors so that the
321: ! output is not jumbled.
323: call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
324: if (rank .eq. 0) write(6,100) n
325: call VecView(x,PETSC_VIEWER_STDOUT_WORLD,ierr)
326: if (rank .eq. 0) write(6,200) n,rnorm
328: 100 format('iteration ',i5,' solution vector:')
329: 200 format('iteration ',i5,' residual norm ',e11.4)
330: 0
331: end
333: ! --------------------------------------------------------------
334: !
335: ! MyKSPConverged - This is a user-defined routine for testing
336: ! convergence of the KSP iterative solvers.
337: !
338: ! Input Parameters:
339: ! ksp - iterative context
340: ! n - iteration number
341: ! rnorm - 2-norm (preconditioned) residual value (may be estimated)
342: ! dummy - optional user-defined monitor context (unused here)
343: !
344: subroutine MyKSPConverged(ksp,n,rnorm,flag,dummy,ierr)
345: use petscksp
346: implicit none
348: KSP ksp
349: PetscErrorCode ierr
350: PetscInt n,dummy
351: KSPConvergedReason flag
352: PetscReal rnorm
354: if (rnorm .le. .05) then
355: flag = 1
356: else
357: flag = 0
358: endif
359: 0
361: end
363: !/*TEST
364: !
365: ! test:
366: ! nsize: 2
367: ! args: -pc_type jacobi -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
368: !
369: ! test:
370: ! suffix: 2
371: ! nsize: 2
372: ! args: -pc_type jacobi -my_ksp_monitor -ksp_gmres_cgs_refinement_type refine_always
373: !
374: !TEST*/