! ! "$Id: ex1f.F,v 1.30 2001/08/07 03:04:00 balay Exp $"; ! ! Description: Solves a tridiagonal linear system with SLES. ! !/*T ! Concepts: SLES^solving a system of linear equations ! Processors: 1 !T*/ ! ----------------------------------------------------------------------- program main implicit none ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Include files ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! ! This program uses CPP for preprocessing, as indicated by the use of ! PETSc include files in the directory petsc/include/finclude. This ! convention enables use of the CPP preprocessor, which allows the use ! of the #include statements that define PETSc objects and variables. ! ! Use of the conventional Fortran include statements is also supported ! In this case, the PETsc include files are located in the directory ! petsc/include/foldinclude. ! ! Since one must be very careful to include each file no more than once ! in a Fortran routine, application programmers must exlicitly list ! each file needed for the various PETSc components within their ! program (unlike the C/C++ interface). ! ! See the Fortran section of the PETSc users manual for details. ! ! The following include statements are required for SLES Fortran programs: ! petsc.h - base PETSc routines ! petscvec.h - vectors ! petscmat.h - matrices ! petscksp.h - Krylov subspace methods ! petscpc.h - preconditioners ! petscsles.h - SLES interface ! Other include statements may be needed if using additional PETSc ! routines in a Fortran program, e.g., ! petscviewer.h - viewers ! petscis.h - index sets ! #include "include/finclude/petsc.h" #include "include/finclude/petscvec.h" #include "include/finclude/petscmat.h" #include "include/finclude/petscksp.h" #include "include/finclude/petscpc.h" #include "include/finclude/petscsles.h" ! ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Variable declarations ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! ! Variables: ! sles - linear solver context ! ksp - Krylov subspace method context ! pc - preconditioner context ! x, b, u - approx solution, right-hand-side, exact solution vectors ! A - matrix that defines linear system ! its - iterations for convergence ! norm - norm of error in solution ! Vec x,b,u Mat A KSP ksp PC pc SLES sles double precision norm,tol integer ierr,i,n,col(3),its,flg,size,rank PetscScalar none,one,value(3) ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Beginning of program ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - call PetscInitialize(PETSC_NULL_CHARACTER,ierr) call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr) if (size .ne. 1) then call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr) if (rank .eq. 0) then write(6,*) 'This is a uniprocessor example only!' endif SETERRQ(1,' ',ierr) endif none = -1.0 one = 1.0 n = 10 call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-n',n,flg,ierr) ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Compute the matrix and right-hand-side vector that define ! the linear system, Ax = b. ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Create matrix. When using MatCreate(), the matrix format can ! be specified at runtime. call MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,A, & & ierr) call MatSetFromOptions(A,ierr) ! Assemble matrix. ! - Note that MatSetValues() uses 0-based row and column numbers ! in Fortran as well as in C (as set here in the array "col"). value(1) = -1.0 value(2) = 2.0 value(3) = -1.0 do 50 i=1,n-2 col(1) = i-1 col(2) = i col(3) = i+1 call MatSetValues(A,1,i,3,col,value,INSERT_VALUES,ierr) 50 continue i = n - 1 col(1) = n - 2 col(2) = n - 1 call MatSetValues(A,1,i,2,col,value,INSERT_VALUES,ierr) i = 0 col(1) = 0 col(2) = 1 value(1) = 2.0 value(2) = -1.0 call MatSetValues(A,1,i,2,col,value,INSERT_VALUES,ierr) call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr) call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr) ! Create vectors. Note that we form 1 vector from scratch and ! then duplicate as needed. call VecCreate(PETSC_COMM_WORLD,x,ierr) call VecSetSizes(x,PETSC_DECIDE,n,ierr) call VecSetFromOptions(x,ierr) call VecDuplicate(x,b,ierr) call VecDuplicate(x,u,ierr) ! Set exact solution; then compute right-hand-side vector. call VecSet(one,u,ierr) call MatMult(A,u,b,ierr) ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Create the linear solver and set various options ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Create linear solver context call SLESCreate(PETSC_COMM_WORLD,sles,ierr) ! Set operators. Here the matrix that defines the linear system ! also serves as the preconditioning matrix. call SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN,ierr) ! Set linear solver defaults for this problem (optional). ! - By extracting the KSP and PC contexts from the SLES context, ! we can then directly directly call any KSP and PC routines ! to set various options. ! - The following four statements are optional; all of these ! parameters could alternatively be specified at runtime via ! SLESSetFromOptions(); call SLESGetKSP(sles,ksp,ierr) call SLESGetPC(sles,pc,ierr) call PCSetType(pc,PCJACOBI,ierr) tol = 1.d-7 call KSPSetTolerances(ksp,tol,PETSC_DEFAULT_DOUBLE_PRECISION, & & PETSC_DEFAULT_DOUBLE_PRECISION,PETSC_DEFAULT_INTEGER,ierr) ! Set runtime options, e.g., ! -ksp_type -pc_type -ksp_monitor -ksp_rtol ! These options will override those specified above as long as ! SLESSetFromOptions() is called _after_ any other customization ! routines. call SLESSetFromOptions(sles,ierr) ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Solve the linear system ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - call SLESSolve(sles,b,x,its,ierr) ! View solver info; we could instead use the option -sles_view call SLESView(sles,PETSC_VIEWER_STDOUT_WORLD,ierr) ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Check solution and clean up ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ! Check the error call VecAXPY(none,u,x,ierr) call VecNorm(x,NORM_2,norm,ierr) if (norm .gt. 1.e-12) then write(6,100) norm,its else write(6,200) its endif 100 format('Norm of error = ',e10.4,', Iterations = ',i5) 200 format('Norm of error < 1.e-12,Iterations = ',i5) ! Free work space. All PETSc objects should be destroyed when they ! are no longer needed. call VecDestroy(x,ierr) call VecDestroy(u,ierr) call VecDestroy(b,ierr) call MatDestroy(A,ierr) call SLESDestroy(sles,ierr) call PetscFinalize(ierr) end