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ex1f.F
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!
!
! Description: Uses the Newton method to solve a two-variable system.
!
!/*T
! Concepts: SNES^basic uniprocessor example
! Processors: 1
!T*/
!
! -----------------------------------------------------------------------
program main
implicit none
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Include files
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
! The following include statements are generally used in SNES Fortran
! programs:
! petscsys.h - base PETSc routines
! petscvec.h - vectors
! petscmat.h - matrices
! petscksp.h - Krylov subspace methods
! petscpc.h - preconditioners
! petscsnes.h - SNES 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 <finclude/petscsys.h>
#include <finclude/petscvec.h>
#include <finclude/petscmat.h>
#include <finclude/petscksp.h>
#include <finclude/petscpc.h>
#include <finclude/petscsnes.h>
!
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Variable declarations
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
! Variables:
! snes - nonlinear solver
! ksp - linear solver
! pc - preconditioner context
! ksp - Krylov subspace method context
! x, r - solution, residual vectors
! J - Jacobian matrix
! its - iterations for convergence
!
SNES snes
PC pc
KSP ksp
Vec x,r
Mat J
SNESLineSearch linesearch
PetscErrorCode ierr
PetscInt its,i2,i20
PetscMPIInt size,rank
PetscScalar pfive
PetscReal tol
PetscBool setls
! Note: Any user-defined Fortran routines (such as FormJacobian)
! MUST be declared as external.
external FormFunction, FormJacobian, MyLineSearch
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Macro definitions
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
! Macros to make clearer the process of setting values in vectors and
! getting values from vectors. These vectors are used in the routines
! FormFunction() and FormJacobian().
! - The element lx_a(ib) is element ib in the vector x
!
#define lx_a(ib) lx_v(lx_i + (ib))
#define lf_a(ib) lf_v(lf_i + (ib))
!
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Beginning of program
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
if (size .ne. 1) then
if (rank .eq. 0) then
write(6,*) 'This is a uniprocessor example only!'
endif
SETERRQ(PETSC_COMM_SELF,1,' ',ierr)
endif
i2 = 2
i20 = 20
! - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -
! Create nonlinear solver context
! - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -
call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Create matrix and vector data structures; set corresponding routines
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Create vectors for solution and nonlinear function
call VecCreateSeq(PETSC_COMM_SELF,i2,x,ierr)
call VecDuplicate(x,r,ierr)
! Create Jacobian matrix data structure
call MatCreate(PETSC_COMM_SELF,J,ierr)
call MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,i2,i2,ierr)
call MatSetFromOptions(J,ierr)
call MatSetUp(J,ierr)
! Set function evaluation routine and vector
call SNESSetFunction(snes,r,FormFunction,PETSC_NULL_OBJECT,ierr)
! Set Jacobian matrix data structure and Jacobian evaluation routine
call SNESSetJacobian(snes,J,J,FormJacobian,PETSC_NULL_OBJECT, &
& ierr)
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Customize nonlinear solver; set runtime options
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Set linear solver defaults for this problem. By extracting the
! KSP, KSP, and PC contexts from the SNES context, we can then
! directly call any KSP, KSP, and PC routines to set various options.
call SNESGetKSP(snes,ksp,ierr)
call KSPGetPC(ksp,pc,ierr)
call PCSetType(pc,PCNONE,ierr)
tol = 1.e-4
call KSPSetTolerances(ksp,tol,PETSC_DEFAULT_REAL, &
& PETSC_DEFAULT_REAL,i20,ierr)
! Set SNES/KSP/KSP/PC runtime options, e.g.,
! -snes_view -snes_monitor -ksp_type <ksp> -pc_type <pc>
! These options will override those specified above as long as
! SNESSetFromOptions() is called _after_ any other customization
! routines.
call SNESSetFromOptions(snes,ierr)
call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-setls',setls,ierr)
if (setls) then
call SNESGetLineSearch(snes, linesearch, ierr)
call SNESLineSearchSetType(linesearch, "shell", ierr)
call SNESLineSearchShellSetUserFunc(linesearch, MyLineSearch, &
&PETSC_NULL_OBJECT, ierr)
endif
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Evaluate initial guess; then solve nonlinear system
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Note: The user should initialize the vector, x, with the initial guess
! for the nonlinear solver prior to calling SNESSolve(). In particular,
! to employ an initial guess of zero, the user should explicitly set
! this vector to zero by calling VecSet().
pfive = 0.5
call VecSet(x,pfive,ierr)
call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
call SNESGetIterationNumber(snes,its,ierr);
if (rank .eq. 0) then
write(6,100) its
endif
100 format('Number of SNES iterations = ',i5)
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! Free work space. All PETSc objects should be destroyed when they
! are no longer needed.
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
call VecDestroy(x,ierr)
call VecDestroy(r,ierr)
call MatDestroy(J,ierr)
call SNESDestroy(snes,ierr)
call PetscFinalize(ierr)
end
!
! ------------------------------------------------------------------------
!
! FormFunction - Evaluates nonlinear function, F(x).
!
! Input Parameters:
! snes - the SNES context
! x - input vector
! dummy - optional user-defined context (not used here)
!
! Output Parameter:
! f - function vector
!
subroutine FormFunction(snes,x,f,dummy,ierr)
implicit none
#include <finclude/petscsys.h>
#include <finclude/petscvec.h>
#include <finclude/petscsnes.h>
SNES snes
Vec x,f
PetscErrorCode ierr
integer dummy(*)
! Declarations for use with local arrays
PetscScalar lx_v(1),lf_v(1)
PetscOffset lx_i,lf_i
! Get pointers to vector data.
! - For default PETSc vectors, VecGetArray() returns a pointer to
! the data array. Otherwise, the routine is implementation dependent.
! - You MUST call VecRestoreArray() when you no longer need access to
! the array.
! - Note that the Fortran interface to VecGetArray() differs from the
! C version. See the Fortran chapter of the users manual for details.
call VecGetArray(x,lx_v,lx_i,ierr)
call VecGetArray(f,lf_v,lf_i,ierr)
! Compute function
lf_a(1) = lx_a(1)*lx_a(1) &
& + lx_a(1)*lx_a(2) - 3.0
lf_a(2) = lx_a(1)*lx_a(2) &
& + lx_a(2)*lx_a(2) - 6.0
! Restore vectors
call VecRestoreArray(x,lx_v,lx_i,ierr)
call VecRestoreArray(f,lf_v,lf_i,ierr)
return
end
! ---------------------------------------------------------------------
!
! FormJacobian - Evaluates Jacobian matrix.
!
! Input Parameters:
! snes - the SNES context
! x - input vector
! dummy - optional user-defined context (not used here)
!
! Output Parameters:
! A - Jacobian matrix
! B - optionally different preconditioning matrix
! flag - flag indicating matrix structure
!
subroutine FormJacobian(snes,X,jac,B,flag,dummy,ierr)
implicit none
#include <finclude/petscsys.h>
#include <finclude/petscvec.h>
#include <finclude/petscmat.h>
#include <finclude/petscpc.h>
#include <finclude/petscsnes.h>
SNES snes
Vec X
Mat jac,B
MatStructure flag
PetscScalar A(4)
PetscErrorCode ierr
PetscInt idx(2),i2
integer dummy(*)
! Declarations for use with local arrays
PetscScalar lx_v(1)
PetscOffset lx_i
! Get pointer to vector data
i2 = 2
call VecGetArray(x,lx_v,lx_i,ierr)
! Compute Jacobian entries and insert into matrix.
! - Since this is such a small problem, we set all entries for
! the matrix at once.
! - Note that MatSetValues() uses 0-based row and column numbers
! in Fortran as well as in C (as set here in the array idx).
idx(1) = 0
idx(2) = 1
A(1) = 2.0*lx_a(1) + lx_a(2)
A(2) = lx_a(1)
A(3) = lx_a(2)
A(4) = lx_a(1) + 2.0*lx_a(2)
call MatSetValues(jac,i2,idx,i2,idx,A,INSERT_VALUES,ierr)
flag = SAME_NONZERO_PATTERN
! Restore vector
call VecRestoreArray(x,lx_v,lx_i,ierr)
! Assemble matrix
call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
return
end
subroutine MyLineSearch(linesearch, lctx, ierr)
#include <finclude/petscsys.h>
#include <finclude/petscvec.h>
#include <finclude/petscmat.h>
#include <finclude/petscksp.h>
#include <finclude/petscpc.h>
#include <finclude/petscsnes.h>
SNES snes
integer lctx
Vec x, f,g, y, w
PetscReal ynorm,gnorm,xnorm
PetscBool flag
PetscErrorCode ierr
PetscScalar mone
mone = -1.0d0
call SNESLineSearchGetSNES(linesearch, snes, ierr)
call SNESLineSearchGetVecs(linesearch, x, f, y, w, g, ierr)
call VecNorm(y,NORM_2,ynorm,ierr)
call VecAXPY(x,mone,y,ierr)
call SNESComputeFunction(snes,x,f,ierr)
call VecNorm(f,NORM_2,gnorm,ierr)
call VecNorm(x,NORM_2,xnorm,ierr)
call VecNorm(y,NORM_2,ynorm,ierr)
call SNESLineSearchSetNorms(linesearch, xnorm, gnorm, ynorm, &
& ierr)
flag = PETSC_FALSE
return
end