1: ! Computes the integral of 2*x/(1+x^2) from x=0..1
  2: ! This is equal to the ln(2).

  4: ! Contributed by Mike McCourt <mccomic@iit.edu> and Nathan Johnston <johnnat@iit.edu>
  5: ! Fortran translation by Arko Bhattacharjee <a.bhattacharjee@mpie.de>

  7: program main
  8: #include <petsc/finclude/petscvec.h>
  9:   use petscvec
 10:   implicit none

 12:   PetscErrorCode :: ierr
 13:   PetscMPIInt :: rank, size
 14:   PetscInt   ::  rstart, rend, i, k, N
 15:   PetscInt, parameter   ::   numPoints = 1000000
 16:   PetscScalar  ::  dummy
 17:   PetscScalar, parameter  :: h = 1.0/numPoints
 18:   PetscScalar, pointer, dimension(:)  :: xarray
 19:   PetscScalar :: myResult = 0
 20:   Vec x, xend
 21:   character(len=PETSC_MAX_PATH_LEN) :: output
 22:   PetscInt, parameter :: one = 1

 24:   PetscCallA(PetscInitialize(ierr))

 26:   PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD, rank, ierr))
 27:   PetscCallMPIA(MPI_Comm_size(PETSC_COMM_WORLD, size, ierr))

 29:   ! Create a parallel vector.
 30:   ! Here we set up our x vector which will be given values below.
 31:   ! The xend vector is a dummy vector to find the value of the
 32:   ! elements at the endpoints for use in the trapezoid rule.

 34:   PetscCallA(VecCreate(PETSC_COMM_WORLD, x, ierr))
 35:   PetscCallA(VecSetSizes(x, PETSC_DECIDE, numPoints, ierr))
 36:   PetscCallA(VecSetFromOptions(x, ierr))
 37:   PetscCallA(VecGetSize(x, N, ierr))
 38:   PetscCallA(VecSet(x, myResult, ierr))
 39:   PetscCallA(VecDuplicate(x, xend, ierr))
 40:   myResult = 0.5
 41:   if (rank == 0) then
 42:     i = 0
 43:     PetscCallA(VecSetValues(xend, one, [i], [myResult], INSERT_VALUES, ierr))
 44:   end if

 46:   if (rank == size - 1) then
 47:     i = N - 1
 48:     PetscCallA(VecSetValues(xend, one, [i], [myResult], INSERT_VALUES, ierr))
 49:   end if

 51:   ! Assemble vector, using the 2-step process:
 52:   ! VecAssemblyBegin(), VecAssemblyEnd()
 53:   ! Computations can be done while messages are in transition
 54:   ! by placing code between these two statements.

 56:   PetscCallA(VecAssemblyBegin(xend, ierr))
 57:   PetscCallA(VecAssemblyEnd(xend, ierr))

 59:   ! Set the x vector elements.
 60:   ! i*h will return 0 for i=0 and 1 for i=N-1.
 61:   ! The function evaluated (2x/(1+x^2)) is defined above.
 62:   ! Each evaluation is put into the local array of the vector without message passing.

 64:   PetscCallA(VecGetOwnershipRange(x, rstart, rend, ierr))
 65:   PetscCallA(VecGetArray(x, xarray, ierr))
 66:   k = 1
 67:   do i = rstart, rend - 1
 68:     xarray(k) = real(i)*h
 69:     xarray(k) = func(xarray(k))
 70:     k = k + 1
 71:   end do
 72:   PetscCallA(VecRestoreArray(x, xarray, ierr))

 74:   ! Evaluates the integral.  First the sum of all the points is taken.
 75:   ! That result is multiplied by the step size for the trapezoid rule.
 76:   ! Then half the value at each endpoint is subtracted,
 77:   ! this is part of the composite trapezoid rule.

 79:   PetscCallA(VecSum(x, myResult, ierr))
 80:   myResult = myResult*h
 81:   PetscCallA(VecDot(x, xend, dummy, ierr))
 82:   myResult = myResult - h*dummy

 84:   !Return the value of the integral.

 86:   write (output, '(a,f9.6,a)') 'ln(2) is', real(myResult), '\n'           ! PetscScalar might be complex
 87:   PetscCallA(PetscPrintf(PETSC_COMM_WORLD, trim(output), ierr))
 88:   PetscCallA(VecDestroy(x, ierr))
 89:   PetscCallA(VecDestroy(xend, ierr))

 91:   PetscCallA(PetscFinalize(ierr))

 93: contains

 95:   function func(a)
 96: #include <petsc/finclude/petscvec.h>
 97:     use petscvec

 99:     implicit none
100:     PetscScalar :: func
101:     PetscScalar, INTENT(IN) :: a

103:     func = 2.0*a/(1.0 + a*a)

105:   end function func

107: end program

109: !/*TEST
110: !
111: !     test:
112: !       nsize: 1
113: !       output_file: output/ex18_1.out
114: !
115: !     test:
116: !       nsize: 2
117: !       suffix: 2
118: !       output_file: output/ex18_1.out
119: !
120: !TEST*/