LobattoEval

Evaluate Lobatto polynomial.

Interface

܀ Interface

INTERFACE
  MODULE PURE FUNCTION LobattoEval(n, x) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    REAL(DFP), INTENT(IN) :: x
    REAL(DFP) :: ans
    !! Evaluate Lobatto polynomial of order n at point x
  END FUNCTION LobattoEval
END INTERFACE

️܀ See example

This example shows the usage of LobattoEval method.

This routine evaluates Lobatto polynomial of order n, at single point

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ) :: ans, x, exact
  real( dfp ), parameter :: tol=1.0E-8

  n = 5
  x = -1.0_DFP; call callme
  exact = (SQRT(9.0/2.0))*(x**2 - 1.0)*(7.0*(x**2)-3.0)*x/8.0_DFP
  call ok( SOFTEQ(ans, exact, tol ))
  x = 0.5_DFP; call callme
  exact = (SQRT(9.0/2.0))*(x**2 - 1.0)*(7.0*(x**2)-3.0)*x/8.0_DFP
  call ok( SOFTEQ(ans, exact, tol ))
  x = +1.0_DFP; call callme
  exact = (SQRT(9.0/2.0))*(x**2 - 1.0)*(7.0*(x**2)-3.0)*x/8.0_DFP
  call ok( SOFTEQ(ans, exact, tol ))

  contains
  subroutine callme
    ans= LobattoEval( n=n, x=x )
  end subroutine callme
end program main

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Interface 2

܀ Interface

INTERFACE
  MODULE PURE FUNCTION LobattoEval(n, x) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    REAL(DFP), INTENT(IN) :: x(:)
    REAL(DFP) :: ans(SIZE(x))
    !! Evaluate Lobatto polynomial of order n at point x
  END FUNCTION LobattoEval
END INTERFACE

️܀ See example

This example shows the usage of LobattoEval method.

This routine evaluates Lobatto polynomial of order n, at several points.

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: ans(:), x(:), exact(:)
  real( dfp ), parameter :: tol=1.0E-08
  type(string) :: astr
  n = 5
  x = [-1.0, 0.5, 1.0]; call callme
  exact = (SQRT(9.0/2.0))*(x**2 - 1.0)*(7.0*(x**2)-3.0)*x/8.0_DFP
  call ok( ALL(SOFTEQ(ans, exact, tol )))
  contains
  subroutine callme
    ans= LobattoEval( n=n, x=x )
  end subroutine callme
end program main

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