LegendreEvalSum

Evaluate the finite sum of Legendre polynomials at point x.

Interface 1

܀ Interface

INTERFACE
  MODULE PURE FUNCTION LegendreEvalSum(n, x, coeff) &
    & RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of polynomial
    REAL(DFP), INTENT(IN) :: x
    !! point
    REAL(DFP), INTENT(IN) :: coeff(0:n)
    !! Coefficient of finite sum, size = n+1
    REAL(DFP) :: ans
    !! Evaluate Legendre polynomial of order n at point x
  END FUNCTION LegendreEvalSum
END INTERFACE

️܀ See example

This example shows the usage of LegendreEvalSum method.

This routine evaluates the finite sum of the Legendre polynomials of order upto n, at several points.

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: ans(:), x(:), exact(:), &
    & coeff(:)
  real( dfp ), parameter :: tol=1.0E-10
  type(string) :: astr
  n = 3
  x = [-0.5, 0.5, 0.25]
  coeff = [1, 0, 0, 0]
  ans = LegendreEvalSum( n=n, x=x, coeff=coeff )
  exact = LegendreEval( n=0_I4B, x=x )
  call ok( ALL(SOFTEQ(ans, exact, tol )))
  n = 3
  x = [-0.5, 0.5, 0.25]
  coeff = [0, 0, 0, 1]
  ans = LegendreEvalSum( n=n, x=x, coeff=coeff )
  exact = LegendreEval( n=3_I4B, x=x)
  call ok( ALL(SOFTEQ(ans, exact, tol )))
  n = 100
  x = [-0.5, 0.5, 0.25]
  coeff = zeros(n+1, 0.0_DFP)
  coeff( n+1 ) = 1.0_DFP
  ans = LegendreEvalSum( n=n, x=x, coeff=coeff )
  exact = LegendreEval( n=n, x=x )
  call ok( ALL(SOFTEQ(ans, exact, tol )))
end program main

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Interface 2

܀ Interface

INTERFACE
  MODULE PURE FUNCTION LegendreEvalSum(n, x, coeff) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of polynomial
    REAL(DFP), INTENT(IN) :: x(:)
    !! point
    REAL(DFP), INTENT(IN) :: coeff(0:n)
    !! Coefficient of finite sum, size = n+1
    REAL(DFP) :: ans(SIZE(x))
    !! Evaluate Legendre polynomial of order n at point x
  END FUNCTION LegendreEvalSum
END INTERFACE

️܀ See example

See above example.

↢