LegendreEvalAll

Evaluate Legendre polynomials from order = 0 to n at single or several points.

Interface 1

܀ Interface

INTERFACE
  MODULE PURE FUNCTION LegendreEvalAll(n, x) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! Highest order of polynomial.
    !! Polynomials from 0 to n will be computed.
    REAL(DFP), INTENT(IN) :: x
    !! Point of evaluation, $x \in [-1, 1]$
    REAL(DFP) :: ans(n + 1)
    !! Evaluate Legendre polynomial of order = 0 to n (total n+1)
    !! at point x
  END FUNCTION LegendreEvalAll
END INTERFACE

️܀ See example

This example shows the usage of LegendreEvalAll method.

This routine evaluates Legendre polynomial upto order n, for many points

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: ans( :, : ), x( : )
  type(string) :: astr
  x = [-1.0, 0.0, 1.0]
  n = 3
  ans= LegendreEvalAll( n=n, x=x )
  astr = MdEncode( ans )
  call display( astr%chars(), "" )
end program main

P0	P1	P2	P3
1	-1	1	-1
1	0	-0.5	-0
1	1	1	1

↢

Interface 2

܀ Interface

INTERFACE
  MODULE PURE FUNCTION LegendreEvalAll(n, x) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! Highest order of polynomial.
    !! Polynomials from 0 to n will be computed.
    REAL(DFP), INTENT(IN) :: x(:)
    !! number of points, SIZE(x)=M
    REAL(DFP) :: ans(SIZE(x), n + 1)
    !! shape (M,N+1)
  END FUNCTION LegendreEvalAll
END INTERFACE

️܀ See example

This example shows the usage of LegendreEvalAll method.

This routine evaluates Legendre polynomial upto order n, for many points

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: ans( : ), x
  type(string) :: astr
  x = -1.0_DFP
  n = 3
  ans= LegendreEvalAll( n=n, x=x )
  astr = MdEncode( ans )
  call display( astr%chars(), "" )
end program main

P0	P1	P2	P3
1	-1	1	-1

↢