UltrasphericalEvalAll

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

Interface 1

܀ Interface

INTERFACE
  MODULE PURE FUNCTION UltrasphericalEvalAll(n, lambda, x) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of polynomial
    REAL(DFP), INTENT(IN) :: lambda
    !! lambda should be greater than -0.5
    REAL(DFP), INTENT(IN) :: x
    REAL(DFP) :: ans(n + 1)
    !! Evaluate Ultraspherical polynomial of order = 0 to n (total n+1)
    !! at point x
  END FUNCTION UltrasphericalEvalAll
END INTERFACE

️܀ See example

This example shows the usage of UltrasphericalEvalAll method.

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

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: ans( :, : ), x( : )
  real( dfp ), parameter :: lambda=0.5_DFP
  type(string) :: astr

  x = [-1.0, -0.5, 0.0, 0.5, 1.0]
  n = 5; call callme

See results

P0	P1	P2	P3	P4	P5
1	-1	1	-1	1	-1
1	-0.5	-0.125	0.4375	-0.28906	-8.98438E-02
1	0	-0.5	-0	0.375	0
1	0.5	-0.125	-0.4375	-0.28906	8.98438E-02
1	1	1	1	1	1

  contains
  subroutine callme
    ans= UltrasphericalEvalAll( n=n, x=x, lambda=lambda )
    astr = MdEncode( ans )
    call display( astr%chars(), "" )
  end subroutine callme

end program main

↢

Interface 2

܀ Interface

INTERFACE
  MODULE PURE FUNCTION UltrasphericalEvalAll(n, lambda, x) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of polynomial
    REAL(DFP), INTENT(IN) :: lambda
    !! lambda should be greater than -0.5
    REAL(DFP), INTENT(IN) :: x(:)
    REAL(DFP) :: ans(SIZE(x), n + 1)
    !! Evaluate Ultraspherical polynomial of order = 0 to n (total n+1)
    !! at point x
  END FUNCTION UltrasphericalEvalAll
END INTERFACE

️܀ See example

This example shows the usage of UltrasphericalEvalAll method.

This routine evaluates Ultraspherical polynomial upto order n, at a single point

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: ans( : ), x
  real( dfp ), parameter :: lambda=0.5_DFP
  type(string) :: astr

  x = 0.5_DFP
  n = 5; call callme

See results

P0	P1	P2	P3	P4	P5
1	0.5	-0.125	-0.4375	-0.28906	8.98438E-02

  contains
  subroutine callme
    ans= UltrasphericalEvalAll( n=n, x=x, lambda=lambda )
    astr = MdEncode( ans )
    call display( astr%chars(), "" )
  end subroutine callme

end program main

↢