UltrasphericalEval

Evaluate Ultraspherical polynomials of order n at single or several points.

Interface 1

܀ Interface

INTERFACE
  MODULE PURE FUNCTION UltrasphericalEval(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
    !! Evaluate Ultraspherical polynomial of order n at point x
  END FUNCTION UltrasphericalEval
END INTERFACE

Evaluate Ultraspherical polynomial of order n at single points.

• N, the order of polynomial to compute.
• lambda is the polynomial parameter.
• x: the point at which the polynomials are to be evaluated.

️܀ See example

This example shows the usage of UltrasphericalEval method.

This routine evaluates Ultraspherical 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-10, lambda=0.5_DFP

  n = 3
  x = -1.0_DFP; call callme
  exact = 0.5_DFP*(5.0 * x**3 - 3.0*x)
  call ok( SOFTEQ(ans, exact, tol ))
  x = 0.0_DFP; call callme
  exact = 0.5_DFP*(5.0 * x**3 - 3.0*x)
  call ok( SOFTEQ(ans, exact, tol ))
  x = +1.0_DFP; call callme
  exact = 0.5_DFP*(5.0 * x**3 - 3.0*x)
  call ok( SOFTEQ(ans, exact, tol ))

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

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Interface 2

܀ Interface

INTERFACE
  MODULE PURE FUNCTION UltrasphericalEval(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))
    !! Evaluate Ultraspherical polynomial of order n at point x
  END FUNCTION UltrasphericalEval
END INTERFACE

• N is order of polynomial to compute.
• lambda is the polynomial parameter.
• x: the point at which the polynomials are to be evaluated.
• ans, the values of the Ultraspherical polynomials at the several points.

️܀ See example

This example shows the usage of UltrasphericalEval method.

This routine evaluates Ultraspherical 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-10, lambda=0.5_DFP
  type(string) :: astr

  n = 3
  x = [-1.0, -0.5, 0.0, 0.5, 1.0]; call callme
  exact = 0.5_DFP*(5.0 * x**3 - 3.0*x)
  call ok( ALL(SOFTEQ(ans, exact, tol )))

  contains
  subroutine callme
    ans= UltrasphericalEval( n=n, x=x, lambda=lambda )
  end subroutine callme

end program main

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