UltrasphericalGradientEval

Evaluate gradient of Ultraspherical polynomials.

Interface 1

܀ Interface

INTERFACE
  MODULE PURE FUNCTION UltrasphericalGradientEval(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
  END FUNCTION UltrasphericalGradientEval
END INTERFACE

️܀ See example

This example shows the usage of UltrasphericalGradientEval method.

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*(3*5.0 * x**2 - 3.0)
  call ok( SOFTEQ(ans, exact, tol ))
  x = 0.0_DFP; call callme
  exact = 0.5_DFP*(3*5.0 * x**2 - 3.0)
  call ok( SOFTEQ(ans, exact, tol ))
  x = +1.0_DFP; call callme
  exact = 0.5_DFP*(3*5.0 * x**2 - 3.0)
  call ok( SOFTEQ(ans, exact, tol ))
  contains
  subroutine callme
    ans= UltrasphericalGradientEval( n=n, x=x, &
      & lambda=lambda )
  end subroutine callme
end program main

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Interface 2

܀ Interface

INTERFACE
  MODULE PURE FUNCTION UltrasphericalGradientEval(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(1:SIZE(x))
  END FUNCTION UltrasphericalGradientEval
END INTERFACE

️܀ See example

This example shows the usage of UltrasphericalGradientEval method.

This routine evaluates gradient of 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, 0.0, 1.0]; call callme
  exact = 0.5_DFP*(3*5.0 * x**2 - 3.0)
  call ok( ALL(SOFTEQ(ans, exact, tol )))
  contains
  subroutine callme
    ans= UltrasphericalGradientEval( n=n, x=x, &
      & lambda=lambda )
  end subroutine callme
end program main

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