UltrasphericalGradientEvalAll

Evaluate gradient of Ultraspherical polynomials.

Interface 1

܀ Interface

INTERFACE
  MODULE PURE FUNCTION UltrasphericalGradientEvalAll(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:n + 1)
  END FUNCTION UltrasphericalGradientEvalAll
END INTERFACE

️܀ See example

This example shows the usage of UltrasphericalGradientEvalAll method.

This routine evaluates the first derivative of 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, 0.0, 1.0]
  n = 3; call callme

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

end program main

See results

dP0	dP1	dP2	dP3
0	1	-3	6
0	1	0	-1.5
0	1	3	6

↢

Interface 2

܀ Interface

INTERFACE
  MODULE PURE FUNCTION UltrasphericalGradientEvalAll(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), 1:n + 1)
  END FUNCTION UltrasphericalGradientEvalAll
END INTERFACE

️܀ See example

This example shows the usage of UltrasphericalGradientEvalAll 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_DFP
  n = 3; call callme

  contains
  subroutine callme
    ans= UltrasphericalGradientEvalAll( n=n, x=x, &
      & lambda=lambda )
    astr = MdEncode( ans )
    call display( astr%chars(), "" )
  end subroutine callme
end program main

See results

P0	P1	P2	P3
0	1	-3	6

↢