JacobiGradientEval

Evaluate gradient of Jacobi polynomials.

Interface 1

INTERFACE
  MODULE PURE FUNCTION JacobiGradientEval(n, alpha, beta, x) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of Jacobi polynomial
    REAL(DFP), INTENT(IN) :: alpha
    !! alpha > -1.0
    REAL(DFP), INTENT(IN) :: beta
    !! beta > -1.0
    REAL(DFP), INTENT(IN) :: x
    !! point
    REAL(DFP) :: ans
    !! Derivative of Jacobi polynomial of order n at point x
  END FUNCTION JacobiGradientEval
END INTERFACE

Interface 2

INTERFACE
  MODULE PURE FUNCTION JacobiGradientEval(n, alpha, beta, x) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    REAL(DFP), INTENT(IN) :: alpha
    REAL(DFP), INTENT(IN) :: beta
    REAL(DFP), INTENT(IN) :: x(:)
    REAL(DFP) :: ans(SIZE(x))
    !! Derivative of Jacobi polynomial of order n at x
  END FUNCTION JacobiGradientEval
END INTERFACE

Examples

️܀ See example

This example shows the usage of JacobiGradientEval method.

In this example $\alpha=\beta=0.0$ (that is, proportional to Legendre polynomial)

program main
  use easifembase
  use easifemclasses
  implicit none
  integer( i4b ) :: n, ii
  real( dfp ) :: exact, ans, x
  real( dfp ), parameter :: alpha=0.0_DFP, beta=0.0_DFP, tol=1.0E-10
  type(string) :: astr

  !!
  n=5
  x = 0.25
  exact = LegendreGradientEval(n=n, x=x)
  ans = JacobiGradientEval(n=n, alpha=alpha, beta=beta, x=x)
  call OK( SOFTEQ( exact, ans, tol), "")
  !!
  n=10
  x = 0.25
  exact = LegendreGradientEval(n=n, x=x)
  ans = JacobiGradientEval(n=n, alpha=alpha, beta=beta, x=x)
  call OK( SOFTEQ( exact, ans, tol), "")
  !!

end program main

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