JacobiGradientEvalAll

Evaluate gradient of Jacobi polynomials.

Interface 1

INTERFACE
  MODULE PURE FUNCTION JacobiGradientEvalAll(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(n + 1)
    !! Derivative of Jacobi polynomial of order n at point x
  END FUNCTION JacobiGradientEvalAll
END INTERFACE

Interface 2

INTERFACE
  MODULE PURE FUNCTION JacobiGradientEvalAll(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), n + 1)
    !! Derivative of Jacobi polynomial of order n at x
  END FUNCTION JacobiGradientEvalAll
END INTERFACE

Examples

️܀ See example

This example shows the usage of JacobiGradientEvalAll method.

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

Module and classes

program main
  use easifembase
  use easifemclasses
  implicit none
  integer( i4b ) :: n, ii
  real( dfp ), allocatable :: exact(:), ans(:)
  real( dfp ) :: 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 = LegendreGradientEvalAll(n=n, x=x)
  ans = JacobiGradientEvalAll(n=n, alpha=alpha, beta=beta, x=x)
  call OK( ALL(SOFTEQ( exact, ans, tol)), "")
  !!
  n=10
  x = 0.25
  exact = LegendreGradientEvalAll(n=n, x=x)
  ans = JacobiGradientEvalAll(n=n, alpha=alpha, beta=beta, x=x)
  call OK( ALL(SOFTEQ( exact, ans, tol)), "")
  !!

end program main

↢

️܀ See example

This example shows the usage of JacobiGradientEvalAll 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 ), allocatable :: exact(:,:), ans(:,:), x(:)
  real( dfp ), parameter :: alpha=0.0_DFP, beta=0.0_DFP, tol=1.0E-10
  type(string) :: astr

  !!
  n=5
  x = [-0.1, 0.0, 0.1]
  exact = LegendreGradientEvalAll(n=n, x=x)
  ans = JacobiGradientEvalAll(n=n, alpha=alpha, beta=beta, x=x)
  call OK( ALL(SOFTEQ( exact, ans, tol)), "")
  !!
  n=10
  x = [-0.1, 0.0, 0.1]
  exact = LegendreGradientEvalAll(n=n, x=x)
  ans = JacobiGradientEvalAll(n=n, alpha=alpha, beta=beta, x=x)
  call OK( ALL(SOFTEQ( exact, ans, tol)), "")
  !!

end program main

↢