JacobiEvalAll

Evaluate Jacobi polynomials from order = 0 to n at single or several points.

Interface 1

INTERFACE
  MODULE PURE FUNCTION JacobiEvalAll(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(n + 1)
    !! Evaluate Jacobi polynomial of order = 0 to n (total n+1)
    !! at point x
  END FUNCTION JacobiEvalAll
END INTERFACE

Evaluate Jacobi polynomials from order = 0 to n at single points

• N, the highest order polynomial to compute. Note that polynomials 0 through N will be computed.
• alpha, beta are parameters
• x: the point at which the polynomials are to be evaluated.
• ans(1:N+1), the values of the first N+1 Jacobi polynomials at x

Interface 2

INTERFACE
  MODULE PURE FUNCTION JacobiEvalAll(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)
    !! Evaluate Jacobi polynomial of order = 0 to n (total n+1)
    !! at point x
  END FUNCTION JacobiEvalAll
END INTERFACE

Evaluate Jacobi polynomials from order = 0 to n at several points

• N, the highest order polynomial to compute. Note that polynomials 0 through N will be computed.
• alpha, beta are parameters
• x: the point at which the polynomials are to be evaluated.
• ans(M,1:N+1), the values of the first N+1 Jacobi polynomials at the point

Examples

️܀ See example

This example shows the usage of JacobiEvalAll method. This routine evaluates Jacobi polynomial upto order n, for many points.

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

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: ans( :, : ), x( : )
  real( dfp ), parameter :: alpha=0.0_DFP, beta=0.0_DFP
  type(string) :: astr

  x = [-1.0, 0.0, 1.0]
  n = 3; call callme

See results

P0	P1	P2	P3
1	-1	1	-1
1	0	-0.5	-0
1	1	1	1

  contains
  subroutine callme
    ans= JacobiEvalAll( n=n, alpha=alpha, beta=beta, x=x )
    astr = MdEncode( ans )
    call display( astr%chars(), "" )
  end subroutine callme

end program main

↢

️܀ See example

This example shows the usage of JacobiEvalAll method. This routine evaluates Jacobi polynomial upto order n, for many points

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

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: ans( : ), x
  real( dfp ), parameter :: alpha=0.0_DFP, beta=0.0_DFP
  type(string) :: astr

  x = -1.0_DFP
  n = 3; call callme

See results

P0	P1	P2	P3
1	-1	1	-1

  contains
  subroutine callme
    ans= JacobiEvalAll( n=n, alpha=alpha, beta=beta, x=x )
    astr = MdEncode( ans )
    call display( astr%chars(), "" )
  end subroutine callme

end program main

↢