JacobiZeros

Zeros of Jacobi polynomials.

INTERFACE
  MODULE FUNCTION JacobiZeros(n, alpha, beta) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of jacobi polynomial
    REAL(DFP), INTENT(IN) :: alpha
    REAL(DFP), INTENT(IN) :: beta
    REAL(DFP) :: ans(n)
  END FUNCTION JacobiZeros
END INTERFACE

Examples

️܀ See example

This example shows the usage of JacobiZeros method which is defined in [[JacobiPolynomialUtility]] MODULE. This routine returns the zeros of a jacobi polynomial.

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

  n = 1; call callme

See results

x
0

  n = 2; call callme

results

Zeros of J(x), n = 2 alpha=0 beta=0

| -0.57735 | 0.57735 |

  n = 3; call callme

See results

Zeros of J(x), n = 3 alpha=0 beta=0

| -0.7746 | 3.71231E-16 | 0.7746 |

  contains
  subroutine callme
    pt = JacobiZeros( n=n, alpha=alpha, beta=beta )
    msg = "Zeros of J(x), n = " &
        & // tostring( n ) // " alpha="//tostring( alpha ) // &
        & " beta="//tostring( beta )
    call display(msg%chars())
    astr = MdEncode( pt )
    call display( astr%chars(), "" )
  end subroutine

end program main

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