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UltrasphericalQuadrature

This routine returns the Quadrature point of Ultraspherical polynomial.

Here n is the number of quadrature points. Please note it is not the order of Ultraspherical polynomial. The order is decided internally depending upon the quadType

pt and wt should be allocated outside, and length should be n.

Interface​

INTERFACE
  MODULE SUBROUTINE UltrasphericalQuadrature(n, lambda, pt, wt, &
    & quadType, onlyInside)
    INTEGER(I4B), INTENT(IN) :: n
    !! number of quadrature points, the order will be computed as follows
    !! for quadType = Gauss, n is same as order of Ultraspherical polynomial
    !! for quadType = GaussRadauLeft or GaussRadauRight n is order+1
    !! for quadType = GaussLobatto, n = order+2
    REAL(DFP), INTENT(IN) :: lambda
    !! lambda should be greater than -0.5
    REAL(DFP), INTENT(OUT) :: pt(n)
    !! n+1 quadrature points from 1 to n+1
    REAL(DFP), OPTIONAL, INTENT(OUT) :: wt(n)
    !! n+1 weights from 1 to n+1
    INTEGER(I4B), INTENT(IN) :: quadType
    !! Gauss
    !! GaussRadauLeft
    !! GaussRadauRight
    !! GaussLobatto
    LOGICAL(LGT), OPTIONAL, INTENT(IN) :: onlyInside
    !! only inside
  END SUBROUTINE UltrasphericalQuadrature
END INTERFACE