Skip to main content

EvalallOrthopol

Evaluate orthogonal polynomials.

Interface​

INTERFACE
  MODULE PURE FUNCTION EvalAllOrthopol(n, x, orthopol, alpha, beta, &
    & lambda) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of polynomial
    REAL(DFP), INTENT(IN) :: x(:)
    !! points of evaluation
    INTEGER(I4B), INTENT(IN) :: orthopol
    !! orthogonal polynomial family
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha
    !! alpha1 needed when orthopol1 is "Jacobi"
    REAL(DFP), OPTIONAL, INTENT(IN) :: beta
    !! beta1 is needed when orthopol1 is "Jacobi"
    REAL(DFP), OPTIONAL, INTENT(IN) :: lambda
    !! lambda1 is needed when orthopol1 is "Ultraspherical"
    REAL(DFP) :: ans(SIZE(x), n + 1)
  END FUNCTION EvalAllOrthopol
END INTERFACE
n

n denotes the order of polynomial space.

x

x denotes the 1D points of evaluation.

orthopol

Currently, we can specify following types of orthogonal polynomials:

  • Jacobi
  • Ultraspherical
  • Legendre
  • Chebyshev
  • Lobatto
  • UnscaledLobatto
alpha, beta

alpha and beta are parameters of Jacobi Polynomials. They should be present when orthopol is equal to Jacobi

lambda

lambda is parameter for Ultraspherical polynomials. They should be present when orthopol is equal to the Ultraspherical

ans
  • The jth col of ans denotes the value of jth polynomial at all points.
  • The ith row of ans denotes the value of all polynomials at ith point.