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LagrangeEvalAll

Evaluate Lagrange polynomials on triangle.

Interface 1​

INTERFACE LagrangeEvalAll_Triangle
  MODULE FUNCTION LagrangeEvalAll_Triangle1(order, x, xij, refTriangle, &
    & coeff, firstCall, basisType) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
    !! order of Lagrange polynomials
    REAL(DFP), INTENT(IN) :: x(2)
    !! point of evaluation
    !! x(1) is x coord
    !! x(2) is y coord
    REAL(DFP), INTENT(INOUT) :: xij(:, :)
    !!
    CHARACTER(*), INTENT(IN) :: refTriangle
    !! interpolation points
    REAL(DFP), OPTIONAL, INTENT(INOUT) :: coeff(SIZE(xij, 2), SIZE(xij, 2))
    !! coefficient of Lagrange polynomials
    LOGICAL(LGT), OPTIONAL :: firstCall
    !! If firstCall is true, then coeff will be made
    !! If firstCall is False, then coeff will be used
    !! Default value of firstCall is True
    INTEGER(I4B), OPTIONAL, INTENT(IN) :: basisType
    !! Monomials *Default
    !! Orthogonal, Jacobi, Legendre, Lobatto, Ultraspherical all are same
    !! Heirarchical
    REAL(DFP) :: ans(SIZE(xij, 2))
    !! Value of n+1 Lagrange polynomials at point x
  END FUNCTION LagrangeEvalAll_Triangle1
END INTERFACE LagrangeEvalAll_Triangle
xij

xij is the interpolation points for Lagrange polynomials. xij is used for constructing the coeff.

basisType

Type of basis functions used for constructing the Lagrange polynomial. Following values are allowed:

  • Monomials
  • Orthogonal, Jacobi, Legendre, Ultraspherical, are all the same.
  • Hierarchical

Interface 2​

INTERFACE LagrangeEvalAll_Triangle
  MODULE FUNCTION LagrangeEvalAll_Triangle2(order, x, xij, refTriangle, &
    & coeff, firstCall, basisType) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
    !! Order of Lagrange polynomials
    REAL(DFP), INTENT(IN) :: x(:, :)
    !! Point of evaluation
    !! x(1, :) is x coord
    !! x(2, :) is y coord
    REAL(DFP), INTENT(INOUT) :: xij(:, :)
    !! Interpolation points
    CHARACTER(*), INTENT(IN) :: refTriangle
    !! Reference triangle
    !! Biunit
    !! Unit
    REAL(DFP), OPTIONAL, INTENT(INOUT) :: coeff(SIZE(xij, 2), SIZE(xij, 2))
    !! Coefficient of Lagrange polynomials
    LOGICAL(LGT), OPTIONAL :: firstCall
    !! If firstCall is true, then coeff will be made
    !! If firstCall is False, then coeff will be used
    !! Default value of firstCall is True
    INTEGER(I4B), OPTIONAL, INTENT(IN) :: basisType
    !! Monomials *Default
    !! Jacobi=Dubiner
    !! Heirarchical
    REAL(DFP) :: ans(SIZE(x, 2), SIZE(xij, 2))
    !! Value of n+1 Lagrange polynomials at point x
  END FUNCTION LagrangeEvalAll_Triangle2
END INTERFACE LagrangeEvalAll_Triangle