hedge.quadrature

Module quadrature

1D quadrature for Jacobi polynomials. Grundmann-Moeller cubature on the simplex.

License: This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see U{http://www.gnu.org/licenses/}.

Classes

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Quadrature
An abstract quadrature rule.

JacobiGaussQuadrature
An Nth order Gauss quadrature associated with the Jacobi polynomials of type (alpha,beta) > -1

LegendreGaussQuadrature
An Nth order Gauss quadrature associated with the Legendre polynomials.

TransformedQuadrature
A quadrature rule on an arbitrary interval (a,b).

SimplexCubature
Cubature on an n-simplex.

Functions

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jacobi_gauss_lobatto_points(alpha, beta, N)
Compute the Nth order Gauss-Lobatto quadrature points, x, associated with the Jacobi polynomial, of type (alpha,beta) > -1 ( <> -0.5).

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legendre_gauss_lobatto_points(N)
Compute the Nth order Gauss-Lobatto quadrature points, x, associated with the Legendre polynomials.

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_extended_euclidean(q, r)
Return a tuple (p, a, b) such that p = aq + br, where p is the greatest common divisor.

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_gcd(q, r)

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_simplify_fraction((a, b))

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