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gauss_legendre_rule.m
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gauss_legendre_rule.m
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% Gauss-Legendre quadrature rule class
%
% q = gauss_legendre_rule(n) creates object q representing a Gauss-Legendre
% rule on [0,1] with n points.
%
% x = q.points() returns vector x containing the quadrature points.
%
% w = q.weights() returns vector w containing the corresponding quadrature
% weights.
%
% Example:
%
% sum(w.*f(x)) approximates the integral of f over the interval [0,1].
%
% Stuart C. Hawkins - 23 August 2021
% Copyright 2019-2022 Stuart C. Hawkins
%
% This file is part of TMATROM3
%
% TMATROM3 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.
%
% TMATROM3 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 TMATROM3. If not, see <http://www.gnu.org/licenses/>.
classdef gauss_legendre_rule < rule
properties
end
methods
%-----------------------------------------
% constructor
%-----------------------------------------
function self = gauss_legendre_rule(n)
% call parent constructor
self = self@rule(n);
end
function val = points(self)
% compute the Gauss-Legendre points
[pp,pw]=gauss_legendre(self.n-1);
% transform from x to theta coordinates... and note we are
% parametrising from [0,1] rather than [0,pi] so divide by pi
val = acos(pp(:))/pi;
end
function val = weights(self)
% compute the Gauss-Legendre points and weigths
[pp,pw]=gauss_legendre(self.n-1);
% return the weights
val = pw;
end
end
end