% CAAM 453 Homework 6, #3 -- GK15.m
%
% Compute nodes and weights for the Gauss-Kronrod (7,15) pair on the
%  interval [a,b].
%
% Inputs:
%      a,b: endpoints of the interval
%
% Outputs:
%        x: length-15 vector of nodes
%    wKron: length-15 vector of Gauss-Kronrod weights
%   wGauss: length-15 vector of Gauss weights
%             (nonzero only on the original 7 Gauss nodes).
%
function [x,wKron,wGauss] = GK15(a,b)

% Nodes and weights for Gauss-Kronrod (7,15) pair on the interval [-1,1].
%
% Data courtesy of QUADPACK's qk15.f, available from:
%    http://www.netlib.org/quadpack/qk15.f
%

x01 = [-0.9914553711208126; 
	-0.9491079123427585;
	-0.8648644233597691; 
	-0.7415311855993944;
	-0.5860872354676911; 
	-0.4058451513773972;
	-0.2077849550078985; 
	0.0
	0.2077849550078985; 
	0.4058451513773972;
	0.5860872354676911; 
	0.7415311855993944;
	0.8648644233597691; 
	0.9491079123427585;
	0.9914553711208126];

wKron01 = [0.02293532201052922; 
	0.06309209262997855;
	0.1047900103222502; 
	0.1406532597155259;
	0.1690047266392679; 
	0.1903505780647854;
	0.2044329400752989; 
	0.2094821410847278
	0.2044329400752989; 
	0.1903505780647854;
	0.1690047266392679; 
	0.1406532597155259;
	0.1047900103222502; 
	0.06309209262997855;
	0.02293532201052922];

wGauss01 = [0;
	0.1294849661688697; 
	0;
	0.2797053914892767;
	0;
	0.3818300505051189; 
	0;
	0.4179591836734694
	0;
	0.3818300505051189; 
	0;
	0.2797053914892767;
	0;
	0.1294849661688697; 
	0];

% Adapt the nodes and weights from [-1,1] to [a,b]:
stretch = 0.5 * (b-a);
x = 0.5 * (b+a) + stretch * x01;
wKron = wKron01 * stretch;
wGauss = wGauss01 * stretch;

end