mlagzo.m

function mlagzo
%This program is a direct conversion of the corresponding Fortran program in
%S. Zhang & J. Jin "Computation of Special Functions" (Wiley, 1996).
%online: http://iris-lee3.ece.uiuc.edu/~jjin/routines/routines.html
%
%Converted by f2matlab open source project:
%online: https://sourceforge.net/projects/f2matlab/
% written by Ben Barrowes (barrowes@alum.mit.edu)
%

%       ===========================================================
%       Purpose : This program computes the zeros of Laguerre
%                 polynomial Ln(x)in the interval[0,∞]and the
%                 corresponding weighting coefficients for Gauss-
%                 Laguerre integration using subroutine LAGZO
%       Input :   n    --- Order of the Laguerre polynomial
%                 X(n)--- Zeros of the Laguerre polynomial
%                 W(n)--- Corresponding weighting coefficients
%       ===========================================================
n=[];x=[];w=[];
x=zeros(1,100);
w=zeros(1,100);
fprintf(1,'%s \n','please enter the order of ln(x), n ');
%        READ(*,*)N
n=5;
fprintf(1,[repmat(' ',1,1),'n =','%3g' ' \n'],n);
[n,x,w]=lagzo(n,x,w);
fprintf(1,'%s \n','  nodes and weights for gauss-lagurre integration');
fprintf(1,'%0.15g \n');
fprintf(1,'%s \n','  i             xi                      wi');
fprintf(1,'%s ',' -----------------------------------------');fprintf(1,'%s \n', '------------');
for  j=1:n;
    fprintf(1,[repmat(' ',1,1),'%3g',repmat(' ',1,3),'%22.13g',repmat(' ',1,3),'%22.13g' ' \n'],j,x(j),w(j));
end;  j=n+1;
%format(1x,',i3);
%format(1x,i3,3x,d22.13,3x,d22.13);
end
function [n,x,w]=lagzo(n,x,w,varargin);
%       =========================================================
%       Purpose : Compute the zeros of Laguerre polynomial Ln(x)
%                 in the interval[0,∞], and the corresponding
%                 weighting coefficients for Gauss-Laguerre
%                 integration
%       Input :   n    --- Order of the Laguerre polynomial
%                 X(n)--- Zeros of the Laguerre polynomial
%                 W(n)--- Corresponding weighting coefficients
%       =========================================================
hn=1.0d0./fix(n);
for  nr=1:n;
    if(nr == 1)z=hn; end;
    if(nr > 1)z=x(nr-1)+hn.*nr.^1.27; end;
    it=0;
    while (1);
        it=it+1;
        z0=z;
        p=1.0d0;
        for  i=1:nr-1;
            p=p.*(z-x(i));
        end;  i=nr-1+1;
        f0=1.0d0;
        f1=1.0d0-z;
        for  k=2:n;
            pf=((2.0d0.*k-1.0d0-z).*f1-(k-1.0d0).*f0)./k;
            pd=k./z.*(pf-f1);
            f0=f1;
            f1=pf;
        end;  k=fix(n)+1;
        fd=pf./p;
        q=0.0d0;
        for  i=1:nr-1;
            wp=1.0d0;
            for  j=1:nr-1;
                if(~(j == i))wp=wp.*(z-x(j)); end;
            end;  j=nr-1+1;
            q=q+wp;
        end;  i=nr-1+1;
        gd=(pd-q.*fd)./p;
        z=z-fd./gd;
        if(~(it <= 40&abs((z-z0)./z)> 1.0d-15))break; end;
    end;
    x(nr)=z;
    w(nr)=1.0d0./(z.*pd.*pd);
end;
return;
end