// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) INRIA - F.D
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution.  The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt

function [y]=%sn(x,m)
    //Jacobi 's elliptic function with parameter m
    //which computes the inverse of the elliptic
    //integral for the parameter m.
    //x may be a vector.
    //The amplitude is computed in fortran and apply
    //the addition formulas for elliptic functions
    //  x :A point inside the fundamental rectangle
    //    :defined by the elliptic integral
    //  m :Parameter of the elliptic integral (0<m<1)
    //  y :Result
    //
    //!

    [n1,n2]=size(x);
    n=n1*n2;
    a=amell(real(x),sqrt(m));
    s=sin(a);
    c=cos(a);
    d=sqrt(ones(n1,n2)-m*s.*s);
    m1=1-m;
    a1=amell(imag(x),sqrt(m1));
    s1=sin(a1);
    c1=cos(a1);
    d1=sqrt(ones(n1,n2)-m1*s1.*s1);
    y=(s.*d1+%i*c.*d.*s1.*c1)./(c1.*c1+m*s.*s.*s1.*s1);
endfunction