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// 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 [K]=%k(m)
//K=%k(m)
//Calculates Jacobi's complete elliptic integral
//of the first kind:
// K = integral from 0 to 1 of
// [(1-t**2)(1-m*t**2)]**(-1/2)
//m is allowed to be a vector
//Ref :Abramowitz and Stegun page 598
// m :Parameter used in calculating the elliptic
// :integral where 0<m<1.
// K :Value of the elliptic integral from 0 to 1
// :on the real axis.
//
//!
[n1,n2]=size(m);
un=ones(n1,n2);
a=un;
b=sqrt(un-m);
c=sqrt(m);
while max(abs(c)) > %eps,
an=0.5*(a+b);
bn=sqrt(a.*b);
cn=0.5*(a-b);
a=an;
b=bn;
c=cn;
end,
K=%pi*un./(2*a);
endfunction
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