halftanh

    Half tanh for x < 0

    Input:
    
        - x: input value [n,m]

    Output:

        - f: function [n,m]
        - df: first derivative [n,m]
        - d2f: second derivative [n,m]

0001 function [f,df,d2f] = halftanh(x)
0002 %
0003 %    Half tanh for x < 0
0004 %
0005 %    Input:
0006 %
0007 %        - x: input value [n,m]
0008 %
0009 %    Output:
0010 %
0011 %        - f: function [n,m]
0012 %        - df: first derivative [n,m]
0013 %        - d2f: second derivative [n,m]
0014 
0015 %
0016 %by Y.PEYSSON CEA-IRFM <yves.peysson@cea.fr> and Joan Decker CEA-IRFM (joan.decker@cea.fr)
0017 %
0018 f = x;
0019 f(x<0) = tanh(x(x<0));
0020 f(x<-400) = -1;
0021 %
0022 df = ones(size(x));
0023 df(x<0) = 1.0./cosh(x(x<0))./cosh(x(x<0));
0024 df(x<-400) = 0;
0025 %
0026 d2f = zeros(size(x));
0027 d2f(x<0) = -2.0*sinh(x(x<0))./cosh(x(x<0)).^3;
0028 d2f(x<-400) = 0;
0029 %
0030