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iCAPs/packages/gspbox/utils/gsp_smooth_step.m
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gsp_smooth_step.m
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function y = gsp_smooth_step(x, a)
%GSP_SMOOTH_STEP Smooth step function from 0 to 1 arround 0.5
% Usage: y = gsp_smooth_step(x);
% y = gsp_smooth_step(x, a)
%
% Input parameters:
% x : input value
% a : smoothing parameter (default 1)
% Ouput parameters:
% y : output value of the function
%
% This function is a smooth step from 0 to 1 arround 0 using the
% following function:
%
% / 0 if x < 0
% s(x) = | exp(-a/x) / ( exp(-a/x) + exp(-a/(1-x)) ) if x in [0, 1]
% \ 1 if x > 1
%
%
% Url: http://lts2research.epfl.ch/gsp/doc/utils/gsp_smooth_step.php
% Copyright (C) 2013-2016 Nathanael Perraudin, Johan Paratte, David I Shuman.
% This file is part of GSPbox version 0.7.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% If you use this toolbox please kindly cite
% N. Perraudin, J. Paratte, D. Shuman, V. Kalofolias, P. Vandergheynst,
% and D. K. Hammond. GSPBOX: A toolbox for signal processing on graphs.
% ArXiv e-prints, Aug. 2014.
% http://arxiv.org/abs/1408.5781
% Author: Nathanael Perraudin
% Date : 5 mai 2016
if nargin<2
a = 1;
end
y=fx(x,a);
y = y./(y+fx(1-x,a));
end
function y=fx(x,a)
y = exp(-a./x);
y(x<0)=0;
end
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