findcorners.m

%  Copyright 2010 Andrew Leifer et al <leifer@fas.harvard.edu>
%  This file is part of Mindcontrol-analysis.
% 
%  Mindcontrol-analysis 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.
% 
%  Mindcontrol-analysis 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 mindcontrol-analysis. If not, see <http://www.gnu.org/licenses/>.


function [tanhCoef,tanhGOF, c1, c2]= findcorners(data);
ymax=max(data);
ymin=min(data);
xmax=length(data);
xmin=0;

%Let's fit to a hyperbolic tangent
%B is the halfway between forward and backwords
%B+A  is one steady state velocity
%B-A is the other steady state velocity
%x0 is the center of the change in speed
%x0 +/- 1/beta is the start and end of the change in speed
 s=fitoptions('Method','NonlinearLeastSquares',...
      'Lower',[ymin, ymin, -Inf, xmin],...
     'Upper',[ymax, ymax, Inf, xmax],...
     'MaxFunEvals',1200,...
     'Startpoint',[(ymax-ymin)/2, (ymax-ymin)/2,1,xmin+0.6*(xmax-xmin)]);
  fitTanh=fittype('A*tanh(beta*(x-x0))+B','options',s);
 x= 1:length(data);
 [tanhCoef,tanhGOF]=fit(x',data',fitTanh);

 A=tanhCoef.A;
 beta=tanhCoef.beta;
 x0=tanhCoef.x0;
 B=tanhCoef.B;
 y=A*tanh(beta.*(x-x0))+B;
 
 
 c1=[x0+1/beta; A+B];
 c2=[x0-1/beta; B-A];
 
 
 
%  %Plot Output:
%
%  figure; hold on;
%  A=tanhCoef.A;
%  beta=tanhCoef.beta;
%  x0=tanhCoef.x0;
%  B=tanhCoef.B;
%  y=A*tanh(beta.*(x-x0))+B;
%  
%  plot(x,data)
%  plot(x,y,'m','linewidth',2)
%  plot([x0+1/beta x0-1/beta],[A+B B-A],'ro','linewidth',3);
%  figure; hold on;
%  plot(data,x)
%  plot(y,x,'m','linewidth',2)
%  plot([A+B B-A],[x0+1/beta x0-1/beta],'ro','linewidth',3);
%