function parameter_estimation_pH_single(filename)
% estimates the parameter of the pH shift using either a exponetial
% function or a hyperbolic tangent
%
% filename refers to the Matlab file (mat--format) that stores the data in
% a vector called time (time points) and a vector pH

% options and preparations
clc
close all

% type of shift experiment
type=1;     % forward shift 5.7 -> 4.5
%type=0;     % reverse shift 4.5 -> 5.7

% load data
load(filename,'time','pH');

% estimate parameters
foptions=fitoptions('Method','NonlinearLeastSquares','Lower',[0.15, 115],'Upper',[1.2, 150],'StartPoint',[0.4, 150]);  
if type==1;
    foptions2=fitoptions('Method','NonlinearLeastSquares','Lower',[0.05, 115],'Upper',[0.5, 150],'StartPoint',[0.1, 130]);
    f=fittype('0.6*(1-tanh(a/2*(x-b)))+4.5','options',foptions);
    f2=fittype('5.7*heaviside(b2-x)+(4.5+1.2*exp(-a2*(x-b2)))*heaviside(x-b2)','options',foptions2);
    [c2,gof2] = fit(time,pH,f);
    par_pH=coeffvalues(c2);
    conf_pH=confint(c2);
    [c3,gof3] = fit(time,pH,f2);
    par_pH2=coeffvalues(c3);
    conf_pH2=confint(c3);
else
    foptions2=fitoptions('Method','NonlinearLeastSquares','Lower',[0.05, 115],'Upper',[0.7, 150],'StartPoint',[0.2, 130]);
    f=fittype('0.6*(tanh(a/2*(x-b))-1)+5.7','options',foptions);
    f2=fittype('4.5*heaviside(b2-x)+(4.5+1.2*(1-exp(-a2*(x-b2))))*heaviside(x-b2)','options',foptions2);
    [c2,gof2] = fit(time,pH,f);
    par_pH=coeffvalues(c2);
    conf_pH=confint(c2);
    [c3,gof3] = fit(time,pH,f2);
    par_pH2=coeffvalues(c3);
    conf_pH2=confint(c3);
end

% vector of parameters and confidence intervals
data_tanh=[par_pH(1) conf_pH(:,1)' par_pH(2) conf_pH(:,2)' gof2.sse gof2.rsquare gof2.dfe gof2.adjrsquare gof2.rmse];
data_exp=[par_pH2(1) conf_pH2(:,1)' par_pH2(2) conf_pH2(:,2)' gof3.sse gof3.rsquare gof3.dfe gof3.adjrsquare gof3.rmse];

display('Parameters: exponential');
display(data_exp);
display('Parameters: hyperbolic tangent');
display(data_tanh);

% compute time-dependent pH value
tm=linspace(0,300,500);
if type==1
    pH_m=0.6*(1-tanh(par_pH(1)/2*(tm-par_pH(2))))+4.5;
    save('./pH_sim.mat','tm','pH_m');
    pH_m2=5.7*heaviside(par_pH2(2)-tm)+(4.5+1.2.*exp(-par_pH2(1)*(tm-par_pH2(2)))).*heaviside(tm-par_pH2(2));
else
    pH_m=0.6*(tanh(par_pH(1)/2*(tm-par_pH(2)))-1)+5.7;
    pH_m2=4.5*heaviside(par_pH2(2)-tm)+(4.5+1.2.*(1-exp(-par_pH2(1)*(tm-par_pH2(2))))).*heaviside(tm-par_pH2(2));
end

% comparison of experimental data and fit
figure
plot(time,pH,'LineStyle','none','Marker','o','MarkerFaceColor',[0 0 1],'Color',[0 0 1]);
xlabel('time [hours]');
ylabel('pH');
hold on
plot(tm,pH_m,tm,pH_m2);
legend('experimental data','hyperbolic tangent','exponential');
hold off
figureprop;