%function [fitresult, gof] = CurvefittingRarefactionCurves(A_spec1, A_spec2,A_met1,A_met2, A_tax1, A_tax2)
%CREATEFITS(A_SPEC1,A_MET1,A_TAX1,A_SPEC2,A_MET2,A_TAX2)
%  Create fits.
%
%  Data for 'Met1' fit:
%      X Input : A_spec1
%      Y Output: A_met1
%  Data for 'Met2' fit:
%      X Input : A_spec2
%      Y Output: A_met2
%  Data for 'Tax1' fit:
%      X Input : A_spec1
%      Y Output: A_tax1
%  Data for 'Tax2' fit:
%      X Input : A_spec2
%      Y Output: A_tax2
%  Output:
%      fitresult : a cell-array of fit objects representing the fits.
%      gof : structure array with goodness-of fit info.
%
%  See also FIT, CFIT, SFIT.

%  Auto-generated by MATLAB on 04-Jan-2018 15:45:28
%  Modified by: Lisa Wenzel

%% Clear
    
close all; clc;

%% Import data from the combined data table

A =  xlsread('Combined-table-Matlab');

% 1D-approach

A_spec1=A(:,1);
A_met1=A(:,4);
A_tax1=A(:,5);

% 2D-approach

A_spec2=A(:,6);
A_met2=A(:,9);
A_tax2=A(:,10);

%% Initialization.

% Initialize arrays to store fits and goodness-of-fit.
fitresult = cell( 4, 1 );
gof = struct( 'sse', cell( 4, 1 ), ...
    'rsquare', [], 'dfe', [], 'adjrsquare', [], 'rmse', [] );

%% Fit: 'Met1'.
[xData_1, yData_1] = prepareCurveData( A_spec1, A_met1 );

% Set up fittype and options.
ft = fittype( '(a*x)/(b+x)', 'independent', 'x', 'dependent', 'y' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.0749443966209411 0.483050724600071];

% Fit model to data.
[fitresult{1}, gof(1)] = fit( xData_1, yData_1, ft, opts );

%% Fit: 'Met2'.
[xData_2, yData_2] = prepareCurveData( A_spec2, A_met2 );

% Set up fittype and options.
ft = fittype( '(a*x)/(b+x)', 'independent', 'x', 'dependent', 'y' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.632251826416449 0.0493137758052661];

% Fit model to data.
[fitresult{2}, gof(2)] = fit( xData_2, yData_2, ft, opts );

%% Fit: 'Tax1'.
[xData_3, yData_3] = prepareCurveData( A_spec1, A_tax1 );

% Set up fittype and options.
ft = fittype( '(a*x)/(b+x)', 'independent', 'x', 'dependent', 'y' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.464533863489609 0.207894030111393];

% Fit model to data.
[fitresult{3}, gof(3)] = fit( xData_3, yData_3, ft, opts );

%% Fit: 'Tax2'.
[xData_4, yData_4] = prepareCurveData( A_spec2, A_tax2 );

% Set up fittype and options.
ft = fittype( '(a*x)/(b+x)', 'independent', 'x', 'dependent', 'y' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.752407459129325 0.595738073442943];

% Fit model to data.
[fitresult{4}, gof(4)] = fit( xData_4, yData_4, ft, opts );


%% Get parameters a, b and R_square from curvefitting for all functions and create one matrix and write a .xlsx-file

% Obtain the parameters a and b from the curvefitting for all 18 functions
for i=1:4
    results_parameter(:,i+1)=coeffvalues(fitresult{i});
end

% Write the results in an array with text in the first column

Text={'Name';'1D-Metaprot';'2D-Metaprot';'1D-Tax';'2D-Tax'};
results_parameter_cell = num2cell(results_parameter');
Results_parameter=[Text,results_parameter_cell];

% Obtain the parameter R_square from the curvefitting for all functions  

R_square=[gof.rsquare]';

% Insert a heading, create a cell-array and the final matrix

Text_rsquare={'R-square'};
R_square_cell=num2cell(R_square);
Results_Rsquare=[Text_rsquare;R_square_cell];

Results=[Results_parameter,Results_Rsquare]; % Final matrix

% Export the Resultsmatrix as .xlsx-file

filename='ResultsCurvefitting.xlsx';
xlswrite(filename,Results)
%% Plot data points for sample 1 (1D and 2D)

% Plot for metaproteins

figure('Name','Curve fitting')
subplot(2,2,1)
plot(fitresult{1},'b-',xData_1, yData_1,'r.')
hold on;
plot(fitresult{2},'k-',xData_2, yData_2,'m.')
xlabel('Number of spectra')
ylabel('Cumulative sum of identified metaproteins')
grid on;
% Subplot title
ta=title('(a) Metaproteins: Data points and fitted curves ');
set(ta,'FontWeight','bold')
% Create a legend
legend('1D-Metaproteins','1D-Metaproteins-Fitting','2D-Metaproteins','2D-Metaproteins-Fitting','Location','SouthEast')

% Plot for species

subplot(2,2,2)
plot(fitresult{3},'b-',xData_1, yData_3,'r.')
hold on;
plot(fitresult{4},'k-',xData_2, yData_4,'m.')
xlabel('Number of spectra')
ylabel('Cumulative sum of identified species')
grid on;
% Subplot title
tb=title('(b) Species: Data points and fitted curves ');
set(tb,'FontWeight','bold')
% Create a legend
legend('1D-Species','1D-Species-Fitting','2D-Species','2D-Species-Fitting','Location','SouthEast')

%% Calculate predicted values with the parameters a and b from curvefitting

% Import the results matrix

B = xlsread('ResultsCurvefitting'); 

% Create a vector with the number of spectra for the prediction

X=[1:100000]';

% Calculate the Cumulative sum of identified metaproteins and
% species for the given vector X

for i=1:4
    y(:,i)=(X.*B(i+1,1))./(B(i+1,2)+X);
end

% Plot the predicted values for metaproteins and species

subplot(2,2,3)
plot(X,y(:,1),'b-',X,y(:,2),'b--',X,y(:,3),'k-',X,y(:,4),'k--')
xlabel('Number of spectra')
ylabel('Cumulative sum of identified metaproteins/species')
grid on;
% Subplot title
tc=title('(c) Predicted curves for 10^5 spectra ');
set(tc,'FontWeight','bold')
% Create a legend
legend('1D-Metaproteins','2D-Metaproteins','1D-Species','2D-Species','Location','SouthEast')

%end