function alpha_value_calculations_082316

%Type in your file name, including the extension
input_file = 'example_areas_and_alpha_values.xlsx';            %input data file name, don't forget the .xls extension
input_sheet = 'sheet1';            %excel sheet name
[input_data] = xlsread(input_file,input_sheet)  %input_data takes in excel data
X=input_data(:,1:12); %Forms a matrx of the area data
u23expt=input_data(:,13); %Array of mu23/RT values
u23err=input_data(:,14);  %Array of mu23/RT errors
format shortG   %Adjusts the length of the float variables
Tdt=transpose(X);  %Transposes areas matrix for calculating alpha values

%This array creates the atom type names for printing a table of the alpha
%values from the fits
AtomType={'Aliphatic C'; 'Hydroxyl O'; 'Amide O'; 'Amide N'; 'Carboxylate O'; 'Cationic N'; 'Aromatic C'; 'Phosph O'; 'K+'; 'Cl-';'Amine N off aromatic ring'; 'Aromatic N'};

mone=(Tdt*X)^-1; %Creating variable used in fitting and error calculation
Alpha_Values = 10000*mone*Tdt*u23expt; %Linear regression producing alpha values

%Creates an array of the error squared
uer=zeros(length(u23err),1); %Zero array for faster calculation of errors
for i=1:length(u23err)
    uer(i) = u23err(i)^2;
end

Ohm = diag(u23err.^2); %Finding the diagonal of the error squared matrix
aei = mone*Tdt*Ohm*X*mone; %Calculating the error in the alpha values
ae=sqrt(aei); %Forming an array of the square root, the diagonal gives the errors

%for loop gets the errors from the 'ae' matrix
for j=1:length(ae)
    Alpha_Error(j,1) = 10000*ae(j,j); %Values are multiplied by 10000 to move the decimal to the ones position for the ease of the user 
end

%Print out table of atom types and their alpha values with their errors
tbl=table(AtomType, Alpha_Values, Alpha_Error)

%This calculates the residuals so that R-square can be calculated
%Calculating predicted mu23/RT values
tpred=X*Alpha_Values/10000;
tperr=X*(Alpha_Values+Alpha_Error)/10000-tpred;

%Determines the residuals
res=tpred-u23expt;

%Calculation of R-square
Rsquare=1-sum(res.^2)/sum((u23expt-mean(u23expt)).^2)

%Predicted u23/RT values
predval = X*Alpha_Values/10000;

%Covariance matrix is used to calculate the residuals of the fits
cov=mean(res.^2)*mone;
fit_a=Alpha_Values/10000; %To adjust the alpha values to their actual value from the prettied calculated values
ci=nlparci(fit_a,res,'covar',cov); %Calculates the confidence intervals for each predicted mu23/RT value
u23_RTerror = fit_a(1,:) - ci(:,2); %Gets the errors of each predicted mu12/RT from the confidence interval


%Prints out the predicted mu23/RT values for each compound plus the
%residual errors for each compound.
Predicted_vals = [predval, res]

%The is to set up the confidence intervals on the plot of mu23/RT versus
%compound number.
ucld=X*ci(:,1);
lcld=X*ci(:,2);

%Gives the predicted u23/RT for Records compounds only.
Recordu23=u23expt(1:27);
Recordpu23=predval(1:27);

%Creates a cutoff line for your data versus Redord's data.
rec_cutoff = [27.5, 27.5];
recx_co = [-1, 2];


gul = [1:length(u23expt)];
%Zero line setup
Zlx = [0, length(u23expt)];
Zly = [0,0];
%Sets up x-values for the lowest and highest experimental mu23/RT values
Zl2=[min(u23expt)-.1,max(u23expt)+.1];

%This gets the linear fit and confidence interval of the predicted versus
%experimental data
fitdata=fit(u23expt,predval,'poly1');
p11=predint(fitdata,u23expt,0.95,'observation','off')

%Plots the data for each compounds and shows confidence intervals of
%predicted data
figure
errorbar(u23expt,u23err, 'bo');
hold on;
errorbar(predval,tperr,'rs');
hold on;
plot(Zlx, Zly, 'm--');
hold on;
plot(gul, ucld, 'b--', gul, lcld, 'b--');
hold on;
plot(rec_cutoff, recx_co, 'k--');
ylabel('u23/RT');
xlabel('Compound Number');
title('Predicted u23/RT values for each compound');
legend('Experimental u23/RT', 'Predicted u23/RT', 'Zero','Upper Confidence Interval', 'Lower Confidence Interval', 'Cutoff between Records and our compounds');

%Plots the predicted vs the experimental data, plus the confidence interval
%of the fit.  Two predicted values show up in the second plot so that error
%bars can be added to the predicted values.  The first green squares are
%for the error bars.  The second gree squares are from the confidence
%interval plot.
figure
plot(Zl2,Zl2,'m--')
hold on
errorbar(u23expt,predval,res,'gs');  %Plots the error bars of the predict values
hold on;
plot(fitdata,u23expt,predval,'gs');  %Plots the confidence intervals for the predicted values
hold on;
plot(u23expt,p11);
hold on;
plot(Recordu23,Recordpu23,'rs');
title('Predicted vs Actual u23/RT values');
legend('Line with slope of 1', 'Predicted data', 'Predicted data', 'Linear fit of plot', 'Lower confidence interval', 'Upper confidence interval', 'Records Compouds');
ylabel('Predicted u23/RT');
xlabel('Experimental u23/RT');