% MATLAB template file for fitting an explicit non-linear model equation 
% "y = f(x1,...,x_nset;p1,...,p_npar)" to experimental 
% (x1,...,xn_set,y_hat) data.
%
% See Supplemental Unit S4 of "A First Course on Kinetics and Reaction
% Engineering" and/or the MATLAB documentation for additional information
% or if questions arise.
%
% Carl R. F. Lund, 4/22/13
%   last rev. 8/26/14
%
% Arguments
%   p_guess (vector) - guesses for the model parameters
%
% This file requires four modifications before each use; the locations
% where editing is required are indicated by the comment "% EDIT HERE"
%
function FitNonlinSR(p_guess)
    % Known quantities and constants (in consistent units)
% EDIT HERE (Required modification 1 of 4):
    % define universal and experimental constants here

% EDIT HERE (Required modification 2 of 4) enter the set variable data
% as a matrix named x with one column for each set variable and one row per
% data point

% EDIT HERE (Required modification 3 of 4) enter the measured response
% variable data as a column vector named y_hat
    
    % Function that calculates the responses using the model
    function y = nlmodel(p,x)
        n_data = size(x,1);
        y = zeros(n_data,1);
        for i = 1:n_data
            % p(i) is the value of parameter i
            % x(i,j) is the value of set variable xj for data point i
% EDIT HERE (Required modification 4 of 4):
            y(i) = ; % insert code to calculate y for data point i
        end
    end % of internal function nlmodel

    % Perform the regression analysis
    [pf,resid,J,sigma,mse] = nlinfit(x,y_hat,@nlmodel,p_guess);
    confint = nlparci(pf,resid,'covar',sigma);
    pf_u = (confint(:,2) - confint(:,1))/2.0;
    
    % Calculate the model-predicted responses
    y = nlmodel(pf,x);
    
    % Display the correlation coefficient, parameters and uncertainties
    format shortE;
    r_squared = 1.0 - (sum(resid.^2))/(sum((y_hat-mean(y_hat)).^2))
    display('Best Values for the Parameters:')
    pf
    display('95% Confidence Intervals for the Parameters:')
    pf_u

    % Generate the graphical output
    n_set = size(x,2);
    if n_set == 1
        % Model plot
        % Use many data points for the model so the curve is smooth
        xx = linspace(min(x),max(x))';
        yy = nlmodel(pf,xx);
        figure;
        plot(x,y,'r',x,y_hat,'o')
        xlabel('X')
        ylabel('Y')
        title('Model Plot')
        legend('Model','Data')
    else
        % Parity plot
        figure;
        plot(y_hat,y_hat,'r',y_hat,y,'o')
        xlabel('Measured Response')
        ylabel('Predicted Response')
        title('Parity Plot')

        % Residuals plots for each set variable
        for n = 1:n_set
            figure;
            plot(x(:,n),zeros(length(y),1),'r',x(:,n),resid,'o')
            xlabel(['x',num2str(n)])
            ylabel('Residual')
            title(['Residuals Plot vs. x',num2str(n)])
        end
    end
end % of FitNonlinSR.m