% MATLAB template file for fitting a model to single response experimental 
% data of the form (y_hat,x(1),...,x(n_set)). An explicit expression, 
% y = f(x(1),...,x(n_set),u(1),...,u(n)) is used to calculate the 
% model-predicted response from the experimental set variables (x) and the
% results (u) of solving a set of n model equations of the form
%   0 = g1(u(1),...,u(n);p(1),...,p(n_par))
%   0 = g2(u(1),...,u(n);p(1),...,p(n_par))
%              .
%              .
%              .
%   0 = gn(u(1),...,u(n);p(1),...,p(n_par))
% where p represents the parameters in the model.
%
% 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. 5/28/14
%
% Arguments
%   p_guess (vector) - guesses for the model parameters
%
% This file requires six modifications before each use; the locations
% where editing is required are indicated by the comment "% EDIT HERE"
%
function FitNumAlgSR(p_guess)
    % Known quantities and constants (in consistent units)
% EDIT HERE (Required modification 1 of 6):
    % define universal and experimental constants here

% EDIT HERE (Required modification 2 of 6) 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 6) enter the measured response
% variable data as a column vector named y_hat
    
    % Function that evaluates the model equations
	function g = nlaeqns(u)
        % Current parameter values are available in column vector p
        % Current set variable values are available in column vector x_set
% EDIT HERE (Required modification 4 of 6):
		g = [
			% evaluate g1(u(1),...,u(n);p(1),...,p(n_par)) here
            % evaluate g2(u(1),...,u(n);p(1),...,p(n_par)) here
            % and so on through gn, one per line
		];
    end % of internal function nlaeqns

    % Function that calculates the responses using the model solution
    function y = nlmodel(p_current,x)
        % Make the current parameters available to the model equations
        p = p_current;
        y = zeros(n_data,1);
        
        for i = 1:n_data
            % Make the set variables available to the model equations
            for j = 1:n_set
                x_set(j) = x(i,j);
            end
            
            % Guesses
            % The measured response is available here as y_hat(i)
% EDIT HERE (Required modification 5 of 6):
            u_guess = [
                % insert/calculate guess for u(1) here
                % insert/calculate guess for u(2) here
                % and so on, one u(i) per line
            ];
        
            % Solve the set of nonlinear modle equations
            u = fsolve(@nlaeqns, u_guess);
            
            % Once you are sure fsolve is obtaining converged solutions,
            % you can suppress the "equations solved" messages by
            % commenting out the line above this comment and uncommenting
            % the next two lines.
            % options = optimoptions('fsolve','Display','off');
            % u = fsolve(@nlaeqns, u_guess, options);
            
            % Calculate the response
% EDIT HERE (Required modification 6 of 6):
            y(i) = ; % insert statement(s) to calculate y for data point i
        end
    end % of internal function nlmodel

    % All the necessary internal functions are now defined

    % get the number of data points and set variables
    n_data = size(x,1);
    n_set = size(x,2);
    
    % create global variables to make parameters and set variables
    % available to the internal function that evaluates the model equations
    p = zeros(length(p_guess),1);
    x_set = zeros(size(x,2),1);
    
    % 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 and the correlation
    % coefficient
    y = zeros(n_data,1);
    y = nlmodel(pf,x);

    % 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
    
    % 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
end % of FitNumAlgSR.m