A4.m

file_name = input('Enter the file name of data, must be in quotes and in the cwd \n');
display(file_name)
data = load(file_name);

type = input('Select type of fit (1: linear, 2: polynomial, 3: exponential, 4: power) \n');
if(type == 2)
    degree = input('Degree of polynomial: ');
end

%Call neccecary fit function based on user input
if(type == 1)
    [result, gof] = get_linear_fit(data);
    plot_with_label(data, result, gof.rsquare);
end
if(type == 2)
    [result, gof] = get_poly_fit(data, degree);
    plot_with_label(data, result, gof.rsquare);
end
if(type == 3)
    [result, gof] = get_exp_fit(data);
    plot_with_label(data, result, gof.rsquare);
end
if(type == 4)
    [result, gof] = get_power_fit(data);
    plot_pow(data, result, gof.rsquare);
end

display(result)

function [result, gof] = get_linear_fit(data)
    [result, gof] = get_poly_fit(data, 1);%call polynomial fit, but with degree 1
end
function [result, gof] = get_poly_fit(data, degree)
    x = data(:,1);%get x components
    y = data(:,2);%get y components
    polystring = strcat('poly', num2str(degree));%Set function type string(depends on degree)
    [result, gof] = fit(x,y, polystring);%fit data
end

function [result, gof] = get_exp_fit(data)
    x = data(:,1);%get x components
    y = data(:,2);%get y components
    [result, gof] = fit(x,y,'exp1');%fit data
end

function [result, gof] = get_power_fit(data)
    x = data(:,1);%get x components
    y = data(:,2);%get y components
    %Set fit options to allow for non zero start point
    FO = fitoptions('Method', 'NonlinearLeastSquares', 'StartPoint',[1 1 1]);
    FT = fittype('a*(x^b) + c', 'options', FO);
    [result, gof] = fit(x, y, FT);%fit data
end


%Plot method to be used if fit is anything but power
function plot_with_label(data, fit, r)
    x = data(:,1);%get x components
    y = data(:,2);%get y components
    s = get_string(fit);%convert cfit type to string
    rs = strcat('r^2=', num2str(r));%Create string storing r^2 value
    plot(fit,x,y)%plot data
    legend("Raw Data",s)%draw legend
    text(min(x),max(y),rs)%Show r^2 in top left corner

end

%Plot method to be used if fit is power
function plot_pow(data, fit, r)
    x = data(:,1);%get x components
    y = data(:,2);%get y components
    %generate string representation of function
    s = num2str(fit.a) + "* (x \^" + num2str(fit.b) + ") + " + num2str(fit.c);
    rs = strcat('r^2=', num2str(r));%Create string storing r^2 value
    plot(fit,x,y)%plot data
    legend("Raw Data",s)%draw legend
    text(min(x),max(y),rs)%Show r^2 in top left corner

end


function eq = get_string(fit)
    %The method below is from MATLAB support
    %https://www.mathworks.com/matlabcentral/answers/99155-how-do-i-extract-the-output-equation-from-a-cfit-object-in-curve-fitting-toolbox-2-0-r2009a
    eq = formula(fit); %Formula of fitted equation
    parameters = coeffnames(fit); %All the parameter names
    values = coeffvalues(fit); %All the parameter values
    for idx = 1:numel(parameters)
          param = parameters{idx};
          l = length(param);
          loc = regexp(eq, param); %Location of the parameter within the string
          while ~isempty(loc)
              %Substitute parameter value
              eq = [eq(1:loc-1) num2str(values(idx)) eq(loc+l:end)];
              loc = regexp(eq, param);
          end
    end
end