function [VOI, STATES, ALGEBRAIC, CONSTANTS] = mainFunction()
    % This is the "main function".  In Matlab, things work best if you rename this function to match the filename.
   [VOI, STATES, ALGEBRAIC, CONSTANTS] = solveModel();
end

function [algebraicVariableCount] = getAlgebraicVariableCount() 
    % Used later when setting a global variable with the number of algebraic variables.
    % Note: This is not the "main method".  
    algebraicVariableCount =4;
end
% There are a total of 2 entries in each of the rate and state variable arrays.
% There are a total of 3 entries in the constant variable array.
%

function [VOI, STATES, ALGEBRAIC, CONSTANTS] = solveModel()
    % Create ALGEBRAIC of correct size
    global algebraicVariableCount;  algebraicVariableCount = getAlgebraicVariableCount();
    % Initialise constants and state variables
    [INIT_STATES, CONSTANTS] = initConsts;

    % Set timespan to solve over 
    tspan = [0, 10];

    % Set numerical accuracy options for ODE solver
    options = odeset('RelTol', 1e-06, 'AbsTol', 1e-06, 'MaxStep', 1);

    % Solve model with ODE solver
    [VOI, STATES] = ode15s(@(VOI, STATES)computeRates(VOI, STATES, CONSTANTS), tspan, INIT_STATES, options);

    % Compute algebraic variables
    [RATES, ALGEBRAIC] = computeRates(VOI, STATES, CONSTANTS);
    ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI);

    % Plot state variables against variable of integration
    [LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends();
    figure();
    plot(VOI, STATES);
    xlabel(LEGEND_VOI);
    l = legend(LEGEND_STATES);
    set(l,'Interpreter','none');
end

function [LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends()
    LEGEND_STATES = ''; LEGEND_ALGEBRAIC = ''; LEGEND_VOI = ''; LEGEND_CONSTANTS = '';
    LEGEND_VOI = strpad('t in component main (second)');
    LEGEND_STATES(:,1) = strpad('q_1 in component main (metre)');
    LEGEND_STATES(:,2) = strpad('v_1 in component main (m_per_s)');
    LEGEND_ALGEBRAIC(:,4) = strpad('a_1 in component main (m_per_s2)');
    LEGEND_ALGEBRAIC(:,1) = strpad('u_C in component main (J_per_m)');
    LEGEND_ALGEBRAIC(:,2) = strpad('u_R in component main (J_per_m)');
    LEGEND_ALGEBRAIC(:,3) = strpad('u_L in component main (J_per_m)');
    LEGEND_CONSTANTS(:,1) = strpad('C in component main (m2_per_J)');
    LEGEND_CONSTANTS(:,2) = strpad('R in component main (Js_per_m2)');
    LEGEND_CONSTANTS(:,3) = strpad('L in component main (Js2_per_m2)');
    LEGEND_RATES(:,1) = strpad('d/dt q_1 in component main (metre)');
    LEGEND_RATES(:,2) = strpad('d/dt v_1 in component main (m_per_s)');
    LEGEND_STATES  = LEGEND_STATES';
    LEGEND_ALGEBRAIC = LEGEND_ALGEBRAIC';
    LEGEND_RATES = LEGEND_RATES';
    LEGEND_CONSTANTS = LEGEND_CONSTANTS';
end

function [STATES, CONSTANTS] = initConsts()
    VOI = 0; CONSTANTS = []; STATES = []; ALGEBRAIC = [];
    STATES(:,1) = 1;
    STATES(:,2) = 0;
    CONSTANTS(:,1) = 20;
    CONSTANTS(:,2) = 0.1;
    CONSTANTS(:,3) = 10;
    if (isempty(STATES)), warning('Initial values for states not set');, end
end

function [RATES, ALGEBRAIC] = computeRates(VOI, STATES, CONSTANTS)
    global algebraicVariableCount;
    statesSize = size(STATES);
    statesColumnCount = statesSize(2);
    if ( statesColumnCount == 1)
        STATES = STATES';
        ALGEBRAIC = zeros(1, algebraicVariableCount);
        utilOnes = 1;
    else
        statesRowCount = statesSize(1);
        ALGEBRAIC = zeros(statesRowCount, algebraicVariableCount);
        RATES = zeros(statesRowCount, statesColumnCount);
        utilOnes = ones(statesRowCount, 1);
    end
    RATES(:,1) = STATES(:,2);
    ALGEBRAIC(:,1) = STATES(:,1)./CONSTANTS(:,1);
    ALGEBRAIC(:,2) =  STATES(:,2).*CONSTANTS(:,2);
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS, STATES, ALGEBRAIC);
    RATES(:,2) = ALGEBRAIC(:,4);
   RATES = RATES';
end

% Calculate algebraic variables
function ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI)
    statesSize = size(STATES);
    statesColumnCount = statesSize(2);
    if ( statesColumnCount == 1)
        STATES = STATES';
        utilOnes = 1;
    else
        statesRowCount = statesSize(1);
        utilOnes = ones(statesRowCount, 1);
    end
    ALGEBRAIC(:,1) = STATES(:,1)./CONSTANTS(:,1);
    ALGEBRAIC(:,2) =  STATES(:,2).*CONSTANTS(:,2);
end

% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
    CONSTANTS = CONSTANTS_IN;
    STATES = STATES_IN;
    ALGEBRAIC = ALGEBRAIC_IN;
    global initialGuess_0;
    if (length(initialGuess_0) ~= 1), initialGuess_0 = 0.1;, end
    options = optimset('Display', 'off', 'TolX', 1E-6);
    if length(VOI) == 1
        residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
        ALGEBRAIC(:,3) = fsolve(residualfn, initialGuess_0, options);
        initialGuess_0 = ALGEBRAIC(:,3);
    else
        SET_ALGEBRAIC(:,3) = logical(1);
        for i=1:length(VOI)
            residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
            TEMP_ALGEBRAIC(:,3) = fsolve(residualfn, initialGuess_0, options);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
            initialGuess_0 = TEMP_ALGEBRAIC(:,3);
        end
    end
end

function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    ALGEBRAIC(:,3) = algebraicCandidate;
    resid = (ALGEBRAIC(:,1)) - ( - ALGEBRAIC(:,2) - ALGEBRAIC(:,3));
end

% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
    CONSTANTS = CONSTANTS_IN;
    STATES = STATES_IN;
    ALGEBRAIC = ALGEBRAIC_IN;
    global initialGuess_1;
    if (length(initialGuess_1) ~= 1), initialGuess_1 = 0.1;, end
    options = optimset('Display', 'off', 'TolX', 1E-6);
    if length(VOI) == 1
        residualfn = @(algebraicCandidate)residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
        ALGEBRAIC(:,4) = fsolve(residualfn, initialGuess_1, options);
        initialGuess_1 = ALGEBRAIC(:,4);
    else
        SET_ALGEBRAIC(:,4) = logical(1);
        for i=1:length(VOI)
            residualfn = @(algebraicCandidate)residualSN_1(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
            TEMP_ALGEBRAIC(:,4) = fsolve(residualfn, initialGuess_1, options);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
            initialGuess_1 = TEMP_ALGEBRAIC(:,4);
        end
    end
end

function resid = residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    ALGEBRAIC(:,4) = algebraicCandidate;
    resid = (ALGEBRAIC(:,3)) - ( ALGEBRAIC(:,4).*CONSTANTS(:,3));
end

% Pad out or shorten strings to a set length
function strout = strpad(strin)
    req_length = 160;
    insize = size(strin,2);
    if insize > req_length
        strout = strin(1:req_length);
    else
        strout = [strin, blanks(req_length - insize)];
    end
end