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 =1;
end
% There are a total of 5 entries in each of the rate and state variable arrays.
% There are a total of 6 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('time in component environment (hour)');
    LEGEND_ALGEBRAIC(:,1) = strpad('GnRH in component GnRH (nanomolar)');
    LEGEND_STATES(:,1) = strpad('F in component F (dimensionless)');
    LEGEND_CONSTANTS(:,1) = strpad('kfb in component model_parameters (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,2) = strpad('kdf in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,2) = strpad('D in component D (dimensionless)');
    LEGEND_CONSTANTS(:,3) = strpad('kbd in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,3) = strpad('B in component B (dimensionless)');
    LEGEND_STATES(:,4) = strpad('R in component R (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('s in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,5) = strpad('a1 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('a2 in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,5) = strpad('C in component C (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt F in component F (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt D in component D (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt B in component B (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt R in component R (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt C in component C (dimensionless)');
    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) = 1.0;
    CONSTANTS(:,1) = 19.35;
    CONSTANTS(:,2) = 2.52;
    STATES(:,2) = 0.0;
    CONSTANTS(:,3) = 9.91;
    STATES(:,3) = 0.0;
    STATES(:,4) = 2115.0;
    CONSTANTS(:,4) = 6.80;
    CONSTANTS(:,5) = 0.0328;
    CONSTANTS(:,6) = 0.0830;
    STATES(:,5) = 0.0;
    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(:,2) =  CONSTANTS(:,3).*STATES(:,3) -  CONSTANTS(:,2).*STATES(:,2);
    RATES(:,4) = CONSTANTS(:,4) -  (CONSTANTS(:,5)+ CONSTANTS(:,6).*STATES(:,3)).*STATES(:,4);
    RATES(:,5) =  (CONSTANTS(:,5)+ CONSTANTS(:,6).*STATES(:,3)).*STATES(:,4);
    ALGEBRAIC(:,1) = piecewise({VOI>=0.00000&VOI<0.0666667, 0.500000 , VOI>=0.0666667&VOI<0.400000, 0.00000 , VOI>=0.400000&VOI<0.466667, 0.500000 , VOI>=0.466667&VOI<2.46667, 0.00000 , VOI>=2.46667&VOI<2.53333, 0.500000 , VOI>=2.53333&VOI<2.61667, 0.00000 , VOI>=2.61667&VOI<2.68333, 0.500000 , VOI>=2.68333&VOI<4.68333, 0.00000 , VOI>=4.68333&VOI<4.75000, 0.500000 , VOI>=4.75000&VOI<4.91667, 0.00000 , VOI>=4.91667&VOI<4.98333, 0.500000 , VOI>=4.98333&VOI<6.98333, 0.00000 , VOI>=6.98333&VOI<7.06667, 0.500000 , VOI>=7.06667&VOI<7.73333, 0.00000 , VOI>=7.73333&VOI<7.80000, 0.500000 , VOI>=7.80000&VOI<9.80000, 0.00000 }, NaN);
    RATES(:,1) =  CONSTANTS(:,2).*STATES(:,2) -  CONSTANTS(:,1).*STATES(:,1).*ALGEBRAIC(:,1);
    RATES(:,3) =  CONSTANTS(:,1).*STATES(:,1).*ALGEBRAIC(:,1) -  CONSTANTS(:,3).*STATES(:,3);
   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) = piecewise({VOI>=0.00000&VOI<0.0666667, 0.500000 , VOI>=0.0666667&VOI<0.400000, 0.00000 , VOI>=0.400000&VOI<0.466667, 0.500000 , VOI>=0.466667&VOI<2.46667, 0.00000 , VOI>=2.46667&VOI<2.53333, 0.500000 , VOI>=2.53333&VOI<2.61667, 0.00000 , VOI>=2.61667&VOI<2.68333, 0.500000 , VOI>=2.68333&VOI<4.68333, 0.00000 , VOI>=4.68333&VOI<4.75000, 0.500000 , VOI>=4.75000&VOI<4.91667, 0.00000 , VOI>=4.91667&VOI<4.98333, 0.500000 , VOI>=4.98333&VOI<6.98333, 0.00000 , VOI>=6.98333&VOI<7.06667, 0.500000 , VOI>=7.06667&VOI<7.73333, 0.00000 , VOI>=7.73333&VOI<7.80000, 0.500000 , VOI>=7.80000&VOI<9.80000, 0.00000 }, NaN);
end

% Compute result of a piecewise function
function x = piecewise(cases, default)
    set = [0];
    for i = 1:2:length(cases)
        if (length(cases{i+1}) == 1)
            x(cases{i} & ~set,:) = cases{i+1};
        else
            x(cases{i} & ~set,:) = cases{i+1}(cases{i} & ~set);
        end
        set = set | cases{i};
        if(set), break, end
    end
    if (length(default) == 1)
        x(~set,:) = default;
    else
        x(~set,:) = default(~set);
    end
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