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 =3;
end
% There are a total of 2 entries in each of the rate and state variable arrays.
% There are a total of 15 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_CONSTANTS(:,1) = strpad('T_a in component model_parameters (celsius)');
    LEGEND_CONSTANTS(:,2) = strpad('T_b in component model_parameters (celsius)');
    LEGEND_CONSTANTS(:,3) = strpad('delta_T in component model_parameters (celsius)');
    LEGEND_CONSTANTS(:,4) = strpad('kinc in component model_parameters (W_per_kg_C2)');
    LEGEND_ALGEBRAIC(:,3) = strpad('M_c in component M_c (W_per_kg)');
    LEGEND_CONSTANTS(:,5) = strpad('t_day in component M_c (hour)');
    LEGEND_CONSTANTS(:,6) = strpad('t_night in component M_c (hour)');
    LEGEND_ALGEBRAIC(:,1) = strpad('tprime in component M_c (second)');
    LEGEND_CONSTANTS(:,7) = strpad('day_length in component M_c (second)');
    LEGEND_CONSTANTS(:,14) = strpad('M_day in component M_day (W_per_kg)');
    LEGEND_CONSTANTS(:,15) = strpad('M_night in component M_night (W_per_kg)');
    LEGEND_STATES(:,1) = strpad('M in component M (W_per_kg)');
    LEGEND_CONSTANTS(:,8) = strpad('km in component M (per_hour)');
    LEGEND_STATES(:,2) = strpad('T in component T (celsius)');
    LEGEND_CONSTANTS(:,9) = strpad('c in component T (kJ_per_kg_C)');
    LEGEND_ALGEBRAIC(:,2) = strpad('k in component k (W_per_kg_C)');
    LEGEND_CONSTANTS(:,13) = strpad('kb in component kb (W_per_kg_C)');
    LEGEND_CONSTANTS(:,11) = strpad('T_day in component T_day (celsius)');
    LEGEND_CONSTANTS(:,12) = strpad('T_night in component T_night (celsius)');
    LEGEND_CONSTANTS(:,10) = strpad('M_b in component kb (W_per_kg)');
    LEGEND_RATES(:,1) = strpad('d/dt M in component M (W_per_kg)');
    LEGEND_RATES(:,2) = strpad('d/dt T in component T (celsius)');
    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 = [];
    CONSTANTS(:,1) = 21.0;
    CONSTANTS(:,2) = 38.0;
    CONSTANTS(:,3) = 1.57;
    CONSTANTS(:,4) = 0.0258;
    CONSTANTS(:,5) = 17.5;
    CONSTANTS(:,6) = 6.73;
    CONSTANTS(:,7) = 86400;
    STATES(:,1) = 3.5;
    CONSTANTS(:,8) = 1.1375;
    STATES(:,2) = 38.785;
    CONSTANTS(:,9) = 3.47;
    CONSTANTS(:,10) = 3.0;
    CONSTANTS(:,11) = CONSTANTS(:,2)+CONSTANTS(:,3)./2.00000;
    CONSTANTS(:,12) = CONSTANTS(:,2) - CONSTANTS(:,3)./2.00000;
    CONSTANTS(:,13) = CONSTANTS(:,10)./(CONSTANTS(:,2) - CONSTANTS(:,1));
    CONSTANTS(:,14) =  (CONSTANTS(:,13)+ CONSTANTS(:,4).*(CONSTANTS(:,11) - CONSTANTS(:,2))).*(CONSTANTS(:,11) - CONSTANTS(:,1));
    CONSTANTS(:,15) =  (CONSTANTS(:,13)+ CONSTANTS(:,4).*(CONSTANTS(:,12) - CONSTANTS(:,2))).*(CONSTANTS(:,12) - CONSTANTS(:,1));
    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
    ALGEBRAIC(:,2) = CONSTANTS(:,13)+ CONSTANTS(:,4).*(STATES(:,2) - CONSTANTS(:,2));
    RATES(:,2) =  power(CONSTANTS(:,9), -1.00000).*(STATES(:,1) -  ALGEBRAIC(:,2).*(STATES(:,2) - CONSTANTS(:,1)));
    ALGEBRAIC(:,1) =  rem( VOI.*3600.00.*1.00000, CONSTANTS(:,7));
    ALGEBRAIC(:,3) = piecewise({ALGEBRAIC(:,1)./3600.00>=CONSTANTS(:,6)&ALGEBRAIC(:,1)./3600.00<CONSTANTS(:,5), CONSTANTS(:,15) }, CONSTANTS(:,14));
    RATES(:,1) =   - CONSTANTS(:,8).*(STATES(:,1) - ALGEBRAIC(:,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(:,2) = CONSTANTS(:,13)+ CONSTANTS(:,4).*(STATES(:,2) - CONSTANTS(:,2));
    ALGEBRAIC(:,1) =  rem( VOI.*3600.00.*1.00000, CONSTANTS(:,7));
    ALGEBRAIC(:,3) = piecewise({ALGEBRAIC(:,1)./3600.00>=CONSTANTS(:,6)&ALGEBRAIC(:,1)./3600.00<CONSTANTS(:,5), CONSTANTS(:,15) }, CONSTANTS(:,14));
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