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 =2;
end
% There are a total of 7 entries in each of the rate and state variable arrays.
% There are a total of 8 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 (second)');
    LEGEND_STATES(:,1) = strpad('Ca_t in component equations (uM_per_kg)');
    LEGEND_STATES(:,2) = strpad('TnCa_t in component equations (uM_per_kg)');
    LEGEND_STATES(:,3) = strpad('CB_on_t in component equations (uM_per_kg)');
    LEGEND_STATES(:,4) = strpad('Ca_released in component equations (uM_per_kg)');
    LEGEND_STATES(:,5) = strpad('Ca_sequestered in component equations (uM_per_kg)');
    LEGEND_STATES(:,6) = strpad('cumCB_on_t in component equations (uM_per_kg)');
    LEGEND_STATES(:,7) = strpad('cumCB_off_t in component equations (uM_per_kg)');
    LEGEND_ALGEBRAIC(:,1) = strpad('Ca_release_rate in component equations (uM_per_kg_per_second)');
    LEGEND_ALGEBRAIC(:,2) = strpad('dTnCa_t_dt in component equations (uM_per_kg_per_second)');
    LEGEND_CONSTANTS(:,1) = strpad('Ca_tot_released in component equations (uM_per_kg)');
    LEGEND_CONSTANTS(:,2) = strpad('total_Tn in component equations (uM_per_kg)');
    LEGEND_CONSTANTS(:,3) = strpad('total_CB in component equations (uM_per_kg)');
    LEGEND_CONSTANTS(:,4) = strpad('k_1 in component equations (kg_per_uM_per_second)');
    LEGEND_CONSTANTS(:,5) = strpad('k_2 in component equations (per_second)');
    LEGEND_CONSTANTS(:,6) = strpad('k_3 in component equations (per_second)');
    LEGEND_CONSTANTS(:,7) = strpad('f in component equations (kg_per_uM_per_second)');
    LEGEND_CONSTANTS(:,8) = strpad('g in component equations (per_second)');
    LEGEND_RATES(:,1) = strpad('d/dt Ca_t in component equations (uM_per_kg)');
    LEGEND_RATES(:,2) = strpad('d/dt TnCa_t in component equations (uM_per_kg)');
    LEGEND_RATES(:,3) = strpad('d/dt CB_on_t in component equations (uM_per_kg)');
    LEGEND_RATES(:,4) = strpad('d/dt Ca_released in component equations (uM_per_kg)');
    LEGEND_RATES(:,5) = strpad('d/dt Ca_sequestered in component equations (uM_per_kg)');
    LEGEND_RATES(:,6) = strpad('d/dt cumCB_on_t in component equations (uM_per_kg)');
    LEGEND_RATES(:,7) = strpad('d/dt cumCB_off_t in component equations (uM_per_kg)');
    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) = 0;
    STATES(:,2) = 0;
    STATES(:,3) = 0;
    STATES(:,4) = 0;
    STATES(:,5) = 0;
    STATES(:,6) = 0;
    STATES(:,7) = 0;
    CONSTANTS(:,1) = 35;
    CONSTANTS(:,2) = 70;
    CONSTANTS(:,3) = 150;
    CONSTANTS(:,4) = 5e6;
    CONSTANTS(:,5) = 10;
    CONSTANTS(:,6) = 1000;
    CONSTANTS(:,7) = 0.4e6;
    CONSTANTS(:,8) = 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(:,2) =  CONSTANTS(:,4).*STATES(:,1).*(CONSTANTS(:,2) - STATES(:,2)) -  CONSTANTS(:,5).*STATES(:,2);
    RATES(:,3) =  CONSTANTS(:,7).*STATES(:,2).*(CONSTANTS(:,3) - STATES(:,3)) -  CONSTANTS(:,8).*STATES(:,3);
    RATES(:,5) =  CONSTANTS(:,6).*STATES(:,1);
    RATES(:,6) =  CONSTANTS(:,7).*STATES(:,2).*(CONSTANTS(:,3) - STATES(:,3));
    RATES(:,7) =  CONSTANTS(:,8).*STATES(:,3);
    ALGEBRAIC(:,1) = piecewise({VOI>0.100000, 0.00000 },  20.0000.*CONSTANTS(:,1).*(1.00000 -  10.0000.*VOI));
    RATES(:,4) = ALGEBRAIC(:,1);
    ALGEBRAIC(:,2) =  CONSTANTS(:,4).*STATES(:,1).*(CONSTANTS(:,2) - STATES(:,2)) -  CONSTANTS(:,5).*STATES(:,2);
    RATES(:,1) = (ALGEBRAIC(:,1) -  CONSTANTS(:,6).*STATES(:,1)) - ALGEBRAIC(:,2);
   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>0.100000, 0.00000 },  20.0000.*CONSTANTS(:,1).*(1.00000 -  10.0000.*VOI));
    ALGEBRAIC(:,2) =  CONSTANTS(:,4).*STATES(:,1).*(CONSTANTS(:,2) - STATES(:,2)) -  CONSTANTS(:,5).*STATES(:,2);
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