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 =5;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 13 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 (minute)');
    LEGEND_CONSTANTS(:,1) = strpad('POT in component non_muscle_autoregulatory_local_blood_flow_control (mmHg)');
    LEGEND_CONSTANTS(:,10) = strpad('POD in component NM_autoregulatory_driving_force (mmHg)');
    LEGEND_CONSTANTS(:,2) = strpad('POR in component parameter_values (mmHg)');
    LEGEND_CONSTANTS(:,11) = strpad('POB in component NM_ST_sensitivity_control (mmHg)');
    LEGEND_CONSTANTS(:,3) = strpad('POK in component parameter_values (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('AR1 in component NM_ST_time_delay_and_damping (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('A1K in component parameter_values (minute)');
    LEGEND_STATES(:,1) = strpad('AR1T in component NM_ST_time_delay_and_damping (dimensionless)');
    LEGEND_CONSTANTS(:,12) = strpad('POA in component NM_I_sensitivity_control (mmHg)');
    LEGEND_CONSTANTS(:,5) = strpad('PON in component parameter_values (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('AR2 in component NM_I_time_delay_and_limit (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('A2K in component parameter_values (minute)');
    LEGEND_STATES(:,2) = strpad('AR2T in component NM_I_time_delay_and_limit (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('POC in component NM_LT_sensitivity_control (mmHg)');
    LEGEND_CONSTANTS(:,7) = strpad('POZ in component parameter_values (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('AR3 in component NM_LT_time_delay_and_limit (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('A3K in component parameter_values (minute)');
    LEGEND_STATES(:,3) = strpad('AR3T in component NM_LT_time_delay_and_limit (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('ARM1 in component total_NM_autoregulation (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('ARM in component global_NM_blood_flow_autoregulation_output (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('AUTOSN in component parameter_values (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt AR1T in component NM_ST_time_delay_and_damping (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt AR2T in component NM_I_time_delay_and_limit (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt AR3T in component NM_LT_time_delay_and_limit (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 = [];
    CONSTANTS(:,1) = 35.1148;
    CONSTANTS(:,2) = 35;
    CONSTANTS(:,3) = 0.1;
    CONSTANTS(:,4) = 0.5;
    STATES(:,1) = 1.02127;
    CONSTANTS(:,5) = 0.1;
    CONSTANTS(:,6) = 60;
    STATES(:,2) = 1.01179;
    CONSTANTS(:,7) = 2;
    CONSTANTS(:,8) = 40000;
    STATES(:,3) = 1.1448;
    CONSTANTS(:,9) = 0.9;
    CONSTANTS(:,10) = CONSTANTS(:,1) - CONSTANTS(:,2);
    CONSTANTS(:,11) =  CONSTANTS(:,10).*CONSTANTS(:,3)+1.00000;
    CONSTANTS(:,12) =  CONSTANTS(:,5).*CONSTANTS(:,10)+1.00000;
    CONSTANTS(:,13) =  CONSTANTS(:,7).*CONSTANTS(:,10)+1.00000;
    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) = ( CONSTANTS(:,11).*1.00000 - STATES(:,1))./CONSTANTS(:,4);
    RATES(:,2) = ( CONSTANTS(:,12).*1.00000 - STATES(:,2))./CONSTANTS(:,6);
    RATES(:,3) = ( CONSTANTS(:,13).*1.00000 - STATES(:,3))./CONSTANTS(:,8);
   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({STATES(:,1)<0.500000, 0.500000 }, STATES(:,1));
    ALGEBRAIC(:,2) = piecewise({STATES(:,2)<0.500000, 0.500000 }, STATES(:,2));
    ALGEBRAIC(:,3) = piecewise({STATES(:,3)<0.300000, 0.300000 }, STATES(:,3));
    ALGEBRAIC(:,4) =  ALGEBRAIC(:,1).*ALGEBRAIC(:,2).*ALGEBRAIC(:,3);
    ALGEBRAIC(:,5) =  (ALGEBRAIC(:,4) - 1.00000).*CONSTANTS(:,9)+1.00000;
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