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 =7;
end
% There are a total of 4 entries in each of the rate and state variable arrays.
% There are a total of 11 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_CONSTANTS(:,1) = strpad('sigma in component parameters (dm)');
    LEGEND_CONSTANTS(:,2) = strpad('CNG_tot in component parameters (mole_per_dm_squared)');
    LEGEND_CONSTANTS(:,3) = strpad('CaM_tot in component parameters (mole_per_dm_cubed)');
    LEGEND_CONSTANTS(:,4) = strpad('km_CNG_0 in component parameters (per_second)');
    LEGEND_CONSTANTS(:,5) = strpad('km_CaM4 in component parameters (per_second)');
    LEGEND_CONSTANTS(:,6) = strpad('kp_CaM4 in component parameters (dm_6_per_second_per_mole_squared)');
    LEGEND_CONSTANTS(:,7) = strpad('kp_CNG_i in component parameters (dm_3_per_second_per_mole)');
    LEGEND_CONSTANTS(:,8) = strpad('km_CNG_i in component parameters (per_second)');
    LEGEND_CONSTANTS(:,9) = strpad('i_Ca in component parameters (per_second)');
    LEGEND_CONSTANTS(:,10) = strpad('k_Ca in component parameters (mole_per_dm_squared_per_second)');
    LEGEND_CONSTANTS(:,11) = strpad('K_Ca in component parameters (mole_per_dm_cubed)');
    LEGEND_ALGEBRAIC(:,1) = strpad('kp_act in component parameters (per_second)');
    LEGEND_STATES(:,1) = strpad('CNG_o in component dCNG_o_dt (mole_per_dm_squared)');
    LEGEND_ALGEBRAIC(:,2) = strpad('CNG_o_normalized in component dCNG_o_dt (dimensionless)');
    LEGEND_STATES(:,2) = strpad('CNG_i in component dCNG_i_dt (mole_per_dm_squared)');
    LEGEND_STATES(:,3) = strpad('CaM4 in component dCaM4_dt (mole_per_dm_cubed)');
    LEGEND_STATES(:,4) = strpad('Ca in component dCa_dt (mole_per_dm_cubed)');
    LEGEND_ALGEBRAIC(:,3) = strpad('Ca_normalized in component dCa_dt (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('CaM4_normalized in component dCaM4_dt (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('CNG_i_normalized in component dCNG_i_dt (dimensionless)');
    LEGEND_ALGEBRAIC(:,6) = strpad('CNG_c in component dCNG_c_dt (mole_per_dm_squared)');
    LEGEND_ALGEBRAIC(:,7) = strpad('CaM in component dCaM_dt (mole_per_dm_cubed)');
    LEGEND_RATES(:,1) = strpad('d/dt CNG_o in component dCNG_o_dt (mole_per_dm_squared)');
    LEGEND_RATES(:,4) = strpad('d/dt Ca in component dCa_dt (mole_per_dm_cubed)');
    LEGEND_RATES(:,3) = strpad('d/dt CaM4 in component dCaM4_dt (mole_per_dm_cubed)');
    LEGEND_RATES(:,2) = strpad('d/dt CNG_i in component dCNG_i_dt (mole_per_dm_squared)');
    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) = 5e-7;
    CONSTANTS(:,2) = 1.3e-13;
    CONSTANTS(:,3) = 2e-5;
    CONSTANTS(:,4) = 1e-2;
    CONSTANTS(:,5) = 2.5;
    CONSTANTS(:,6) = 1.1e9;
    CONSTANTS(:,7) = 2.1e6;
    CONSTANTS(:,8) = 3.4e-1;
    CONSTANTS(:,9) = 2e4;
    CONSTANTS(:,10) = 1e-10;
    CONSTANTS(:,11) = 1.2e-7;
    STATES(:,1) = 0;
    STATES(:,2) = 0;
    STATES(:,3) = 0;
    STATES(:,4) = 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(:,4) = ( (STATES(:,1)./CONSTANTS(:,1)).*CONSTANTS(:,9) - ( (CONSTANTS(:,10)./CONSTANTS(:,1)).*STATES(:,4))./(STATES(:,4)+CONSTANTS(:,11))) -  4.00000.*( CONSTANTS(:,6).*power(STATES(:,4), 2.00000).*((CONSTANTS(:,3) - STATES(:,3)) - STATES(:,2)./CONSTANTS(:,1)) -  CONSTANTS(:,5).*STATES(:,3));
    RATES(:,3) = (( CONSTANTS(:,6).*power(STATES(:,4), 2.00000).*((CONSTANTS(:,3) - STATES(:,3)) - STATES(:,2)./CONSTANTS(:,1)) -  CONSTANTS(:,5).*STATES(:,3)) -  (CONSTANTS(:,7)./CONSTANTS(:,1)).*STATES(:,3).*(CONSTANTS(:,2) - STATES(:,1)))+ (CONSTANTS(:,8)./CONSTANTS(:,1)).*STATES(:,2);
    RATES(:,2) =   - CONSTANTS(:,8).*STATES(:,2)+ CONSTANTS(:,7).*STATES(:,3).*(CONSTANTS(:,2) - STATES(:,2));
    ALGEBRAIC(:,1) = piecewise({VOI>0.100000&VOI<0.200000, 5.50000 , VOI>4.10000&VOI<4.20000, 5.50000 }, 1.60000e-05);
    RATES(:,1) = ( ALGEBRAIC(:,1).*((CONSTANTS(:,2) - STATES(:,1)) - STATES(:,2)) -  CONSTANTS(:,4).*STATES(:,1)) -  CONSTANTS(:,7).*STATES(:,1).*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>0.100000&VOI<0.200000, 5.50000 , VOI>4.10000&VOI<4.20000, 5.50000 }, 1.60000e-05);
    ALGEBRAIC(:,2) = STATES(:,1)./CONSTANTS(:,2);
    ALGEBRAIC(:,3) =  STATES(:,4).*10000.0;
    ALGEBRAIC(:,4) = STATES(:,3)./CONSTANTS(:,3);
    ALGEBRAIC(:,5) = STATES(:,2)./CONSTANTS(:,2);
    ALGEBRAIC(:,6) = (CONSTANTS(:,2) - STATES(:,1)) - STATES(:,2);
    ALGEBRAIC(:,7) = (CONSTANTS(:,3) - STATES(:,3)) -  (1.00000./CONSTANTS(:,1)).*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