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 =4;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 19 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('Qv in component v (per_second)');
    LEGEND_STATES(:,1) = strpad('Vv in component v (mV)');
    LEGEND_CONSTANTS(:,1) = strpad('tau_v in component v (second)');
    LEGEND_CONSTANTS(:,2) = strpad('v_vm in component v (mV_second)');
    LEGEND_CONSTANTS(:,3) = strpad('awake_start in component v (hour)');
    LEGEND_CONSTANTS(:,4) = strpad('awake_end in component v (hour)');
    LEGEND_ALGEBRAIC(:,2) = strpad('Qm in component m (per_second)');
    LEGEND_CONSTANTS(:,5) = strpad('Qmax in component model_parameters (per_second)');
    LEGEND_ALGEBRAIC(:,4) = strpad('D in component D (mV)');
    LEGEND_CONSTANTS(:,6) = strpad('theta in component model_parameters (mV)');
    LEGEND_CONSTANTS(:,7) = strpad('sigma in component model_parameters (mV)');
    LEGEND_STATES(:,2) = strpad('Vm in component m (mV)');
    LEGEND_CONSTANTS(:,8) = strpad('tau_m in component m (second)');
    LEGEND_CONSTANTS(:,9) = strpad('v_mv in component m (mV_second)');
    LEGEND_CONSTANTS(:,10) = strpad('A in component m (mV)');
    LEGEND_CONSTANTS(:,11) = strpad('awake_start in component m (hour)');
    LEGEND_CONSTANTS(:,12) = strpad('awake_end in component m (hour)');
    LEGEND_STATES(:,3) = strpad('H in component H (nM)');
    LEGEND_CONSTANTS(:,13) = strpad('chi in component H (hour)');
    LEGEND_CONSTANTS(:,14) = strpad('mu in component H (nM_second)');
    LEGEND_ALGEBRAIC(:,3) = strpad('C in component D (dimensionless)');
    LEGEND_CONSTANTS(:,15) = strpad('c0 in component D (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('omega in component D (per_hour)');
    LEGEND_CONSTANTS(:,16) = strpad('alpha in component D (hour)');
    LEGEND_CONSTANTS(:,17) = strpad('v_vc in component D (mV)');
    LEGEND_CONSTANTS(:,18) = strpad('v_vh in component D (mV_per_nM)');
    LEGEND_RATES(:,1) = strpad('d/dt Vv in component v (mV)');
    LEGEND_RATES(:,2) = strpad('d/dt Vm in component m (mV)');
    LEGEND_RATES(:,3) = strpad('d/dt H in component H (nM)');
    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) = -12.5;
    CONSTANTS(:,1) = 10.0;
    CONSTANTS(:,2) = -2.1;
    CONSTANTS(:,3) = 167.04;
    CONSTANTS(:,4) = 240.0;
    CONSTANTS(:,5) = 100.0;
    CONSTANTS(:,6) = 10.0;
    CONSTANTS(:,7) = 3.0;
    STATES(:,2) = 0.0;
    CONSTANTS(:,8) = 10.0;
    CONSTANTS(:,9) = -1.8;
    CONSTANTS(:,10) = 1.3;
    CONSTANTS(:,11) = 160.0;
    CONSTANTS(:,12) = 240.0;
    STATES(:,3) = 15.0;
    CONSTANTS(:,13) = 45.0;
    CONSTANTS(:,14) = 4.4;
    CONSTANTS(:,15) = 4.5;
    CONSTANTS(:,16) = 0;
    CONSTANTS(:,17) = -2.9;
    CONSTANTS(:,18) = 1.0;
    CONSTANTS(:,19) = ( 2.00000.* pi)./24.0000;
    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(:,1) = CONSTANTS(:,5)./(1.00000+exp( - (STATES(:,1) - CONSTANTS(:,6))./CONSTANTS(:,7)));
    RATES(:,2) = piecewise({VOI>=CONSTANTS(:,11)&VOI<CONSTANTS(:,12), 0.00000 }, ((CONSTANTS(:,10)+ CONSTANTS(:,9).*ALGEBRAIC(:,1)) - STATES(:,2))./(CONSTANTS(:,8)./3600.00));
    ALGEBRAIC(:,2) = CONSTANTS(:,5)./(1.00000+exp( - (STATES(:,2) - CONSTANTS(:,6))./CONSTANTS(:,7)));
    RATES(:,3) = ( CONSTANTS(:,14).*ALGEBRAIC(:,2) - STATES(:,3))./CONSTANTS(:,13);
    ALGEBRAIC(:,3) = CONSTANTS(:,15)+cos( CONSTANTS(:,19).*(VOI - CONSTANTS(:,16)));
    ALGEBRAIC(:,4) =  CONSTANTS(:,17).*ALGEBRAIC(:,3)+ CONSTANTS(:,18).*STATES(:,3);
    RATES(:,1) = piecewise({VOI>=CONSTANTS(:,3)&VOI<CONSTANTS(:,4), 0.00000 }, (( CONSTANTS(:,2).*ALGEBRAIC(:,2)+ALGEBRAIC(:,4)) - STATES(:,1))./(CONSTANTS(:,1)./3600.00));
   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) = CONSTANTS(:,5)./(1.00000+exp( - (STATES(:,1) - CONSTANTS(:,6))./CONSTANTS(:,7)));
    ALGEBRAIC(:,2) = CONSTANTS(:,5)./(1.00000+exp( - (STATES(:,2) - CONSTANTS(:,6))./CONSTANTS(:,7)));
    ALGEBRAIC(:,3) = CONSTANTS(:,15)+cos( CONSTANTS(:,19).*(VOI - CONSTANTS(:,16)));
    ALGEBRAIC(:,4) =  CONSTANTS(:,17).*ALGEBRAIC(:,3)+ CONSTANTS(:,18).*STATES(:,3);
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