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 =9;
end
% There are a total of 7 entries in each of the rate and state variable arrays.
% There are a total of 35 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('IP3 in component IP3_dynamics (micromolar)');
    LEGEND_ALGEBRAIC(:,1) = strpad('j_IP3 in component IP3_dynamics (micromolar_micrometre_per_second)');
    LEGEND_CONSTANTS(:,1) = strpad('J_IP3 in component IP3_dynamics (micromolar_micrometre_per_second)');
    LEGEND_CONSTANTS(:,2) = strpad('k_0 in component IP3_dynamics (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,3) = strpad('k_degr in component IP3_dynamics (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('IP3_0 in component IP3_dynamics (micromolar)');
    LEGEND_CONSTANTS(:,5) = strpad('Ca_ER in component ER (micromolar)');
    LEGEND_STATES(:,2) = strpad('Ca in component Calcium_dynamics (micromolar)');
    LEGEND_CONSTANTS(:,6) = strpad('alpha in component Calcium_dynamics (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('J_channel in component Channel_kinetics (flux)');
    LEGEND_ALGEBRAIC(:,8) = strpad('J_pump in component SERCA_pump_kinetics (flux)');
    LEGEND_ALGEBRAIC(:,9) = strpad('J_leak in component Leak (flux)');
    LEGEND_CONSTANTS(:,28) = strpad('R_buffering in component Calcium_buffering (flux)');
    LEGEND_CONSTANTS(:,7) = strpad('J_max in component Channel_kinetics (flux)');
    LEGEND_STATES(:,3) = strpad('h in component Channel_kinetics (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('K_act in component Channel_kinetics (micromolar)');
    LEGEND_CONSTANTS(:,9) = strpad('K_IP3 in component Channel_kinetics (micromolar)');
    LEGEND_CONSTANTS(:,10) = strpad('K_inh in component Channel_kinetics (micromolar)');
    LEGEND_CONSTANTS(:,11) = strpad('k_on in component Channel_kinetics (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,12) = strpad('V_max in component SERCA_pump_kinetics (flux)');
    LEGEND_CONSTANTS(:,13) = strpad('K_p in component SERCA_pump_kinetics (micromolar)');
    LEGEND_CONSTANTS(:,14) = strpad('L in component Leak (flux)');
    LEGEND_CONSTANTS(:,15) = strpad('R1 in component Calcium_buffering (flux)');
    LEGEND_CONSTANTS(:,16) = strpad('R2 in component Calcium_buffering (flux)');
    LEGEND_STATES(:,4) = strpad('B1 in component Calcium_buffering (micromolar)');
    LEGEND_STATES(:,5) = strpad('B2 in component Calcium_buffering (micromolar)');
    LEGEND_STATES(:,6) = strpad('CaB1 in component Calcium_buffering (micromolar)');
    LEGEND_STATES(:,7) = strpad('CaB2 in component Calcium_buffering (micromolar)');
    LEGEND_ALGEBRAIC(:,3) = strpad('k1_on in component Calcium_buffering (second_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,4) = strpad('k1_off in component Calcium_buffering (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,5) = strpad('k2_on in component Calcium_buffering (second_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,6) = strpad('k2_off in component Calcium_buffering (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,17) = strpad('K1 in component Calcium_buffering (micromolar)');
    LEGEND_CONSTANTS(:,18) = strpad('K2 in component Calcium_buffering (micromolar)');
    LEGEND_CONSTANTS(:,19) = strpad('soma_or_neurite in component Plasma_membrane_extrusion_mechanisms (dimensionless)');
    LEGEND_ALGEBRAIC(:,7) = strpad('j_Ca in component Plasma_membrane_extrusion_mechanisms (micromolar_micrometre_per_second)');
    LEGEND_CONSTANTS(:,20) = strpad('gamma_0 in component Plasma_membrane_extrusion_mechanisms (micrometre_per_second)');
    LEGEND_CONSTANTS(:,31) = strpad('gamma in component Plasma_membrane_extrusion_mechanisms (micrometre_per_second)');
    LEGEND_CONSTANTS(:,29) = strpad('gamma_s in component Plasma_membrane_extrusion_mechanisms (micrometre_per_second)');
    LEGEND_CONSTANTS(:,30) = strpad('gamma_n in component Plasma_membrane_extrusion_mechanisms (micrometre_per_second)');
    LEGEND_CONSTANTS(:,21) = strpad('delta in component Plasma_membrane_extrusion_mechanisms (dimensionless)');
    LEGEND_CONSTANTS(:,22) = strpad('sigma in component Plasma_membrane_extrusion_mechanisms (per_micrometre)');
    LEGEND_CONSTANTS(:,23) = strpad('w_n in component Plasma_membrane_extrusion_mechanisms (dimensionless)');
    LEGEND_CONSTANTS(:,24) = strpad('w_s in component Plasma_membrane_extrusion_mechanisms (dimensionless)');
    LEGEND_CONSTANTS(:,25) = strpad('sigma_soma_2D in component Plasma_membrane_extrusion_mechanisms (per_micrometre)');
    LEGEND_CONSTANTS(:,26) = strpad('sigma_neurite_2D in component Plasma_membrane_extrusion_mechanisms (per_micrometre)');
    LEGEND_CONSTANTS(:,27) = strpad('Ca_c in component Plasma_membrane_extrusion_mechanisms (micromolar)');
    LEGEND_RATES(:,1) = strpad('d/dt IP3 in component IP3_dynamics (micromolar)');
    LEGEND_RATES(:,2) = strpad('d/dt Ca in component Calcium_dynamics (micromolar)');
    LEGEND_RATES(:,3) = strpad('d/dt h in component Channel_kinetics (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt B1 in component Calcium_buffering (micromolar)');
    LEGEND_RATES(:,6) = strpad('d/dt CaB1 in component Calcium_buffering (micromolar)');
    LEGEND_RATES(:,5) = strpad('d/dt B2 in component Calcium_buffering (micromolar)');
    LEGEND_RATES(:,7) = strpad('d/dt CaB2 in component Calcium_buffering (micromolar)');
    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) = 3.0;
    CONSTANTS(:,1) = 20.86;
    CONSTANTS(:,2) = 1.188;
    CONSTANTS(:,3) = 0.14;
    CONSTANTS(:,4) = 0.16;
    CONSTANTS(:,5) = 400.0;
    STATES(:,2) = 0.05;
    CONSTANTS(:,6) = 0.0;
    CONSTANTS(:,7) = 3500.0;
    STATES(:,3) = 0.8;
    CONSTANTS(:,8) = 0.3;
    CONSTANTS(:,9) = 0.8;
    CONSTANTS(:,10) = 0.2;
    CONSTANTS(:,11) = 2.7;
    CONSTANTS(:,12) = 3.75;
    CONSTANTS(:,13) = 0.27;
    CONSTANTS(:,14) = 0.1;
    CONSTANTS(:,15) = 0.1;
    CONSTANTS(:,16) = 0.1;
    STATES(:,4) = 450.0;
    STATES(:,5) = 75.0;
    STATES(:,6) = 0;
    STATES(:,7) = 0;
    CONSTANTS(:,17) = 10.0;
    CONSTANTS(:,18) = 0.24;
    CONSTANTS(:,19) = -1;
    CONSTANTS(:,20) = 8.0;
    CONSTANTS(:,21) = 1.45;
    CONSTANTS(:,22) = 0.263;
    CONSTANTS(:,23) = 0.377;
    CONSTANTS(:,24) = 0.623;
    CONSTANTS(:,25) = 0.132;
    CONSTANTS(:,26) = 0.479;
    CONSTANTS(:,27) = 0.2;
    CONSTANTS(:,28) = CONSTANTS(:,15)+CONSTANTS(:,16);
    CONSTANTS(:,29) = ( CONSTANTS(:,20).*CONSTANTS(:,22))./( CONSTANTS(:,21).*CONSTANTS(:,26).*CONSTANTS(:,23)+ CONSTANTS(:,25).*CONSTANTS(:,24));
    CONSTANTS(:,31) = CONSTANTS(:,15);
    CONSTANTS(:,32) =  - CONSTANTS(:,15);
    CONSTANTS(:,33) = CONSTANTS(:,16);
    CONSTANTS(:,34) =  - CONSTANTS(:,16);
    CONSTANTS(:,30) = ( CONSTANTS(:,20).*CONSTANTS(:,22).*CONSTANTS(:,21))./( CONSTANTS(:,21).*CONSTANTS(:,26).*CONSTANTS(:,23)+ CONSTANTS(:,25).*CONSTANTS(:,24));
    CONSTANTS(:,31) = piecewise({CONSTANTS(:,19)<=0.00000, CONSTANTS(:,29) }, CONSTANTS(:,30));
    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) = CONSTANTS(:,31);
    RATES(:,6) = CONSTANTS(:,32);
    RATES(:,5) = CONSTANTS(:,33);
    RATES(:,7) = CONSTANTS(:,34);
    RATES(:,1) =  - ( CONSTANTS(:,3).*(STATES(:,1) - CONSTANTS(:,4)));
    RATES(:,3) =  CONSTANTS(:,11).*(CONSTANTS(:,10) -  STATES(:,3).*(STATES(:,2)+CONSTANTS(:,10)));
    ALGEBRAIC(:,2) =  CONSTANTS(:,7).*power( (STATES(:,1)./(STATES(:,1)+CONSTANTS(:,9))).*(STATES(:,2)./(STATES(:,2)+CONSTANTS(:,8))).*STATES(:,3), 3.00000).*(1.00000 - STATES(:,2)./CONSTANTS(:,5));
    ALGEBRAIC(:,8) =  CONSTANTS(:,12).*(power(STATES(:,2), 2.00000)./(power(STATES(:,2), 2.00000)+power(CONSTANTS(:,13), 2.00000)));
    ALGEBRAIC(:,9) =  CONSTANTS(:,14).*(1.00000 - STATES(:,2)./CONSTANTS(:,5));
    RATES(:,2) =  CONSTANTS(:,6).*(ALGEBRAIC(:,2)+ - ALGEBRAIC(:,8)+ALGEBRAIC(:,9))+CONSTANTS(:,28);
   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(:,7).*power( (STATES(:,1)./(STATES(:,1)+CONSTANTS(:,9))).*(STATES(:,2)./(STATES(:,2)+CONSTANTS(:,8))).*STATES(:,3), 3.00000).*(1.00000 - STATES(:,2)./CONSTANTS(:,5));
    ALGEBRAIC(:,8) =  CONSTANTS(:,12).*(power(STATES(:,2), 2.00000)./(power(STATES(:,2), 2.00000)+power(CONSTANTS(:,13), 2.00000)));
    ALGEBRAIC(:,9) =  CONSTANTS(:,14).*(1.00000 - STATES(:,2)./CONSTANTS(:,5));
    ALGEBRAIC(:,1) =  CONSTANTS(:,1).*exp(  - CONSTANTS(:,2).*VOI);
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS, STATES, ALGEBRAIC);
    ALGEBRAIC(:,7) = piecewise({STATES(:,2)>CONSTANTS(:,27),  CONSTANTS(:,31).*(STATES(:,2) - CONSTANTS(:,27)) }, 0.00000);
end

% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
    ALGEBRAIC = ALGEBRAIC_IN;
    CONSTANTS = CONSTANTS_IN;
    STATES = STATES_IN;
    global initialGuess_0;
    if (length(initialGuess_0) ~= 2), initialGuess_0 = [0.1,0.1];, end
    options = optimset('Display', 'off', 'TolX', 1E-6);
    if length(VOI) == 1
        residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
        soln = fsolve(residualfn, initialGuess_0, options);
        initialGuess_0 = soln;
        ALGEBRAIC(:,3) = soln(1);
        ALGEBRAIC(:,4) = soln(2);
    else
        SET_ALGEBRAIC(:,3) = logical(1);
        SET_ALGEBRAIC(:,4) = logical(1);
        for i=1:length(VOI)
            residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
            soln = fsolve(residualfn, initialGuess_0, options);
            initialGuess_0 = soln;
            TEMP_ALGEBRAIC(:,3) = soln(1);
            TEMP_ALGEBRAIC(:,4) = soln(2);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
        end
    end
end

function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    ALGEBRAIC(:,3) = algebraicCandidate(1);
    ALGEBRAIC(:,4) = algebraicCandidate(2);
    resid(1) = CONSTANTS(:,15) - ( - ( ALGEBRAIC(:,3).*STATES(:,2).*STATES(:,4))+ ALGEBRAIC(:,4).*STATES(:,6));
    resid(2) = CONSTANTS(:,17) - ALGEBRAIC(:,4)./ALGEBRAIC(:,3);
end

% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
    ALGEBRAIC = ALGEBRAIC_IN;
    CONSTANTS = CONSTANTS_IN;
    STATES = STATES_IN;
    global initialGuess_1;
    if (length(initialGuess_1) ~= 2), initialGuess_1 = [0.1,0.1];, end
    options = optimset('Display', 'off', 'TolX', 1E-6);
    if length(VOI) == 1
        residualfn = @(algebraicCandidate)residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
        soln = fsolve(residualfn, initialGuess_1, options);
        initialGuess_1 = soln;
        ALGEBRAIC(:,5) = soln(1);
        ALGEBRAIC(:,6) = soln(2);
    else
        SET_ALGEBRAIC(:,5) = logical(1);
        SET_ALGEBRAIC(:,6) = logical(1);
        for i=1:length(VOI)
            residualfn = @(algebraicCandidate)residualSN_1(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
            soln = fsolve(residualfn, initialGuess_1, options);
            initialGuess_1 = soln;
            TEMP_ALGEBRAIC(:,5) = soln(1);
            TEMP_ALGEBRAIC(:,6) = soln(2);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
        end
    end
end

function resid = residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    ALGEBRAIC(:,5) = algebraicCandidate(1);
    ALGEBRAIC(:,6) = algebraicCandidate(2);
    resid(1) = CONSTANTS(:,16) - ( - ( ALGEBRAIC(:,5).*STATES(:,2).*STATES(:,5))+ ALGEBRAIC(:,6).*STATES(:,7));
    resid(2) = CONSTANTS(:,18) - ALGEBRAIC(:,6)./ALGEBRAIC(:,5);
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