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 =40;
end
% There are a total of 7 entries in each of the rate and state variable arrays.
% There are a total of 38 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('V in component membrane (millivolt)');
    LEGEND_CONSTANTS(:,1) = strpad('V_T in component membrane (millivolt)');
    LEGEND_CONSTANTS(:,2) = strpad('V_S in component membrane (millivolt)');
    LEGEND_CONSTANTS(:,3) = strpad('C_m in component membrane (mF_per_cm_squared)');
    LEGEND_CONSTANTS(:,4) = strpad('F in component membrane (coulomb_per_mole)');
    LEGEND_CONSTANTS(:,5) = strpad('R in component membrane (joule_per_mole_per_kelvin)');
    LEGEND_CONSTANTS(:,6) = strpad('T in component membrane (kelvin)');
    LEGEND_ALGEBRAIC(:,17) = strpad('I_leak in component I_leak (milliampere_per_cm_squared)');
    LEGEND_ALGEBRAIC(:,22) = strpad('I_Na in component I_Na (milliampere_per_cm_squared)');
    LEGEND_ALGEBRAIC(:,23) = strpad('I_KD in component I_KD (milliampere_per_cm_squared)');
    LEGEND_ALGEBRAIC(:,24) = strpad('I_KM in component I_KM (milliampere_per_cm_squared)');
    LEGEND_ALGEBRAIC(:,26) = strpad('I_CaL in component I_CaL (milliampere_per_cm_squared)');
    LEGEND_ALGEBRAIC(:,40) = strpad('I_h in component I_h (milliampere_per_cm_squared)');
    LEGEND_ALGEBRAIC(:,12) = strpad('I_app in component stimulus_protocol (milliampere_per_cm_squared)');
    LEGEND_CONSTANTS(:,7) = strpad('i_stimStart in component stimulus_protocol (second)');
    LEGEND_CONSTANTS(:,8) = strpad('i_stimEnd in component stimulus_protocol (second)');
    LEGEND_CONSTANTS(:,9) = strpad('i_stimAmplitude in component stimulus_protocol (milliampere_per_cm_squared)');
    LEGEND_ALGEBRAIC(:,6) = strpad('tau in component stimulus_protocol (second)');
    LEGEND_CONSTANTS(:,10) = strpad('period in component stimulus_protocol (second)');
    LEGEND_CONSTANTS(:,11) = strpad('g_leak in component I_leak (millisiemens_per_cm_squared)');
    LEGEND_CONSTANTS(:,12) = strpad('E_leak in component I_leak (millivolt)');
    LEGEND_CONSTANTS(:,13) = strpad('g_Na in component I_Na (millisiemens_per_cm_squared)');
    LEGEND_CONSTANTS(:,14) = strpad('E_Na in component I_Na (millivolt)');
    LEGEND_STATES(:,2) = strpad('m in component Na_m_gate (dimensionless)');
    LEGEND_STATES(:,3) = strpad('h in component Na_h_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('alpha in component Na_m_gate (per_second)');
    LEGEND_ALGEBRAIC(:,7) = strpad('beta in component Na_m_gate (per_second)');
    LEGEND_ALGEBRAIC(:,13) = strpad('tau_m in component Na_m_gate (second)');
    LEGEND_ALGEBRAIC(:,18) = strpad('m_inf in component Na_m_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('alpha_h in component Na_h_gate (per_second)');
    LEGEND_ALGEBRAIC(:,8) = strpad('beta_h in component Na_h_gate (per_second)');
    LEGEND_ALGEBRAIC(:,19) = strpad('h_inf in component Na_h_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,14) = strpad('tau_h in component Na_h_gate (second)');
    LEGEND_CONSTANTS(:,15) = strpad('g_KD in component I_KD (millisiemens_per_cm_squared)');
    LEGEND_CONSTANTS(:,16) = strpad('E_K in component I_KD (millivolt)');
    LEGEND_STATES(:,4) = strpad('n in component KD_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('alpha_n in component KD_n_gate (per_second)');
    LEGEND_ALGEBRAIC(:,9) = strpad('beta_n in component KD_n_gate (per_second)');
    LEGEND_ALGEBRAIC(:,15) = strpad('tau_n in component KD_n_gate (second)');
    LEGEND_ALGEBRAIC(:,20) = strpad('n_inf in component KD_n_gate (dimensionless)');
    LEGEND_CONSTANTS(:,17) = strpad('g_KM in component I_KM (millisiemens_per_cm_squared)');
    LEGEND_STATES(:,5) = strpad('p in component KM_p_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('p_inf in component KM_p_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,10) = strpad('tau_p in component KM_p_gate (second)');
    LEGEND_CONSTANTS(:,18) = strpad('tau_max in component KM_p_gate (second)');
    LEGEND_CONSTANTS(:,19) = strpad('P_Ca in component I_CaL (cm_per_second)');
    LEGEND_ALGEBRAIC(:,25) = strpad('G in component G_nonlin (coulomb_per_cm_cubed)');
    LEGEND_STATES(:,6) = strpad('q in component CaL_q_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('alpha_q in component CaL_q_gate (per_second)');
    LEGEND_ALGEBRAIC(:,11) = strpad('beta_q in component CaL_q_gate (per_second)');
    LEGEND_ALGEBRAIC(:,16) = strpad('tau_q in component CaL_q_gate (second)');
    LEGEND_ALGEBRAIC(:,21) = strpad('q_inf in component CaL_q_gate (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('Z in component G_nonlin (dimensionless)');
    LEGEND_CONSTANTS(:,21) = strpad('Ca_o in component G_nonlin (mM)');
    LEGEND_STATES(:,7) = strpad('Ca_i in component dCa_i_dt (mM)');
    LEGEND_CONSTANTS(:,22) = strpad('Ca_inf in component dCa_i_dt (mM)');
    LEGEND_CONSTANTS(:,23) = strpad('tau_r in component dCa_i_dt (second)');
    LEGEND_CONSTANTS(:,24) = strpad('d in component dCa_i_dt (centimeter)');
    LEGEND_ALGEBRAIC(:,27) = strpad('drive_channel in component dCa_i_dt (mM_per_second)');
    LEGEND_CONSTANTS(:,25) = strpad('k in component dCa_i_dt (fixer)');
    LEGEND_ALGEBRAIC(:,39) = strpad('m in component I_h (dimensionless)');
    LEGEND_CONSTANTS(:,26) = strpad('E_h in component I_h (millivolt)');
    LEGEND_CONSTANTS(:,27) = strpad('g_hbar in component I_h (millisiemens_per_cm_squared)');
    LEGEND_CONSTANTS(:,28) = strpad('cac in component I_h (mM)');
    LEGEND_CONSTANTS(:,29) = strpad('V_S in component I_h (millivolt)');
    LEGEND_ALGEBRAIC(:,36) = strpad('o_1 in component kinetic (dimensionless)');
    LEGEND_ALGEBRAIC(:,37) = strpad('o_2 in component kinetic (dimensionless)');
    LEGEND_CONSTANTS(:,30) = strpad('g_inc in component I_h (dimensionless)');
    LEGEND_ALGEBRAIC(:,33) = strpad('p_0 in component kinetic (dimensionless)');
    LEGEND_ALGEBRAIC(:,34) = strpad('p_1 in component kinetic (dimensionless)');
    LEGEND_ALGEBRAIC(:,38) = strpad('c_1 in component kinetic (dimensionless)');
    LEGEND_ALGEBRAIC(:,30) = strpad('alpha in component rate_constants (dimensionless)');
    LEGEND_ALGEBRAIC(:,31) = strpad('beta in component rate_constants (dimensionless)');
    LEGEND_ALGEBRAIC(:,32) = strpad('k_1Ca in component rate_constants (per_second)');
    LEGEND_CONSTANTS(:,31) = strpad('k_2 in component rate_constants (per_second)');
    LEGEND_ALGEBRAIC(:,35) = strpad('k_3p in component rate_constants (per_second)');
    LEGEND_CONSTANTS(:,32) = strpad('k_4 in component rate_constants (per_second)');
    LEGEND_ALGEBRAIC(:,28) = strpad('h_inf in component rate_constants (second)');
    LEGEND_ALGEBRAIC(:,29) = strpad('tau_s in component rate_constants (second)');
    LEGEND_CONSTANTS(:,33) = strpad('P_c in component rate_constants (dimensionless)');
    LEGEND_CONSTANTS(:,34) = strpad('n_Ca in component rate_constants (dimensionless)');
    LEGEND_CONSTANTS(:,35) = strpad('n_exp in component rate_constants (dimensionless)');
    LEGEND_CONSTANTS(:,36) = strpad('p_C in component rate_constants (dimensionless)');
    LEGEND_CONSTANTS(:,37) = strpad('Ca_c in component rate_constants (mM)');
    LEGEND_CONSTANTS(:,38) = strpad('tau_m in component rate_constants (second)');
    LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)');
    LEGEND_RATES(:,2) = strpad('d/dt m in component Na_m_gate (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt h in component Na_h_gate (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt n in component KD_n_gate (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt p in component KM_p_gate (dimensionless)');
    LEGEND_RATES(:,6) = strpad('d/dt q in component CaL_q_gate (dimensionless)');
    LEGEND_RATES(:,7) = strpad('d/dt Ca_i in component dCa_i_dt (mM)');
    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) = -70;
    CONSTANTS(:,1) = -55;
    CONSTANTS(:,2) = 0;
    CONSTANTS(:,3) = 1e-3;
    CONSTANTS(:,4) = 96489;
    CONSTANTS(:,5) = 8.314;
    CONSTANTS(:,6) = 296.65;
    CONSTANTS(:,7) = 5;
    CONSTANTS(:,8) = 9;
    CONSTANTS(:,9) = -0.3;
    CONSTANTS(:,10) = 9;
    CONSTANTS(:,11) = 1;
    CONSTANTS(:,12) = -70;
    CONSTANTS(:,13) = 70;
    CONSTANTS(:,14) = 50;
    STATES(:,2) = 0;
    STATES(:,3) = 0;
    CONSTANTS(:,15) = 7;
    CONSTANTS(:,16) = -95;
    STATES(:,4) = 0;
    CONSTANTS(:,17) = 0.004;
    STATES(:,5) = 0;
    CONSTANTS(:,18) = 4;
    CONSTANTS(:,19) = 2.76e-4;
    STATES(:,6) = 0.00247262;
    CONSTANTS(:,20) = 2;
    CONSTANTS(:,21) = 2;
    STATES(:,7) = 100e-6;
    CONSTANTS(:,22) = 100e-6;
    CONSTANTS(:,23) = 17e-3;
    CONSTANTS(:,24) = 1e-4;
    CONSTANTS(:,25) = 0.1;
    CONSTANTS(:,26) = -20;
    CONSTANTS(:,27) = 0.02;
    CONSTANTS(:,28) = 0.006;
    CONSTANTS(:,29) = 0;
    CONSTANTS(:,30) = 2;
    CONSTANTS(:,31) = 0.1;
    CONSTANTS(:,32) = 1;
    CONSTANTS(:,33) = 0.01;
    CONSTANTS(:,34) = 4;
    CONSTANTS(:,35) = 1;
    CONSTANTS(:,36) = 0.01;
    CONSTANTS(:,37) = 0.006;
    CONSTANTS(:,38) = 20e-3;
    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(:,4) = piecewise({ - (STATES(:,1)+35.0000)./10.0000<25.0000& - (STATES(:,1)+35.0000)./10.0000> - 25.0000, 1.00000./(1.00000+exp( - (STATES(:,1)+35.0000)./10.0000)) }, 1.00000);
    ALGEBRAIC(:,10) = piecewise({(STATES(:,1)+35.0000)./20.0000<25.0000&(STATES(:,1)+35.0000)./20.0000> - 25.0000, CONSTANTS(:,18)./( 3.30000.*exp((STATES(:,1)+35.0000)./20.0000)+exp( - (STATES(:,1)+35.0000)./20.0000)) }, 1.00000);
    RATES(:,5) = (ALGEBRAIC(:,4) - STATES(:,5))./ALGEBRAIC(:,10);
    ALGEBRAIC(:,1) = piecewise({abs(((13.0000+CONSTANTS(:,1)) - STATES(:,1))./4.00000)<1.00000e-06,  0.320000.*4.00000.*(1.00000 - ((13.0000+CONSTANTS(:,1)) - STATES(:,1))./( 2.00000.*4.00000)) }, ( 0.320000.*((13.0000+CONSTANTS(:,1)) - STATES(:,1)))./(exp(((13.0000+CONSTANTS(:,1)) - STATES(:,1))./4.00000) - 1.00000));
    ALGEBRAIC(:,7) = piecewise({abs( - ((STATES(:,1) - CONSTANTS(:,1)) - 40.0000)./5.00000)<1.00000e-06,   - 0.280000.*5.00000.*(1.00000 -  - ((STATES(:,1) - CONSTANTS(:,1)) - 40.0000)./( 2.00000.*5.00000)) }, (  - 0.280000.*((STATES(:,1) - CONSTANTS(:,1)) - 40.0000))./(exp( - ((STATES(:,1) - CONSTANTS(:,1)) - 40.0000)./5.00000) - 1.00000));
    ALGEBRAIC(:,13) = 1.00000./(ALGEBRAIC(:,1)+ALGEBRAIC(:,7));
    ALGEBRAIC(:,18) = ALGEBRAIC(:,1)./(ALGEBRAIC(:,1)+ALGEBRAIC(:,7));
    RATES(:,2) = (ALGEBRAIC(:,18) - STATES(:,2))./ALGEBRAIC(:,13);
    ALGEBRAIC(:,2) =  0.128000.*exp(((17.0000+CONSTANTS(:,1)+CONSTANTS(:,2)) - STATES(:,1))./18.0000);
    ALGEBRAIC(:,8) = 4.00000./(1.00000+exp(((40.0000+CONSTANTS(:,2)+CONSTANTS(:,1)) - STATES(:,1))./5.00000));
    ALGEBRAIC(:,19) = ALGEBRAIC(:,2)./(ALGEBRAIC(:,2)+ALGEBRAIC(:,8));
    ALGEBRAIC(:,14) = 1.00000./(ALGEBRAIC(:,2)+ALGEBRAIC(:,8));
    RATES(:,3) = (ALGEBRAIC(:,19) - STATES(:,3))./ALGEBRAIC(:,14);
    ALGEBRAIC(:,3) = piecewise({abs(((STATES(:,1) - CONSTANTS(:,1)) - 15.0000)./5.00000)<1.00000e-06,   - 0.0320000.*5.00000.*(1.00000 - ((STATES(:,1) - CONSTANTS(:,1)) - 15.0000)./( 2.00000.*5.00000)) }, (  - 0.0320000.*((STATES(:,1) - CONSTANTS(:,1)) - 15.0000))./(exp(((STATES(:,1) - CONSTANTS(:,1)) - 15.0000)./5.00000) - 1.00000));
    ALGEBRAIC(:,9) = piecewise({abs( - ((STATES(:,1) - CONSTANTS(:,1)) - 10.0000)./40.0000)<1.00000e-06,  0.500000.*40.0000.*(1.00000+((STATES(:,1) - CONSTANTS(:,1)) - 10.0000)./( 2.00000.*40.0000)) }, ( 0.500000.* - ((STATES(:,1) - CONSTANTS(:,1)) - 10.0000))./(exp( - ((STATES(:,1) - CONSTANTS(:,1)) - 10.0000)./40.0000) - 1.00000));
    ALGEBRAIC(:,15) = 1.00000./(ALGEBRAIC(:,3)+ALGEBRAIC(:,9));
    ALGEBRAIC(:,20) = ALGEBRAIC(:,3)./(ALGEBRAIC(:,3)+ALGEBRAIC(:,9));
    RATES(:,4) = (ALGEBRAIC(:,20) - STATES(:,4))./ALGEBRAIC(:,15);
    ALGEBRAIC(:,5) = 6.32000./(1.00000+exp( - (STATES(:,1) - 5.00000)./13.8900));
    ALGEBRAIC(:,11) = piecewise({abs((1.31000 - STATES(:,1))./5.36000)<1.00000e-06,  0.0200000.*(5.36000+(1.31000 - STATES(:,1))./2.00000) }, ( 0.0200000.*(1.31000 - STATES(:,1)))./(1.00000 - exp((STATES(:,1) - 1.31000)./5.36000)));
    ALGEBRAIC(:,16) = 1.00000./(ALGEBRAIC(:,5)+ALGEBRAIC(:,11));
    ALGEBRAIC(:,21) = 1.00000./(1.00000+exp((STATES(:,1)+10.0000)./ - 10.0000));
    RATES(:,6) = (ALGEBRAIC(:,21) - STATES(:,6))./ALGEBRAIC(:,16);
    ALGEBRAIC(:,25) = ( (( power(CONSTANTS(:,20), 2.00000).*power(CONSTANTS(:,4), 2.00000).*0.00100000.*STATES(:,1))./( CONSTANTS(:,5).*CONSTANTS(:,6))).*1.00000e-06.*(STATES(:,7) -  CONSTANTS(:,21).*exp(( CONSTANTS(:,20).*CONSTANTS(:,4).*0.00100000.*STATES(:,1))./( CONSTANTS(:,5).*CONSTANTS(:,6)))))./(1.00000 - exp(( 0.00100000.*CONSTANTS(:,20).*CONSTANTS(:,4).*STATES(:,1))./( CONSTANTS(:,5).*CONSTANTS(:,6))));
    ALGEBRAIC(:,26) =  1000.00.*CONSTANTS(:,19).*power(STATES(:,6), 2.00000).*ALGEBRAIC(:,25);
    ALGEBRAIC(:,27) = ( CONSTANTS(:,25).*ALGEBRAIC(:,26))./( 2.00000.*CONSTANTS(:,4).*CONSTANTS(:,24));
    RATES(:,7) = piecewise({ALGEBRAIC(:,27)<=0.00000, (CONSTANTS(:,22) - STATES(:,7))./CONSTANTS(:,23) }, ALGEBRAIC(:,27)+(CONSTANTS(:,22) - STATES(:,7))./CONSTANTS(:,23));
    ALGEBRAIC(:,17) =  1000.00.*CONSTANTS(:,11).*(STATES(:,1) - CONSTANTS(:,12));
    ALGEBRAIC(:,22) =  1000.00.*CONSTANTS(:,13).*power(STATES(:,2), 3.00000).*STATES(:,3).*(STATES(:,1) - CONSTANTS(:,14));
    ALGEBRAIC(:,23) =  1000.00.*CONSTANTS(:,15).*power(STATES(:,4), 4.00000).*(STATES(:,1) - CONSTANTS(:,16));
    ALGEBRAIC(:,24) =  1000.00.*CONSTANTS(:,17).*STATES(:,5).*(STATES(:,1) - CONSTANTS(:,16));
    ALGEBRAIC(:,28) = 1.00000./(1.00000+exp(((STATES(:,1)+75.0000) - CONSTANTS(:,29))./5.50000));
    ALGEBRAIC(:,29) = CONSTANTS(:,38)+1000.00./(exp(((STATES(:,1)+71.5500) - CONSTANTS(:,29))./14.2000)+exp( - ((STATES(:,1)+89.0000) - CONSTANTS(:,29))./11.6000));
    ALGEBRAIC(:,30) = ALGEBRAIC(:,28)./ALGEBRAIC(:,29);
    ALGEBRAIC(:,31) = (1.00000 - ALGEBRAIC(:,28))./ALGEBRAIC(:,29);
    ALGEBRAIC(:,32) =  CONSTANTS(:,31).*power(STATES(:,7)./CONSTANTS(:,37), CONSTANTS(:,34));
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
    ALGEBRAIC(:,35) =  CONSTANTS(:,32).*power(ALGEBRAIC(:,34)./CONSTANTS(:,36), CONSTANTS(:,35));
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS, STATES, ALGEBRAIC);
    ALGEBRAIC(:,39) = ALGEBRAIC(:,36)+CONSTANTS(:,30)+ALGEBRAIC(:,37);
    ALGEBRAIC(:,40) =  1000.00.*CONSTANTS(:,27).*ALGEBRAIC(:,39).*(STATES(:,1) - CONSTANTS(:,26));
    ALGEBRAIC(:,6) = VOI -  CONSTANTS(:,10).*floor(VOI./CONSTANTS(:,10));
    ALGEBRAIC(:,12) = piecewise({ALGEBRAIC(:,6)>=CONSTANTS(:,7)&ALGEBRAIC(:,6)<=CONSTANTS(:,8), CONSTANTS(:,9) }, 0.00000);
    RATES(:,1) = ( 0.00100000.*((((((ALGEBRAIC(:,12)+ - ALGEBRAIC(:,17)) - ALGEBRAIC(:,22)) - ALGEBRAIC(:,23)) - ALGEBRAIC(:,24)) - ALGEBRAIC(:,26)) - ALGEBRAIC(:,40)))./CONSTANTS(:,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(:,4) = piecewise({ - (STATES(:,1)+35.0000)./10.0000<25.0000& - (STATES(:,1)+35.0000)./10.0000> - 25.0000, 1.00000./(1.00000+exp( - (STATES(:,1)+35.0000)./10.0000)) }, 1.00000);
    ALGEBRAIC(:,10) = piecewise({(STATES(:,1)+35.0000)./20.0000<25.0000&(STATES(:,1)+35.0000)./20.0000> - 25.0000, CONSTANTS(:,18)./( 3.30000.*exp((STATES(:,1)+35.0000)./20.0000)+exp( - (STATES(:,1)+35.0000)./20.0000)) }, 1.00000);
    ALGEBRAIC(:,1) = piecewise({abs(((13.0000+CONSTANTS(:,1)) - STATES(:,1))./4.00000)<1.00000e-06,  0.320000.*4.00000.*(1.00000 - ((13.0000+CONSTANTS(:,1)) - STATES(:,1))./( 2.00000.*4.00000)) }, ( 0.320000.*((13.0000+CONSTANTS(:,1)) - STATES(:,1)))./(exp(((13.0000+CONSTANTS(:,1)) - STATES(:,1))./4.00000) - 1.00000));
    ALGEBRAIC(:,7) = piecewise({abs( - ((STATES(:,1) - CONSTANTS(:,1)) - 40.0000)./5.00000)<1.00000e-06,   - 0.280000.*5.00000.*(1.00000 -  - ((STATES(:,1) - CONSTANTS(:,1)) - 40.0000)./( 2.00000.*5.00000)) }, (  - 0.280000.*((STATES(:,1) - CONSTANTS(:,1)) - 40.0000))./(exp( - ((STATES(:,1) - CONSTANTS(:,1)) - 40.0000)./5.00000) - 1.00000));
    ALGEBRAIC(:,13) = 1.00000./(ALGEBRAIC(:,1)+ALGEBRAIC(:,7));
    ALGEBRAIC(:,18) = ALGEBRAIC(:,1)./(ALGEBRAIC(:,1)+ALGEBRAIC(:,7));
    ALGEBRAIC(:,2) =  0.128000.*exp(((17.0000+CONSTANTS(:,1)+CONSTANTS(:,2)) - STATES(:,1))./18.0000);
    ALGEBRAIC(:,8) = 4.00000./(1.00000+exp(((40.0000+CONSTANTS(:,2)+CONSTANTS(:,1)) - STATES(:,1))./5.00000));
    ALGEBRAIC(:,19) = ALGEBRAIC(:,2)./(ALGEBRAIC(:,2)+ALGEBRAIC(:,8));
    ALGEBRAIC(:,14) = 1.00000./(ALGEBRAIC(:,2)+ALGEBRAIC(:,8));
    ALGEBRAIC(:,3) = piecewise({abs(((STATES(:,1) - CONSTANTS(:,1)) - 15.0000)./5.00000)<1.00000e-06,   - 0.0320000.*5.00000.*(1.00000 - ((STATES(:,1) - CONSTANTS(:,1)) - 15.0000)./( 2.00000.*5.00000)) }, (  - 0.0320000.*((STATES(:,1) - CONSTANTS(:,1)) - 15.0000))./(exp(((STATES(:,1) - CONSTANTS(:,1)) - 15.0000)./5.00000) - 1.00000));
    ALGEBRAIC(:,9) = piecewise({abs( - ((STATES(:,1) - CONSTANTS(:,1)) - 10.0000)./40.0000)<1.00000e-06,  0.500000.*40.0000.*(1.00000+((STATES(:,1) - CONSTANTS(:,1)) - 10.0000)./( 2.00000.*40.0000)) }, ( 0.500000.* - ((STATES(:,1) - CONSTANTS(:,1)) - 10.0000))./(exp( - ((STATES(:,1) - CONSTANTS(:,1)) - 10.0000)./40.0000) - 1.00000));
    ALGEBRAIC(:,15) = 1.00000./(ALGEBRAIC(:,3)+ALGEBRAIC(:,9));
    ALGEBRAIC(:,20) = ALGEBRAIC(:,3)./(ALGEBRAIC(:,3)+ALGEBRAIC(:,9));
    ALGEBRAIC(:,5) = 6.32000./(1.00000+exp( - (STATES(:,1) - 5.00000)./13.8900));
    ALGEBRAIC(:,11) = piecewise({abs((1.31000 - STATES(:,1))./5.36000)<1.00000e-06,  0.0200000.*(5.36000+(1.31000 - STATES(:,1))./2.00000) }, ( 0.0200000.*(1.31000 - STATES(:,1)))./(1.00000 - exp((STATES(:,1) - 1.31000)./5.36000)));
    ALGEBRAIC(:,16) = 1.00000./(ALGEBRAIC(:,5)+ALGEBRAIC(:,11));
    ALGEBRAIC(:,21) = 1.00000./(1.00000+exp((STATES(:,1)+10.0000)./ - 10.0000));
    ALGEBRAIC(:,25) = ( (( power(CONSTANTS(:,20), 2.00000).*power(CONSTANTS(:,4), 2.00000).*0.00100000.*STATES(:,1))./( CONSTANTS(:,5).*CONSTANTS(:,6))).*1.00000e-06.*(STATES(:,7) -  CONSTANTS(:,21).*exp(( CONSTANTS(:,20).*CONSTANTS(:,4).*0.00100000.*STATES(:,1))./( CONSTANTS(:,5).*CONSTANTS(:,6)))))./(1.00000 - exp(( 0.00100000.*CONSTANTS(:,20).*CONSTANTS(:,4).*STATES(:,1))./( CONSTANTS(:,5).*CONSTANTS(:,6))));
    ALGEBRAIC(:,26) =  1000.00.*CONSTANTS(:,19).*power(STATES(:,6), 2.00000).*ALGEBRAIC(:,25);
    ALGEBRAIC(:,27) = ( CONSTANTS(:,25).*ALGEBRAIC(:,26))./( 2.00000.*CONSTANTS(:,4).*CONSTANTS(:,24));
    ALGEBRAIC(:,17) =  1000.00.*CONSTANTS(:,11).*(STATES(:,1) - CONSTANTS(:,12));
    ALGEBRAIC(:,22) =  1000.00.*CONSTANTS(:,13).*power(STATES(:,2), 3.00000).*STATES(:,3).*(STATES(:,1) - CONSTANTS(:,14));
    ALGEBRAIC(:,23) =  1000.00.*CONSTANTS(:,15).*power(STATES(:,4), 4.00000).*(STATES(:,1) - CONSTANTS(:,16));
    ALGEBRAIC(:,24) =  1000.00.*CONSTANTS(:,17).*STATES(:,5).*(STATES(:,1) - CONSTANTS(:,16));
    ALGEBRAIC(:,28) = 1.00000./(1.00000+exp(((STATES(:,1)+75.0000) - CONSTANTS(:,29))./5.50000));
    ALGEBRAIC(:,29) = CONSTANTS(:,38)+1000.00./(exp(((STATES(:,1)+71.5500) - CONSTANTS(:,29))./14.2000)+exp( - ((STATES(:,1)+89.0000) - CONSTANTS(:,29))./11.6000));
    ALGEBRAIC(:,30) = ALGEBRAIC(:,28)./ALGEBRAIC(:,29);
    ALGEBRAIC(:,31) = (1.00000 - ALGEBRAIC(:,28))./ALGEBRAIC(:,29);
    ALGEBRAIC(:,32) =  CONSTANTS(:,31).*power(STATES(:,7)./CONSTANTS(:,37), CONSTANTS(:,34));
    ALGEBRAIC(:,35) =  CONSTANTS(:,32).*power(ALGEBRAIC(:,34)./CONSTANTS(:,36), CONSTANTS(:,35));
    ALGEBRAIC(:,39) = ALGEBRAIC(:,36)+CONSTANTS(:,30)+ALGEBRAIC(:,37);
    ALGEBRAIC(:,40) =  1000.00.*CONSTANTS(:,27).*ALGEBRAIC(:,39).*(STATES(:,1) - CONSTANTS(:,26));
    ALGEBRAIC(:,6) = VOI -  CONSTANTS(:,10).*floor(VOI./CONSTANTS(:,10));
    ALGEBRAIC(:,12) = piecewise({ALGEBRAIC(:,6)>=CONSTANTS(:,7)&ALGEBRAIC(:,6)<=CONSTANTS(:,8), CONSTANTS(:,9) }, 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(:,33) = soln(1);
        ALGEBRAIC(:,34) = soln(2);
    else
        SET_ALGEBRAIC(:,33) = logical(1);
        SET_ALGEBRAIC(:,34) = 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(:,33) = soln(1);
            TEMP_ALGEBRAIC(:,34) = soln(2);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
        end
    end
end

function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    ALGEBRAIC(:,33) = algebraicCandidate(1);
    ALGEBRAIC(:,34) = algebraicCandidate(2);
    resid(1) = ALGEBRAIC(:,33) - ( ALGEBRAIC(:,34).*CONSTANTS(:,31))./ALGEBRAIC(:,32);
    resid(2) = ALGEBRAIC(:,34) - (1.00000 - ALGEBRAIC(:,33));
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) ~= 3), initialGuess_1 = [0.1,0.1,0.1];, 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(:,36) = soln(1);
        ALGEBRAIC(:,37) = soln(2);
        ALGEBRAIC(:,38) = soln(3);
    else
        SET_ALGEBRAIC(:,36) = logical(1);
        SET_ALGEBRAIC(:,37) = logical(1);
        SET_ALGEBRAIC(:,38) = 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(:,36) = soln(1);
            TEMP_ALGEBRAIC(:,37) = soln(2);
            TEMP_ALGEBRAIC(:,38) = soln(3);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
        end
    end
end

function resid = residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    ALGEBRAIC(:,36) = algebraicCandidate(1);
    ALGEBRAIC(:,37) = algebraicCandidate(2);
    ALGEBRAIC(:,38) = algebraicCandidate(3);
    resid(1) = ALGEBRAIC(:,38) -  (ALGEBRAIC(:,31)./ALGEBRAIC(:,30)).*ALGEBRAIC(:,36);
    resid(2) = ALGEBRAIC(:,36) -  (CONSTANTS(:,32)./ALGEBRAIC(:,35)).*ALGEBRAIC(:,37);
    resid(3) = ALGEBRAIC(:,37) - ((1.00000 - ALGEBRAIC(:,38)) - ALGEBRAIC(:,36));
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