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 =34;
end
% There are a total of 15 entries in each of the rate and state variable arrays.
% There are a total of 59 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_ALGEBRAIC(:,1) = strpad('L_iso in component beta_1_adrenergic_parameters (uM)');
    LEGEND_CONSTANTS(:,1) = strpad('K_H in component beta_1_adrenergic_parameters (uM)');
    LEGEND_CONSTANTS(:,2) = strpad('K_L in component beta_1_adrenergic_parameters (uM)');
    LEGEND_CONSTANTS(:,3) = strpad('K_C in component beta_1_adrenergic_parameters (uM)');
    LEGEND_ALGEBRAIC(:,2) = strpad('L_ach in component muscarinic_parameters (uM)');
    LEGEND_CONSTANTS(:,4) = strpad('K_H in component muscarinic_parameters (uM)');
    LEGEND_CONSTANTS(:,5) = strpad('K_L in component muscarinic_parameters (uM)');
    LEGEND_CONSTANTS(:,6) = strpad('K_C in component muscarinic_parameters (uM)');
    LEGEND_CONSTANTS(:,7) = strpad('k_PDE2 in component PDE_parameters (per_sec)');
    LEGEND_CONSTANTS(:,8) = strpad('Km_PDE2 in component PDE_parameters (uM)');
    LEGEND_CONSTANTS(:,9) = strpad('k_PDE3 in component PDE_parameters (per_sec)');
    LEGEND_CONSTANTS(:,10) = strpad('Km_PDE3 in component PDE_parameters (uM)');
    LEGEND_CONSTANTS(:,11) = strpad('k_PDE4 in component PDE_parameters (per_sec)');
    LEGEND_CONSTANTS(:,12) = strpad('Km_PDE4 in component PDE_parameters (uM)');
    LEGEND_CONSTANTS(:,13) = strpad('k_act1 in component G_s_parameters (per_sec)');
    LEGEND_CONSTANTS(:,14) = strpad('k_act2 in component G_s_parameters (per_sec)');
    LEGEND_CONSTANTS(:,15) = strpad('k_hydr in component G_s_parameters (per_sec)');
    LEGEND_CONSTANTS(:,16) = strpad('k_reas in component G_s_parameters (per_uM_per_sec)');
    LEGEND_CONSTANTS(:,17) = strpad('k_act1 in component G_i_parameters (per_sec)');
    LEGEND_CONSTANTS(:,18) = strpad('k_act2 in component G_i_parameters (per_sec)');
    LEGEND_CONSTANTS(:,19) = strpad('k_hydr in component G_i_parameters (per_sec)');
    LEGEND_CONSTANTS(:,20) = strpad('k_reas in component G_i_parameters (per_uM_per_sec)');
    LEGEND_ALGEBRAIC(:,13) = strpad('R in component caveolar_beta_1_adrenergic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,14) = strpad('LR in component caveolar_beta_1_adrenergic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,15) = strpad('LRG in component caveolar_beta_1_adrenergic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,16) = strpad('RG in component caveolar_beta_1_adrenergic_receptor_module (uM)');
    LEGEND_CONSTANTS(:,21) = strpad('R_Total in component caveolar_beta_1_adrenergic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,6) = strpad('Gs_alpha_beta_gamma in component caveolar_G_s_protein_activation_module (uM)');
    LEGEND_ALGEBRAIC(:,17) = strpad('R in component caveolar_muscarinic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,18) = strpad('LR in component caveolar_muscarinic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,19) = strpad('LRG in component caveolar_muscarinic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,20) = strpad('RG in component caveolar_muscarinic_receptor_module (uM)');
    LEGEND_CONSTANTS(:,22) = strpad('R_Total in component caveolar_muscarinic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,7) = strpad('Gi_alpha_beta_gamma in component caveolar_G_i_protein_activation_module (uM)');
    LEGEND_STATES(:,1) = strpad('Gs_alpha_GTP in component caveolar_G_s_protein_activation_module (uM)');
    LEGEND_STATES(:,2) = strpad('Gs_beta_gamma in component caveolar_G_s_protein_activation_module (uM)');
    LEGEND_STATES(:,3) = strpad('Gs_alpha_GDP in component caveolar_G_s_protein_activation_module (uM)');
    LEGEND_CONSTANTS(:,23) = strpad('Gs_Total in component caveolar_G_s_protein_activation_module (uM)');
    LEGEND_STATES(:,4) = strpad('Gi_alpha_GTP in component caveolar_G_i_protein_activation_module (uM)');
    LEGEND_STATES(:,5) = strpad('Gi_beta_gamma in component caveolar_G_i_protein_activation_module (uM)');
    LEGEND_STATES(:,6) = strpad('Gi_alpha_GDP in component caveolar_G_i_protein_activation_module (uM)');
    LEGEND_CONSTANTS(:,24) = strpad('Gi_Total in component caveolar_G_i_protein_activation_module (uM)');
    LEGEND_ALGEBRAIC(:,21) = strpad('R in component extracaveolar_beta_1_adrenergic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,22) = strpad('LR in component extracaveolar_beta_1_adrenergic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,23) = strpad('LRG in component extracaveolar_beta_1_adrenergic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,24) = strpad('RG in component extracaveolar_beta_1_adrenergic_receptor_module (uM)');
    LEGEND_CONSTANTS(:,25) = strpad('R_Total in component extracaveolar_beta_1_adrenergic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,8) = strpad('Gs_alpha_beta_gamma in component extracaveolar_G_s_protein_activation_module (uM)');
    LEGEND_ALGEBRAIC(:,25) = strpad('R in component extracaveolar_muscarinic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,26) = strpad('LR in component extracaveolar_muscarinic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,27) = strpad('LRG in component extracaveolar_muscarinic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,28) = strpad('RG in component extracaveolar_muscarinic_receptor_module (uM)');
    LEGEND_CONSTANTS(:,26) = strpad('R_Total in component extracaveolar_muscarinic_receptor_module (uM)');
    LEGEND_ALGEBRAIC(:,9) = strpad('Gi_alpha_beta_gamma in component extracaveolar_G_i_protein_activation_module (uM)');
    LEGEND_STATES(:,7) = strpad('Gs_alpha_GTP in component extracaveolar_G_s_protein_activation_module (uM)');
    LEGEND_STATES(:,8) = strpad('Gs_beta_gamma in component extracaveolar_G_s_protein_activation_module (uM)');
    LEGEND_STATES(:,9) = strpad('Gs_alpha_GDP in component extracaveolar_G_s_protein_activation_module (uM)');
    LEGEND_CONSTANTS(:,27) = strpad('Gs_Total in component extracaveolar_G_s_protein_activation_module (uM)');
    LEGEND_STATES(:,10) = strpad('Gi_alpha_GTP in component extracaveolar_G_i_protein_activation_module (uM)');
    LEGEND_STATES(:,11) = strpad('Gi_beta_gamma in component extracaveolar_G_i_protein_activation_module (uM)');
    LEGEND_STATES(:,12) = strpad('Gi_alpha_GDP in component extracaveolar_G_i_protein_activation_module (uM)');
    LEGEND_CONSTANTS(:,28) = strpad('Gi_Total in component extracaveolar_G_i_protein_activation_module (uM)');
    LEGEND_ALGEBRAIC(:,10) = strpad('dcAMP_AC_56_dt in component AC56_module (uM_per_sec)');
    LEGEND_ALGEBRAIC(:,3) = strpad('k_AC56 in component AC56_module (per_sec)');
    LEGEND_CONSTANTS(:,29) = strpad('AC_56 in component AC56_module (uM)');
    LEGEND_CONSTANTS(:,30) = strpad('AF56 in component AC56_module (dimensionless)');
    LEGEND_CONSTANTS(:,31) = strpad('MW_AC56 in component AC56_module (kDa)');
    LEGEND_CONSTANTS(:,32) = strpad('ATP in component AC56_module (uM)');
    LEGEND_CONSTANTS(:,33) = strpad('Km_ATP in component AC56_module (uM)');
    LEGEND_ALGEBRAIC(:,11) = strpad('dcAMP_AC_47_ecav_dt in component AC47_ecav_module (uM_per_sec)');
    LEGEND_ALGEBRAIC(:,4) = strpad('k_AC47_ecav in component AC47_ecav_module (per_sec)');
    LEGEND_CONSTANTS(:,34) = strpad('AC_47_ecav in component AC47_ecav_module (uM)');
    LEGEND_CONSTANTS(:,35) = strpad('AF47 in component AC47_ecav_module (dimensionless)');
    LEGEND_CONSTANTS(:,36) = strpad('MW_AC47 in component AC47_ecav_module (kDa)');
    LEGEND_CONSTANTS(:,37) = strpad('ATP in component AC47_ecav_module (uM)');
    LEGEND_CONSTANTS(:,38) = strpad('Km_ATP in component AC47_ecav_module (uM)');
    LEGEND_CONSTANTS(:,56) = strpad('dcAMP_AC_47_cyt_dt in component AC47_cyt_module (uM_per_sec)');
    LEGEND_CONSTANTS(:,39) = strpad('k_AC47_cyt in component AC47_cyt_module (per_sec)');
    LEGEND_CONSTANTS(:,40) = strpad('AC_47_cyt in component AC47_cyt_module (uM)');
    LEGEND_CONSTANTS(:,41) = strpad('AF47 in component AC47_cyt_module (dimensionless)');
    LEGEND_CONSTANTS(:,42) = strpad('ATP in component AC47_cyt_module (uM)');
    LEGEND_CONSTANTS(:,43) = strpad('Km_ATP in component AC47_cyt_module (uM)');
    LEGEND_ALGEBRAIC(:,29) = strpad('dcAMP_cav_PDE2_dt in component caveolar_PDE_module (uM_per_sec)');
    LEGEND_ALGEBRAIC(:,32) = strpad('dcAMP_cav_PDE3_dt in component caveolar_PDE_module (uM_per_sec)');
    LEGEND_ALGEBRAIC(:,34) = strpad('dcAMP_cav_PDE4_dt in component caveolar_PDE_module (uM_per_sec)');
    LEGEND_STATES(:,13) = strpad('cAMP_cav in component cAMP_flux_module (uM)');
    LEGEND_CONSTANTS(:,44) = strpad('PDE2 in component caveolar_PDE_module (uM)');
    LEGEND_CONSTANTS(:,45) = strpad('PDE3 in component caveolar_PDE_module (uM)');
    LEGEND_CONSTANTS(:,46) = strpad('PDE4 in component caveolar_PDE_module (uM)');
    LEGEND_ALGEBRAIC(:,30) = strpad('dcAMP_ecav_PDE2_dt in component extracaveolar_PDE_module (uM_per_sec)');
    LEGEND_ALGEBRAIC(:,33) = strpad('dcAMP_ecav_PDE4_dt in component extracaveolar_PDE_module (uM_per_sec)');
    LEGEND_STATES(:,14) = strpad('cAMP_ecav in component cAMP_flux_module (uM)');
    LEGEND_CONSTANTS(:,47) = strpad('PDE2 in component extracaveolar_PDE_module (uM)');
    LEGEND_CONSTANTS(:,48) = strpad('PDE4 in component extracaveolar_PDE_module (uM)');
    LEGEND_ALGEBRAIC(:,5) = strpad('dcAMP_cyt_PDE2_dt in component bulk_cytoplasmic_PDE_module (uM_per_sec)');
    LEGEND_ALGEBRAIC(:,12) = strpad('dcAMP_cyt_PDE3_dt in component bulk_cytoplasmic_PDE_module (uM_per_sec)');
    LEGEND_ALGEBRAIC(:,31) = strpad('dcAMP_cyt_PDE4_dt in component bulk_cytoplasmic_PDE_module (uM_per_sec)');
    LEGEND_STATES(:,15) = strpad('cAMP_cyt in component cAMP_flux_module (uM)');
    LEGEND_CONSTANTS(:,49) = strpad('PDE2 in component bulk_cytoplasmic_PDE_module (uM)');
    LEGEND_CONSTANTS(:,50) = strpad('PDE3 in component bulk_cytoplasmic_PDE_module (uM)');
    LEGEND_CONSTANTS(:,51) = strpad('PDE4 in component bulk_cytoplasmic_PDE_module (uM)');
    LEGEND_CONSTANTS(:,57) = strpad('V_cav in component cAMP_flux_module (liter)');
    LEGEND_CONSTANTS(:,58) = strpad('V_ecav in component cAMP_flux_module (liter)');
    LEGEND_CONSTANTS(:,59) = strpad('V_cyt in component cAMP_flux_module (liter)');
    LEGEND_CONSTANTS(:,52) = strpad('V_cell in component cAMP_flux_module (liter)');
    LEGEND_CONSTANTS(:,53) = strpad('J_cav_ecav in component cAMP_flux_module (liters_per_second)');
    LEGEND_CONSTANTS(:,54) = strpad('J_cav_cyt in component cAMP_flux_module (liters_per_second)');
    LEGEND_CONSTANTS(:,55) = strpad('J_ecav_cyt in component cAMP_flux_module (liters_per_second)');
    LEGEND_RATES(:,1) = strpad('d/dt Gs_alpha_GTP in component caveolar_G_s_protein_activation_module (uM)');
    LEGEND_RATES(:,2) = strpad('d/dt Gs_beta_gamma in component caveolar_G_s_protein_activation_module (uM)');
    LEGEND_RATES(:,3) = strpad('d/dt Gs_alpha_GDP in component caveolar_G_s_protein_activation_module (uM)');
    LEGEND_RATES(:,4) = strpad('d/dt Gi_alpha_GTP in component caveolar_G_i_protein_activation_module (uM)');
    LEGEND_RATES(:,5) = strpad('d/dt Gi_beta_gamma in component caveolar_G_i_protein_activation_module (uM)');
    LEGEND_RATES(:,6) = strpad('d/dt Gi_alpha_GDP in component caveolar_G_i_protein_activation_module (uM)');
    LEGEND_RATES(:,7) = strpad('d/dt Gs_alpha_GTP in component extracaveolar_G_s_protein_activation_module (uM)');
    LEGEND_RATES(:,8) = strpad('d/dt Gs_beta_gamma in component extracaveolar_G_s_protein_activation_module (uM)');
    LEGEND_RATES(:,9) = strpad('d/dt Gs_alpha_GDP in component extracaveolar_G_s_protein_activation_module (uM)');
    LEGEND_RATES(:,10) = strpad('d/dt Gi_alpha_GTP in component extracaveolar_G_i_protein_activation_module (uM)');
    LEGEND_RATES(:,11) = strpad('d/dt Gi_beta_gamma in component extracaveolar_G_i_protein_activation_module (uM)');
    LEGEND_RATES(:,12) = strpad('d/dt Gi_alpha_GDP in component extracaveolar_G_i_protein_activation_module (uM)');
    LEGEND_RATES(:,13) = strpad('d/dt cAMP_cav in component cAMP_flux_module (uM)');
    LEGEND_RATES(:,14) = strpad('d/dt cAMP_ecav in component cAMP_flux_module (uM)');
    LEGEND_RATES(:,15) = strpad('d/dt cAMP_cyt in component cAMP_flux_module (uM)');
    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) = 0.035;
    CONSTANTS(:,2) = 0.386;
    CONSTANTS(:,3) = 8.809;
    CONSTANTS(:,4) = 0.16;
    CONSTANTS(:,5) = 11;
    CONSTANTS(:,6) = 30;
    CONSTANTS(:,7) = 20;
    CONSTANTS(:,8) = 50;
    CONSTANTS(:,9) = 1.25;
    CONSTANTS(:,10) = 0.08;
    CONSTANTS(:,11) = 2.5;
    CONSTANTS(:,12) = 2.2;
    CONSTANTS(:,13) = 5;
    CONSTANTS(:,14) = 0.1;
    CONSTANTS(:,15) = 0.8;
    CONSTANTS(:,16) = 1.21e3;
    CONSTANTS(:,17) = 2.5;
    CONSTANTS(:,18) = 0.05;
    CONSTANTS(:,19) = 0.8;
    CONSTANTS(:,20) = 1.21e3;
    CONSTANTS(:,21) = 0.633;
    CONSTANTS(:,22) = 0.633;
    STATES(:,1) = 0.041983438;
    STATES(:,2) = 0.042634499;
    STATES(:,3) = 0.000651061;
    CONSTANTS(:,23) = 10;
    STATES(:,4) = 0.012644961;
    STATES(:,5) = 0.013274751;
    STATES(:,6) = 0.00062979;
    CONSTANTS(:,24) = 20;
    CONSTANTS(:,25) = 0.633;
    CONSTANTS(:,26) = 0.633;
    STATES(:,7) = 0.083866891;
    STATES(:,8) = 0.084522918;
    STATES(:,9) = 0.000656025;
    CONSTANTS(:,27) = 10;
    STATES(:,10) = 0.001018705;
    STATES(:,11) = 0.001475253;
    STATES(:,12) = 0.000456548;
    CONSTANTS(:,28) = 1;
    CONSTANTS(:,29) = 3.379;
    CONSTANTS(:,30) = 500;
    CONSTANTS(:,31) = 130;
    CONSTANTS(:,32) = 5000;
    CONSTANTS(:,33) = 315;
    CONSTANTS(:,34) = 0.2;
    CONSTANTS(:,35) = 130;
    CONSTANTS(:,36) = 130;
    CONSTANTS(:,37) = 5000;
    CONSTANTS(:,38) = 315;
    CONSTANTS(:,39) = 1.08e-3;
    CONSTANTS(:,40) = 0.136;
    CONSTANTS(:,41) = 130;
    CONSTANTS(:,42) = 5000;
    CONSTANTS(:,43) = 315;
    STATES(:,13) = 0.11750433;
    CONSTANTS(:,44) = 4.5;
    CONSTANTS(:,45) = 5.6;
    CONSTANTS(:,46) = 2;
    STATES(:,14) = 1.092200547;
    CONSTANTS(:,47) = 0.02;
    CONSTANTS(:,48) = 0.16;
    STATES(:,15) = 0.992583576;
    CONSTANTS(:,49) = 5e-3;
    CONSTANTS(:,50) = 7.5e-3;
    CONSTANTS(:,51) = 5e-3;
    CONSTANTS(:,52) = 38e-12;
    CONSTANTS(:,53) = 7.5e-15;
    CONSTANTS(:,54) = 7.5e-14;
    CONSTANTS(:,55) = 1.5e-17;
    CONSTANTS(:,56) = ( CONSTANTS(:,39).*CONSTANTS(:,40).*CONSTANTS(:,41).*CONSTANTS(:,42))./(CONSTANTS(:,43)+CONSTANTS(:,42));
    CONSTANTS(:,57) =  0.0100000.*CONSTANTS(:,52);
    CONSTANTS(:,58) =  0.0200000.*CONSTANTS(:,52);
    CONSTANTS(:,59) =  0.500000.*CONSTANTS(:,52);
    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(:,3) =  STATES(:,1).*CONSTANTS(:,15) -  STATES(:,3).*STATES(:,2).*CONSTANTS(:,16);
    RATES(:,6) =  STATES(:,4).*CONSTANTS(:,19) -  STATES(:,6).*STATES(:,5).*CONSTANTS(:,20);
    RATES(:,9) =  STATES(:,7).*CONSTANTS(:,15) -  STATES(:,9).*STATES(:,8).*CONSTANTS(:,16);
    RATES(:,12) =  STATES(:,10).*CONSTANTS(:,19) -  STATES(:,12).*STATES(:,11).*CONSTANTS(:,20);
    ALGEBRAIC(:,1) = piecewise({VOI>120.000&VOI<=720.000, 1.00000 }, 1.00000);
    ALGEBRAIC(:,6) = (CONSTANTS(:,23) - STATES(:,1)) - STATES(:,3);
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
    RATES(:,1) = ( ALGEBRAIC(:,16).*CONSTANTS(:,14)+ ALGEBRAIC(:,15).*CONSTANTS(:,13)) -  STATES(:,1).*CONSTANTS(:,15);
    RATES(:,2) = ( ALGEBRAIC(:,16).*CONSTANTS(:,14)+ ALGEBRAIC(:,15).*CONSTANTS(:,13)) -  STATES(:,3).*STATES(:,2).*CONSTANTS(:,16);
    ALGEBRAIC(:,2) = piecewise({VOI>240.000&VOI<=540.000, 0.00000 }, 0.00000);
    ALGEBRAIC(:,7) = (CONSTANTS(:,24) - STATES(:,4)) - STATES(:,6);
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS, STATES, ALGEBRAIC);
    RATES(:,4) = ( ALGEBRAIC(:,20).*CONSTANTS(:,18)+ ALGEBRAIC(:,19).*CONSTANTS(:,17)) -  STATES(:,4).*CONSTANTS(:,19);
    RATES(:,5) = ( ALGEBRAIC(:,20).*CONSTANTS(:,18)+ ALGEBRAIC(:,19).*CONSTANTS(:,17)) -  STATES(:,6).*STATES(:,5).*CONSTANTS(:,20);
    ALGEBRAIC(:,8) = (CONSTANTS(:,27) - STATES(:,7)) - STATES(:,9);
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_2(VOI, CONSTANTS, STATES, ALGEBRAIC);
    RATES(:,7) = ( ALGEBRAIC(:,24).*CONSTANTS(:,14)+ ALGEBRAIC(:,23).*CONSTANTS(:,13)) -  STATES(:,7).*CONSTANTS(:,15);
    RATES(:,8) = ( ALGEBRAIC(:,24).*CONSTANTS(:,14)+ ALGEBRAIC(:,23).*CONSTANTS(:,13)) -  STATES(:,9).*STATES(:,8).*CONSTANTS(:,16);
    ALGEBRAIC(:,9) = (CONSTANTS(:,28) - STATES(:,10)) - STATES(:,12);
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_3(VOI, CONSTANTS, STATES, ALGEBRAIC);
    RATES(:,10) = ( ALGEBRAIC(:,28).*CONSTANTS(:,18)+ ALGEBRAIC(:,27).*CONSTANTS(:,17)) -  STATES(:,10).*CONSTANTS(:,19);
    RATES(:,11) = ( ALGEBRAIC(:,28).*CONSTANTS(:,18)+ ALGEBRAIC(:,27).*CONSTANTS(:,17)) -  STATES(:,12).*STATES(:,11).*CONSTANTS(:,20);
    ALGEBRAIC(:,5) = ( CONSTANTS(:,7).*CONSTANTS(:,49).*STATES(:,15))./(CONSTANTS(:,8)+STATES(:,15));
    ALGEBRAIC(:,12) = ( CONSTANTS(:,9).*CONSTANTS(:,50).*STATES(:,15))./(CONSTANTS(:,10)+STATES(:,15));
    ALGEBRAIC(:,31) = ( CONSTANTS(:,11).*CONSTANTS(:,51).*STATES(:,15))./(CONSTANTS(:,12)+STATES(:,15));
    RATES(:,15) = (CONSTANTS(:,56) - (ALGEBRAIC(:,5)+ALGEBRAIC(:,12)+ALGEBRAIC(:,31)))+( CONSTANTS(:,54).*(STATES(:,13) - STATES(:,15)))./CONSTANTS(:,59)+( CONSTANTS(:,55).*(STATES(:,14) - STATES(:,15)))./CONSTANTS(:,59);
    ALGEBRAIC(:,4) =  (( (0.0630000+( 2.01000.*power( STATES(:,7).*1000.00, 1.00430))./(31.5440+power( STATES(:,7).*1000.00, 1.00430))).*(1.00000+( (1.00000./3.01000).*49.1000.*power( STATES(:,11).*1000.00, 0.892100))./(25.4400+power( STATES(:,11).*1000.00, 0.892100))).*CONSTANTS(:,36))./60.0000).*0.00100000;
    ALGEBRAIC(:,11) = ( ALGEBRAIC(:,4).*CONSTANTS(:,34).*CONSTANTS(:,35).*CONSTANTS(:,37))./(CONSTANTS(:,38)+CONSTANTS(:,37));
    ALGEBRAIC(:,30) = ( CONSTANTS(:,7).*CONSTANTS(:,47).*STATES(:,14))./(CONSTANTS(:,8)+STATES(:,14));
    ALGEBRAIC(:,33) = ( CONSTANTS(:,11).*CONSTANTS(:,48).*STATES(:,14))./(CONSTANTS(:,12)+STATES(:,14));
    RATES(:,14) = ((ALGEBRAIC(:,11) - (ALGEBRAIC(:,30)+ALGEBRAIC(:,33)))+( CONSTANTS(:,53).*(STATES(:,13) - STATES(:,14)))./CONSTANTS(:,58)) - ( CONSTANTS(:,55).*(STATES(:,14) - STATES(:,15)))./CONSTANTS(:,58);
    ALGEBRAIC(:,3) =  (( (0.700000+( 3.82340.*power(STATES(:,1)./1.00000, 0.978700))./(0.198600+power(STATES(:,1)./1.00000, 0.978700))).*(1.00000+( (1.00000./1.44320).* - 1.00610.*power(STATES(:,4)./1.00000, 0.835600))./(0.191800+power(STATES(:,4)./1.00000, 0.835600))).*CONSTANTS(:,31))./60.0000).*0.00100000;
    ALGEBRAIC(:,10) = ( ALGEBRAIC(:,3).*CONSTANTS(:,29).*CONSTANTS(:,30).*CONSTANTS(:,32))./(CONSTANTS(:,33)+CONSTANTS(:,32));
    ALGEBRAIC(:,29) = ( CONSTANTS(:,7).*CONSTANTS(:,44).*STATES(:,13))./(CONSTANTS(:,8)+STATES(:,13));
    ALGEBRAIC(:,32) = ( CONSTANTS(:,9).*CONSTANTS(:,45).*STATES(:,13))./(CONSTANTS(:,10)+STATES(:,13));
    ALGEBRAIC(:,34) = ( CONSTANTS(:,11).*CONSTANTS(:,46).*STATES(:,13))./(CONSTANTS(:,12)+STATES(:,13));
    RATES(:,13) = ((ALGEBRAIC(:,10) - (ALGEBRAIC(:,29)+ALGEBRAIC(:,32)+ALGEBRAIC(:,34))) - ( CONSTANTS(:,53).*(STATES(:,13) - STATES(:,14)))./CONSTANTS(:,57)) - ( CONSTANTS(:,54).*(STATES(:,13) - STATES(:,15)))./CONSTANTS(:,57);
   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>120.000&VOI<=720.000, 1.00000 }, 1.00000);
    ALGEBRAIC(:,6) = (CONSTANTS(:,23) - STATES(:,1)) - STATES(:,3);
    ALGEBRAIC(:,2) = piecewise({VOI>240.000&VOI<=540.000, 0.00000 }, 0.00000);
    ALGEBRAIC(:,7) = (CONSTANTS(:,24) - STATES(:,4)) - STATES(:,6);
    ALGEBRAIC(:,8) = (CONSTANTS(:,27) - STATES(:,7)) - STATES(:,9);
    ALGEBRAIC(:,9) = (CONSTANTS(:,28) - STATES(:,10)) - STATES(:,12);
    ALGEBRAIC(:,5) = ( CONSTANTS(:,7).*CONSTANTS(:,49).*STATES(:,15))./(CONSTANTS(:,8)+STATES(:,15));
    ALGEBRAIC(:,12) = ( CONSTANTS(:,9).*CONSTANTS(:,50).*STATES(:,15))./(CONSTANTS(:,10)+STATES(:,15));
    ALGEBRAIC(:,31) = ( CONSTANTS(:,11).*CONSTANTS(:,51).*STATES(:,15))./(CONSTANTS(:,12)+STATES(:,15));
    ALGEBRAIC(:,4) =  (( (0.0630000+( 2.01000.*power( STATES(:,7).*1000.00, 1.00430))./(31.5440+power( STATES(:,7).*1000.00, 1.00430))).*(1.00000+( (1.00000./3.01000).*49.1000.*power( STATES(:,11).*1000.00, 0.892100))./(25.4400+power( STATES(:,11).*1000.00, 0.892100))).*CONSTANTS(:,36))./60.0000).*0.00100000;
    ALGEBRAIC(:,11) = ( ALGEBRAIC(:,4).*CONSTANTS(:,34).*CONSTANTS(:,35).*CONSTANTS(:,37))./(CONSTANTS(:,38)+CONSTANTS(:,37));
    ALGEBRAIC(:,30) = ( CONSTANTS(:,7).*CONSTANTS(:,47).*STATES(:,14))./(CONSTANTS(:,8)+STATES(:,14));
    ALGEBRAIC(:,33) = ( CONSTANTS(:,11).*CONSTANTS(:,48).*STATES(:,14))./(CONSTANTS(:,12)+STATES(:,14));
    ALGEBRAIC(:,3) =  (( (0.700000+( 3.82340.*power(STATES(:,1)./1.00000, 0.978700))./(0.198600+power(STATES(:,1)./1.00000, 0.978700))).*(1.00000+( (1.00000./1.44320).* - 1.00610.*power(STATES(:,4)./1.00000, 0.835600))./(0.191800+power(STATES(:,4)./1.00000, 0.835600))).*CONSTANTS(:,31))./60.0000).*0.00100000;
    ALGEBRAIC(:,10) = ( ALGEBRAIC(:,3).*CONSTANTS(:,29).*CONSTANTS(:,30).*CONSTANTS(:,32))./(CONSTANTS(:,33)+CONSTANTS(:,32));
    ALGEBRAIC(:,29) = ( CONSTANTS(:,7).*CONSTANTS(:,44).*STATES(:,13))./(CONSTANTS(:,8)+STATES(:,13));
    ALGEBRAIC(:,32) = ( CONSTANTS(:,9).*CONSTANTS(:,45).*STATES(:,13))./(CONSTANTS(:,10)+STATES(:,13));
    ALGEBRAIC(:,34) = ( CONSTANTS(:,11).*CONSTANTS(:,46).*STATES(:,13))./(CONSTANTS(:,12)+STATES(:,13));
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) ~= 4), initialGuess_0 = [0.1,0.1,0.1,0.1];, 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(:,13) = soln(1);
        ALGEBRAIC(:,14) = soln(2);
        ALGEBRAIC(:,15) = soln(3);
        ALGEBRAIC(:,16) = soln(4);
    else
        SET_ALGEBRAIC(:,13) = logical(1);
        SET_ALGEBRAIC(:,14) = logical(1);
        SET_ALGEBRAIC(:,15) = logical(1);
        SET_ALGEBRAIC(:,16) = 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(:,13) = soln(1);
            TEMP_ALGEBRAIC(:,14) = soln(2);
            TEMP_ALGEBRAIC(:,15) = soln(3);
            TEMP_ALGEBRAIC(:,16) = soln(4);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
        end
    end
end

function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    ALGEBRAIC(:,13) = algebraicCandidate(1);
    ALGEBRAIC(:,14) = algebraicCandidate(2);
    ALGEBRAIC(:,15) = algebraicCandidate(3);
    ALGEBRAIC(:,16) = algebraicCandidate(4);
    resid(1) = ALGEBRAIC(:,13) - (((CONSTANTS(:,21) - ALGEBRAIC(:,14)) - ALGEBRAIC(:,15)) - ALGEBRAIC(:,16));
    resid(2) = ALGEBRAIC(:,14) - ( ALGEBRAIC(:,1).*ALGEBRAIC(:,13))./CONSTANTS(:,2);
    resid(3) = ALGEBRAIC(:,15) - ( ALGEBRAIC(:,1).*ALGEBRAIC(:,13).*ALGEBRAIC(:,6))./(( CONSTANTS(:,1).*CONSTANTS(:,3))./CONSTANTS(:,2));
    resid(4) = ALGEBRAIC(:,16) - ( ALGEBRAIC(:,13).*ALGEBRAIC(:,6))./CONSTANTS(:,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) ~= 4), initialGuess_1 = [0.1,0.1,0.1,0.1];, 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(:,17) = soln(1);
        ALGEBRAIC(:,18) = soln(2);
        ALGEBRAIC(:,19) = soln(3);
        ALGEBRAIC(:,20) = soln(4);
    else
        SET_ALGEBRAIC(:,17) = logical(1);
        SET_ALGEBRAIC(:,18) = logical(1);
        SET_ALGEBRAIC(:,19) = logical(1);
        SET_ALGEBRAIC(:,20) = 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(:,17) = soln(1);
            TEMP_ALGEBRAIC(:,18) = soln(2);
            TEMP_ALGEBRAIC(:,19) = soln(3);
            TEMP_ALGEBRAIC(:,20) = soln(4);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
        end
    end
end

function resid = residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    ALGEBRAIC(:,17) = algebraicCandidate(1);
    ALGEBRAIC(:,18) = algebraicCandidate(2);
    ALGEBRAIC(:,19) = algebraicCandidate(3);
    ALGEBRAIC(:,20) = algebraicCandidate(4);
    resid(1) = ALGEBRAIC(:,17) - (((CONSTANTS(:,22) - ALGEBRAIC(:,18)) - ALGEBRAIC(:,19)) - ALGEBRAIC(:,20));
    resid(2) = ALGEBRAIC(:,18) - ( ALGEBRAIC(:,2).*ALGEBRAIC(:,17))./CONSTANTS(:,5);
    resid(3) = ALGEBRAIC(:,19) - ( ALGEBRAIC(:,2).*ALGEBRAIC(:,17).*ALGEBRAIC(:,7))./(( CONSTANTS(:,4).*CONSTANTS(:,6))./CONSTANTS(:,5));
    resid(4) = ALGEBRAIC(:,20) - ( ALGEBRAIC(:,17).*ALGEBRAIC(:,7))./CONSTANTS(:,6);
end

% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_2(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
    ALGEBRAIC = ALGEBRAIC_IN;
    CONSTANTS = CONSTANTS_IN;
    STATES = STATES_IN;
    global initialGuess_2;
    if (length(initialGuess_2) ~= 4), initialGuess_2 = [0.1,0.1,0.1,0.1];, end
    options = optimset('Display', 'off', 'TolX', 1E-6);
    if length(VOI) == 1
        residualfn = @(algebraicCandidate)residualSN_2(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
        soln = fsolve(residualfn, initialGuess_2, options);
        initialGuess_2 = soln;
        ALGEBRAIC(:,21) = soln(1);
        ALGEBRAIC(:,22) = soln(2);
        ALGEBRAIC(:,23) = soln(3);
        ALGEBRAIC(:,24) = soln(4);
    else
        SET_ALGEBRAIC(:,21) = logical(1);
        SET_ALGEBRAIC(:,22) = logical(1);
        SET_ALGEBRAIC(:,23) = logical(1);
        SET_ALGEBRAIC(:,24) = logical(1);
        for i=1:length(VOI)
            residualfn = @(algebraicCandidate)residualSN_2(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
            soln = fsolve(residualfn, initialGuess_2, options);
            initialGuess_2 = soln;
            TEMP_ALGEBRAIC(:,21) = soln(1);
            TEMP_ALGEBRAIC(:,22) = soln(2);
            TEMP_ALGEBRAIC(:,23) = soln(3);
            TEMP_ALGEBRAIC(:,24) = soln(4);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
        end
    end
end

function resid = residualSN_2(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    ALGEBRAIC(:,21) = algebraicCandidate(1);
    ALGEBRAIC(:,22) = algebraicCandidate(2);
    ALGEBRAIC(:,23) = algebraicCandidate(3);
    ALGEBRAIC(:,24) = algebraicCandidate(4);
    resid(1) = ALGEBRAIC(:,21) - (((CONSTANTS(:,25) - ALGEBRAIC(:,22)) - ALGEBRAIC(:,23)) - ALGEBRAIC(:,24));
    resid(2) = ALGEBRAIC(:,22) - ( ALGEBRAIC(:,1).*ALGEBRAIC(:,21))./CONSTANTS(:,2);
    resid(3) = ALGEBRAIC(:,23) - ( ALGEBRAIC(:,1).*ALGEBRAIC(:,21).*ALGEBRAIC(:,8))./(( CONSTANTS(:,1).*CONSTANTS(:,3))./CONSTANTS(:,2));
    resid(4) = ALGEBRAIC(:,24) - ( ALGEBRAIC(:,21).*ALGEBRAIC(:,8))./CONSTANTS(:,3);
end

% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_3(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
    ALGEBRAIC = ALGEBRAIC_IN;
    CONSTANTS = CONSTANTS_IN;
    STATES = STATES_IN;
    global initialGuess_3;
    if (length(initialGuess_3) ~= 4), initialGuess_3 = [0.1,0.1,0.1,0.1];, end
    options = optimset('Display', 'off', 'TolX', 1E-6);
    if length(VOI) == 1
        residualfn = @(algebraicCandidate)residualSN_3(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
        soln = fsolve(residualfn, initialGuess_3, options);
        initialGuess_3 = soln;
        ALGEBRAIC(:,25) = soln(1);
        ALGEBRAIC(:,26) = soln(2);
        ALGEBRAIC(:,27) = soln(3);
        ALGEBRAIC(:,28) = soln(4);
    else
        SET_ALGEBRAIC(:,25) = logical(1);
        SET_ALGEBRAIC(:,26) = logical(1);
        SET_ALGEBRAIC(:,27) = logical(1);
        SET_ALGEBRAIC(:,28) = logical(1);
        for i=1:length(VOI)
            residualfn = @(algebraicCandidate)residualSN_3(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
            soln = fsolve(residualfn, initialGuess_3, options);
            initialGuess_3 = soln;
            TEMP_ALGEBRAIC(:,25) = soln(1);
            TEMP_ALGEBRAIC(:,26) = soln(2);
            TEMP_ALGEBRAIC(:,27) = soln(3);
            TEMP_ALGEBRAIC(:,28) = soln(4);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
        end
    end
end

function resid = residualSN_3(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    ALGEBRAIC(:,25) = algebraicCandidate(1);
    ALGEBRAIC(:,26) = algebraicCandidate(2);
    ALGEBRAIC(:,27) = algebraicCandidate(3);
    ALGEBRAIC(:,28) = algebraicCandidate(4);
    resid(1) = ALGEBRAIC(:,25) - (((CONSTANTS(:,26) - ALGEBRAIC(:,26)) - ALGEBRAIC(:,27)) - ALGEBRAIC(:,28));
    resid(2) = ALGEBRAIC(:,26) - ( ALGEBRAIC(:,2).*ALGEBRAIC(:,25))./CONSTANTS(:,5);
    resid(3) = ALGEBRAIC(:,27) - ( ALGEBRAIC(:,2).*ALGEBRAIC(:,25).*ALGEBRAIC(:,9))./(( CONSTANTS(:,4).*CONSTANTS(:,6))./CONSTANTS(:,5));
    resid(4) = ALGEBRAIC(:,28) - ( ALGEBRAIC(:,25).*ALGEBRAIC(:,9))./CONSTANTS(:,6);
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