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 =17;
end
% There are a total of 7 entries in each of the rate and state variable arrays.
% There are a total of 40 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 (millisecond)');
    LEGEND_CONSTANTS(:,1) = strpad('V_cell in component environment (picoL)');
    LEGEND_CONSTANTS(:,2) = strpad('Ca_e in component environment (millimolar)');
    LEGEND_CONSTANTS(:,3) = strpad('K_e in component environment (millimolar)');
    LEGEND_CONSTANTS(:,4) = strpad('K_i in component environment (millimolar)');
    LEGEND_CONSTANTS(:,5) = strpad('V_tau in component environment (millivolt)');
    LEGEND_CONSTANTS(:,6) = strpad('k_tau in component environment (millivolt)');
    LEGEND_STATES(:,1) = strpad('V in component membrane (millivolt)');
    LEGEND_CONSTANTS(:,7) = strpad('R in component membrane (joule_per_kilomole_kelvin)');
    LEGEND_CONSTANTS(:,8) = strpad('T in component membrane (kelvin)');
    LEGEND_CONSTANTS(:,9) = strpad('F in component membrane (coulomb_per_mole)');
    LEGEND_CONSTANTS(:,10) = strpad('Cm in component membrane (picoF)');
    LEGEND_ALGEBRAIC(:,6) = strpad('i_Ca_L in component L_type_calcium_current (picoA)');
    LEGEND_ALGEBRAIC(:,9) = strpad('i_Ca_T in component T_type_calcium_current (picoA)');
    LEGEND_ALGEBRAIC(:,12) = strpad('i_K_DR in component voltage_sensitive_K_current (picoA)');
    LEGEND_ALGEBRAIC(:,14) = strpad('i_K_Ca in component Ca_activated_K_current (picoA)');
    LEGEND_ALGEBRAIC(:,16) = strpad('i_leak in component leak_current (picoA)');
    LEGEND_ALGEBRAIC(:,1) = strpad('phi_Ca in component L_type_calcium_current (millivolt_millimolar)');
    LEGEND_CONSTANTS(:,11) = strpad('g_Ca_L in component L_type_calcium_current (nanoS_per_millimolar)');
    LEGEND_STATES(:,2) = strpad('Ca_i in component cytosolic_calcium (millimolar)');
    LEGEND_STATES(:,3) = strpad('m_L in component L_type_calcium_current_m_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('m_L_infinity in component L_type_calcium_current_m_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,7) = strpad('tau_m_L in component L_type_calcium_current_m_gate (millisecond)');
    LEGEND_CONSTANTS(:,12) = strpad('tau_m_L_max in component L_type_calcium_current_m_gate (millisecond)');
    LEGEND_CONSTANTS(:,13) = strpad('V_m_L in component L_type_calcium_current_m_gate (millivolt)');
    LEGEND_CONSTANTS(:,14) = strpad('k_m_L in component L_type_calcium_current_m_gate (millivolt)');
    LEGEND_CONSTANTS(:,15) = strpad('g_Ca_T in component T_type_calcium_current (nanoS_per_millimolar)');
    LEGEND_STATES(:,4) = strpad('m_T in component T_type_calcium_current_m_gate (dimensionless)');
    LEGEND_STATES(:,5) = strpad('h_T in component T_type_calcium_current_h_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('m_T_infinity in component T_type_calcium_current_m_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,8) = strpad('tau_m_T in component T_type_calcium_current_m_gate (millisecond)');
    LEGEND_CONSTANTS(:,16) = strpad('tau_m_T_max in component T_type_calcium_current_m_gate (millisecond)');
    LEGEND_CONSTANTS(:,17) = strpad('V_m_T in component T_type_calcium_current_m_gate (millivolt)');
    LEGEND_CONSTANTS(:,18) = strpad('k_m_T in component T_type_calcium_current_m_gate (millivolt)');
    LEGEND_ALGEBRAIC(:,4) = strpad('h_T_infinity in component T_type_calcium_current_h_gate (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('tau_h_T in component T_type_calcium_current_h_gate (millisecond)');
    LEGEND_CONSTANTS(:,20) = strpad('V_h_T in component T_type_calcium_current_h_gate (millivolt)');
    LEGEND_CONSTANTS(:,21) = strpad('k_h_T in component T_type_calcium_current_h_gate (millivolt)');
    LEGEND_ALGEBRAIC(:,10) = strpad('phi_K in component voltage_sensitive_K_current (millivolt_millimolar)');
    LEGEND_CONSTANTS(:,22) = strpad('g_K_DR in component voltage_sensitive_K_current (nanoS_per_millimolar)');
    LEGEND_STATES(:,6) = strpad('n in component voltage_sensitive_K_current_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('n_infinity in component voltage_sensitive_K_current_n_gate (dimensionless)');
    LEGEND_CONSTANTS(:,23) = strpad('tau_n in component voltage_sensitive_K_current_n_gate (millisecond)');
    LEGEND_CONSTANTS(:,24) = strpad('V_n in component voltage_sensitive_K_current_n_gate (millivolt)');
    LEGEND_CONSTANTS(:,25) = strpad('k_n in component voltage_sensitive_K_current_n_gate (millivolt)');
    LEGEND_CONSTANTS(:,26) = strpad('g_K_Ca in component Ca_activated_K_current (nanoS_per_millimolar)');
    LEGEND_CONSTANTS(:,27) = strpad('Kc in component Ca_activated_K_current (millimolar)');
    LEGEND_CONSTANTS(:,28) = strpad('g_L in component leak_current (nanoS)');
    LEGEND_CONSTANTS(:,29) = strpad('V_L in component leak_current (millivolt)');
    LEGEND_STATES(:,7) = strpad('Ca_er in component ER_calcium (millimolar)');
    LEGEND_ALGEBRAIC(:,11) = strpad('J_rel in component ER_calcium (millimolar_picoL_per_millisecond)');
    LEGEND_ALGEBRAIC(:,13) = strpad('J_up in component ER_calcium (millimolar_picoL_per_millisecond)');
    LEGEND_CONSTANTS(:,39) = strpad('V_er in component ER_calcium (picoL)');
    LEGEND_CONSTANTS(:,30) = strpad('K_er in component ER_calcium (millimolar)');
    LEGEND_CONSTANTS(:,31) = strpad('f_er in component ER_calcium (dimensionless)');
    LEGEND_CONSTANTS(:,32) = strpad('P in component ER_calcium (picoL_per_millisecond)');
    LEGEND_CONSTANTS(:,33) = strpad('v_er in component ER_calcium (millimolar_picoL_per_millisecond)');
    LEGEND_CONSTANTS(:,40) = strpad('V_c in component cytosolic_calcium (picoL)');
    LEGEND_CONSTANTS(:,34) = strpad('K_p in component cytosolic_calcium (millimolar)');
    LEGEND_CONSTANTS(:,35) = strpad('f_cyt in component cytosolic_calcium (dimensionless)');
    LEGEND_CONSTANTS(:,36) = strpad('v_p in component cytosolic_calcium (millimolar_micrometre_per_millisecond)');
    LEGEND_ALGEBRAIC(:,15) = strpad('J_in in component cytosolic_calcium (millimolar_micrometre_per_millisecond)');
    LEGEND_ALGEBRAIC(:,17) = strpad('J_eff in component cytosolic_calcium (millimolar_micrometre_per_millisecond)');
    LEGEND_CONSTANTS(:,37) = strpad('alpha in component cytosolic_calcium (millimolar_micrometre_per_millisecond_per_picoA)');
    LEGEND_CONSTANTS(:,38) = strpad('beta in component cytosolic_calcium (per_micrometre)');
    LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)');
    LEGEND_RATES(:,3) = strpad('d/dt m_L in component L_type_calcium_current_m_gate (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt m_T in component T_type_calcium_current_m_gate (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt h_T in component T_type_calcium_current_h_gate (dimensionless)');
    LEGEND_RATES(:,6) = strpad('d/dt n in component voltage_sensitive_K_current_n_gate (dimensionless)');
    LEGEND_RATES(:,7) = strpad('d/dt Ca_er in component ER_calcium (millimolar)');
    LEGEND_RATES(:,2) = strpad('d/dt Ca_i in component cytosolic_calcium (millimolar)');
    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) = 1.77;
    CONSTANTS(:,2) = 20;
    CONSTANTS(:,3) = 5.6;
    CONSTANTS(:,4) = 140;
    CONSTANTS(:,5) = -60;
    CONSTANTS(:,6) = 22;
    STATES(:,1) = -70;
    CONSTANTS(:,7) = 8314;
    CONSTANTS(:,8) = 310;
    CONSTANTS(:,9) = 96845;
    CONSTANTS(:,10) = 7;
    CONSTANTS(:,11) = 9;
    STATES(:,2) = 0.00026;
    STATES(:,3) = 0;
    CONSTANTS(:,12) = 27;
    CONSTANTS(:,13) = -18;
    CONSTANTS(:,14) = 12;
    CONSTANTS(:,15) = 10;
    STATES(:,4) = 0;
    STATES(:,5) = 0;
    CONSTANTS(:,16) = 10;
    CONSTANTS(:,17) = -30;
    CONSTANTS(:,18) = 10.5;
    CONSTANTS(:,19) = 15;
    CONSTANTS(:,20) = -57;
    CONSTANTS(:,21) = 5;
    CONSTANTS(:,22) = 0.1;
    STATES(:,6) = 0;
    CONSTANTS(:,23) = 20;
    CONSTANTS(:,24) = -20;
    CONSTANTS(:,25) = 4.5;
    CONSTANTS(:,26) = 0.09;
    CONSTANTS(:,27) = 0.0004;
    CONSTANTS(:,28) = 0.3;
    CONSTANTS(:,29) = -67;
    STATES(:,7) = 0.0172;
    CONSTANTS(:,30) = 0.0002;
    CONSTANTS(:,31) = 0.0025;
    CONSTANTS(:,32) = 0.0012;
    CONSTANTS(:,33) = 0.00005;
    CONSTANTS(:,34) = 0.00008;
    CONSTANTS(:,35) = 0.01;
    CONSTANTS(:,36) = 0.000045;
    CONSTANTS(:,37) = 0.0000074;
    CONSTANTS(:,38) = 0.47;
    CONSTANTS(:,39) =  CONSTANTS(:,1).*0.150000;
    CONSTANTS(:,40) =  CONSTANTS(:,1).*0.850000;
    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) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,20))./CONSTANTS(:,21)));
    RATES(:,5) = (ALGEBRAIC(:,4) - STATES(:,5))./CONSTANTS(:,19);
    ALGEBRAIC(:,5) = 1.00000./(1.00000+exp((CONSTANTS(:,24) - STATES(:,1))./CONSTANTS(:,25)));
    RATES(:,6) = (ALGEBRAIC(:,5) - STATES(:,6))./CONSTANTS(:,23);
    ALGEBRAIC(:,2) = 1.00000./(1.00000+exp((CONSTANTS(:,13) - STATES(:,1))./CONSTANTS(:,14)));
    ALGEBRAIC(:,7) = CONSTANTS(:,12)./(exp((STATES(:,1) - CONSTANTS(:,5))./CONSTANTS(:,6))+ 2.00000.*exp(( 2.00000.*(CONSTANTS(:,5) - STATES(:,1)))./CONSTANTS(:,6)));
    RATES(:,3) = (ALGEBRAIC(:,2) - STATES(:,3))./ALGEBRAIC(:,7);
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((CONSTANTS(:,17) - STATES(:,1))./CONSTANTS(:,18)));
    ALGEBRAIC(:,8) = CONSTANTS(:,16)./(exp((STATES(:,1) - CONSTANTS(:,5))./CONSTANTS(:,6))+ 2.00000.*exp(( 2.00000.*(CONSTANTS(:,5) - STATES(:,1)))./CONSTANTS(:,6)));
    RATES(:,4) = (ALGEBRAIC(:,3) - STATES(:,4))./ALGEBRAIC(:,8);
    ALGEBRAIC(:,11) =  CONSTANTS(:,32).*(STATES(:,7) - STATES(:,2));
    ALGEBRAIC(:,13) = ( CONSTANTS(:,33).*power(STATES(:,2), 2.00000))./(power(STATES(:,2), 2.00000)+power(CONSTANTS(:,30), 2.00000));
    RATES(:,7) =  ( - CONSTANTS(:,31)./CONSTANTS(:,39)).*(ALGEBRAIC(:,11) - ALGEBRAIC(:,13));
    ALGEBRAIC(:,1) = ( STATES(:,1).*(STATES(:,2) - CONSTANTS(:,2)).*exp((  - 2.00000.*CONSTANTS(:,9).*STATES(:,1))./( CONSTANTS(:,7).*CONSTANTS(:,8))))./(1.00000 - exp((  - 2.00000.*CONSTANTS(:,9).*STATES(:,1))./( CONSTANTS(:,7).*CONSTANTS(:,8))));
    ALGEBRAIC(:,6) =  CONSTANTS(:,11).*power(STATES(:,3), 2.00000).*ALGEBRAIC(:,1);
    ALGEBRAIC(:,9) =  CONSTANTS(:,15).*power(STATES(:,4), 2.00000).*STATES(:,5).*ALGEBRAIC(:,1);
    ALGEBRAIC(:,10) = ( STATES(:,1).*(CONSTANTS(:,4) - CONSTANTS(:,3)).*exp((  - 1.00000.*CONSTANTS(:,9).*STATES(:,1))./( CONSTANTS(:,7).*CONSTANTS(:,8))))./(1.00000 - exp((  - 1.00000.*CONSTANTS(:,9).*STATES(:,1))./( CONSTANTS(:,7).*CONSTANTS(:,8))));
    ALGEBRAIC(:,12) =  CONSTANTS(:,22).*STATES(:,6).*ALGEBRAIC(:,10);
    ALGEBRAIC(:,14) =  (( CONSTANTS(:,26).*power(STATES(:,2), 4.00000))./(power(STATES(:,2), 4.00000)+power(CONSTANTS(:,27), 4.00000))).*ALGEBRAIC(:,10);
    ALGEBRAIC(:,16) =  CONSTANTS(:,28).*(STATES(:,1) - CONSTANTS(:,29));
    RATES(:,1) =  - (ALGEBRAIC(:,6)+ALGEBRAIC(:,9)+ALGEBRAIC(:,12)+ALGEBRAIC(:,14)+ALGEBRAIC(:,16))./CONSTANTS(:,10);
    ALGEBRAIC(:,15) =   - CONSTANTS(:,37).*(ALGEBRAIC(:,6)+ALGEBRAIC(:,9));
    ALGEBRAIC(:,17) = ( CONSTANTS(:,36).*power(STATES(:,2), 2.00000))./(power(STATES(:,2), 2.00000)+power(CONSTANTS(:,34), 2.00000));
    RATES(:,2) =  (CONSTANTS(:,35)./CONSTANTS(:,40)).*(ALGEBRAIC(:,11) - ALGEBRAIC(:,13))+ CONSTANTS(:,35).*CONSTANTS(:,38).*(ALGEBRAIC(:,15) - ALGEBRAIC(:,17));
   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) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,20))./CONSTANTS(:,21)));
    ALGEBRAIC(:,5) = 1.00000./(1.00000+exp((CONSTANTS(:,24) - STATES(:,1))./CONSTANTS(:,25)));
    ALGEBRAIC(:,2) = 1.00000./(1.00000+exp((CONSTANTS(:,13) - STATES(:,1))./CONSTANTS(:,14)));
    ALGEBRAIC(:,7) = CONSTANTS(:,12)./(exp((STATES(:,1) - CONSTANTS(:,5))./CONSTANTS(:,6))+ 2.00000.*exp(( 2.00000.*(CONSTANTS(:,5) - STATES(:,1)))./CONSTANTS(:,6)));
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((CONSTANTS(:,17) - STATES(:,1))./CONSTANTS(:,18)));
    ALGEBRAIC(:,8) = CONSTANTS(:,16)./(exp((STATES(:,1) - CONSTANTS(:,5))./CONSTANTS(:,6))+ 2.00000.*exp(( 2.00000.*(CONSTANTS(:,5) - STATES(:,1)))./CONSTANTS(:,6)));
    ALGEBRAIC(:,11) =  CONSTANTS(:,32).*(STATES(:,7) - STATES(:,2));
    ALGEBRAIC(:,13) = ( CONSTANTS(:,33).*power(STATES(:,2), 2.00000))./(power(STATES(:,2), 2.00000)+power(CONSTANTS(:,30), 2.00000));
    ALGEBRAIC(:,1) = ( STATES(:,1).*(STATES(:,2) - CONSTANTS(:,2)).*exp((  - 2.00000.*CONSTANTS(:,9).*STATES(:,1))./( CONSTANTS(:,7).*CONSTANTS(:,8))))./(1.00000 - exp((  - 2.00000.*CONSTANTS(:,9).*STATES(:,1))./( CONSTANTS(:,7).*CONSTANTS(:,8))));
    ALGEBRAIC(:,6) =  CONSTANTS(:,11).*power(STATES(:,3), 2.00000).*ALGEBRAIC(:,1);
    ALGEBRAIC(:,9) =  CONSTANTS(:,15).*power(STATES(:,4), 2.00000).*STATES(:,5).*ALGEBRAIC(:,1);
    ALGEBRAIC(:,10) = ( STATES(:,1).*(CONSTANTS(:,4) - CONSTANTS(:,3)).*exp((  - 1.00000.*CONSTANTS(:,9).*STATES(:,1))./( CONSTANTS(:,7).*CONSTANTS(:,8))))./(1.00000 - exp((  - 1.00000.*CONSTANTS(:,9).*STATES(:,1))./( CONSTANTS(:,7).*CONSTANTS(:,8))));
    ALGEBRAIC(:,12) =  CONSTANTS(:,22).*STATES(:,6).*ALGEBRAIC(:,10);
    ALGEBRAIC(:,14) =  (( CONSTANTS(:,26).*power(STATES(:,2), 4.00000))./(power(STATES(:,2), 4.00000)+power(CONSTANTS(:,27), 4.00000))).*ALGEBRAIC(:,10);
    ALGEBRAIC(:,16) =  CONSTANTS(:,28).*(STATES(:,1) - CONSTANTS(:,29));
    ALGEBRAIC(:,15) =   - CONSTANTS(:,37).*(ALGEBRAIC(:,6)+ALGEBRAIC(:,9));
    ALGEBRAIC(:,17) = ( CONSTANTS(:,36).*power(STATES(:,2), 2.00000))./(power(STATES(:,2), 2.00000)+power(CONSTANTS(:,34), 2.00000));
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