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 =11;
end
% There are a total of 10 entries in each of the rate and state variable arrays.
% There are a total of 27 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(:,3) = strpad('Rate_Ca_influx_across_the_SR in component Ca_influx_across_the_SR (flux)');
    LEGEND_CONSTANTS(:,1) = strpad('Ca_e in component extracellular_calcium (molar)');
    LEGEND_STATES(:,1) = strpad('Ca_f in component fuzzy_space_calcium (molar)');
    LEGEND_CONSTANTS(:,2) = strpad('k1 in component Ca_influx_across_the_SR (first_order_rate_constant)');
    LEGEND_STATES(:,2) = strpad('Ca_2_S1 in component Ca_bound_to_the_SRRC_fast_activating_binding_site (molar)');
    LEGEND_STATES(:,3) = strpad('Ca_S2 in component Ca_bound_to_the_SRRC_slow_inactivating_binding_site (molar)');
    LEGEND_STATES(:,4) = strpad('S1 in component SRRC_fast_activating_binding_site (molar)');
    LEGEND_STATES(:,5) = strpad('S2 in component SRRC_slow_inactivating_binding_site (molar)');
    LEGEND_STATES(:,6) = strpad('Ca_s in component SR_calcium (molar)');
    LEGEND_ALGEBRAIC(:,1) = strpad('dCa2_S1_dt in component Ca_movement_through_the_SRRC (flux)');
    LEGEND_ALGEBRAIC(:,2) = strpad('dCa_S2_dt in component Ca_movement_through_the_SRRC (flux)');
    LEGEND_CONSTANTS(:,3) = strpad('k_on1 in component Ca_movement_through_the_SRRC (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('k_off1 in component Ca_movement_through_the_SRRC (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,5) = strpad('k_on2 in component Ca_movement_through_the_SRRC (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('k_off2 in component Ca_movement_through_the_SRRC (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('k_s in component Ca_movement_through_the_SRRC (first_order_rate_constant)');
    LEGEND_STATES(:,7) = strpad('cas1 in component Ca_movement_through_the_SRRC (dimensionless)');
    LEGEND_STATES(:,8) = strpad('cas2 in component Ca_movement_through_the_SRRC (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('dcas1_dt in component Ca_movement_through_the_SRRC (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,6) = strpad('dcas2_dt in component Ca_movement_through_the_SRRC (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,4) = strpad('r_o in component Ca_movement_through_the_SRRC (dimensionless)');
    LEGEND_ALGEBRAIC(:,7) = strpad('Rate_Ca_movement_through_the_SRRC in component Ca_movement_through_the_SRRC (flux)');
    LEGEND_CONSTANTS(:,8) = strpad('Km_NaCaX in component Ca_efflux_across_the_SR_by_NaCa_exchange (molar)');
    LEGEND_CONSTANTS(:,9) = strpad('Vmax_NaCaX in component Ca_efflux_across_the_SR_by_NaCa_exchange (flux)');
    LEGEND_ALGEBRAIC(:,8) = strpad('Rate_Ca_efflux_across_the_SR_by_NaCa_exchange in component Ca_efflux_across_the_SR_by_NaCa_exchange (flux)');
    LEGEND_STATES(:,9) = strpad('Ca_c in component cytosolic_calcium (molar)');
    LEGEND_CONSTANTS(:,10) = strpad('kf in component Ca_movement_between_the_fuzzy_space_and_cytosol (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,9) = strpad('Rate_Ca_movement_between_the_fuzzy_space_and_cytosol in component Ca_movement_between_the_fuzzy_space_and_cytosol (flux)');
    LEGEND_CONSTANTS(:,11) = strpad('Km_s in component Ca_uptake_by_SR_Ca_ATPase (molar)');
    LEGEND_CONSTANTS(:,12) = strpad('Vmax_s in component Ca_uptake_by_SR_Ca_ATPase (flux)');
    LEGEND_ALGEBRAIC(:,10) = strpad('Rate_Ca_uptake_by_SR_Ca_ATPase in component Ca_uptake_by_SR_Ca_ATPase (flux)');
    LEGEND_STATES(:,10) = strpad('Ca_CSQ in component calsequestrin_bound_calcium (molar)');
    LEGEND_CONSTANTS(:,13) = strpad('K_ons in component Ca_buffering_in_the_SR (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,14) = strpad('K_offs in component Ca_buffering_in_the_SR (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,15) = strpad('Bmax_s in component Ca_buffering_in_the_SR (molar)');
    LEGEND_ALGEBRAIC(:,11) = strpad('Rate_Ca_buffering_in_the_SR in component Ca_buffering_in_the_SR (flux)');
    LEGEND_CONSTANTS(:,16) = strpad('Rt in component fuzzy_space_calcium (molar)');
    LEGEND_CONSTANTS(:,17) = strpad('Bmax_f1 in component fuzzy_space_calcium (molar)');
    LEGEND_CONSTANTS(:,18) = strpad('Bmax_f2 in component fuzzy_space_calcium (molar)');
    LEGEND_CONSTANTS(:,19) = strpad('Kb_f1 in component fuzzy_space_calcium (molar)');
    LEGEND_CONSTANTS(:,20) = strpad('Kb_f2 in component fuzzy_space_calcium (molar)');
    LEGEND_CONSTANTS(:,21) = strpad('V_f in component fuzzy_space_calcium (dimensionless)');
    LEGEND_CONSTANTS(:,22) = strpad('Bmax_c in component cytosolic_calcium (molar)');
    LEGEND_CONSTANTS(:,23) = strpad('dye_c in component cytosolic_calcium (molar)');
    LEGEND_CONSTANTS(:,24) = strpad('Kb_c in component cytosolic_calcium (molar)');
    LEGEND_CONSTANTS(:,25) = strpad('Kb_dye in component cytosolic_calcium (molar)');
    LEGEND_CONSTANTS(:,26) = strpad('V_c in component cytosolic_calcium (dimensionless)');
    LEGEND_CONSTANTS(:,27) = strpad('V_s in component SR_calcium (dimensionless)');
    LEGEND_RATES(:,7) = strpad('d/dt cas1 in component Ca_movement_through_the_SRRC (dimensionless)');
    LEGEND_RATES(:,8) = strpad('d/dt cas2 in component Ca_movement_through_the_SRRC (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt Ca_f in component fuzzy_space_calcium (molar)');
    LEGEND_RATES(:,9) = strpad('d/dt Ca_c in component cytosolic_calcium (molar)');
    LEGEND_RATES(:,6) = strpad('d/dt Ca_s in component SR_calcium (molar)');
    LEGEND_RATES(:,10) = strpad('d/dt Ca_CSQ in component calsequestrin_bound_calcium (molar)');
    LEGEND_RATES(:,4) = strpad('d/dt S1 in component SRRC_fast_activating_binding_site (molar)');
    LEGEND_RATES(:,5) = strpad('d/dt S2 in component SRRC_slow_inactivating_binding_site (molar)');
    LEGEND_RATES(:,2) = strpad('d/dt Ca_2_S1 in component Ca_bound_to_the_SRRC_fast_activating_binding_site (molar)');
    LEGEND_RATES(:,3) = strpad('d/dt Ca_S2 in component Ca_bound_to_the_SRRC_slow_inactivating_binding_site (molar)');
    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) = 0.002;
    STATES(:,1) = 0.12e-6;
    CONSTANTS(:,2) = 0.2;
    STATES(:,2) = 0;
    STATES(:,3) = 0;
    STATES(:,4) = 0;
    STATES(:,5) = 0;
    STATES(:,6) = 201e-6;
    CONSTANTS(:,3) = 2000000000;
    CONSTANTS(:,4) = 1400;
    CONSTANTS(:,5) = 13000000;
    CONSTANTS(:,6) = 3.9;
    CONSTANTS(:,7) = 9;
    STATES(:,7) = 0;
    STATES(:,8) = 0;
    CONSTANTS(:,8) = 0.000036;
    CONSTANTS(:,9) = 0.0012;
    STATES(:,9) = 1e-7;
    CONSTANTS(:,10) = 2500;
    CONSTANTS(:,11) = 0.00000025;
    CONSTANTS(:,12) = 0.000525;
    STATES(:,10) = 0;
    CONSTANTS(:,13) = 8772;
    CONSTANTS(:,14) = 5.596536;
    CONSTANTS(:,15) = 0.008;
    CONSTANTS(:,16) = 0.00000015;
    CONSTANTS(:,17) = 0.0002;
    CONSTANTS(:,18) = 0.0011;
    CONSTANTS(:,19) = 0.000017;
    CONSTANTS(:,20) = 0.000013;
    CONSTANTS(:,21) = 0.0013;
    CONSTANTS(:,22) = 0.00012;
    CONSTANTS(:,23) = 0;
    CONSTANTS(:,24) = 0.00000096;
    CONSTANTS(:,25) = 2e-7;
    CONSTANTS(:,26) = 0.9287;
    CONSTANTS(:,27) = 0.07;
    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(:,3).*STATES(:,1).*STATES(:,4) -  (power(CONSTANTS(:,4), 2.00000)./( CONSTANTS(:,3).*STATES(:,1))).*STATES(:,2);
    RATES(:,4) =  - ALGEBRAIC(:,1);
    ALGEBRAIC(:,2) =  CONSTANTS(:,5).*STATES(:,1).*STATES(:,5) -  CONSTANTS(:,6).*STATES(:,3);
    RATES(:,5) =  - ALGEBRAIC(:,2);
    RATES(:,2) = ALGEBRAIC(:,1);
    RATES(:,3) = ALGEBRAIC(:,2);
    ALGEBRAIC(:,5) =  CONSTANTS(:,3).*STATES(:,1).*(1.00000 - STATES(:,7)) -  (power(CONSTANTS(:,4), 2.00000)./( CONSTANTS(:,3).*STATES(:,1))).*STATES(:,7);
    RATES(:,7) = ALGEBRAIC(:,5);
    ALGEBRAIC(:,6) =  CONSTANTS(:,5).*STATES(:,1).*(1.00000 - STATES(:,8)) -  CONSTANTS(:,6).*STATES(:,8);
    RATES(:,8) = ALGEBRAIC(:,6);
    ALGEBRAIC(:,3) =  CONSTANTS(:,2).*(CONSTANTS(:,1) - STATES(:,1));
    ALGEBRAIC(:,4) =  STATES(:,7).*(1.00000 - STATES(:,8));
    ALGEBRAIC(:,7) =  CONSTANTS(:,7).*ALGEBRAIC(:,4).*(STATES(:,6) - STATES(:,1));
    ALGEBRAIC(:,8) = ( CONSTANTS(:,9).*STATES(:,1))./(CONSTANTS(:,8)+STATES(:,1));
    ALGEBRAIC(:,9) =  CONSTANTS(:,10).*(STATES(:,1) - STATES(:,9));
    RATES(:,1) = ((ALGEBRAIC(:,7) - ( CONSTANTS(:,16).*(ALGEBRAIC(:,5)+ALGEBRAIC(:,6))+ALGEBRAIC(:,9)+ALGEBRAIC(:,8)))+ALGEBRAIC(:,3))./(( CONSTANTS(:,17).*CONSTANTS(:,19))./power(STATES(:,1)+CONSTANTS(:,19), 2.00000)+( CONSTANTS(:,18).*CONSTANTS(:,20))./power(STATES(:,1)+CONSTANTS(:,20), 2.00000)+CONSTANTS(:,21));
    ALGEBRAIC(:,10) = ( CONSTANTS(:,12).*(power(STATES(:,9), 2.00000) - power(STATES(:,6), 2.00000)./power(7000.00, 2.00000)))./(power(CONSTANTS(:,11), 2.00000)+power(STATES(:,9), 2.00000)+power(STATES(:,6), 2.00000)./power(7000.00, 2.00000));
    RATES(:,9) = (ALGEBRAIC(:,9) - ALGEBRAIC(:,10))./(( CONSTANTS(:,22).*CONSTANTS(:,24))./power(STATES(:,9)+CONSTANTS(:,24), 2.00000)+( CONSTANTS(:,23).*CONSTANTS(:,25))./power(STATES(:,9)+CONSTANTS(:,25), 2.00000)+CONSTANTS(:,26));
    ALGEBRAIC(:,11) =  CONSTANTS(:,13).*STATES(:,6).*(CONSTANTS(:,15) - STATES(:,10)) -  CONSTANTS(:,14).*STATES(:,10);
    RATES(:,6) = (ALGEBRAIC(:,10) - ALGEBRAIC(:,7))./CONSTANTS(:,27) - ALGEBRAIC(:,11);
    RATES(:,10) = ALGEBRAIC(:,11);
   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(:,3).*STATES(:,1).*STATES(:,4) -  (power(CONSTANTS(:,4), 2.00000)./( CONSTANTS(:,3).*STATES(:,1))).*STATES(:,2);
    ALGEBRAIC(:,2) =  CONSTANTS(:,5).*STATES(:,1).*STATES(:,5) -  CONSTANTS(:,6).*STATES(:,3);
    ALGEBRAIC(:,5) =  CONSTANTS(:,3).*STATES(:,1).*(1.00000 - STATES(:,7)) -  (power(CONSTANTS(:,4), 2.00000)./( CONSTANTS(:,3).*STATES(:,1))).*STATES(:,7);
    ALGEBRAIC(:,6) =  CONSTANTS(:,5).*STATES(:,1).*(1.00000 - STATES(:,8)) -  CONSTANTS(:,6).*STATES(:,8);
    ALGEBRAIC(:,3) =  CONSTANTS(:,2).*(CONSTANTS(:,1) - STATES(:,1));
    ALGEBRAIC(:,4) =  STATES(:,7).*(1.00000 - STATES(:,8));
    ALGEBRAIC(:,7) =  CONSTANTS(:,7).*ALGEBRAIC(:,4).*(STATES(:,6) - STATES(:,1));
    ALGEBRAIC(:,8) = ( CONSTANTS(:,9).*STATES(:,1))./(CONSTANTS(:,8)+STATES(:,1));
    ALGEBRAIC(:,9) =  CONSTANTS(:,10).*(STATES(:,1) - STATES(:,9));
    ALGEBRAIC(:,10) = ( CONSTANTS(:,12).*(power(STATES(:,9), 2.00000) - power(STATES(:,6), 2.00000)./power(7000.00, 2.00000)))./(power(CONSTANTS(:,11), 2.00000)+power(STATES(:,9), 2.00000)+power(STATES(:,6), 2.00000)./power(7000.00, 2.00000));
    ALGEBRAIC(:,11) =  CONSTANTS(:,13).*STATES(:,6).*(CONSTANTS(:,15) - STATES(:,10)) -  CONSTANTS(:,14).*STATES(:,10);
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