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 =10;
end
% There are a total of 5 entries in each of the rate and state variable arrays.
% There are a total of 13 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('t in component environment (second)');
    LEGEND_CONSTANTS(:,1) = strpad('C_m in component environment (fF)');
    LEGEND_CONSTANTS(:,2) = strpad('w_i in component environment (pL)');
    LEGEND_CONSTANTS(:,3) = strpad('w_o in component environment (pL)');
    LEGEND_STATES(:,1) = strpad('q_mem in component environment (fC)');
    LEGEND_CONSTANTS(:,4) = strpad('R in component environment (J_per_K_per_mol)');
    LEGEND_CONSTANTS(:,5) = strpad('T in component environment (kelvin)');
    LEGEND_CONSTANTS(:,6) = strpad('F in component environment (C_per_mol)');
    LEGEND_ALGEBRAIC(:,8) = strpad('v_pCa_R1 in component pCa (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,9) = strpad('v_pCa_R2 in component pCa (fmol_per_sec)');
    LEGEND_STATES(:,2) = strpad('q_Ca_o in component environment (fmol)');
    LEGEND_STATES(:,3) = strpad('q_Ca_i in component environment (fmol)');
    LEGEND_STATES(:,4) = strpad('q_pCa in component environment (fmol)');
    LEGEND_STATES(:,5) = strpad('q_pCa_Ca in component environment (fmol)');
    LEGEND_ALGEBRAIC(:,2) = strpad('V_mem in component environment (J_per_C)');
    LEGEND_ALGEBRAIC(:,10) = strpad('I_mem_pCa in component pCa (fA)');
    LEGEND_ALGEBRAIC(:,3) = strpad('Ca_T in component environment (fmol)');
    LEGEND_ALGEBRAIC(:,4) = strpad('channel_T in component environment (fmol)');
    LEGEND_CONSTANTS(:,7) = strpad('kappa_pCa_R1 in component pCa_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,8) = strpad('kappa_pCa_R2 in component pCa_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,9) = strpad('K_Ca_i in component pCa_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,10) = strpad('K_Ca_o in component pCa_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,11) = strpad('K_pCa in component pCa_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,12) = strpad('K_pCa_Ca in component pCa_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,13) = strpad('zCa in component pCa_parameters (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('mu_Ca_i in component pCa (J_per_mol)');
    LEGEND_ALGEBRAIC(:,5) = strpad('mu_Ca_o in component pCa (J_per_mol)');
    LEGEND_ALGEBRAIC(:,6) = strpad('mu_pCa in component pCa (J_per_mol)');
    LEGEND_ALGEBRAIC(:,7) = strpad('mu_pCa_Ca in component pCa (J_per_mol)');
    LEGEND_RATES(:,3) = strpad('d/dt q_Ca_i in component environment (fmol)');
    LEGEND_RATES(:,2) = strpad('d/dt q_Ca_o in component environment (fmol)');
    LEGEND_RATES(:,4) = strpad('d/dt q_pCa in component environment (fmol)');
    LEGEND_RATES(:,5) = strpad('d/dt q_pCa_Ca in component environment (fmol)');
    LEGEND_RATES(:,1) = strpad('d/dt q_mem in component environment (fC)');
    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) = 153400;
    CONSTANTS(:,2) = 25.8;
    CONSTANTS(:,3) = 3.52;
    STATES(:,1) = -8.5e4;
    CONSTANTS(:,4) = 8.31;
    CONSTANTS(:,5) = 310;
    CONSTANTS(:,6) = 96500;
    STATES(:,2) = 9.3276;
    STATES(:,3) = 0.00456;
    STATES(:,4) = 0.0032;
    STATES(:,5) = 1e-9;
    CONSTANTS(:,7) = 1451.43;
    CONSTANTS(:,8) = 0.00014695;
    CONSTANTS(:,9) = 32.3484;
    CONSTANTS(:,10) = 0.00010737;
    CONSTANTS(:,11) = 0.0179984;
    CONSTANTS(:,12) = 0.0100142;
    CONSTANTS(:,13) = 2;
    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(:,4).*CONSTANTS(:,5).*log( CONSTANTS(:,9).*STATES(:,3));
    ALGEBRAIC(:,6) =  CONSTANTS(:,4).*CONSTANTS(:,5).*log( CONSTANTS(:,11).*STATES(:,4));
    ALGEBRAIC(:,7) =  CONSTANTS(:,4).*CONSTANTS(:,5).*log( CONSTANTS(:,12).*STATES(:,5));
    ALGEBRAIC(:,8) =  CONSTANTS(:,7).*(exp((ALGEBRAIC(:,1)+ALGEBRAIC(:,6))./( CONSTANTS(:,4).*CONSTANTS(:,5))) - exp(ALGEBRAIC(:,7)./( CONSTANTS(:,4).*CONSTANTS(:,5))));
    RATES(:,3) =  - ALGEBRAIC(:,8);
    ALGEBRAIC(:,5) =  CONSTANTS(:,4).*CONSTANTS(:,5).*log( CONSTANTS(:,10).*STATES(:,2));
    ALGEBRAIC(:,9) =  CONSTANTS(:,8).*(exp(ALGEBRAIC(:,7)./( CONSTANTS(:,4).*CONSTANTS(:,5))) - exp((ALGEBRAIC(:,5)+ALGEBRAIC(:,6))./( CONSTANTS(:,4).*CONSTANTS(:,5))));
    RATES(:,2) = ALGEBRAIC(:,9);
    RATES(:,4) =  - ALGEBRAIC(:,8)+ALGEBRAIC(:,9);
    RATES(:,5) = ALGEBRAIC(:,8) - ALGEBRAIC(:,9);
    ALGEBRAIC(:,10) =   - CONSTANTS(:,13).*CONSTANTS(:,6).*ALGEBRAIC(:,9);
    RATES(:,1) = ALGEBRAIC(:,10);
   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(:,4).*CONSTANTS(:,5).*log( CONSTANTS(:,9).*STATES(:,3));
    ALGEBRAIC(:,6) =  CONSTANTS(:,4).*CONSTANTS(:,5).*log( CONSTANTS(:,11).*STATES(:,4));
    ALGEBRAIC(:,7) =  CONSTANTS(:,4).*CONSTANTS(:,5).*log( CONSTANTS(:,12).*STATES(:,5));
    ALGEBRAIC(:,8) =  CONSTANTS(:,7).*(exp((ALGEBRAIC(:,1)+ALGEBRAIC(:,6))./( CONSTANTS(:,4).*CONSTANTS(:,5))) - exp(ALGEBRAIC(:,7)./( CONSTANTS(:,4).*CONSTANTS(:,5))));
    ALGEBRAIC(:,5) =  CONSTANTS(:,4).*CONSTANTS(:,5).*log( CONSTANTS(:,10).*STATES(:,2));
    ALGEBRAIC(:,9) =  CONSTANTS(:,8).*(exp(ALGEBRAIC(:,7)./( CONSTANTS(:,4).*CONSTANTS(:,5))) - exp((ALGEBRAIC(:,5)+ALGEBRAIC(:,6))./( CONSTANTS(:,4).*CONSTANTS(:,5))));
    ALGEBRAIC(:,10) =   - CONSTANTS(:,13).*CONSTANTS(:,6).*ALGEBRAIC(:,9);
    ALGEBRAIC(:,2) = STATES(:,1)./CONSTANTS(:,1);
    ALGEBRAIC(:,3) = STATES(:,3)+STATES(:,2)+STATES(:,5);
    ALGEBRAIC(:,4) = STATES(:,4)+STATES(:,5);
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