BYOM function call_deri.m (calculates the model output)

Syntax: [Xout TE] = call_deri(t,par,X0v)

This function calls the ODE solver to solve the system of differential equations specified in derivatives.m, or the explicit function(s) in simplefun.m. As input, it gets:

The output Xout provides a matrix with time in rows, and states in columns. This function calls derivatives.m. The optional output TE is the time at which an event takes place (specified using the events function, set it up to catch discontinuities). If you want to use parameters that are (or influence) initial states, they have to be included in this function.

Contents

Start

The function statement, and make the global structure glo known here (we don't use zvd in this demo).

function [Xout, TE] = call_deri(t,par,X0v)
global glo   % allow for global parameters in structure glo
global zvd   % global structure for zero-variate data

Initial settings

This part extracts optional settings for the ODE solver that can be set in the main script (defaults are set in prelim_checks). The useode option decides whether to calculate the model results using the ODEs in derivatives.m, or an analytical solution that has to be provided in simplefun.m. Using eventson=1 turns on the events handling. Also modify the sub-function at the bottom of this function! See the example BYOM files for more information.

useode   = glo.useode;   % calculate model using ODE solver (1) or analytical solution (2)
eventson = glo.eventson; % events function on (1) or off (0)
stiff    = glo.stiff;    % set to 1 to use a stiff solver instead of the standard one

% Unpack the vector X0v, which is X0mat for one scenario
X0 = X0v(2:end); % these are the intitial states for a scenario

Calculations

This part calls the ODE solver (or the explicit model in simplefun.m) to calculate the output (the value of the state variables over time). There is generally no need to modify this part. The solver ode45 generally works well. For stiff problems, the solver might become very slow; you can try ode15s instead.

c  = X0v(1);     % the concentration (or scenario number)
t  = t(:);       % force t to be a row vector (needed when useode=0)

% specify options for the ODE solver
options = odeset; % start with default options
if eventson == 1
    options = odeset(options, 'Events',@eventsfun); % add an events function
end
options = odeset(options, 'RelTol',1e-4,'AbsTol',1e-7); % specify tightened tolerances

TE = 0; % dummy for time of events

if useode == 1 % use the ODE solver to calculate the solution
    % call the ODE solver (use ode15s for stiff problems, escpecially for pulses)
    if isempty(options.Events) % if no events function is specified ...
        switch stiff
            case 0
                [~,Xout] = ode45(@derivatives,t,X0,options,par,c);
            case 1
                [~,Xout] = ode113(@derivatives,t,X0,options,par,c);
            case 2
                [~,Xout] = ode15s(@derivatives,t,X0,options,par,c);
        end
    else % with an events functions ... additional output arguments for events:
        % TE catches the time of an event, YE the states at the event, and IE the number of the event
        switch stiff
            case 0
                [~,Xout,TE,YE,IE] = ode45(@derivatives,t,X0,options,par,c);
            case 1
                [~,Xout,TE,YE,IE] = ode113(@derivatives,t,X0,options,par,c);
            case 2
                [~,Xout,TE,YE,IE] = ode15s(@derivatives,t,X0,options,par,c);
        end
    end
else % alternatively, use an explicit function provided in simplefun!
    Xout = simplefun(t,X0,par,c);
end

if isempty(TE) || all(TE == 0) % if there is no event caught
    TE = +inf; % return infinity
end

Output mapping

The matrix Xout contains a row for each state variable. It can be mapped to the data. If you need to transform the model values to match the data, do it here.

% Xout(:,1) = Xout(:,1).^3; % e.g., do something on first state variable, like cube it ...

Events function

Modify this part of the code if eventson=1. This subfunction catches the 'events': in this case, it looks for the start of depuration at t=7. This is rather trivial, as we already know exactly when this event happens. However, it is useful as the ODE solver will now stop and restart at t=7 and will not be hampered by the sudden shift in states at this discontinuity.

Note that the eventsfun has the same inputs, in the same sequence, as derivatives.m.

function [value,isterminal,direction] = eventsfun(t,X,par,c)

nevents = 1;         % number of events that we try to catch

value       = zeros(nevents,1); % initialise with zeros
value(1)    = t - 7;            % thing to follow is when depuration starts at t=7
isterminal  = zeros(nevents,1); % do NOT stop the solver at an event
direction   = zeros(nevents,1); % catch ALL zero crossing when function is increasing or decreasing