BYOM function call_deri.m (calculates the model output)

Syntax: [Xout,TE,Xout2,zvd] = call_deri(t,par,X0v,glo)

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). The events function is set up to catch discontinuities. It should be specified according to the problem you are simulating. If you want to use parameters that are (or influence) initial states, they have to be included in this function. Optional output Xout2 is for additional uni-variate data (not used here), and zvd is for zero-variate data (used in byom_bioconc_extra.m).

Copyright (c) 2012-2021, Tjalling Jager, all rights reserved.
This source code is licensed under the MIT-style license found in the
LICENSE.txt file in the root directory of BYOM.



function [Xout,TE,Xout2,zvd] = call_deri(t,par,X0v,glo)
% initialise extra outputs as empty for when they are not used
Xout2    = []; % additional uni-variate output
zvd      = []; % additional zero-variate output

% Note: if these options are not used, these variables must be defined as
% empty as they are outputs of this function.

% if needed, calculate model values for zero-variate data from parameter
% set; these lines can be removed if no zero-variate data are used
if ~isempty(glo.zvd) % if there are zero-variate data defined (see byom_bioconc_extra)
    zvd       = glo.zvd; % copy zero-variate data structure to zvd
    zvd.ku(3) = par.Piw(1) *; % add model prediction as third value in zvd
else % if there are no zero-variate data defined (as in byom_bioconc_start)
    zvd       = []; % additional zero-variate output, output defined as empty matrix

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 the analytical solution in simplefun.m. Using eventson=1 turns on the events handling. Also modify the sub-function at the bottom of this function! Further in this section, initial values can be determined by a parameter (overwrite parts of X0), and zero-variate data can be calculated. See the example BYOM files for more information.

useode   = glo.useode; % calculate model using ODE solver (1) or analytical solution (0)
eventson = glo.eventson; % events function on (1) or off (0)
stiff    = glo.stiff; % set to 1 or 2 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
% % if needed, extract parameters from par that influence initial states in X0
% Ci0   = par.Ci0(1); % example: parameter for the internal concentration
% X0(2) = Ci0; % put this parameter in the correct location of the initial vector


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)

TE = 0; % dummy for time of events

if useode == 1 % use the ODE solver to calculate the solution
    % Note: set options AFTER the 'if useode == 1' as odeset takes
    % considerable calculation time, which is not needed when using the
    % analytical solution. Also note that the global _glo_ is now input to
    % the derivatives function. This increases calculation speed.

    % specify options for the ODE solver; feel free to change the
    % tolerances, if you know what you're doing (for some problems, it is
    % better to set them much tighter, e.g., both to 1e-9)
    reltol = 1e-4;
    abstol = 1e-7;
    options = odeset; % start with default options
    if eventson == 1
        options = odeset(options,'Events',@eventsfun,'RelTol',reltol,'AbsTol',abstol); % add an events function and tigher tolerances
        options = odeset(options,'RelTol',reltol,'AbsTol',abstol); % only specify tightened tolerances
    % options = odeset(options,'InitialStep',max(t)/1000,'MaxStep',max(t)/100); % specify smaller stepsize

    % call the ODE solver (try ode15s for stiff problems, and possibly with for pulsed forcings)
    if isempty(options.Events) % if no events function is specified ...
        switch stiff
            case 0
                [~,Xout] = ode45(@derivatives,t,X0,options,par,c,glo);
            case 1
                [~,Xout] = ode113(@derivatives,t,X0,options,par,c,glo);
            case 2
                [~,Xout] = ode15s(@derivatives,t,X0,options,par,c,glo);
    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,glo);
            case 1
                [~,Xout,TE,YE,IE] = ode113(@derivatives,t,X0,options,par,c,glo);
            case 2
                [~,Xout,TE,YE,IE] = ode15s(@derivatives,t,X0,options,par,c,glo);
else % alternatively, use an explicit function provided in simplefun
    Xout = simplefun(t,X0,par,c,glo);

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

Output mapping

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 column, like cube it ...

% % To obtain the output of the derivatives at each time point. The values in
% % dXout might be used to replace values in Xout, if the data to be fitted
% % are the changes (rates) instead of the state variable itself.
% % dXout = zeros(size(Xout)); % initialise with zeros
% for i = 1:length(t) % run through all time points
%     dXout(i,:) = derivatives(t(i),Xout(i,:),par,c,glo);
%     % derivatives for each stage at each time
% end

Events function

Modify this part of the code if eventson=1. This subfunction catches the 'events': in this case, it looks for the external concentration where degradation stops. This function should be adapted to the problem you are modelling (this one matches the byom_bioconc_... files). You can catch more events by making a vector out of values.

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

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

Ct      = par.Ct(1); % threshold external concentration where degradation stops
nevents = 1;         % number of events that we try to catch

value       = zeros(nevents,1); % initialise with zeros
value(1)    = X(1) - Ct;        % thing to follow is external concentration (state 1) minus threshold
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