This part of the documentation is deprecated. Several changes are currently performed on the library. A new stable version of Codac will be released in the coming weeks.

Using external integration methods for ODEs

Installing CAPD

It is now possible to use CAPD to compute a guaranteed integration of an ODE. The result is enclosed in a TubeVector object of Codac.

To do so, you need to have CAPD and its DynSys module installed. You may need to install the following packages in order to compile CAPD:

sudo apt-get install subversion autoconf libtool

Then you can proceed to the compilation of the sources of CAPD:

svn co https://svn.capdnet.ii.uj.edu.pl/capd/ --non-interactive --trust-server-cert-failures=unknown-ca,cn-mismatch,expired,not-yet-valid,other
cd capd
svn co https://svn.capdnet.ii.uj.edu.pl/capdDynSys4 --non-interactive --trust-server-cert-failures=unknown-ca,cn-mismatch,expired,not-yet-valid,other
autoreconf --install
./configure --with-filib=check --with-mpfr=check # other options are available on the documentation website
sudo make install


For additional options on CAPD compilation and integration please visit the CAPD official documentation.

Finally, you need to compile Codac again:

cmake <other_options> -DWITH_CAPD=ON ..
sudo make install

How to use

The module works with reading a JSON configuration that gives the parameters of the integration for CAPD.

To use the module you need to add at the beginning of your code:

#include <codac-capd.h>

Here is an example of use:

#include <codac.h>
#include <codac-capd.h>

int main()
  auto j = R"(
      "function":"var:x,y;fun: x^3+x*y^2-x+y, y^3+x^2*y-x-y;",
      "fixed_step": true,
      "integration_time": 5,
      "integration_step": 0.001,
      "dimensions": 2,
      "initial_coordinates": [[0.5,0.5],[0,0]],

      "output_file": "reference_output.txt",
      "codac_output": "tube.tube"

  vector<IntervalVector> ibex_curve = capd2ibex(j); // list of IBEX format IntervalVector
  // or
  TubeVector output = capd2codac(j); // one tube of Codac format

All the different options are given in the above example.

Note that you can also define the configuration in a separated file with:

ifstream i("parameters/travis_test.json");
json j;
i >> j;

You can then use any Codac operator on this new generated tube.