ODES is a scikit offering extra ode/dae solvers, as an extension to what is available in scipy. The main solvers to use are the Sundials solvers.
- You need scipy,
- Tested with python 2.7 and 3.3-3.5
- Available solvers:
- BDF linear multistep method for stiff problems. This is done or via cvode, which is an improvement on the ode (vode/dvode) solver in scipy.integrate, or for DAE systems via ida. Both are part of the sundials package. Use it to have modern features: root (event) finding, error control, (Krylov-)preconditioning, and more
- Adams-Moulton linear multistep method for nonstiff problems. This is done also via cvode or ida (option lmm_type='ADAMS')
- Explicit Runge-Kutta method of order (4)5 with stepsize control. This is done via dopri5 from scipy.integrate.
- Explicit Runge-Kutta method of order 8(5,3) with stepsize control. This is done via dop853 from scipy.integrate.
- Historical solvers: lsodi and ddaspk are available for comparison reasons. Use ida instead!
Since 2.2.0, a new API is available, which will become the default. Typical usage is:
import pylab import numpy as np from scikits.odes import ode t0, y0 = 1, np.array([0.5, 0.5]) # initial condition def van_der_pol(t, y, ydot): """ we create rhs equations for the problem""" ydot = y ydot = 1000*(1.0-y**2)*y-y solution = ode('cvode', van_der_pol, old_api=False).solve(np.linspace(t0,500,200), y0) pylab.plot(solution.values.t, solution.values.y[:,0], label='Van der Pol oscillator') pylab.show()
For simplicity there is also a convenience function odeint wrapping the ode solver class. See example use in simple.py.
- Double pendulum Example of using classes to pass residual and jacobian functions to IDA, and of how to implement roots functionality.
- Cython to speed up integration Example of using a cython rhs to speed up the ODE integration. As sundials mostly uses internal C code, the benefits of using cython for the rhs are normally small.
A comparison of different methods is given in following image. In this BDF, RK23, RK45 and Radau are python implementations; cvode is the method cvode of this scikit odes; lsoda, odeint and vode are the scipy integrators (2016), dopxxx are the RK methods in scipy. For this problem, cvode performs fastest at a preset tolerance.
You can generate above graph via the Performance notebook.
Projects that use odes
You can learn by example from following code that uses odes
- Centrifuge simulation, a wrapper around the ida solver: see centrifuge-1d
You have a project using odes? Do a pull request to add your project.
Requirements before install
- You need numpy and scipy installed, as the aim is to extend scipy.integrate
- You need to have cython installed and executable
- You need python development files available (python-dev package)
- You need a fortran compiler to install from source.
- If you use python < 3.4, you need the enum34 package (eg via command: pip install enum34)
- You need to have the sundials package version 2.7.0 installed, see (https://computation.llnl.gov/casc/sundials/download/download.html)
It is required that the Blas/Lapack interface in included in sundials, so check the Fortran Settings section. A typical install if sundials download package is extracted into directory sundials-2.7.0 is on a *nix system:
mkdir build-sundials-2.7.0 cd build-sundials-2.7.0/ cmake -DLAPACK_ENABLE=ON ../sundials-2.7.0/ make
This should install sundials in /usr/local/lib Make sure you use the fortran compiler as used for your lapack/blas install!
Installation of ODES scikit from sources
You can copy the git repository locally in directory odes with:
git clone git://github.com/bmcage/odes.git odes
In the top directory (the same as the file you are reading now), just do as root:
python setup.py build
This builds the packages in the build directory.
Libraries are searched in
/usr/local/lib by default.
You can also set
$SUNDIALS_INST in your environment to the directory you have installed SUNDIALS into.
It should contain
For a working scikit compile, LAPACK, ATLAS and BLAS must be found. A typical output of the build is:
lapack_info: FOUND: libraries = ['lapack'] library_dirs = ['/usr/lib'] language = f77 blas_info: FOUND: libraries = ['blas'] library_dirs = ['/usr/lib'] language = f77 FOUND: libraries = ['lapack', 'blas'] library_dirs = ['/usr/lib'] define_macros = [('NO_ATLAS_INFO', 1)] language = f77
You can try it without installation by using
PYTHONPATH and if needed adding local sundials install to
LD_LIBRARY_PATH. For example:
On my box, the build libs are in odes/build/lib.linux-x86_64-2.7/, hence I can
use them with:
PYTHONPATH=/path-to-odes/odes/build/lib.linux-x86_64-2.7/ python -c'import scikits.odes.sundials'
To install, as root:
python setup.py install
This installs the scikit, to use it in your python scripts use eg:
from scikits.odes import dae
Note: you need to add the local sundials install to
LD_LIBRARY_PATH if not installed in the standard locations.
See the examples for more info.
You need nose to run the tests. Eg, to install it, run
pip install nose
To run the tests do in the python shell:
>>> import scikits.odes as od; od.test()
or shorter, in a terminal:
PYTHONPATH=/path-to-build python -c 'import scikits.odes as od; od.test()'
Please submit extra ipython notebook examples of usage of odes scikit. To install and use ipython, typical install instructions would be (use
pip instead of
pip3 for python2):
pip3 install jupyter jupyter-notebook
Which should open a browser window from the current directory to work on a python notebook. Do this in the directory
odes/docs/ipython. You might obtain errors due to missing dependencies. For example, if simplegeneric missing, install it via
pip3. Typical problem is that several conflicting versions are installed. If so, remove the versions installed on your system, and use
pip3 to install the most recent version. For example, an old ipython install will create problems, removing it (
sudo apt-get remove --purge ipython3 ipython) fixes those issues.
- set in common.py version string and DEV=False, commit this.
- tag like:
git tag -a v2.2.0 -m "version 2.2.0"
- push tag:
git push --tags
- update to pypi repo:
python setup.py sdist --formats=gztar,zip register upload
- update version string to a higher number, and DEV=True
For the documentation, you need following packages
sudo apt-get install python-sphinx python-numpydoc
After local install, create the new documentation via
- go to the sphinx directory:
- create the documentation:
- upload the new html doc.
linking errors - Lapack not found
Most issues with using the scikit are due to incorrectly setting the lapack libraries, resulting in error, typically:
AttributeError: module 'scikits.odes.sundials.cvode' has no attribute 'CVODE'
undefined reference to dcopy_
This is an indication the scikit does not link correctly to the lapack directories. You can solve this as follows: When installing sundials, look at output of cmake. If it has:
-- A library with BLAS API not found. Please specify library location. -- LAPACK requires BLAS -- A library with LAPACK API not found. Please specify library location.
then the scikit will not work ! First make sure you install sundials with BLAS and LAPACK found!
Eg on ubuntu one needs
sudo apt-get install libblas-dev libatlas-base-dev libopenblas-dev liblapack-dev gfortran
Once installed correctly, the sundials cmake output should be
-- A library with BLAS API found. -- Looking for Fortran cheev -- Looking for Fortran cheev - found -- A library with LAPACK API found. -- Looking for LAPACK libraries... OK -- Checking if Lapack works... OK
You can check the CMakeCache.txt file to see which libraries are found. It should have output as eg:
//Blas and Lapack libraries LAPACK_LIBRARIES:STRING=/usr/lib/liblapack.so;/usr/lib/libf77blas.so;/usr/lib/libatlas.so //Path to a library. LAPACK_lapack_LIBRARY:FILEPATH=/usr/lib/liblapack.so
With above output, you can set the LAPACK directories and libs correctly. To force the scikit to find these directories you can set them by force by editing the file
scikits/odes/sundials/setup.py, and passing the directories and libs as used by sundials:
INCL_DIRS_LAPACK = ['/usr/include', '/usr/include/atlas'] LIB_DIRS_LAPACK = ['/usr/lib'] LIBS_LAPACK = ['lapack', 'f77blas', 'atlas']
Note that on your install, these directories and libs might be different than the example above! With these variables set, installation of the scikit should be successful.
Verify you link to the correct sundials version. Easiest to ensure you only have one libsundials_xxx installed. If several are installed, pass the correct one via the
$SUNDIALS_INST environment variable.
Most common reason for errors with the tests is because they are run in the scikits.odes download directory. This is not supported. The tests must be run from a different location, passing the install location if not installed globally. See info above on how to set PYTHONPATH if needed.