Pade_PyCpp

Padé approximation in Python and C++ (with Python link)

Source Files

src/expm.py

This file contains an implementation of the Padé approximation method. The standard scipy version (scipy.linalg.expm) will be replaced with this version in the future, however currently it is much faster than the scipy version.

src/expmat.cpp

This file contains the C++ implementation of the matrix exponential, along with the boost::python link. Internally, it uses the Eigen implementation of the matrix exponential. Thus, it contains a way to efficiently access the data of an instance of a numpy.ndarray without needing to copy the data.

Testing

src/test/demo_expm.py

This file executes the Python and C++ versions of the Padé approximation and does some timings. It produced the output plots src/test/results/expmtimings_*.pdf.

src/test/demo_cores.py

This file does some timings for the multithreaded C++ implementation. It stores results in the files src/test/results/<N>threads_gcc.npz where the values for <N> is determined by the OMP_NUM_THREADS environment variable.

If multiple runs are needed (better results), this file can just be executed multiple times. It then reads the existing timing information and stores the minimum of that and the new timings.

evalcores.py

This file evaluates the information in src/test/results/<N>threads_gcc.npz and creates some nice plots.

Docstring

The docstring of the expmat.expmc function is as follows:

expmc( A, expmA ) :
    Compute the matrix exponential using Pade approximation.
        Parameters
            A : array, shape(M,M)
                Matrix to be exponentiated
            expA : array, shape(M,M)
                Matrix exponential of A (overwritten by function)