PyArnoldi

Arnoldi algorithm in Python and C++ (with Python link)

Dependencies

• Eigen matrix library (http://eigen.tuxfamily.org)
• boost::python (http://www.boost.org/doc/libs/1_48_0/libs/python)

Debian

• Eigen matrix library in packet libeigen3-dev
• boost::python in packet libboost-python1.46-dev (At this time the version 1.46 is the most recent one from sid.)

Brutus

The following brutus modules must be loaded:

module load python/2.7.2
module load boost

The Eigen matrix library must be in the current directory (currently, brutus has no global eigen installation)

• edit the Makefile and uncomment the brutus includes
• copy an eigen3 directory into the current directory, eg:

wget http://bitbucket.org/eigen/eigen/get/3.0.5.tar.gz
tar xvzf 3.0.5.tar.gz
mv eigen-eigen-6e7488e20373 eigen3

In order to be able to load the compiled module on Brutus, the library path must be updated:

export LD_LIBRARY_PATH=/cluster/apps/boost/1_47_0_nompi/x86_64/gcc_4.1.2/lib64:$LD_LIBRARY_PATH

Compilation

• edit the makefile to contain your correct library paths
• make python to compile the python module
• make prog to compile a small test program

Usage

• test_arnoldi.py unit tests using nose. install python-nose and run nosetests from the console
• demo_arnoldi.py timing script which calls Python and C++ versions for various N and plots the resulting times.
• to directly use in python, just compile (make python) and run:

>>> import arnoldi
>>> arnoldi.arnoldi(A,v,k,V,H)

Docstring

The docstring of the arnoldi function is as follows:

Arnoldi algorithm (Krylov approximation of a matrix)
    input:
        A: matrix to approximate
        v0: initial vector (should be in matrix form)
        k: number of Krylov steps
    output:
        V: matrix (large, N*k) containing the orthogonal vectors
        H: matrix (small, k*k) containing the Krylov approximation of A

Example:
    >>> A=rand(10,10); v=rand(10,1)
    >>> V=zeros((10,5)); H=zeros((6,5))
    >>> arnoldi(A,v,5,V,H)