=================================================================
           	SYMEIG Python Module
=================================================================

	Authors: Pietro Berkes and Tiziano Zito
        Email:   berkes@brandeis.edu, tiziano.zito@bccn-berlin.de
 	Homepage: http://mdp-toolkit.sourceforge.net/symeig.html
	Download: http://sourceforge.net/projects/mdp-toolkit
	Current release: 1.4
	License: BSD (see COPYRIGHT file)
	Date: Wed Nov 19 2008

=================================================================

Semi-automatically generated by links from
  http://mdp-toolkit.sourceforge.net/symeig.html .


               Symeig - Symmetrical eigenvalue routines for NumPy

   The symeig module contains  a Python wrapper for  the LAPACK functions  to
   solve the standard and generalized  eigenvalue problems for symmetric  and
   hermitian  matrices.  Those  specialized  algorithms  give  an   important
   speed-up with respect to the generic LAPACK eigenvalue problem solver used
   by NumPy (linalg.eig and linalg.eigh).

   The wrapper function symeig  automatically selects the appropriate  LAPACK
   routine. It is also possible to request only a subset of all  eigenvalues,
   which  consumes  less  memory  and  results  sometimes  in  an  additional
   speed-up, especially for large matrices.

   The symeig  routine is  integrated in  the  0.7 release  of SciPy.  It  is
   available there as scipy.linalg.eigh with a slightly different signature.

   --------------------------------------------------------------------------

Installation

     * Requirements:

          * A complete LAPACK library, possibly complemented by ATLAS
            optimized routines
          * Python >= 2.4
          * NumPy >= 1.0

     * Download: Download symeig at SourceForge
     * Installation: Unpack the archive file and enter the project directory.
       To build the module type:
       python setup.py build
       To install it:
       python setup.py install
       If you want to use symeig without installing it on the system Python
       path:
       python setup.py install --prefix=/some_dir_in_your_PYTHONPATH/
     * Testing: Check your installation in a Python shell as follows:

 >>> import symeig
 >>> symeig.test()

   --------------------------------------------------------------------------

Mantainers

   symeig has been written by Pietro Berkes and Tiziano Zito at the Institute
   for Theoretical Biology of the Humboldt University, Berlin.
   For comments, patches, feature requests, support requests, and bug reports
   please send a message to the MDP users mailing list.

   --------------------------------------------------------------------------

Documentation

     * symeig docstring:

    """Solve standard and generalized eigenvalue problem for symmetric
 and hermitian matrices.

     Syntax:

       w,Z = symeig(A)
       w = symeig(A,eigenvectors=0)
       w,Z = symeig(A,range=(lo,hi))
       w,Z = symeig(A,B,range=(lo,hi))

     Inputs:

       A     -- An N x N real symmetric or complex hermitian matrix.
       B     -- An N x N real symmetric or complex hermitian definite
                positive matrix.
       eigenvectors -- if set return eigenvalues and eigenvectors, otherwise
                       only eigenvalues
       turbo -- (only for generalized eigenvalue problem and if range=None)
                if turbo = "on", use divide and conquer algorithm
                (faster but expensive in memory)
       range -- the tuple (lo,hi) represent the indexes of the smallest and
                largest (in ascending order) eigenvalues to be returned.
                1 <= lo < hi <= N
                if range = None, returns all eigenvalues and eigenvectors.
       type  -- (only for generalized eigenvalue problem)
                Specifies the problem type to be solved:
                       type = 1:  A*x = (lambda)*B*x
                            = 2:  A*B*x = (lambda)*x
                            = 3:  B*A*x = (lambda)*x
       overwrite -- if 'overwrite' is set, computations are done inplace,
                    A and B are overwritten during calculation (you save
                    memory but loose the matrices).
                    If matrices are complex this argument is ignored.

     Outputs:

       w     -- (selected) eigenvalues in ascending order.
       Z     -- if range = None, Z contains the matrix of eigenvectors,
                normalized as follows:
                   Z^H * A * Z = lambda and
                     - type = 1 or 2: Z^H * B * Z = I
                     - type = 3     : Z^H * B^(-1) * Z = I
                where ^H means conjugate transpose.
                if range, an N x M matrix containing the orthonormal
                eigenvectors of the matrix A corresponding to the selected
                eigenvalues, with the i-th column of Z holding the eigenvector
                associated with w[i]. The eigenvectors are normalized as above.
     """

     * Wrapped LAPACK functions:
       symeig wraps the following LAPACK functions for standard and
       generalized symmetric eigenvalue problems:

          +----------------------------------------------------------+
          | EVR routines | ssyevr.f | dsyevr.f | cheevr.f | zheevr.f |
          |--------------+----------+----------+----------+----------|
          | GV routines  | ssygv.f  | dsygv.f  | chegv.f  | zhegv.f  |
          |--------------+----------+----------+----------+----------|
          | GVD routines | ssygvd.f | dsygvd.f | chegvd.f | zhegvd.f |
          |--------------+----------+----------+----------+----------|
          | GVX routines | ssygvx.f | dsygvx.f | chegvx.f | zhegvx.f |
          +----------------------------------------------------------+

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References

   Visible links
   . http://sourceforge.net/mail/?group_id=116959
   . http://mdp-toolkit.sourceforge.net/symeig.html
   . http://numpy.scipy.org/
   . http://www.scipy.org/
   . http://www.netlib.org/lapack/
   . http://math-atlas.sourceforge.net/
   . http://www.python.org/
   . http://numpy.scipy.org/
   . http://sourceforge.net/project/showfiles.php?group_id=116959
   . http://people.brandeis.edu/~berkes/
   . http://itb.biologie.hu-berlin.de/~zito
   . http://itb.biologie.hu-berlin.de/
   . http://www.hu-berlin.de/
   . http://sourceforge.net/mail/?group_id=116959
   . http://www.netlib.org/lapack/lug/node30.html
   . http://www.netlib.org/lapack/lug/node34.html
   . http://sourceforge.net/
   . http://validator.w3.org/check?uri=referer;verbose=1
