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

	Authors: Pietro Berkes and Tiziano Zito
        Email:   berkes@gatsby.ucl.ac.uk, 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: LGPL v3 (see COPYING and COPYING.LESSER files)
	Date: Fri May 15 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
   (hermitian) positive definite 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.

   Update for SciPy >=  0.5.2: some of  the routines used  in symeig are  now
   included in SciPy as well. They are available under
   scipy.lib.lapack.flapack and can be accessed with the function
   scipy.lib.lapack.get_lapack_funcs. Some of them are still missing, though.
   symeig uses its  own wrappers and  offers a unified  interface to all  the
   relevant LAPACK routines.

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

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
 (hermitian) definite positive 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 matrix.
       B     -- An N x N 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.
     """

     * Benchmark results:

       +--------------------------------------------------------------------+
       |                 | Standard eigenproblem | Generalized eigenproblem |
       |                 | (sec/100)             | (sec/100)                |
       |-----------------+-----------------------+--------------------------|
       | Matrix          | symeig    | numpy     | symeig     | numpy       |
       | dimension       |           |           |            |             |
       |-----------------+-----------+-----------+------------+-------------|
       | 16x16           | 0.04      | 0.14      | 0.06       | >0.06       |
       |-----------------+-----------+-----------+------------+-------------|
       | 32x32           | 0.07      | 0.16      | 0.11       | 0.26        |
       |-----------------+-----------+-----------+------------+-------------|
       | 64x64           | 0.23      | 0.86      | 0.39       | 1.33        |
       |-----------------+-----------+-----------+------------+-------------|
       | 128x128         | 1.19      | 5.92      | 2.01       | 8.92        |
       |-----------------+-----------+-----------+------------+-------------|
       | 256x256         | 6.49      | 40.42     | 10.71      | 86.40       |
       |-----------------+-----------+-----------+------------+-------------|
       | 512x512         | 60.04     | 540.57    | 65.31      | 2233.41     |
       |-----------------+-----------+-----------+------------+-------------|
       | 1024x1024       | 338.93    | 4883.13   | 345.84     | 14802.98    |
       |-----------------+-----------+-----------+------------+-------------|
       | 2048x2048       | 1952.03   | 69594.75  | 2020.79    | 97749.95    |
       +--------------------------------------------------------------------+

     * 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
   . click to see the animated logo!
	http://mdp-toolkit.sourceforge.net/logo_animation.html
   . http://mdp-toolkit.sourceforge.net/index.html
   . http://mdp-toolkit.sourceforge.net/tutorial.html
   . http://mdp-toolkit.sourceforge.net/index.html#DOWINS
   . http://mdp-toolkit.sourceforge.net/tutorial.html#node-list
   . http://mdp-toolkit.sourceforge.netdocs/api/index.html
   . 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://www.gatsby.ucl.ac.uk/~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
