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rogues 0.2.0

Python and numpy port of Nicholas Higham's m*lab test matrices

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Rogues is a Python and numpy/scipy port of Nicholas Higham's m*lab test matrices.

These matrices are a collection of interesting matrices that appear
in m*lab's 'gallery' collection.  This collection was originally defined
and implemented by Prof. Nicholas Higham of Manchester University and is
more fully discussed in "The Test Matrix Toolbox for Matlab (Version 3.0)",
N.J. Higham, Numerical Analysis Report No. 276, September 1995 and can be
found at

http://www.maths.manchester.ac.uk/~nareports

By 'interesting' we mean that these matrices either present some challenges
to numerical algorithms or have some a set of interesting properties. The
documentation of the individual functions contains much more info, as well
as references.

Also included are a set of matrix utility functions that are needed for
generating some of members of the collection as well as a few functions
from Prof. Higham's matrixcomp package.  One of the more interesting
routines here is mdsmax, a direct search optimization algorithm.

The rogues package depends on numpy and scipy, both of which must be installed.
Additionally, there are a few routines that deal with plotting, and these
use matplotlib.  While ipython is not strictly necessary, it is a very
convenient environment for numpy / scipy / matplotlib. Finally, the unit
tests utilize the nose package and the numpy wrappers around nose. To run
the tests from inside ipython, for example, type the following::

import rogues.matrices.tests at rmt
import rogues.utils.tests as rut
rmt.check()
rut.check()

The inluded matrix generation functions are:

*   cauchy    Cauchy matrix
*   chebspec  Chebyshev spectral differentiation matrix
*   chebvand  Vandermonde-like matrix for the Chebyshev polynomials
*   chow      Chow matrix - a singular Toeplitz lower Hessenberg matrix
*   clement   Clement matrix - tridiagonal with zero diagonal entries
*   comp      Comparison matrices
*   compan    Companion matrix
*   condex    Counterexamples to matrix condition number estimators
*   cycol     Matrix whose columns repeat cyclically
*   dingdong  Dingdong matrix - a symmetric Hankel matrix
*   dorr      Dorr matrix - diagonally dominant, ill conditioned, tridiagonal.
*   dramadah  A (0,1) matrix whose inverse has large integer entries
*   fiedler   Fiedler matrix - symmetric
*   forsythe  Forsythe matrix - a perturbed Jordan block
*   frank     Frank matrix - ill conditioned eigenvalues.
*   gearm     Gear matrix
*   gfpp      Matrix giving maximal growth factor for GW with partial pivoting
*   grcar     Grcar matrix - a Toeplitz matrix with sensitive eigenvalues.
*   hadamard  Hadamard matrix
*   hankel    Hankel matrix
*   hanowa    A matrix whose eigenvalues lie on a vertical line in C
*   hilb      Hilbert matrix
*   invhess   Inverse of an upper Hessenberg matrix
*   invol     An involutory matrix
*   ipjfact   A Hankel matrix with factorial elements
*   jordbloc  Jordan block matrix
*   kahan     Kahan matrix - upper trapezoidal
*   kms       Kar-Murdock-Szego Toeplitz matrix
*   krylov    Krylov matrix
*   lauchli   Lauchli matrix - rectangular
*   lehmer    Lehmer matrix - symmetric positive definite
*   lesp      A tridiagonal matrix with real, sensitve eigenvalues
*   lotkin    Lotkin matrix
*   minij     Symmetric positive definite matrix min(i,j)
*   moler     Moler matrix symmetric positive definite
*   neumann   Singular matrix from the descrete Neumann problem (sparse)
*   ohess     Random, orthogonal upper Hessenberg matrix
*   parter    Parter matrix - a Toeplitz matrix with singular values near pi
*   pascal    Pascal matrix
*   pdtoep    Symmetric positive definite Toeplitz matrix
*   pei       Pei matrix
*   pentoep   Tentadiagonal Toeplitz matrix (sparse)
*   poisson   Block tridiagonal matrix from Poisson's equation (sparse)
*   prolate   Prolate matrix - symmetric, ill-conditioned Toeplitz matrix
*   qmult     Pre-multiply by random orthogonal matrix
*   rando     Random matrix with elements -1, 0, or 1
*   randsvd   Random matrix with pre-assigned singular values
*   redheff   A (0,1) matrix of Redheffer associated with the Riemann hypothesis
*   riemann   A matrix associated with the Riemann hypothesis
*   smoke     Smoke matrix - complex, with a 'smoke ring' pseudospectrum
*   triw      Upper triangular matrix discussed by Wilkinson and others
*   wathen    Wathen matrix - a finite element matrix (sparse, random entries)
*   wilk      Various specific matrices devised /discussed by Wilkenson
*   wilkinson Wilkinson matrix of size n, where n must be odd

Some of generally useful matrix utility functions:

*   augment   Agumented system matrix
*   bandred   Band reduction by two-sided unitary transformations
*   cgs       Classical Gram-Schmidt QR factorization
*   cond      Matrix condition number in 1,2,Frobenius, or infinity norm
*   condeig   Condition numbers for eigenvalues of a matrix
*   cpltaxes  Determine suitable axis for plot of complex vector
*   dual      Dual vector with respect to Holder p-norm
*   ge        Gaussian elimination without pivoting
*   hankel    Given first row, returns a Toeplitz type matrix
*   house     Householder matrix
*   mdsmax    Multidimensional search method for direct search optimization
*   mgs       Modified Gram-Schmidt QR factorization
*   pow2      Vector whose i-th element is 2 ** x[i], where x[] is input
*   ps        Dot plot of a pseudospectrum
*   repmat    Simple re-implementation of m*lab's repmat function
*   rq        Rayleigh quotient
*   skewpart  Skew-symmetric (skew-Hermitian) part
*   sparsify  Randomly sets matrix elements to zero
*   sub       Principal submatrix
*   symmpart  Symmetric (Hermitian) part
*   toeplitz  Returns toeplitz matrix given first row of the matrix
*   treshape  Reshape vector to or from (unit) triangular matrix
*   tridiag   Sparse tridiagonl matrix given the diagonals
*   vand      Vandermonde matrix
*   vecperm   Vector permutation matrix

   More information is available on any of these functions by typing
   "help <funcname>"

Release 0.2.0 Notes
The unit tests are now included in the distribution.  They work with nosetests
and if you have installed the source (not the zip'd egg file) you can do the
following

import rogues.matrices.tests as rmt
rmt.check()
import rogues.utils.tests as rut
rut.check()
rut.check_see()    # matrix visualization
rut.check_ps()     # matrix visualization

Sadly, this does not work with zipped egg files.

Fixed several small bugs in the use of np.max.  Added matrix visualization
routing 'see'
 
File Type Py Version Uploaded on Size # downloads
rogues-0.2.0-py2.6.egg (md5) Python Egg 2.6 2010-11-11 212KB 355
rogues-0.2.0.tar.gz (md5) Source 2010-11-11 57KB 364