Metadata-Version: 1.0
Name: rogues
Version: 0.2.0
Summary: Python and numpy port of Nicholas Higham's m*lab test matrices
Home-page: UNKNOWN
Author: Don MacMillen
Author-email: don@macmillen.net
License: MIT
Description: 
        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'
        
Keywords: numpy scipy matplotlib linalg
Platform: UNKNOWN
Classifier: Development Status :: 3 - Alpha
Classifier: Intended Audience :: Developers
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Classifier: Topic :: Scientific/Engineering :: Mathematics
