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comparison toolbox/contents.m @ 2:c124219d7bfa draft

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Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author Antonio Pino Robles <data.script93@gmail.com>
date Thu, 07 May 2015 18:36:24 +0200
parents 8f23314345f4
children
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1:e471a92d17be 2:c124219d7bfa
1 % Test Matrix Toolbox.
2 % Version 3.0, September 19 1995
3 % Copyright (c) 1995 by N. J. Higham
4 %
5 % Demonstration
6 %TMTDEMO Demonstration of Test Matrix Toolbox.
7 %
8 % Test Matrices
9 %AUGMENT Augmented system matrix.
10 %CAUCHY Cauchy matrix.
11 %CHEBSPEC Chebyshev spectral differentiation matrix.
12 %CHEBVAND Vandermonde-like matrix for the Chebyshev polynomials.
13 %CHOW Chow matrix - a singular Toeplitz lower Hessenberg matrix.
14 %CIRCUL Circulant matrix.
15 %CLEMENT Clement matrix - tridiagonal with zero diagonal entries.
16 %COMPAN Companion matrix.
17 %CONDEX `Counterexamples' to matrix condition estimators.
18 %CYCOL Matrix whose columns repeat cyclically.
19 %DINGDONG Dingdong matrix - a symmetric Hankel matrix.
20 %DORR Dorr matrix - diag. dominant, ill-conditioned, tridiagonal (sparse).
21 %DRAMADAH A (0,1) matrix with large inverse.
22 %FIEDLER Fiedler matrix - symmetric.
23 %FORSYTHE Forsythe matrix - a perturbed Jordan block.
24 %FRANK Frank matrix - ill-conditioned eigenvalues.
25 %GALLERY Famous, and not so famous, test matrices.
26 %GEARM Gear matrix.
27 %GFPP Matrix giving maximal growth factor for Gaussian elim. with pivoting.
28 %GRCAR Grcar matrix - a Toeplitz matrix with sensitive eigenvalues.
29 %HADAMARD Hadamard matrix.
30 %HANOWA Hanowa matrix.
31 %HILB Hilbert matrix.
32 %INVHESS Inverse of an upper Hessenberg matrix.
33 %INVOL An involutory matrix.
34 %IPJFACT A Hankel matrix with factorial elements.
35 %JORDBLOC Jordan block.
36 %KAHAN Kahan matrix - upper trapezoidal.
37 %KMS Kac-Murdock-Szego Toeplitz matrix.
38 %KRYLOV Krylov matrix.
39 %LAUCHLI Lauchli matrix.
40 %LEHMER Lehmer matrix - symmetric positive definite.
41 %LESP A tridiagonal matrix with real, sensitive eigenvalues.
42 %LOTKIN Lotkin matrix.
43 %MAKEJCF A matrix with given Jordan canonical form.
44 %MINIJ Symmetric positive definite matrix MIN(i,j).
45 %MOLER Moler matrix - symmetric positive definite.
46 %NEUMANN Singular matrix from the discrete Neumann problem.
47 %OHESS Random, orthogonal upper Hessenberg matrix.
48 %ORTHOG Orthogonal and nearly orthogonal matrices.
49 %PARTER Parter matrix - a Toeplitz matrix with singular values near PI.
50 %PASCAL Pascal matrix.
51 %PDTOEP Symmetric positive definite Toeplitz matrix.
52 %PEI Pei matrix.
53 %PENTOEP Pentadiagonal Toeplitz matrix (sparse).
54 %POISSON Block tridiagonal matrix from Poisson's equation (sparse).
55 %PROLATE Prolate matrix - symmetric, ill-conditioned Toeplitz matrix.
56 %RANDO Random matrix with elements -1, 0 or 1.
57 %RANDSVD Random matrices with pre-assigned singular values.
58 %REDHEFF A matrix of 0s and 1s of Redheffer.
59 %RIEMANN A matrix associated with the Riemann hypothesis.
60 %RSCHUR An upper quasi-triangular matrix.
61 %SMOKE Smoke matrix - complex, with a `smoke ring' pseudospectrum.
62 %TRIDIAG Tridiagonal matrix (sparse).
63 %TRIW Upper triangular matrix discussed by Wilkinson and others.
64 %VAND Vandermonde matrix.
65 %WATHEN Wathen matrix - a finite element matrix (sparse, random entries).
66 %WILK Various specific matrices devised/discussed by Wilkinson.
67 %
68 % Visualization
69 %FV Field of values (or numerical range).
70 %GERSH Gershgorin disks.
71 %PS Approximation to the pseudospectrum.
72 %PSCONT Contours and colour pictures of pseudospectra.
73 %SEE Pictures of a matrix and its (pseudo-) inverse.
74 %
75 % Decompositions and factorizations.
76 %CGS Gram-Schmidt QR factorization.
77 %CHOLP Cholesky factorization with pivoting of a pos. semidefinite matrix.
78 %COD Complete orthogonal decomposition.
79 %DIAGPIV Diagonal pivoting factorization with partial pivoting.
80 %GE Gaussian elimination without pivoting.
81 %GECP Gaussian elimination with complete pivoting.
82 %GJ Gauss-Jordan elimination to solve Ax = b.
83 %MGS Modified Gram-Schmidt QR factorization.
84 %POLDEC Polar decomposition.
85 %SIGNM Matrix sign decomposition.
86 %
87 % Direct Search Optimization.
88 %ADSMAX Alternating directions direct search method.
89 %MDSMAX Multidirectional search method for direct search optimization.
90 %NMSMAX Nedler-Mead simplex method for direct search optimization.
91 %
92 % Miscellaneous
93 %BANDRED Band reduction by two-sided orthogonal transformations.
94 %CHOP Round matrix elements.
95 %COMP Comparison matrices.
96 %COND Matrix condition number in 1, 2, Frobenius, or infinity norm.
97 %CPLTAXES Determine suitable AXIS for plot of complex vector.
98 %DUAL Dual vector with respect to Holder p-norm.
99 %EIGSENS Eigenvalue condition numbers.
100 %HOUSE Householder matrix.
101 %MATRIX Test Matrix Collection information and access by number.
102 %MATSIGNT Matrix sign function of a triangular matrix.
103 %PNORM Estimate of matrix p-norm (1 <= p <= inf).
104 %QMULT Pre-multiply by random orthogonal matrix.
105 %RQ Rayleigh quotient.
106 %SEQA An additive sequence.
107 %SEQCHEB Sequence of points related to Chebyshev polynomials, T_N.
108 %SEQM A multiplicative sequence.
109 %SHOW Display signs of matrix elements.
110 %SKEWPART Skew-symmetric (Hermitian) part.
111 %SPARSIFY Randomly sets matrix elements to zero.
112 %SUB Principal submatrix.
113 %SYMMPART Symmetric (Hermitian) part.
114 %TRAP2TRI Trapezoidal matrix to triangular form.