annotate toolbox/contents.m @ 2:c124219d7bfa draft

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