www.gusucode.com > elmat工具箱matlab源码程序 > elmat/gallery.m
function varargout = gallery(matname,varargin)
%GALLERY Higham test matrices.
% [out1,out2,...] = GALLERY(matname, param1, param2, ...)
% takes matname, a string that is the name of a matrix family, and
% the family's input parameters. See the listing below for available
% matrix families. Most of the functions take an input argument
% that specifies the order of the matrix, and unless otherwise
% stated, return a single output.
%
% GALLERY(matname,param1, param2, ..., CLASSNAME) produces a matrix
% of class CLASSNAME, which must be either 'single' or 'double' (unless
% matname is 'integerdata', in which case 'int8', 'int16', 'int32',
% 'uint8', 'uint16', and 'uint32' are also allowed.)
% If CLASSNAME is not specified then the class of the matrix is
% determined from those arguments among param 1, param2, ..., that do
% not specify dimensions or select an option:
% if any of these arguments is of class single then the matrix is
% single; otherwise the matrix is double.
%
% For additional information, type "help private/matname", where matname
% is the name of the matrix family.
%
% binomial Binomial matrix -- multiple of involutory matrix.
% 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.
% circul Circulant matrix.
% clement Clement matrix -- tridiagonal with zero diagonal entries.
% compar Comparison matrices.
% condex Counter-examples to matrix condition number estimators.
% cycol Matrix whose columns repeat cyclically.
% dorr Dorr matrix -- diagonally dominant, ill-conditioned, tridiagonal.
% (One or three output arguments, sparse)
% dramadah Matrix of ones and zeroes whose inverse has large integer entries.
% fiedler Fiedler matrix -- symmetric.
% forsythe Forsythe matrix -- a perturbed Jordan block.
% frank Frank matrix -- ill-conditioned eigenvalues.
% gcdmat GCD matrix.
% gearmat Gear matrix.
% grcar Grcar matrix -- a Toeplitz matrix with sensitive eigenvalues.
% hanowa Matrix whose eigenvalues lie on a vertical line in the complex
% plane.
% house Householder matrix. (Three output arguments)
% integerdata Array of arbitrary data from uniform distribution on
% specified range of integers
% invhess Inverse of an upper Hessenberg matrix.
% invol Involutory matrix.
% ipjfact Hankel matrix with factorial elements. (Two output arguments)
% jordbloc Jordan block matrix.
% kahan Kahan matrix -- upper trapezoidal.
% kms Kac-Murdock-Szego Toeplitz matrix.
% krylov Krylov matrix.
% lauchli Lauchli matrix -- rectangular.
% lehmer Lehmer matrix -- symmetric positive definite.
% leslie Leslie matrix.
% lesp Tridiagonal matrix with real, sensitive eigenvalues.
% lotkin Lotkin matrix.
% minij Symmetric positive definite matrix MIN(i,j).
% moler Moler matrix -- symmetric positive definite.
% neumann Singular matrix from the discrete Neumann problem (sparse).
% normaldata Array of arbitrary data from standard normal distribution
% orthog Orthogonal and nearly orthogonal matrices.
% parter Parter matrix -- a Toeplitz matrix with singular values near PI.
% pei Pei matrix.
% poisson Block tridiagonal matrix from Poisson's equation (sparse).
% prolate Prolate matrix -- symmetric, ill-conditioned Toeplitz matrix.
% qmult Pre-multiply matrix by random orthogonal matrix.
% randcolu Random matrix with normalized cols and specified singular values.
% randcorr Random correlation matrix with specified eigenvalues.
% randhess Random, orthogonal upper Hessenberg matrix.
% randjorth Random J-orthogonal (hyperbolic, pseudo-orthogonal) matrix.
% rando Random matrix with elements -1, 0 or 1.
% randsvd Random matrix with pre-assigned singular values and specified
% bandwidth.
% redheff Matrix of 0s and 1s of Redheffer.
% riemann Matrix associated with the Riemann hypothesis.
% ris Ris matrix -- a symmetric Hankel matrix.
% sampling Nonsymmetric matrix with integer, ill conditioned eigenvalues.
% smoke Smoke matrix -- complex, with a "smoke ring" pseudospectrum.
% toeppd Symmetric positive definite Toeplitz matrix.
% toeppen Pentadiagonal Toeplitz matrix (sparse).
% tridiag Tridiagonal matrix (sparse).
% triw Upper triangular matrix discussed by Wilkinson and others.
% uniformdata Array of arbitrary data from standard uniform distribution
% wathen Wathen matrix -- a finite element matrix (sparse, random entries).
% wilk Various specific matrices devised/discussed by Wilkinson.
% (Two output arguments)
%
% GALLERY(3) is a badly conditioned 3-by-3 matrix.
% GALLERY(5) is an interesting eigenvalue problem. Try to find
% its EXACT eigenvalues and eigenvectors.
%
% See also MAGIC, HILB, INVHILB, HADAMARD, PASCAL, ROSSER, VANDER, WILKINSON.
% References:
% [1] N. J. Higham, Accuracy and Stability of Numerical Algorithms,
% Second edition, Society for Industrial and Applied Mathematics,
% Philadelphia, 2002; Chapter 28.
% [2] J. R. Westlake, A Handbook of Numerical Matrix Inversion and
% Solution of Linear Equations, John Wiley, New York, 1968.
% [3] J. H. Wilkinson, The Algebraic Eigenvalue Problem,
% Oxford University Press, 1965.
%
% Nicholas J. Higham
% Copyright 1984-2010 The MathWorks, Inc.
if isnumeric(matname)
if matname == 3 || matname == 5
matname = ['gallery' num2str(matname)];
% Next line since need nonempty varargin below.
if nargin == 1, varargin = {'double'}; end
else
error(message('MATLAB:gallery:invalidN'))
end
end
if isempty(varargin)
error(message('MATLAB:gallery:parametersRequired'));
else
len1 = length(varargin{1});
end
% arg_inds is indices of arguments that should determine the class.
% It excludes arguments that specify a dimension or select an option.
arg_inds = []; % Default: none of the arguments determine the class.
switch matname
case {'binomial','chebspec','clement','cycol','dramadah','gearmat',...
'frank','gallery3','gallery5','gcdmat','grcar','invol','ipjfact',...
'lehmer','lesp','lotkin','minij','neumann', 'orthog', ...
'parter','poisson','redheff','riemann','rando','ris','smoke', ...
'wathen','wilk'}
% These all take the default arg_inds.
case {'cauchy','invhess','leslie'}
if len1 ~= 1, arg_inds = [1 2]; end
case 'chebvand'
if len1 > 1
arg_inds = 1;
elseif length(varargin) >= 2 && length(varargin{2}) > 1
arg_inds = 2;
end
case {'chow','forsythe','kahan'}
arg_inds = [2 3];
case {'compar','house','qmult','randhess'}
arg_inds = 1;
case {'condex','randjorth'}
arg_inds = 3;
case {'circul','fiedler','randcorr','randcolu','sampling'}
if len1 ~= 1, arg_inds = 1; end
case {'dorr','hanowa','jordbloc','kms','lauchli','moler','pei',...
'prolate','randsvd','triw'}
arg_inds = 2;
case 'krylov'
arg_inds = [1 2];
case 'toeppd'
arg_inds = [3 4];
case 'toeppen'
arg_inds = [2 3 4 5 6];
case 'tridiag'
if len1 > 1
arg_inds = [1 2 3];
elseif length(varargin) > 2
arg_inds = [2 3 4];
end
case {'normaldata', 'uniformdata', 'integerdata'}
% These functions perform their own class and input argument
% checking, so just call them directly.
F = str2func(matname);
[varargout{1:max(nargout,1)}] = F(varargin{:});
return;
otherwise
error(message('MATLAB:gallery:invalidMatName'))
end
nargs = nargin(matname);
if ischar(varargin{end})
if strcmp(varargin{end},'single') || strcmp(varargin{end},'double')
% CLASSNAME was passed to GALLERY.
% ARGCLASS will make all relevant arguments of class CLASSNAME.
[classname,varargin{1:end-1}] = ...
argclass(arg_inds,varargin{end},varargin{1:end-1});
% Next lines allow classname to be specified as trailing
% input argument without giving full argument list.
if length(varargin) < nargs
varargin{end} = [];
varargin{nargs} = classname;
end
else
error(message('MATLAB:gallery:invalidClassName'))
end
else
% CLASSNAME was not passed to GALLERY.
% ARGCLASS will determine appropriate CLASSNAME and
% make all relevant arguments of class CLASSNAME.
[classname,varargin{:}] = argclass(arg_inds,[],varargin{:});
varargin{nargs} = classname;
end
if strcmp(classname,'single') && ...
( strcmp(matname,'dorr') || strcmp(matname,'neumann') ...
|| strcmp(matname,'toeppen') || strcmp(matname,'tridiag') ...
|| strcmp(matname,'wathen') )
error(message('MATLAB:gallery:SparseSingle'))
end
F = str2func(matname);
[varargout{1:max(nargout,1)}] = F(varargin{:});
function A = gallery3(classname)
A = [ -149 -50 -154
537 180 546
-27 -9 -25 ];
A = cast(A,classname);
function A = gallery5(classname)
A = [ -9 11 -21 63 -252
70 -69 141 -421 1684
-575 575 -1149 3451 -13801
3891 -3891 7782 -23345 93365
1024 -1024 2048 -6144 24572 ];
A = cast(A,classname);