/usr/share/freemat/toolbox/matrix/cond.m is in freemat-data 4.0-5.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | % COND COND Condition Number of a Matrix
%
% Usage
%
% Calculates the condition number of a matrix. To compute the
% 2-norm condition number of a matrix (ratio of largest to smallest
% singular values), use the syntax
%
% y = cond(A)
%
% where A is a matrix. If you want to compute the condition number
% in a different norm (e.g., the 1-norm), use the second syntax
%
% y = cond(A,p)
%
% where p is the norm to use when computing the condition number.
% The following choices of p are supported
% - p = 1 returns the 1-norm, or the max column sum of A
%
% - p = 2 returns the 2-norm (largest singular value of A)
%
% - p = inf returns the infinity norm, or the max row sum of A
%
% - p = 'fro' returns the Frobenius-norm (vector Euclidean norm, or RMS value)
%
% Copyright (c) 2002-2007 Samit Basu
% Licensed under the GPL
function y = cond(A,p)
if (nargin < 2)
p = 2;
end
if (nargin < 1)
error('expect at least 1 input to cond function');
end
if (isempty(A)) y = 0; return; end;
if (p ~= 2)
y = norm(A,p)*norm(inv(A),p);
else
if (isscalar(A) && (A == 0))
y = inf;
return;
end
s = svd(A);
y = s(1)/s(end);
end
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