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annotate toolbox/cond.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
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1 function y = cond(A, p)
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2 %COND Matrix condition number in 1, 2, Frobenius, or infinity norm.
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3 % For p = 1, 2, 'fro', inf, COND(A,p) = NORM(A,p) * NORM(INV(A),p).
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4 % If p is omitted then p = 2 is used.
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5 % A may be a rectangular matrix if p = 2; in this case COND(A)
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6 % is the ratio of the largest singular value of A to the smallest
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7 % (and hence is infinite if A is rank deficient).
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8
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9 % See also RCOND, NORM, CONDEST, NORMEST.
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10 % Generalises and incorporates MATFUN/COND.M from Matlab 4.
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11
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12 if length(A) == 0 % Handle null matrix.
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13 y = NaN;
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14 return
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15 end
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16 if issparse(A)
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17 error('Matrix must be non-sparse.')
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18 end
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19
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20 if nargin == 1, p = 2; end
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21
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22 [m, n] = size(A);
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23 if m ~= n & p ~= 2
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24 error('A is rectangular. Use the 2 norm.')
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25 end
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26
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27 if p == 2
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28 s = svd(A);
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29 if any(s == 0) % Handle singular matrix
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30 disp('Condition is infinite')
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31 y = Inf;
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32 return
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33 end
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34 y = max(s)./min(s);
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35 else
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36 % We'll let NORM pick up any invalid p argument.
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37 y = norm(A, p) * norm(inv(A), p);
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38 end