Mercurial > matrix-functions
comparison toolbox/cond.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 |
| parents | 8f23314345f4 |
| children |
comparison
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| 1:e471a92d17be | 2:c124219d7bfa |
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| 1 function y = cond(A, p) | |
| 2 %COND Matrix condition number in 1, 2, Frobenius, or infinity norm. | |
| 3 % For p = 1, 2, 'fro', inf, COND(A,p) = NORM(A,p) * NORM(INV(A),p). | |
| 4 % If p is omitted then p = 2 is used. | |
| 5 % A may be a rectangular matrix if p = 2; in this case COND(A) | |
| 6 % is the ratio of the largest singular value of A to the smallest | |
| 7 % (and hence is infinite if A is rank deficient). | |
| 8 | |
| 9 % See also RCOND, NORM, CONDEST, NORMEST. | |
| 10 % Generalises and incorporates MATFUN/COND.M from Matlab 4. | |
| 11 | |
| 12 if length(A) == 0 % Handle null matrix. | |
| 13 y = NaN; | |
| 14 return | |
| 15 end | |
| 16 if issparse(A) | |
| 17 error('Matrix must be non-sparse.') | |
| 18 end | |
| 19 | |
| 20 if nargin == 1, p = 2; end | |
| 21 | |
| 22 [m, n] = size(A); | |
| 23 if m ~= n & p ~= 2 | |
| 24 error('A is rectangular. Use the 2 norm.') | |
| 25 end | |
| 26 | |
| 27 if p == 2 | |
| 28 s = svd(A); | |
| 29 if any(s == 0) % Handle singular matrix | |
| 30 disp('Condition is infinite') | |
| 31 y = Inf; | |
| 32 return | |
| 33 end | |
| 34 y = max(s)./min(s); | |
| 35 else | |
| 36 % We'll let NORM pick up any invalid p argument. | |
| 37 y = norm(A, p) * norm(inv(A), p); | |
| 38 end |