% 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) % 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 (p ~= 2) y = norm(A,p)*norm(inv(A),p); else s = svd(A); y = s(1)/s(end); end