time   calls  line
                  1 function [c, v] = condest(A,t)
                  2 %CONDEST 1-norm condition number estimate.
                  3 %   C = CONDEST(A) computes a lower bound C for the 1-norm condition
                  4 %   number of a square matrix A.
                  5 %
                  6 %   C = CONDEST(A,T) changes T, a positive integer parameter equal to
                  7 %   the number of columns in an underlying iteration matrix.  Increasing the
                  8 %   number of columns usually gives a better condition estimate but increases
                  9 %   the cost.  The default is T = 2, which almost always gives an estimate
                 10 %   correct to within a factor 2.
                 11 %
                 12 %   [C,V] = CONDEST(A) also computes a vector V which is an approximate null
                 13 %   vector if C is large.  V satisfies NORM(A*V,1) = NORM(A,1)*NORM(V,1)/C.
                 14 %
                 15 %   Note: CONDEST invokes RAND.  If repeatable results are required,  then
                 16 %   see RAND for details on how to set the default stream state.
                 17 %
                 18 %   CONDEST is based on the 1-norm condition estimator of Hager [1] and a
                 19 %   block oriented generalization of Hager's estimator given by Higham and
                 20 %   Tisseur [2].  The heart of the algorithm involves an iterative search
                 21 %   to estimate ||A^{-1}||_1 without computing A^{-1}. This is posed as the
                 22 %   convex, but nondifferentiable, optimization problem: 
                 23 %
                 24 %         max ||A^{-1}x||_1 subject to ||x||_1 = 1. 
                 25 %
                 26 %   See also NORMEST1, COND, NORM, RAND.
                 27 
                 28 %   Reference:
                 29 %   [1] William W. Hager, Condition estimates, 
                 30 %       SIAM J. Sci. Stat. Comput. 5, 1984, 311-316, 1984.
                 31 % 
                 32 %   [2] Nicholas J. Higham and Fran\c{c}oise Tisseur, 
                 33 %       A Block Algorithm for Matrix 1-Norm Estimation 
                 34 %       with an Application to 1-Norm Pseudospectra, 
                 35 %       SIAM J. Matrix Anal. App. 21, 1185-1201, 2000. 
                 36 %
                 37 %   Nicholas J. Higham
                 38 %   Copyright 1984-2010 The MathWorks, Inc.
                 39 %   $Revision: 5.18.4.6 $  $Date: 2010/11/22 02:46:32 $
                 40 
           240   41 if size(A,1) ~= size(A,2) 
                 42    error(message('MATLAB:condest:NonSquareMatrix'))
                 43 end
           240   44 if isempty(A), c = 0; v = []; return, end 
           240   45 if nargin < 2, t = []; end 
                 46 
           240   47 if issparse(A) 
                 48    [L,U,~,~] = lu(A,'vector');
           240   49 else 
           240   50    [L,U,~] = lu(A,'vector'); 
           240   51 end 
           240   52 k = find(abs(diag(U))==0); 
  0.01     240   53 warns = warning('query','all'); 
  0.02     240   54 temp = onCleanup(@()warning(warns)); 
           240   55 warning('off','all'); 
           240   56 if ~isempty(k) 
                 57    c = Inf;
                 58    n = length(A);
                 59    v = zeros(n,1);
                 60    k = min(k);
                 61    v(k) = 1;
                 62    if k > 1
                 63       v(1:k-1) = -U(1:k-1,1:k-1)\U(1:k-1,k);
                 64    end
           240   65 else 
  0.08     240   66    [Ainv_norm, ~, v] = normest1(@condestf,t); 
  0.01     240   67    A_norm = norm(A,1); 
           240   68    c = Ainv_norm*A_norm; 
           240   69 end 
           240   70 v = v/norm(v,1); 
                 71 
                 72     function f = condestf(flag, X)
                 73         %CONDESTF   Function used by CONDEST.        
                 74         if isequal(flag,'dim')
                 75             f = max(size(L));
                 76         elseif isequal(flag,'real')
                 77             f = isreal(L) && isreal(U);
                 78         elseif isequal(flag,'notransp')
                 79             f = U\(L\X);
                 80         elseif isequal(flag,'transp')
                 81             f = L'\(U'\X);
                 82         end
                 83     end
                 84 
  0.02     240   85 end 

Other subfunctions in this file are not included in this listing.