function [x,E,C]=verhullparam(varargin) % uses jz and, inside it, ea % VERHULLPARAM Verified enclosure of the solution set of a family of parametric interval linear equations. % % This is an INTLAB file. It requires to have INTLAB installed under % MATLAB to function properly. % % For real n-by-n matrices A0, A1, ..., Ap, real n-by-1 vectors b0, b1, ..., bp, % and a p-by-1 interval vector t, % [X,E,C]=verhullparam(A0,A1,...,Ap,b0,b1,...,bp,t) % computes an interval vector X verified to enclose the set % { x | A(to)*x = b(to) for some to in t } (1) % where % A(to)=A0+to(1)*A1+...+to(p)*Ap % b(to)=b0+to(1)*b1+...+to(p)*bp % for to in t (hence, (1) is the solution set of a family of parametric % interval linear equations). If no verified enclosure is found, then X % consists of NaN's. The structured array E explains reasons for NaN output. % It has three fields: E.error, E.where, E.value. The output variable C % records some intermediate values. % % It is also possible to issue the command in the form % [X,E,C]=verhullparam(cellarray) % where "cellarray" is a cell array satisfying % cellarray{1}= A0, cellarray{2}= A1, ..., cellarray{p+1}= Ap, % cellarray{p+2}= b0, cellarray{p+3}=b1, ..., cellarray{2*p+2}=bp, % cellarray{2*p+3)=t. % This helps to prepare the data in advance, in particular when the % number of parameters p is large (as it may happen with special types % of matrices). % % See also VERINTERVALHULL, VERHULLPATT. % % Built-in function. % Copyright 2008 Jiri Rohn % % Based on ideas sketched in J. Rohn, A Method for Handling Dependent % Data in Interval Linear Systems, Technical Report No. 911, Institute % of Computer Science, Academy of Sciences of the Czech Republic, % Prague 2004. % % WARRANTY % % Because the program is licensed free of charge, there is % no warranty for the program, to the extent permitted by applicable % law. Except when otherwise stated in writing the copyright holder % and/or other parties provide the program "as is" without warranty % of any kind, either expressed or implied, including, but not % limited to, the implied warranties of merchantability and fitness % for a particular purpose. The entire risk as to the quality and % performance of the program is with you. Should the program prove % defective, you assume the cost of all necessary servicing, repair % or correction. % % History % % 2008-11-16 started (versolver created; up to construction of D; called verintervalhulldep) % 2008-11-17 upper and lower loops added, input of a cell array enabled, % renamed as jz, called by verhullpar; working version % 2008-11-20 output parameter C added % 2008-12-04 reworded to "parametric interval linear equations" % 2008-12-20 jz p-coded, final version (html) % [x,E,C]=jz(varargin); % computation done by JZ