%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/LPnetlib/lp_fit2d
% name: LPnetlib/lp_fit2d
% [Netlib LP problem fit2d: minimize c'*x, where Ax=b, lo<=x<=hi]
% id: 626
% date: 1990
% author: R. Fourer
% ed: R. Fourer
% fields: title name A b id aux kind date author ed notes
% aux: c lo hi z0
% kind: linear programming problem
%-------------------------------------------------------------------------------
% notes:
% A Netlib LP problem, in lp/data.  For more information                    
% send email to netlib@ornl.gov with the message:                           
%                                                                           
% 	 send index from lp                                                      
% 	 send readme from lp/data                                                
%                                                                           
% The following are relevant excerpts from lp/data/readme (by David M. Gay):
%                                                                           
% The column and nonzero counts in the PROBLEM SUMMARY TABLE below exclude  
% slack and surplus columns and the right-hand side vector, but include     
% the cost row.  We have omitted other free rows and all but the first      
% right-hand side vector, as noted below.  The byte count is for the        
% MPS compressed file; it includes a newline character at the end of each   
% line.  These files start with a blank initial line intended to prevent    
% mail programs from discarding any of the data.  The BR column indicates   
% whether a problem has bounds or ranges:  B stands for "has bounds", R     
% for "has ranges".  The BOUND-TYPE TABLE below shows the bound types       
% present in those problems that have bounds.                               
%                                                                           
% The optimal value is from MINOS version 5.3 (of Sept. 1988)               
% running on a VAX with default options.                                    
%                                                                           
%                        PROBLEM SUMMARY TABLE                              
%                                                                           
% Name       Rows   Cols   Nonzeros    Bytes  BR      Optimal Value         
% FIT2D        26  10500   138018     482330  B    -6.8464293294E+04        
%                                                                           
%         BOUND-TYPE TABLE                                                  
% FIT2D      UP                                                             
%                                                                           
% Supplied by Bob Fourer.                                                   
% When included in Netlib: Cost coefficients negated.                       
%                                                                           
% Concerning FIT1D, FIT1P, FIT2D, FIT2P, Bob Fourer says                    
%     The pairs FIT1P/FIT1D and FIT2P/FIT2D are primal and                  
%     dual versions of the same two problems [except that we                
%     have negated the cost coefficients of the dual problems               
%     so all are minimization problems].  They originate from               
%     a model for fitting linear inequalities to data, by                   
%     minimization of a sum of piecewise-linear penalties.                  
%     The FIT1 problems are based on 627 data points and 2-3                
%     pieces per primal pl penalty term.  The FIT2 problems                 
%     are based on 3000 data points (from a different sample                
%     altogether) and 4-5 pieces per pl term.                               
%                                                                           
% Bob Bixby reports that the CPLEX solver (running on a Sparc station)      
% finds slightly different optimal values for some of the problems.         
% On a MIPS processor, MINOS version 5.3 (with crash and scaling of         
% December 1989) also finds different optimal values for some of the        
% problems.  The following table shows the values that differ from those    
% shown above.  (Whether CPLEX finds different values on the recently       
% added problems remains to be seen.)                                       
%                                                                           
% Problem        CPLEX(Sparc)          MINOS(MIPS)                          
% FIT2D                            -6.8464293232E+04                        
%                                                                           
% Added to Netlib on  31 Jan. 1990                                          
%-------------------------------------------------------------------------------
