Netlib LP problem fit2d: minimize c'*x, where Ax=b, lo<=x<=hi
Name lp_fit2d
Group LPnetlib
Matrix ID 626
Num Rows 25
Num Cols 10,524
Nonzeros 129,042
Pattern Entries 129,042
Kind Linear Programming Problem
Symmetric No
Date 1990
Author R. Fourer
Editor R. Fourer
Structural Rank 25
Structural Rank Full true
Num Dmperm Blocks 1
Strongly Connect Components 1
Num Explicit Zeros 0
Pattern Symmetry 0%
Numeric Symmetry 0%
Cholesky Candidate no
Positive Definite no
Type real
SVD Statistics
Matrix Norm 1.751323e+04
Minimum Singular Value 1.008801e+01
Condition Number 1.736045e+03
Rank 25
sprank(A)-rank(A) 0
Null Space Dimension 0
Full Numerical Rank? yes
Download Singular Values MATLAB
Download MATLAB Rutherford Boeing Matrix Market
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