Netlib LP problem maros_r7: minimize c'*x, where Ax=b, lo<=x<=hi
Name lp_maros_r7
Group LPnetlib
Matrix ID 643
Num Rows 3,136
Num Cols 9,408
Nonzeros 144,848
Pattern Entries 144,848
Kind Linear Programming Problem
Symmetric No
Date 1994
Author I. Maros
Editor D. Gay
Structural Rank 3,136
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 3.403268e+00
Minimum Singular Value 1.464952e+00
Condition Number 2.323126e+00
Rank 3,136
sprank(A)-rank(A) 0
Null Space Dimension 0
Full Numerical Rank? yes
Download Singular Values MATLAB
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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 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         
MAROS-R7   3137   9408   151120    4812587        1.4971851665E+06        
From Istvan Maros.                                                        
Concerning the problems he submitted, Istvan Maros says that              
MAROS-R7 is "an interesting                                               
real-life LP problem which appeared hard to some solvers."  It "is an     
image restoration problem done via a goal programming approach.  It is    
structured, namely, its first section is a band matrix with the           
dominating number of nonzeros, while the second section is also a band    
matrix with bandwidth equals 2 and coefficients +1, -1.  The problem is   
a representative of a family of problems in which the number of rows and  
the bandwidth of the first section can vary.  This one is a medium size   
problem from the family.  MAROS-R7 became available in cooperation with   
Roni Levkovitz and Carison Tong."                                         
Added to Netlib on  17 Jan. 1994