Matrix: LPnetlib/lp_maros_r7

Description: Netlib LP problem maros_r7: minimize c'*x, where Ax=b, lo<=x<=hi

LPnetlib/lp_maros_r7 graph
(bipartite graph drawing)


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  • download as a MATLAB mat-file, file size: 179 KB. Use UFget(643) or UFget('LPnetlib/lp_maros_r7') in MATLAB.
  • download in Matrix Market format, file size: 528 KB.
  • download in Rutherford/Boeing format, file size: 165 KB.

    Matrix properties
    number of rows3,136
    number of columns9,408
    structural full rank?yes
    structural rank3,136
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorI. Maros
    editorD. Gay
    kindlinear programming problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 3136-by-1
    cfull 9408-by-1
    lofull 9408-by-1
    hifull 9408-by-1
    z0full 1-by-1


    A Netlib LP problem, in lp/data.  For more information                    
    send email to 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                                          

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD9,862,844
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD853,785

    SVD-based statistics:
    null space dimension0
    full numerical rank?yes

    singular values (MAT file):click here
    SVD method used:s = svd (full (A)) ;

    LPnetlib/lp_maros_r7 svd

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.