Matrix: LPnetlib/lp_greenbea

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

LPnetlib/lp_greenbea graph
(bipartite graph drawing)

LPnetlib/lp_greenbea dmperm of LPnetlib/lp_greenbea
scc of LPnetlib/lp_greenbea

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  • Matrix group: LPnetlib
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  • download as a MATLAB mat-file, file size: 128 KB. Use UFget(630) or UFget('LPnetlib/lp_greenbea') in MATLAB.
  • download in Matrix Market format, file size: 137 KB.
  • download in Rutherford/Boeing format, file size: 102 KB.

    Matrix properties
    number of rows2,392
    number of columns5,598
    structural full rank?no
    structural rank2,389
    # of blocks from dmperm75
    # strongly connected comp.9
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorK. Palmer
    editorR. Fourer
    kindlinear programming problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 2392-by-1
    cfull 5598-by-1
    lofull 5598-by-1
    hifull 5598-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 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         
    GREENBEA   2393   5405    31499     235711  B    -7.2462405908E+07        
            BOUND-TYPE TABLE                                                  
    GREENBEA   UP LO FX                                                       
    Supplied by Bob Fourer.                                                   
    When included in Netlib: Extra bound sets omitted; Extra free rows        
    Empty RHS section.                                                        
    Problems GREENBEA and GREENBEB differ only in their BOUNDS sections.      
    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)                          
    GREENBEA    -7.2555248130E+07                                             
    Source:  GREENBEA, GREENBEB: a large refinery model; see the book         
    "A Model-Management Framework for Mathematical Programming" by Kenneth    
    H. Palmer et al. (John Wiley & Sons, New York, 1984).                     
    Added to Netlib on  6 May 1988                                            

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD700,189
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD79,425

    SVD-based statistics:
    null space dimension3
    full numerical rank?no
    singular value gap4.59607e+13

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

    LPnetlib/lp_greenbea 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.