• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
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  • Matrix: LPnetlib/lpi_greenbea
  • Description: Netlib LP problem greenbea: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 144 KB. Use SJget(372) or SJget('LPnetlib/lpi_greenbea') in MATLAB.
  • download in Matrix Market format, file size: 139 KB.
  • download in Rutherford/Boeing format, file size: 102 KB.

    LPnetlib/lpi_greenbea

    Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

    LPnetlib/lpi_greenbea

    dmperm of LPnetlib/lpi_greenbea

    scc of LPnetlib/lpi_greenbea

    Matrix properties (click for a legend)  
    number of rows2,393
    number of columns5,596
    structural full rank?no
    structural rank2,390
    numerical rank 2,390
    dimension of the numerical null space3,206
    numerical rank / min(size(A))0.99875
    Euclidean norm of A 106.23
    calculated singular value # 23900.024208
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    7.9524e-011
    calculated singular value # 23916.765e-016
    gap in the singular values at the numerical rank:
    singular value # 2390 / singular value # 2391
    3.5784e+013
    calculated condition number2.6425e+066
    condest-2
    nonzeros31,074
    # of blocks from dmperm75
    # strongly connected comp.9
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorR. Fourer
    editorR. Fourer
    date1988
    kindlinear programming problem
    2D/3D problem?no
    SJid372
    UFid718

    Additional fieldssize and type
    bfull 2393-by-1
    cfull 5596-by-1
    lofull 5596-by-1
    hifull 5596-by-1
    z0full 1-by-1

    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         
    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        
    omitted.                                                                  
    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:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU704,268 580,104
    nnz(R) for QR, upper bound nnz(U) for LU79,738 88,011

    Maintained by Leslie Foster, last updated 24-Apr-2009.

    Entries 5 through 14 in the table of matrix properties and the singular
    value plot were created using SJsingular code. The other plots
    and statistics are produced using utilities from the SuiteSparse package.
    Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.