• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
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  • Matrix: LPnetlib/lp_bnl1
  • Description: Netlib LP problem bnl1: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 25 KB. Use SJget(323) or SJget('LPnetlib/lp_bnl1') in MATLAB.
  • download in Matrix Market format, file size: 24 KB.
  • download in Rutherford/Boeing format, file size: 20 KB.

    LPnetlib/lp_bnl1

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

    LPnetlib/lp_bnl1

    dmperm of LPnetlib/lp_bnl1

    scc of LPnetlib/lp_bnl1

    Matrix properties (click for a legend)  
    number of rows643
    number of columns1,586
    structural full rank?no
    structural rank642
    numerical rank 642
    dimension of the numerical null space944
    numerical rank / min(size(A))0.99844
    Euclidean norm of A 170.48
    calculated singular value # 6420.050808
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    4.5077e-011
    calculated singular value # 6431.2221e-060
    gap in the singular values at the numerical rank:
    singular value # 642 / singular value # 643
    4.1573e+058
    calculated condition number1.395e+062
    condest-2
    nonzeros5,532
    # of blocks from dmperm12
    # strongly connected comp.12
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorJ. Tomlin
    editorD. Gay
    date1989
    kindlinear programming problem
    2D/3D problem?no
    SJid323
    UFid604

    Additional fieldssize and type
    bfull 643-by-1
    cfull 1586-by-1
    lofull 1586-by-1
    hifull 1586-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 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         
    BNL1        644   1175     6129      42473        1.9776292856E+03        
                                                                              
    From John Tomlin.                                                         
                                                                              
    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)                          
    BNL1         1.9776295615E+03     1.9776293385E+03                        
                                                                              
    On the problems supplied by John Tomlin, MINOS 5.3 reports that about     
    10% to 57% of its steps are degenerate:                                   
         Name     Steps  Degen  Percent                                       
         BNL1      1614    169   10.47                                        
                                                                              
    Added to Netlib on 30 Oct. 1989                                           
                                                                              
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU95,006 90,893
    nnz(R) for QR, upper bound nnz(U) for LU12,073 13,070

    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.