• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
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  • Matrix: LPnetlib/lp_degen2
  • Description: Netlib LP problem degen2: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 14 KB. Use SJget(312) or SJget('LPnetlib/lp_degen2') in MATLAB.
  • download in Matrix Market format, file size: 15 KB.
  • download in Rutherford/Boeing format, file size: 10 KB.

    LPnetlib/lp_degen2

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

    LPnetlib/lp_degen2

    Matrix properties (click for a legend)  
    number of rows444
    number of columns757
    structural full rank?yes
    structural rank444
    numerical rank 442
    dimension of the numerical null space315
    numerical rank / min(size(A))0.9955
    Euclidean norm of A 17.672
    calculated singular value # 4420.17845
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.6894e-012
    calculated singular value # 4435.7573e-015
    gap in the singular values at the numerical rank:
    singular value # 442 / singular value # 443
    3.0996e+013
    calculated condition number4.1128e+015
    condest-2
    nonzeros4,201
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typeinteger
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorJ. Tomlin
    editorD. Gay
    date1989
    kindlinear programming problem
    2D/3D problem?no
    SJid312
    UFid617

    Additional fieldssize and type
    bfull 444-by-1
    cfull 757-by-1
    lofull 757-by-1
    hifull 757-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         
    DEGEN2      445    534     4449      24657       -1.4351780000E+03        
                                                                              
    From John Tomlin.                                                         
    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                                       
         DEGEN2    1075    610   56.74                                        
                                                                              
    When included in Netlib: Cost coefficients negated.                       
                                                                              
    Added to Netlib on  30 Oct. 1989                                          
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU37,804 35,681
    nnz(R) for QR, upper bound nnz(U) for LU16,368 17,457

    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.