Matrix: LPnetlib/lp_degen3

Description: Netlib LP problem degen3: minimize c'*x, where Ax=b, lo<=x<=hi

LPnetlib/lp_degen3 graph
(bipartite graph drawing)


LPnetlib/lp_degen3

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  • Matrix group: LPnetlib
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  • download as a MATLAB mat-file, file size: 34 KB. Use UFget(618) or UFget('LPnetlib/lp_degen3') in MATLAB.
  • download in Matrix Market format, file size: 70 KB.
  • download in Rutherford/Boeing format, file size: 36 KB.

    Matrix properties
    number of rows1,503
    number of columns2,604
    nonzeros25,432
    structural full rank?yes
    structural rank1,503
    # of blocks from dmperm1
    # strongly connected comp.1
    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

    Additional fieldssize and type
    bfull 1503-by-1
    cfull 2604-by-1
    lofull 2604-by-1
    hifull 2604-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         
    DEGEN3     1504   1818    26230     130252       -9.8729400000E+02        
                                                                              
    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                                       
         DEGEN3    6283   3299   52.51                                        
                                                                              
    When included in Netlib: Cost coefficients negated.                       
                                                                              
    Added to Netlib on  30 Oct. 1989                                          
    

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD334,792
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD123,387

    SVD-based statistics:
    norm(A)54.6509
    min(svd(A))1.00663e-14
    cond(A)5.4291e+15
    rank(A)1,501
    sprank(A)-rank(A)2
    null space dimension2
    full numerical rank?no
    singular value gap5.8764e+12

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

    LPnetlib/lp_degen3 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.