Matrix: LPnetlib/lp_ken_13

Description: Netlib LP problem ken_13: minimize c'*x, where Ax=b, lo<=x<=hi

LPnetlib/lp_ken_13 graph
(bipartite graph drawing)


LPnetlib/lp_ken_13 dmperm of LPnetlib/lp_ken_13

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  • Matrix group: LPnetlib
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  • download as a MATLAB mat-file, file size: 367 KB. Use UFget(639) or UFget('LPnetlib/lp_ken_13') in MATLAB.
  • download in Matrix Market format, file size: 523 KB.
  • download in Rutherford/Boeing format, file size: 445 KB.

    Matrix properties
    number of rows28,632
    number of columns42,659
    nonzeros97,246
    structural full rank?yes
    structural rank28,632
    # of blocks from dmperm6,099
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typeinteger
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorJ. Kennington
    editorD. Gay
    date1991
    kindlinear programming problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 28632-by-1
    cfull 42659-by-1
    lofull 42659-by-1
    hifull 42659-by-1
    z0full 1-by-1

    Notes:

    A Netlib LP problem, in lp/data/kennington.  For more information             
    send email to netlib@ornl.gov with the message:                               
                                                                                  
    	 send index from lp                                                          
    	 send readme from lp/data                                                    
    	 send readme from lp/data/kennington                                         
                                                                                  
    The following are relevant excerpts from lp/data/kennington/readme:           
                                                                                  
    The "Kennington" problems: sixteen problems described in "An Empirical        
    Evaluation of the KORBX Algorithms for Military Airlift Applications"         
    by W. J. Carolan, J. E. Hill, J. L. Kennington, S. Niemi, S. J.               
    Wichmann (Operations Research vol. 38, no. 2 (1990), pp. 240-248).            
                                                                                  
    The following table gives some statistics for the "Kennington"                
    problems.  The number of columns excludes slacks and surpluses.               
    The bounds column tells how many entries appear in the BOUNDS                 
    section of the MPS file.  The mpc column shows the bytes in                   
    the problem after "uncompress" and before "emps"; MPS shows                   
    the bytes after "emps".  The optimal values were computed by                  
    Vanderbei's ALPO, running on an SGI computer (with binary IEEE                
    arithmetic).                                                                  
                                                                                  
    Name       rows  columns  nonzeros  bounds      mpc      MPS     optimal value
    KEN-13    28633   42659    139834    85318   1836457   8254122  -1.0257395e+10
                                                                                  
    Submitted to Netlib by Irv Lustig.                                            
                                                                                  
    

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD2,207,416
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD353,474

    SVD-based statistics:
    norm(A)13.3255
    min(svd(A))6.7931e-47
    cond(A)1.96162e+47
    rank(A)28,463
    sprank(A)-rank(A)169
    null space dimension169
    full numerical rank?no
    singular value gap3.29015e+12

    singular values (MAT file):click here
    SVD method used:s = svd (full (R)) ; where [~,R,E] = spqr (A') with droptol of zero
    status:ok

    LPnetlib/lp_ken_13 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.