Matrix: LPnetlib/lp_ken_11

Description: Netlib LP problem ken_11: minimize c'*x, where Ax=b, lo<=x<=hi

LPnetlib/lp_ken_11 graph
(bipartite graph drawing)


LPnetlib/lp_ken_11 dmperm of LPnetlib/lp_ken_11

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  • Matrix group: LPnetlib
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  • download as a MATLAB mat-file, file size: 184 KB. Use UFget(638) or UFget('LPnetlib/lp_ken_11') in MATLAB.
  • download in Matrix Market format, file size: 266 KB.
  • download in Rutherford/Boeing format, file size: 228 KB.

    Matrix properties
    number of rows14,694
    number of columns21,349
    nonzeros49,058
    structural full rank?yes
    structural rank14,694
    # of blocks from dmperm4,610
    # 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 14694-by-1
    cfull 21349-by-1
    lofull 21349-by-1
    hifull 21349-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-11    14695   21349     70354    42698    928171   4167698  -6.9723823e+09
                                                                                  
    Submitted to Netlib by Irv Lustig.                                            
                                                                                  
    

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD618,040
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD133,221

    SVD-based statistics:
    norm(A)11.462
    min(svd(A))3.1051e-15
    cond(A)3.69135e+15
    rank(A)14,573
    sprank(A)-rank(A)121
    null space dimension121
    full numerical rank?no
    singular value gap5.61076e+11

    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_11 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.