• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
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  • Matrix: LPnetlib/lp_ken_07
  • Description: Netlib LP problem ken_07: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 38 KB. Use SJget(318) or SJget('LPnetlib/lp_ken_07') in MATLAB.
  • download in Matrix Market format, file size: 48 KB.
  • download in Rutherford/Boeing format, file size: 42 KB.

    LPnetlib/lp_ken_07

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

    LPnetlib/lp_ken_07

    dmperm of LPnetlib/lp_ken_07

    Matrix properties (click for a legend)  
    number of rows2,426
    number of columns3,602
    structural full rank?yes
    structural rank2,426
    numerical rank 2,377
    dimension of the numerical null space1,225
    numerical rank / min(size(A))0.9798
    Euclidean norm of A 7.5241
    calculated singular value # 23770.057008
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    3.1992e-012
    calculated singular value # 23782.1691e-014
    gap in the singular values at the numerical rank:
    singular value # 2377 / singular value # 2378
    2.6282e+012
    calculated condition number4.693e+015
    condest-2
    nonzeros8,404
    # of blocks from dmperm990
    # strongly connected comp.1
    entries not in dmperm blocks1,421
    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
    SJid318
    UFid637

    Additional fieldssize and type
    bfull 2426-by-1
    cfull 3602-by-1
    lofull 3602-by-1
    hifull 3602-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-07     2427    3602     11981     7204    150525    718748  -6.7952044e+08
                                                                                  
    Submitted to Netlib by Irv Lustig.                                            
                                                                                  
    

    Ordering statistics:AMD METIS DMPERM+
    nnz(V) for QR, upper bound nnz(L) for LU67,547 40,802 30,748
    nnz(R) for QR, upper bound nnz(U) for LU15,529 16,151 12,493

    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.