• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
  • Click here for a description of the LPnetlib group.
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  • Matrix: LPnetlib/lp_pds_02
  • Description: Netlib LP problem pds_02: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 48 KB. Use SJget(361) or SJget('LPnetlib/lp_pds_02') in MATLAB.
  • download in Matrix Market format, file size: 71 KB.
  • download in Rutherford/Boeing format, file size: 50 KB.

    LPnetlib/lp_pds_02

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

    LPnetlib/lp_pds_02

    dmperm of LPnetlib/lp_pds_02

    Matrix properties (click for a legend)  
    number of rows2,953
    number of columns7,716
    structural full rank?yes
    structural rank2,953
    numerical rank 2,942
    dimension of the numerical null space4,774
    numerical rank / min(size(A))0.99627
    Euclidean norm of A 9.5939
    calculated singular value # 29420.23688
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.3706e-011
    calculated singular value # 29434.743e-015
    gap in the singular values at the numerical rank:
    singular value # 2942 / singular value # 2943
    4.9942e+013
    calculated condition number5.5819e+015
    condest-2
    nonzeros16,571
    # of blocks from dmperm300
    # strongly connected comp.1
    entries not in dmperm blocks308
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typeinteger
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorJ. Kennington
    editorI. Lustig
    date1990
    kindlinear programming problem
    2D/3D problem?no
    SJid361
    UFid649

    Additional fieldssize and type
    bfull 2953-by-1
    cfull 7716-by-1
    lofull 7716-by-1
    hifull 7716-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
    PDS-02     2954    7535     21252     2134    197821    801690   2.8857862e+10
                                                                                  
    Submitted to Netlib by Irv Lustig.                                            
                                                                                  
    

    Ordering statistics:AMD METIS DMPERM+
    nnz(V) for QR, upper bound nnz(L) for LU790,391 719,697 650,676
    nnz(R) for QR, upper bound nnz(U) for LU44,486 48,250 43,259

    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.