• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
  • Click here for a description of the LPnetlib group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups


  • Matrix: LPnetlib/lp_cre_a
  • Description: Netlib LP problem cre_a: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 67 KB. Use SJget(348) or SJget('LPnetlib/lp_cre_a') in MATLAB.
  • download in Matrix Market format, file size: 71 KB.
  • download in Rutherford/Boeing format, file size: 59 KB.

    LPnetlib/lp_cre_a

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

    LPnetlib/lp_cre_a

    dmperm of LPnetlib/lp_cre_a

    scc of LPnetlib/lp_cre_a

    Matrix properties (click for a legend)  
    number of rows3,516
    number of columns7,248
    structural full rank?no
    structural rank3,428
    numerical rank 3,423
    dimension of the numerical null space3,825
    numerical rank / min(size(A))0.97355
    Euclidean norm of A 193.02
    calculated singular value # 34230.009165
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.06e-010
    calculated singular value # 34241.7105e-015
    gap in the singular values at the numerical rank:
    singular value # 3423 / singular value # 3424
    5.3582e+012
    calculated condition numberInf
    condest-2
    nonzeros18,168
    # of blocks from dmperm8
    # strongly connected comp.89
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorJ. Kennington
    editorI. Lustig
    date1990
    kindlinear programming problem
    2D/3D problem?no
    SJid348
    UFid609

    Additional fieldssize and type
    bfull 3516-by-1
    cfull 7248-by-1
    lofull 7248-by-1
    hifull 7248-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
    CRE-A      3517    4067     19054        0    152726    659682   2.3595407e+07
                                                                                  
    Submitted to Netlib by Irv Lustig.                                            
                                                                                  
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU363,400 351,413
    nnz(R) for QR, upper bound nnz(U) for LU37,116 37,719

    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.