• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
  • Click here for a description of the LPnetlib group.
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  • Matrix: LPnetlib/lpi_gran
  • Description: Netlib LP problem gran: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 66 KB. Use SJget(391) or SJget('LPnetlib/lpi_gran') in MATLAB.
  • download in Matrix Market format, file size: 92 KB.
  • download in Rutherford/Boeing format, file size: 56 KB.

    LPnetlib/lpi_gran

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

    LPnetlib/lpi_gran

    dmperm of LPnetlib/lpi_gran

    scc of LPnetlib/lpi_gran

    Matrix properties (click for a legend)  
    number of rows2,658
    number of columns2,525
    structural full rank?no
    structural rank2,311
    numerical rank 1,938
    dimension of the numerical null space587
    numerical rank / min(size(A))0.76752
    Euclidean norm of A 2079
    calculated singular value # 19383.8268e-008
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.2087e-009
    calculated singular value # 19392.9062e-010
    gap in the singular values at the numerical rank:
    singular value # 1938 / singular value # 1939
    131.67
    calculated condition number1.5142e+020
    condest-2
    nonzeros20,111
    # of blocks from dmperm1,267
    # strongly connected comp.1,243
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorR. Main
    editorJ. Chinneck
    date1993
    kindlinear programming problem
    2D/3D problem?no
    SJid391
    UFid717

    Additional fieldssize and type
    bfull 2658-by-1
    cfull 2525-by-1
    lofull 2525-by-1
    hifull 2525-by-1
    z0full 1-by-1

    Notes:

    An infeasible Netlib LP problem, in lp/infeas.  For more information        
    send email to netlib@ornl.gov with the message:                             
                                                                                
    	send index from lp                                                         
    	send readme from lp/infeas                                                 
                                                                                
    The lp/infeas directory contains infeasible linear programming test problems
    collected by John W. Chinneck, Carleton Univ, Ontario Canada.  The following
    are relevant excerpts from lp/infeas/readme (by John W. Chinneck):          
                                                                                
    PROBLEM DESCRIPTION                                                         
    -------------------                                                         
                                                                                
    GOSH, GRAN, PANG:  these very large, large, and medium size models,         
    respectively, problems arose from British Petroleum operations models.      
    Contributor:  Roger Main, BP Oil.                                           
                                                                                
    Name       Rows   Cols   Nonzeros Bounds      Notes                         
    gran       2569   2520    20151   B    FX                                   
                                                                                
    Added to Netlib on Sept. 19, 1993                                           
                                                                                
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU206,097 112,467
    nnz(R) for QR, upper bound nnz(U) for LU190,918 147,973

    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.