• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
  • Click here for a description of the LPnetlib group.
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  • Matrix: LPnetlib/lpi_gosh
  • Description: Netlib LP problem gosh: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 333 KB. Use SJget(536) or SJget('LPnetlib/lpi_gosh') in MATLAB.
  • download in Matrix Market format, file size: 382 KB.
  • download in Rutherford/Boeing format, file size: 221 KB.

    LPnetlib/lpi_gosh

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

    LPnetlib/lpi_gosh

    dmperm of LPnetlib/lpi_gosh

    scc of LPnetlib/lpi_gosh

    Matrix properties (click for a legend)  
    number of rows3,792
    number of columns13,455
    structural full rank?no
    structural rank3,790
    numerical rank 3,790
    dimension of the numerical null space9,665
    numerical rank / min(size(A))0.99947
    Euclidean norm of A 323.67
    calculated singular value # 37900.0057761
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    7.6483e-010
    calculated singular value # 37913.3981e-014
    gap in the singular values at the numerical rank:
    singular value # 3790 / singular value # 3791
    1.6998e+011
    calculated condition number1.5863e+017
    condest-2
    nonzeros99,953
    # of blocks from dmperm130
    # strongly connected comp.105
    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
    SJid536
    UFid716

    Additional fieldssize and type
    bfull 3792-by-1
    cfull 13455-by-1
    lofull 13455-by-1
    hifull 13455-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                         
    gosh       3793  10733    97257   B FR         242 free cols                
                                                                                
    Added to Netlib on Sept. 19, 1993                                           
                                                                                
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU4,605,419 3,556,493
    nnz(R) for QR, upper bound nnz(U) for LU275,933 252,052

    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.