• SJSU Singular Matrix Database
  • Matrix group: JGD_Groebner
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  • Matrix: JGD_Groebner/HFE18_96_in
  • Description: Groebner basis from Jean-Charles Fauge`res
  • download as a MATLAB mat-file, file size: 1 MB. Use SJget(652) or SJget('JGD_Groebner/HFE18_96_in') in MATLAB.
  • download in Matrix Market format, file size: 2 MB.
  • download in Rutherford/Boeing format, file size: 1 MB.

    JGD_Groebner/HFE18_96_in

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

    JGD_Groebner/HFE18_96_in

    dmperm of JGD_Groebner/HFE18_96_in

    scc of JGD_Groebner/HFE18_96_in

    Matrix properties (click for a legend)  
    number of rows2,372
    number of columns4,096
    structural full rank?no
    structural rank2,371
    numerical rank 2,371
    dimension of the numerical null space1,725
    numerical rank / min(size(A))0.99958
    Euclidean norm of A 555.31
    calculated singular value # 23710.00042403
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    4.6566e-010
    calculated singular value # 23729.4212e-015
    gap in the singular values at the numerical rank:
    singular value # 2371 / singular value # 2372
    4.5008e+010
    calculated condition number5.8942e+016
    condest-2
    nonzeros933,343
    # of blocks from dmperm2
    # strongly connected comp.1,726
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typebinary
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorJ.-C. Faugeres
    editorJ.-G. Dumas
    date2008
    kindcombinatorial problem
    2D/3D problem?no
    SJid652
    UFid2,004

    Notes:

    Gro"bner basis from Jean-Charles Fauge`res,                 
    From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,
    http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html   
                                                                
    http://www-calfor.lip6.fr/~jcf/                             
                                                                
    Filename in JGD collection: Grobner/HFE18_96.in.sms         
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU2,341,530 2,610,280
    nnz(R) for QR, upper bound nnz(U) for LU2,807,609 2,814,378

    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.