• 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.


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


    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)) =
    calculated singular value # 23729.4212e-015
    gap in the singular values at the numerical rank:
    singular value # 2371 / singular value # 2372
    calculated condition number5.8942e+016
    # of blocks from dmperm2
    # strongly connected comp.1,726
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorJ.-C. Faugeres
    editorJ.-G. Dumas
    kindcombinatorial problem
    2D/3D problem?no


    Gro"bner basis from Jean-Charles Fauge`res,                 
    From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,
    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.