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


  • Matrix: Gset/G56
  • Description: Random matrix, 0.05% uniformly distributed. G55=pattern of G56
  • download as a MATLAB mat-file, file size: 108 KB. Use SJget(10) or SJget('Gset/G56') in MATLAB.
  • download in Matrix Market format, file size: 52 KB.
  • download in Rutherford/Boeing format, file size: 42 KB.

    Gset/G56

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

    Gset/G56

    scc of Gset/G56

    Matrix properties (click for a legend)  
    number of rows5,000
    number of columns5,000
    structural full rank?no
    structural rank4,966
    numerical rank 4,966
    dimension of the numerical null space34
    numerical rank / min(size(A))0.9932
    Euclidean norm of A 4.9941
    calculated singular value # 49660.00024622
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    4.4409e-012
    calculated singular value # 49672.1839e-015
    gap in the singular values at the numerical rank:
    singular value # 4966 / singular value # 4967
    1.1274e+011
    calculated condition number6.9717e+019
    condestInf
    nonzeros24,996
    # of blocks from dmperm411
    # strongly connected comp.32
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typeinteger
    structuresymmetric
    Cholesky candidate?yes
    positive definite?no

    authorC. Helmberg
    editorY. Ye
    date1996
    kindundirected weighted random graph
    2D/3D problem?no
    SJid10
    UFid520

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))1,091,404 1,317,912
    Cholesky flop count1.0e+009 1.3e+009
    nnz(L+U), no partial pivoting2,177,808 2,630,824
    nnz(V) for QR, upper bound nnz(L) for LU3,896,150 3,680,788
    nnz(R) for QR, upper bound nnz(U) for LU4,732,160 5,432,189

    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.