• 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/G49
  • Description: 2D torus, 100-by-30
  • download as a MATLAB mat-file, file size: 28 KB. Use SJget(7) or SJget('Gset/G49') in MATLAB.
  • download in Matrix Market format, file size: 20 KB.
  • download in Rutherford/Boeing format, file size: 19 KB.


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


    Matrix properties (click for a legend)  
    number of rows3,000
    number of columns3,000
    structural full rank?yes
    structural rank3,000
    numerical rank 2,982
    dimension of the numerical null space18
    numerical rank / min(size(A))0.994
    Euclidean norm of A 4
    calculated singular value # 29820.0039465
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 29831.0745e-015
    gap in the singular values at the numerical rank:
    singular value # 2982 / singular value # 2983
    calculated condition number4.8929e+017
    # of blocks from dmperm2
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?unknown

    authorC. Helmberg
    editorY. Ye
    kindundirected random graph
    2D/3D problem?no

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))60,814 58,902 -
    Cholesky flop count2.9e+006 2.6e+006 -
    nnz(L+U), no partial pivoting118,628 114,804 -
    nnz(V) for QR, upper bound nnz(L) for LU61,153 55,382 61,153
    nnz(R) for QR, upper bound nnz(U) for LU109,213 99,782 109,213

    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.