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

  • Matrix: Grund/bayer05
  • Description: Unsymmetric Matrix bayer05, Bayer AG, F. Grund, Oct 1995.
  • download as a MATLAB mat-file, file size: 85 KB. Use SJget(54) or SJget('Grund/bayer05') in MATLAB.
  • download in Matrix Market format, file size: 130 KB.
  • download in Rutherford/Boeing format, file size: 89 KB.


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


    dmperm of Grund/bayer05

    Matrix properties (click for a legend)  
    number of rows3,268
    number of columns3,268
    structural full rank?yes
    structural rank3,268
    numerical rank 1,666
    dimension of the numerical null space1,602
    numerical rank / min(size(A))0.50979
    Euclidean norm of A 2.4972e+012
    calculated singular value # 16661.5976
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 16671.58
    gap in the singular values at the numerical rank:
    singular value # 1666 / singular value # 1667
    calculated condition number7.1897e+026
    # of blocks from dmperm3,037
    # strongly connected comp.1
    entries not in dmperm blocks16,467
    explicit zero entries7,124
    nonzero pattern symmetry 1%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    editorF. Grund
    kindchemical process simulation problem
    2D/3D problem?no

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))555,007 486,480 4,552
    Cholesky flop count3.1e+008 1.8e+008 1.4e+004
    nnz(L+U), no partial pivoting1,106,746 969,692 22,303
    nnz(V) for QR, upper bound nnz(L) for LU92,975 99,954 6,666
    nnz(R) for QR, upper bound nnz(U) for LU199,278 211,160 25,113

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 7124 explicit zero entries.

    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.