• 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/bayer04
  • Description: Unsymmetric Matrix bayer04, Bayer AG, F. Grund, Aug 1995.
  • download as a MATLAB mat-file, file size: 479 KB. Use SJget(365) or SJget('Grund/bayer04') in MATLAB.
  • download in Matrix Market format, file size: 923 KB.
  • download in Rutherford/Boeing format, file size: 752 KB.


    A singular value of A is guaranteed1 to be in the interval pictured by the blue bars around each of the calculated singular values.

    Routine svds_err, version 1.0, used with Matlab (R2008a) to calculate the 6 largest singular values and associated error bounds.
    Routine spnrank, version 1.0, used with Matlab (R2008a) to calculate singular values 14829 to 14834 and associated error bounds.


    dmperm of Grund/bayer04

    scc of Grund/bayer04

    Matrix properties (click for a legend)  
    number of rows20,545
    number of columns20,545
    structural full rank?yes
    structural rank20,545
    numerical rank 14,831
    dimension of the numerical null space5,714
    numerical rank / min(size(A))0.72188
    Euclidean norm of A 3.3796e+009
    calculated singular value # 148310.0097968
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 148320.0097965
    gap in the singular values at the numerical rank:
    singular value # 14831 / singular value # 14832
    calculated condition number-2
    # of blocks from dmperm8,168
    # strongly connected comp.6
    entries not in dmperm blocks14,470
    explicit zero entries73,545
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    bfull 20545-by-1

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))26,089,441 15,577,878 295,395
    Cholesky flop count1.2e+011 3.4e+010 1.7e+007
    nnz(L+U), no partial pivoting52,158,337 31,135,211 584,715
    nnz(V) for QR, upper bound nnz(L) for LU266,355 261,690 204,829
    nnz(R) for QR, upper bound nnz(U) for LU553,570 574,775 435,471

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 73545 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.