• SJSU Singular Matrix Database
  • Matrix group: Grund
  • Click here for a description of the Grund group.
  • Click here for a list of all matrices
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  • Matrix: Grund/bayer02
  • Description: Unsymmetric Matrix bayer02, Bayer AG, F. Grund, Mar 1995.
  • download as a MATLAB mat-file, file size: 384 KB. Use SJget(364) or SJget('Grund/bayer02') in MATLAB.
  • download in Matrix Market format, file size: 584 KB.
  • download in Rutherford/Boeing format, file size: 514 KB.

    Grund/bayer02

    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 7.6.0.324 (R2008a) to calculate the 6 largest singular values and associated error bounds.
    Routine spnrank, version 1.0 with opts.tol_eigs = 1e-010, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 12608 to 12613 and associated error bounds.

    Grund/bayer02

    dmperm of Grund/bayer02

    Matrix properties (click for a legend)  
    number of rows13,935
    number of columns13,935
    structural full rank?yes
    structural rank13,935
    numerical rank 12,610
    dimension of the numerical null space1,325
    numerical rank / min(size(A))0.90492
    Euclidean norm of A 1.26e+005
    calculated singular value # 126102.1243e-007
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.0278e-007
    calculated singular value # 126112.0274e-007
    gap in the singular values at the numerical rank:
    singular value # 12610 / singular value # 12611
    1.0478
    calculated condition number-2
    condest2.3531e+018
    nonzeros63,307
    # of blocks from dmperm2,226
    # strongly connected comp.1
    entries not in dmperm blocks6,828
    explicit zero entries372
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorBayer
    editorF. Grund
    date1997
    kindchemical process simulation problem
    2D/3D problem?no
    SJid364
    UFid453

    Additional fieldssize and type
    bfull 13935-by-1

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))12,891,970 7,317,986 200,894
    Cholesky flop count4.0e+010 9.9e+009 7.8e+006
    nnz(L+U), no partial pivoting25,770,005 14,622,037 394,681
    nnz(V) for QR, upper bound nnz(L) for LU161,526 199,050 155,054
    nnz(R) for QR, upper bound nnz(U) for LU323,903 399,395 321,665

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 372 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.