• 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/bayer10
  • Description: Unsymmetric Matrix bayer10, Bayer AG, F. Grund, Jul 1995.
  • download as a MATLAB mat-file, file size: 398 KB. Use SJget(359) or SJget('Grund/bayer10') in MATLAB.
  • download in Matrix Market format, file size: 663 KB.
  • download in Rutherford/Boeing format, file size: 552 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 with opts.tol_eigs = 1e-010, used with Matlab (R2008a) to calculate singular values 13307 to 13312 and associated error bounds.


    dmperm of Grund/bayer10

    Matrix properties (click for a legend)  
    number of rows13,436
    number of columns13,436
    structural full rank?yes
    structural rank13,436
    numerical rank 13,309
    dimension of the numerical null space127
    numerical rank / min(size(A))0.99055
    Euclidean norm of A 14143
    calculated singular value # 133092.5525e-008
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 133102.1913e-008
    gap in the singular values at the numerical rank:
    singular value # 13309 / singular value # 13310
    calculated condition number-2
    # of blocks from dmperm2,545
    # strongly connected comp.1
    entries not in dmperm blocks6,611
    explicit zero entries23,332
    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 13436-by-1

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))12,726,035 7,228,854 242,390
    Cholesky flop count4.0e+010 1.1e+010 1.1e+007
    nnz(L+U), no partial pivoting25,438,634 14,444,272 477,955
    nnz(V) for QR, upper bound nnz(L) for LU170,063 194,681 161,659
    nnz(R) for QR, upper bound nnz(U) for LU385,588 426,704 365,771

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 23332 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.