• 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/bayer01
  • Description: Unsymmetric Matrix bayer01, Bayer AG, F. Grund, Apr 1996.
  • download as a MATLAB mat-file, file size: 1 MB. Use SJget(418) or SJget('Grund/bayer01') in MATLAB.
  • download in Matrix Market format, file size: 2 MB.
  • download in Rutherford/Boeing format, file size: 2 MB.


    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 51607 to 51612 and associated error bounds.


    dmperm of Grund/bayer01

    Matrix properties (click for a legend)  
    number of rows57,735
    number of columns57,735
    structural full rank?yes
    structural rank57,735
    numerical rank 51,609
    dimension of the numerical null space6,126
    numerical rank / min(size(A))0.89389
    Euclidean norm of A 1.26e+005
    calculated singular value # 516098.4181e-007
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 516108.3961e-007
    gap in the singular values at the numerical rank:
    singular value # 51609 / singular value # 51610
    calculated condition number-2
    # of blocks from dmperm9,133
    # strongly connected comp.1
    entries not in dmperm blocks28,203
    explicit zero entries2,680
    nonzero pattern symmetry 0%
    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'))230,553,822 69,960,978 898,313
    Cholesky flop count3.1e+012 2.6e+011 3.7e+007
    nnz(L+U), no partial pivoting461,049,909 139,864,221 1,767,094
    nnz(V) for QR, upper bound nnz(L) for LU762,409 820,455 714,068
    nnz(R) for QR, upper bound nnz(U) for LU1,565,498 1,655,102 1,473,688

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 2680 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.