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


  • Matrix: Boeing/pcrystk02
  • Description: FEM CRYSTAL FREE VIBRATION STIFFNESS MATRIX
  • download as a MATLAB mat-file, file size: 379 KB. Use SJget(513) or SJget('Boeing/pcrystk02') in MATLAB.
  • download in Matrix Market format, file size: 904 KB.
  • download in Rutherford/Boeing format, file size: 326 KB.

    Boeing/pcrystk02

    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, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 4622 to 4627 and associated error bounds.

    Boeing/pcrystk02

    Matrix properties (click for a legend)  
    number of rows13,965
    number of columns13,965
    structural full rank?yes
    structural rank13,965
    numerical rank 4,624
    dimension of the numerical null space9,341
    numerical rank / min(size(A))0.33111
    Euclidean norm of A 76.044
    calculated singular value # 46240.010251
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.9845e-010
    calculated singular value # 46258.0737e-016
    gap in the singular values at the numerical rank:
    singular value # 4624 / singular value # 4625
    1.2697e+013
    calculated condition number-2
    condestInf
    nonzeros968,583
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typebinary
    structuresymmetric
    Cholesky candidate?yes
    positive definite?no

    authorR. Grimes
    editorT. Davis
    date1995
    kindduplicate materials problem
    2D/3D problem?yes
    SJid513
    UFid366

    Notes:

    This matrix is the nonzero pattern of Boeing/crystk02
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))6,118,928 4,273,248
    Cholesky flop count4.5e+009 1.9e+009
    nnz(L+U), no partial pivoting12,223,891 8,532,531
    nnz(V) for QR, upper bound nnz(L) for LU5,340,099 6,306,789
    nnz(R) for QR, upper bound nnz(U) for LU10,693,425 11,979,822

    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.