• SJSU Singular Matrix Database
  • Matrix group: Schenk_IBMSDS
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  • Matrix: Schenk_IBMSDS/3D_28984_Tetra
  • Description: Olaf Schenk, Univ. Basel: IBM TJ Watson, Yorktown, semiconductor device
  • download as a MATLAB mat-file, file size: 3 MB. Use SJget(517) or SJget('Schenk_IBMSDS/3D_28984_Tetra') in MATLAB.
  • download in Matrix Market format, file size: 3 MB.
  • download in Rutherford/Boeing format, file size: 3 MB.

    Schenk_IBMSDS/3D_28984_Tetra

    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-008, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 844 to 849 and associated error bounds.

    Schenk_IBMSDS/3D_28984_Tetra

    dmperm of Schenk_IBMSDS/3D_28984_Tetra

    Matrix properties (click for a legend)  
    number of rows28,984
    number of columns28,984
    structural full rank?yes
    structural rank28,984
    numerical rank 846
    dimension of the numerical null space28,138
    numerical rank / min(size(A))0.029189
    Euclidean norm of A 1.3523e+021
    calculated singular value # 8465.4744e+012
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    7.598e+009
    calculated singular value # 847182.24
    gap in the singular values at the numerical rank:
    singular value # 846 / singular value # 847
    3.0039e+010
    calculated condition number-2
    condest2.6176e+042
    nonzeros285,092
    # of blocks from dmperm5,439
    # strongly connected comp.5,439
    entries not in dmperm blocks1,548
    explicit zero entries314,078
    nonzero pattern symmetry 99%
    numeric value symmetry 36%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorIBM
    editorO. Schenk
    date2003
    kindsemiconductor device problem
    2D/3D problem?yes
    SJid517
    UFid956

    Additional fieldssize and type
    bfull 28984-by-1

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))6,646,202 4,128,442 4,317,757
    Cholesky flop count4.0e+009 1.8e+009 2.0e+009
    nnz(L+U), no partial pivoting13,263,420 8,227,900 8,608,078
    nnz(V) for QR, upper bound nnz(L) for LU8,104,405 7,059,175 7,173,130
    nnz(R) for QR, upper bound nnz(U) for LU15,049,119 13,240,927 13,418,309

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 314078 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.