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  • Matrix group: Schenk_IBMSDS
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  • Matrix: Schenk_IBMSDS/2D_27628_bjtcai
  • Description: Olaf Schenk, Univ. Basel: IBM TJ Watson, Yorktown, semiconductor device
  • download as a MATLAB mat-file, file size: 2 MB. Use SJget(479) or SJget('Schenk_IBMSDS/2D_27628_bjtcai') in MATLAB.
  • download in Matrix Market format, file size: 2 MB.
  • download in Rutherford/Boeing format, file size: 2 MB.

    Schenk_IBMSDS/2D_27628_bjtcai

    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 18440 to 18445 and associated error bounds.

    Schenk_IBMSDS/2D_27628_bjtcai

    dmperm of Schenk_IBMSDS/2D_27628_bjtcai

    Matrix properties (click for a legend)  
    number of rows27,628
    number of columns27,628
    structural full rank?yes
    structural rank27,628
    numerical rank 18,442
    dimension of the numerical null space9,186
    numerical rank / min(size(A))0.66751
    Euclidean norm of A 4.7256e+005
    calculated singular value # 184420.00067736
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.6082e-006
    calculated singular value # 184433.8813e-010
    gap in the singular values at the numerical rank:
    singular value # 18442 / singular value # 18443
    1.7452e+006
    calculated condition number-2
    condest6.4611e+019
    nonzeros206,670
    # of blocks from dmperm6,361
    # strongly connected comp.6,361
    entries not in dmperm blocks272
    explicit zero entries236,228
    nonzero pattern symmetry 100%
    numeric value symmetry 22%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorIBM
    editorO. Schenk
    date2003
    kindsemiconductor device problem
    2D/3D problem?yes
    SJid479
    UFid954

    Additional fieldssize and type
    bfull 27628-by-1

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))1,306,054 993,292 1,000,926
    Cholesky flop count1.9e+008 1.0e+008 9.8e+007
    nnz(L+U), no partial pivoting2,584,480 1,958,956 1,974,496
    nnz(V) for QR, upper bound nnz(L) for LU1,655,386 1,549,878 1,646,257
    nnz(R) for QR, upper bound nnz(U) for LU3,115,120 2,957,621 3,128,439

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 236228 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.