• SJSU Singular Matrix Database
  • Matrix group: VanVelzen
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  • Matrix: VanVelzen/std1_Jac2_db
  • Description: Chemical process simulation, Nils van Velzen (diagonal blocks only)
  • download as a MATLAB mat-file, file size: 3 MB. Use SJget(433) or SJget('VanVelzen/std1_Jac2_db') in MATLAB.
  • download in Matrix Market format, file size: 5 MB.
  • download in Rutherford/Boeing format, file size: 4 MB.

    VanVelzen/std1_Jac2_db

    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-010, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 8938 to 8943 and associated error bounds.

    VanVelzen/std1_Jac2_db

    dmperm of VanVelzen/std1_Jac2_db

    Matrix properties (click for a legend)  
    number of rows21,982
    number of columns21,982
    structural full rank?yes
    structural rank21,982
    numerical rank 8,940
    dimension of the numerical null space13,042
    numerical rank / min(size(A))0.4067
    Euclidean norm of A 4.4592e+011
    calculated singular value # 89401.3424
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.3417
    calculated singular value # 89411.3355
    gap in the singular values at the numerical rank:
    singular value # 8940 / singular value # 8941
    1.0052
    calculated condition number-2
    condest3.3622e+022
    nonzeros498,771
    # of blocks from dmperm11,091
    # strongly connected comp.11,091
    entries not in dmperm blocks1,428
    explicit zero entries0
    nonzero pattern symmetry 33%
    numeric value symmetry 0%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorN. van Velzen
    editorT. Davis
    date2006
    kindchemical process simulation problem
    2D/3D problem?no
    SJid433
    UFid1,333

    Additional fieldssize and type
    bfull 21982-by-1

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))2,315,950 2,012,803 1,941,211
    Cholesky flop count1.3e+009 7.8e+008 7.7e+008
    nnz(L+U), no partial pivoting4,609,918 4,003,624 3,861,868
    nnz(V) for QR, upper bound nnz(L) for LU1,484,010 1,728,653 1,476,390
    nnz(R) for QR, upper bound nnz(U) for LU2,995,888 3,197,474 2,649,897

    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.