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

  • Matrix: VanVelzen/Zd_Jac3_db
  • Description: Chemical process simulation, Nils van Velzen (diagonal blocks only)
  • download as a MATLAB mat-file, file size: 5 MB. Use SJget(498) or SJget('VanVelzen/Zd_Jac3_db') in MATLAB.
  • download in Matrix Market format, file size: 8 MB.
  • download in Rutherford/Boeing format, file size: 6 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-008, used with Matlab (R2008a) to calculate singular values 22372 to 22377 and associated error bounds.


    dmperm of VanVelzen/Zd_Jac3_db

    Matrix properties (click for a legend)  
    number of rows22,835
    number of columns22,835
    structural full rank?yes
    structural rank22,835
    numerical rank 22,374
    dimension of the numerical null space461
    numerical rank / min(size(A))0.97981
    Euclidean norm of A 1.1941e+009
    calculated singular value # 223740.0054812
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 223750.0051149
    gap in the singular values at the numerical rank:
    singular value # 22374 / singular value # 22375
    calculated condition number-2
    # of blocks from dmperm9,833
    # strongly connected comp.9,833
    entries not in dmperm blocks1,071
    explicit zero entries0
    nonzero pattern symmetry 33%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorN. van Velzen
    editorT. Davis
    kindchemical process simulation problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 22835-by-1

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))3,255,295 2,980,245 2,863,295
    Cholesky flop count1.9e+009 1.3e+009 1.2e+009
    nnz(L+U), no partial pivoting6,487,755 5,937,655 5,704,826
    nnz(V) for QR, upper bound nnz(L) for LU1,292,142 2,169,660 2,113,403
    nnz(R) for QR, upper bound nnz(U) for LU3,875,673 4,299,757 3,611,623

    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.