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

  • Matrix: Schenk_IBMNA/c-52
  • Description: IBM TJ Watson, non-linear optimization
  • download as a MATLAB mat-file, file size: 1 MB. Use SJget(401) or SJget('Schenk_IBMNA/c-52') in MATLAB.
  • download in Matrix Market format, file size: 994 KB.
  • download in Rutherford/Boeing format, file size: 915 KB.


    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 7 to 12 and associated error bounds.


    dmperm of Schenk_IBMNA/c-52

    Matrix properties (click for a legend)  
    number of rows23,948
    number of columns23,948
    structural full rank?yes
    structural rank23,948
    numerical rank 9
    dimension of the numerical null space23,939
    numerical rank / min(size(A))0.00037581
    Euclidean norm of A 1.9435e+015
    calculated singular value # 96595.2
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 102874
    gap in the singular values at the numerical rank:
    singular value # 9 / singular value # 10
    calculated condition number-2
    # of blocks from dmperm5
    # strongly connected comp.5
    entries not in dmperm blocks12
    explicit zero entries8
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

    editorO. Schenk
    kindoptimization problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 23948-by-1

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))308,197 329,594 318,057
    Cholesky flop count2.1e+007 2.1e+007 1.8e+007
    nnz(L+U), no partial pivoting592,446 635,240 612,178
    nnz(V) for QR, upper bound nnz(L) for LU2,350,021 2,127,671 2,436,962
    nnz(R) for QR, upper bound nnz(U) for LU4,229,867 4,534,116 4,989,915

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 8 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.