• 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-41
  • Description: IBM TJ Watson, non-linear optimization
  • download as a MATLAB mat-file, file size: 692 KB. Use SJget(413) or SJget('Schenk_IBMNA/c-41') in MATLAB.
  • download in Matrix Market format, file size: 516 KB.
  • download in Rutherford/Boeing format, file size: 475 KB.

    Schenk_IBMNA/c-41

    Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

    Schenk_IBMNA/c-41

    dmperm of Schenk_IBMNA/c-41

    Matrix properties (click for a legend)  
    number of rows9,769
    number of columns9,769
    structural full rank?yes
    structural rank9,769
    numerical rank 9,705
    dimension of the numerical null space64
    numerical rank / min(size(A))0.99345
    Euclidean norm of A 47782
    calculated singular value # 97058.3276e-008
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    7.1079e-008
    calculated singular value # 97063.2613e-008
    gap in the singular values at the numerical rank:
    singular value # 9705 / singular value # 9706
    2.5534
    calculated condition number4.7782e+012
    condest4.9514e+012
    nonzeros101,635
    # of blocks from dmperm8
    # strongly connected comp.8
    entries not in dmperm blocks21
    explicit zero entries110
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typereal
    structuresymmetric
    Cholesky candidate?no
    positive definite?no

    authorIBM
    editorO. Schenk
    date2006
    kindoptimization problem
    2D/3D problem?no
    SJid413
    UFid1,560

    Additional fieldssize and type
    bfull 9769-by-1

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))153,504 167,079 153,490
    Cholesky flop count1.0e+007 1.1e+007 1.0e+007
    nnz(L+U), no partial pivoting297,239 324,389 297,232
    nnz(V) for QR, upper bound nnz(L) for LU1,630,571 1,611,386 1,618,484
    nnz(R) for QR, upper bound nnz(U) for LU2,709,653 2,927,174 2,923,786

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 110 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.