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

  • Matrix: GHS_indef/c-68
  • Description: Schenk: IBM TJ Watson, Yorktown, nonlinear optimization
  • download as a MATLAB mat-file, file size: 3 MB. Use SJget(514) or SJget('GHS_indef/c-68') in MATLAB.
  • download in Matrix Market format, file size: 2 MB.
  • download in Rutherford/Boeing format, file size: 2 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, used with Matlab (R2008a) to calculate singular values 64799 to 64804 and associated error bounds.


    dmperm of GHS_indef/c-68

    Matrix properties (click for a legend)  
    number of rows64,810
    number of columns64,810
    structural full rank?yes
    structural rank64,810
    numerical rank 64,801
    dimension of the numerical null space9
    numerical rank / min(size(A))0.99986
    Euclidean norm of A 4.1067e+008
    calculated singular value # 648010.0039293
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 648020.0036578
    gap in the singular values at the numerical rank:
    singular value # 64801 / singular value # 64802
    calculated condition number-2
    # of blocks from dmperm6
    # strongly connected comp.6
    entries not in dmperm blocks15
    explicit zero entries10
    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 64810-by-1


    Revised Nov 2006; relative eps changes to A, right-hand-side added.
    Note that this matrix should have been placed in the Schenk_IBMNA/ 
    directory when it was first added in August 2004, but moving it now
    would disrupt exising users of the collection.                     

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))6,523,400 5,247,637 5,522,952
    Cholesky flop count1.2e+010 5.1e+009 5.7e+009
    nnz(L+U), no partial pivoting12,981,990 10,430,464 10,981,109
    nnz(V) for QR, upper bound nnz(L) for LU70,689,995 34,052,057 33,801,713
    nnz(R) for QR, upper bound nnz(U) for LU115,405,123 70,190,882 69,487,093

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 10 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.