• 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/ncvxqp9
  • Description: Gould, Hu, & Scott: KKT matrix - nonconvex QP (CUTEr)
  • download as a MATLAB mat-file, file size: 210 KB. Use SJget(398) or SJget('GHS_indef/ncvxqp9') in MATLAB.
  • download in Matrix Market format, file size: 203 KB.
  • download in Rutherford/Boeing format, file size: 200 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, used with Matlab (R2008a) to calculate singular values 14615 to 14620 and associated error bounds.


    dmperm of GHS_indef/ncvxqp9

    scc of GHS_indef/ncvxqp9

    Matrix properties (click for a legend)  
    number of rows16,554
    number of columns16,554
    structural full rank?yes
    structural rank16,554
    numerical rank 14,617
    dimension of the numerical null space1,937
    numerical rank / min(size(A))0.88299
    Euclidean norm of A 1.2705e+011
    calculated singular value # 146170.25269
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 146180.25226
    gap in the singular values at the numerical rank:
    singular value # 14617 / singular value # 14618
    calculated condition number-2
    # of blocks from dmperm555
    # strongly connected comp.555
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?no

    authorN. Gould
    editorN. Gould
    kindoptimization problem
    2D/3D problem?no

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))142,666 134,665 384,442
    Cholesky flop count1.0e+007 5.9e+006 4.0e+007
    nnz(L+U), no partial pivoting268,778 252,776 752,330
    nnz(V) for QR, upper bound nnz(L) for LU360,371 328,079 315,723
    nnz(R) for QR, upper bound nnz(U) for LU680,921 695,753 673,342

    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.