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


  • Matrix: HB/zenios
  • Description: S AIR-TRAFFIC CONTROL MODEL BY STAVROS A. ZENIOS
  • download as a MATLAB mat-file, file size: 46 KB. Use SJget(228) or SJget('HB/zenios') in MATLAB.
  • download in Matrix Market format, file size: 49 KB.
  • download in Rutherford/Boeing format, file size: 33 KB.

    HB/zenios

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

    HB/zenios

    dmperm of HB/zenios

    scc of HB/zenios

    Matrix properties (click for a legend)  
    number of rows2,873
    number of columns2,873
    structural full rank?no
    structural rank266
    numerical rank 265
    dimension of the numerical null space2,608
    numerical rank / min(size(A))0.092238
    Euclidean norm of A 3.3379
    calculated singular value # 2657.0905e-012
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.2759e-012
    calculated singular value # 2661.3375e-015
    gap in the singular values at the numerical rank:
    singular value # 265 / singular value # 266
    5301.5
    calculated condition numberInf
    condestInf
    nonzeros1,314
    # of blocks from dmperm84
    # strongly connected comp.2,650
    explicit zero entries25,877
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typereal
    structuresymmetric
    Cholesky candidate?yes
    positive definite?no

    authorS. Zenios
    editorI. Duff, R. Grimes, J. Lewis
    date1985
    kindoptimization problem
    2D/3D problem?no
    SJid228
    UFid282

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))3,546 3,559
    Cholesky flop count7.3e+003 7.4e+003
    nnz(L+U), no partial pivoting4,219 4,245
    nnz(V) for QR, upper bound nnz(L) for LU3,507 3,547
    nnz(R) for QR, upper bound nnz(U) for LU3,862 3,833

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 25877 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.