• 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/sherman3
  • Description: U BLACK OIL, IMPES SIMULATION, 35 BY 11 BY 13 GRID, ONE UNK
  • download as a MATLAB mat-file, file size: 179 KB. Use SJget(336) or SJget('HB/sherman3') in MATLAB.
  • download in Matrix Market format, file size: 136 KB.
  • download in Rutherford/Boeing format, file size: 124 KB.

    HB/sherman3

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

    HB/sherman3

    dmperm of HB/sherman3

    Matrix properties (click for a legend)  
    number of rows5,005
    number of columns5,005
    structural full rank?yes
    structural rank5,005
    numerical rank 2,898
    dimension of the numerical null space2,107
    numerical rank / min(size(A))0.57902
    Euclidean norm of A 6.7584e+006
    calculated singular value # 28981.3177
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    4.6613e-006
    calculated singular value # 28996.7127e-009
    gap in the singular values at the numerical rank:
    singular value # 2898 / singular value # 2899
    1.963e+008
    calculated condition number6.7101e+018
    condest6.8981e+016
    nonzeros20,033
    # of blocks from dmperm2,111
    # strongly connected comp.2,111
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetry 45%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorA. Sherman
    editorI. Duff, R. Grimes, J. Lewis
    date1984
    kindcomputational fluid dynamics problem
    2D/3D problem?yes
    SJid336
    UFid244

    Additional fieldssize and type
    bfull 5005-by-1

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))96,048 101,317 96,048
    Cholesky flop count7.5e+006 8.2e+006 7.5e+006
    nnz(L+U), no partial pivoting187,091 197,629 187,091
    nnz(V) for QR, upper bound nnz(L) for LU190,653 190,440 195,368
    nnz(R) for QR, upper bound nnz(U) for LU340,378 351,863 359,042

    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.