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

  • Matrix: Graham/graham1
  • Description: Galerkin FE disc. of Nav.Stokes 2phase fluid flow. D Graham, U Illinois
  • download as a MATLAB mat-file, file size: 3 MB. Use SJget(450) or SJget('Graham/graham1') in MATLAB.
  • download in Matrix Market format, file size: 4 MB.
  • download in Rutherford/Boeing format, file size: 3 MB.


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


    dmperm of Graham/graham1

    scc of Graham/graham1

    Matrix properties (click for a legend)  
    number of rows9,035
    number of columns9,035
    structural full rank?yes
    structural rank9,035
    numerical rank 8,924
    dimension of the numerical null space111
    numerical rank / min(size(A))0.98771
    Euclidean norm of A 82013
    calculated singular value # 89241.3189e-007
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 89251.2991e-007
    gap in the singular values at the numerical rank:
    singular value # 8924 / singular value # 8925
    calculated condition number1.2155e+014
    # of blocks from dmperm478
    # strongly connected comp.474
    entries not in dmperm blocks25,829
    explicit zero entries32
    nonzero pattern symmetry 72%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorD. Graham
    editorT. Davis
    kindcomputational fluid dynamics problem
    2D/3D problem?yes

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))602,647 653,632 1,232,080
    Cholesky flop count7.0e+007 7.4e+007 2.7e+008
    nnz(L+U), no partial pivoting1,196,259 1,298,229 2,480,954
    nnz(V) for QR, upper bound nnz(L) for LU1,689,616 1,342,042 1,251,139
    nnz(R) for QR, upper bound nnz(U) for LU5,071,066 4,055,430 3,710,633

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 32 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.