• 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/stokes64
  • Description: Gould, Hu, & Scott: Stokes equation, from Mario Arioli
  • download as a MATLAB mat-file, file size: 287 KB. Use SJget(443) or SJget('GHS_indef/stokes64') in MATLAB.
  • download in Matrix Market format, file size: 340 KB.
  • download in Rutherford/Boeing format, file size: 228 KB.

    GHS_indef/stokes64

    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 7.6.0.324 (R2008a) to calculate the 6 largest singular values and associated error bounds.
    Routine spnrank, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 12542 to 12546 and associated error bounds.

    GHS_indef/stokes64

    Matrix properties (click for a legend)  
    number of rows12,546
    number of columns12,546
    structural full rank?yes
    structural rank12,546
    numerical rank 12,544
    dimension of the numerical null space2
    numerical rank / min(size(A))0.99984
    Euclidean norm of A 3.9978
    calculated singular value # 125441.7624e-006
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    5.5715e-012
    calculated singular value # 125456.4234e-014
    gap in the singular values at the numerical rank:
    singular value # 12544 / singular value # 12545
    2.7437e+007
    calculated condition number3.2369e+014
    condest2.8044e+016
    nonzeros140,034
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typereal
    structuresymmetric
    Cholesky candidate?yes
    positive definite?no

    authorM. Arioli
    editorN. Gould, Y. Hu, J. Scott
    date2004
    kindcomputational fluid dynamics problem
    2D/3D problem?yes
    SJid443
    UFid1,247

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))487,299 496,730
    Cholesky flop count4.3e+007 4.0e+007
    nnz(L+U), no partial pivoting962,052 980,914
    nnz(V) for QR, upper bound nnz(L) for LU1,046,650 965,696
    nnz(R) for QR, upper bound nnz(U) for LU2,348,996 2,185,536

    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.