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

  • Matrix: Shyy/shyy161
  • Description: Wei Shyy, Univ. Florida. CFD/Navier-Stokes,viscous flow, fully coupled
  • download as a MATLAB mat-file, file size: 2 MB. Use SJget(438) or SJget('Shyy/shyy161') in MATLAB.
  • download in Matrix Market format, file size: 2 MB.
  • download in Rutherford/Boeing format, file size: 2 MB.


    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 with opts.tol_eigs = 1e-010, used with Matlab (R2008a) to calculate singular values 76430 to 76435 and associated error bounds.


    dmperm of Shyy/shyy161

    scc of Shyy/shyy161

    Matrix properties (click for a legend)  
    number of rows76,480
    number of columns76,480
    structural full rank?yes
    structural rank76,480
    numerical rank 76,432
    dimension of the numerical null space48
    numerical rank / min(size(A))0.99937
    Euclidean norm of A 62.798
    calculated singular value # 764321.0797e-009
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 764333.1056e-012
    gap in the singular values at the numerical rank:
    singular value # 76432 / singular value # 76433
    calculated condition number-2
    # of blocks from dmperm25,761
    # strongly connected comp.321
    entries not in dmperm blocks76,161
    explicit zero entries0
    nonzero pattern symmetry 73%
    numeric value symmetry 18%
    Cholesky candidate?no
    positive definite?no

    authorW. Shyy
    editorT. Davis
    kindcomputational fluid dynamics problem
    2D/3D problem?yes

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))2,371,970 2,232,764 1,062,100
    Cholesky flop count2.7e+008 2.5e+008 1.1e+008
    nnz(L+U), no partial pivoting4,667,460 4,389,048 2,123,881
    nnz(V) for QR, upper bound nnz(L) for LU3,357,830 2,957,745 1,654,111
    nnz(R) for QR, upper bound nnz(U) for LU6,259,276 5,572,965 3,096,274

    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.