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

  • Matrix: Goodwin/rim
  • Description: FEM, fluid mechanics problem. From Ralph Goodwin, Univ. Illinois
  • download as a MATLAB mat-file, file size: 8 MB. Use SJget(497) or SJget('Goodwin/rim') in MATLAB.
  • download in Matrix Market format, file size: 12 MB.
  • download in Rutherford/Boeing format, file size: 10 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, used with Matlab (R2008a) to calculate singular values 22477 to 22482 and associated error bounds.


    dmperm of Goodwin/rim

    scc of Goodwin/rim

    Matrix properties (click for a legend)  
    number of rows22,560
    number of columns22,560
    structural full rank?yes
    structural rank22,560
    numerical rank 22,479
    dimension of the numerical null space81
    numerical rank / min(size(A))0.99641
    Euclidean norm of A 82346
    calculated singular value # 224793.2913e-007
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 224803.2695e-007
    gap in the singular values at the numerical rank:
    singular value # 22479 / singular value # 22480
    calculated condition number-2
    # of blocks from dmperm2
    # strongly connected comp.2
    entries not in dmperm blocks12
    explicit zero entries0
    nonzero pattern symmetry 64%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorR. Goodwin
    editorT. Davis
    kindcomputational fluid dynamics problem
    2D/3D problem?yes

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))1,927,907 1,730,524 3,576,250
    Cholesky flop count2.6e+008 1.8e+008 7.4e+008
    nnz(L+U), no partial pivoting3,833,254 3,438,488 7,129,952
    nnz(V) for QR, upper bound nnz(L) for LU4,940,213 3,350,250 2,997,226
    nnz(R) for QR, upper bound nnz(U) for LU16,753,049 9,521,901 8,973,829

    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.