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

  • Matrix: Rothberg/struct3
  • Description: Finite element matrix, from Ed Rothberg, Silicon Graphics, Inc.
  • download as a MATLAB mat-file, file size: 753 KB. Use SJget(510) or SJget('Rothberg/struct3') in MATLAB.
  • download in Matrix Market format, file size: 1 MB.
  • download in Rutherford/Boeing format, file size: 643 KB.


    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 41591 to 41596 and associated error bounds.


    dmperm of Rothberg/struct3

    Matrix properties (click for a legend)  
    number of rows53,570
    number of columns53,570
    structural full rank?yes
    structural rank53,570
    numerical rank 41,593
    dimension of the numerical null space11,977
    numerical rank / min(size(A))0.77642
    Euclidean norm of A 26.147
    calculated singular value # 415933.6237e-006
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 415944.4303e-013
    gap in the singular values at the numerical rank:
    singular value # 41593 / singular value # 41594
    calculated condition number-2
    # of blocks from dmperm2
    # strongly connected comp.2
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?no

    authorE. Rothberg
    editorT. Davis
    kindstructural problem
    2D/3D problem?yes

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))4,945,868 4,600,416 4,488,562
    Cholesky flop count1.0e+009 7.9e+008 7.0e+008
    nnz(L+U), no partial pivoting9,838,166 9,147,262 8,923,554
    nnz(V) for QR, upper bound nnz(L) for LU9,586,863 6,964,487 6,806,585
    nnz(R) for QR, upper bound nnz(U) for LU18,314,276 13,182,923 12,885,627

    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.