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

  • Matrix: TKK/tube1
  • Description: Tube problem from R. Kouhia
  • download as a MATLAB mat-file, file size: 255 KB. Use SJget(697) or SJget('TKK/tube1') in MATLAB.
  • download in Matrix Market format, file size: 854 KB.
  • download in Rutherford/Boeing format, file size: 327 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 3581 to 3586 and associated error bounds.


    Matrix properties (click for a legend)  
    number of rows21,498
    number of columns21,498
    structural full rank?yes
    structural rank21,498
    numerical rank 3,583
    dimension of the numerical null space17,915
    numerical rank / min(size(A))0.16667
    Euclidean norm of A 43.257
    calculated singular value # 35830.0027604
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 35841.337e-012
    gap in the singular values at the numerical rank:
    singular value # 3583 / singular value # 3584
    calculated condition number-2
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?unknown

    authorR. Kouhia
    editorT. Davis
    kindstructural problem
    2D/3D problem?yes


    Matrix problems from Reijo Kouhia, Structural Mechanics, Helsinki  
    University of Technology.   http://users.tkk.fi/~kouhia/sparse.html

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))2,258,376 2,375,329
    Cholesky flop count4.7e+008 4.5e+008
    nnz(L+U), no partial pivoting4,495,254 4,729,160
    nnz(V) for QR, upper bound nnz(L) for LU6,666,632 3,487,803
    nnz(R) for QR, upper bound nnz(U) for LU12,131,864 6,675,094

    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.