• 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/cyl6
  • Description: Cylindrical shell, non-linear analysis, 3 RHS vectors at step 6. R Kouhia
  • download as a MATLAB mat-file, file size: 416 KB. Use SJget(694) or SJget('TKK/cyl6') in MATLAB.
  • download in Matrix Market format, file size: 1 MB.
  • download in Rutherford/Boeing format, file size: 564 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 2241 to 2246 and associated error bounds.


    Matrix properties (click for a legend)  
    number of rows13,681
    number of columns13,681
    structural full rank?yes
    structural rank13,681
    numerical rank 2,243
    dimension of the numerical null space11,438
    numerical rank / min(size(A))0.16395
    Euclidean norm of A 321.97
    calculated singular value # 22430.29575
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 22448.4752e-015
    gap in the singular values at the numerical rank:
    singular value # 2243 / singular value # 2244
    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

    Additional fieldssize and type
    bfull 13681-by-3


    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'))1,617,535 1,787,005
    Cholesky flop count2.7e+008 3.3e+008
    nnz(L+U), no partial pivoting3,221,389 3,560,329
    nnz(V) for QR, upper bound nnz(L) for LU6,302,305 3,214,165
    nnz(R) for QR, upper bound nnz(U) for LU14,813,011 5,921,011

    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.