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


  • Matrix: JGD_Homology/D6-6
  • Description: Simplicial complexes from Homology from Volkmar Welker.
  • download as a MATLAB mat-file, file size: 675 KB. Use SJget(699) or SJget('JGD_Homology/D6-6') in MATLAB.
  • download in Matrix Market format, file size: 917 KB.
  • download in Rutherford/Boeing format, file size: 788 KB.

    JGD_Homology/D6-6

    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 7.6.0.324 (R2008a) to calculate the 6 largest singular values and associated error bounds.
    Routine spnrank, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 14407 to 14412 and associated error bounds.

    JGD_Homology/D6-6

    dmperm of JGD_Homology/D6-6

    scc of JGD_Homology/D6-6

    Matrix properties (click for a legend)  
    number of rows120,576
    number of columns23,740
    structural full rank?no
    structural rank18,660
    numerical rank 14,409
    dimension of the numerical null space9,331
    numerical rank / min(size(A))0.60695
    Euclidean norm of A 5.4772
    calculated singular value # 144090.91233
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.0709e-010
    calculated singular value # 144109.7861e-016
    gap in the singular values at the numerical rank:
    singular value # 14409 / singular value # 14410
    9.3227e+014
    calculated condition number-2
    condest-2
    nonzeros146,520
    # of blocks from dmperm2
    # strongly connected comp.75,727
    explicit zero entries360
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typeinteger
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorV. Welker
    editorJ.-G. Dumas
    date2008
    kindcombinatorial problem
    2D/3D problem?no
    SJid699
    UFid2,052

    Additional fieldssize and type
    Tfull 147240-by-3

    Notes:

    Simplicial complexes from Homology from Volkmar Welker.     
    From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,
    http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html   
                                                                
    http://www.mathematik.uni-marburg.de/~welker/               
                                                                
    Filename in JGD collection: Homology/D6-6.sms               
    The original file contains 720 duplicate entries,           
    and is the only file in the JGD collection with             
    duplicates.  The original triplets can be found             
    in Problem.aux.T, where the kth triplet is row k            
    of T: row index T(k,1), column index T(k,2), value T(k,3),  
    so that A = spconvert (Problem.aux.T)                       
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU1,478,161 1,501,913
    nnz(R) for QR, upper bound nnz(U) for LU440,884 460,417

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 360 explicit zero entries.

    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.