• SJSU Singular Matrix Database
  • Matrix group: JGD_SL6
  • Click here for a description of the JGD_SL6 group.
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  • Matrix: JGD_SL6/D_6
  • Description: Differentials of the Voronoi complex of perfect forms
  • download as a MATLAB mat-file, file size: 20 KB. Use SJget(611) or SJget('JGD_SL6/D_6') in MATLAB.
  • download in Matrix Market format, file size: 21 KB.
  • download in Rutherford/Boeing format, file size: 16 KB.

    JGD_SL6/D_6

    Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

    JGD_SL6/D_6

    dmperm of JGD_SL6/D_6

    scc of JGD_SL6/D_6

    Matrix properties (click for a legend)  
    number of rows970
    number of columns435
    structural full rank?no
    structural rank433
    numerical rank 339
    dimension of the numerical null space96
    numerical rank / min(size(A))0.77931
    Euclidean norm of A 65.992
    calculated singular value # 3391.9308
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.3785e-011
    calculated singular value # 3408.1573e-015
    gap in the singular values at the numerical rank:
    singular value # 339 / singular value # 340
    2.367e+014
    calculated condition numberInf
    condest-2
    nonzeros6,491
    # of blocks from dmperm2
    # strongly connected comp.6
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typeinteger
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorP. Elbaz-Vincent
    editorJ.-G. Dumas
    date2008
    kindcombinatorial problem
    2D/3D problem?no
    SJid611
    UFid2,188

    Notes:

    Differentials of the Voronoi complex of perfect forms                    
    from Philippe Elbaz-Vincent, Institut Fourier, Grenoble, France.         
                                                                             
    From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,             
    http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html                
                                                                             
    http://www-fourier.ujf-grenoble.fr/-Informations-personnelles-.html?P=pev
                                                                             
    D_5  Smith Invariants = [ 1:92 3:2 18:1 ]                                
    D_6  Smith Invariants = [ 1:338 2:1 ]                                    
    D_7  Smith Invariants = [ 1:621 2:5 6:1 60:2 ]                           
    D_8  Smith Invariants = [ 1:637 3:3 12:1 ]                               
    D_9  Smith Invariants = [ 1:491 ]                                        
    D_10 Smith Invariants = [ 1:318 2:3 4:2 ]                                
    D_11 Smith Invariants = [ 1:129 2:6 6:1 ]                                
                                                                             
    Filename in JGD collection: SL6/D_6.sms                                  
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU225,116 204,929
    nnz(R) for QR, upper bound nnz(U) for LU69,344 71,333

    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.