• 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_8
  • Description: Differentials of the Voronoi complex of perfect forms
  • download as a MATLAB mat-file, file size: 44 KB. Use SJget(630) or SJget('JGD_SL6/D_8') in MATLAB.
  • download in Matrix Market format, file size: 49 KB.
  • download in Rutherford/Boeing format, file size: 37 KB.

    JGD_SL6/D_8

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

    JGD_SL6/D_8

    dmperm of JGD_SL6/D_8

    scc of JGD_SL6/D_8

    Matrix properties (click for a legend)  
    number of rows1,132
    number of columns1,271
    structural full rank?no
    structural rank1,126
    numerical rank 641
    dimension of the numerical null space630
    numerical rank / min(size(A))0.56625
    Euclidean norm of A 22.465
    calculated singular value # 6412.448
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    4.5155e-012
    calculated singular value # 6424.2093e-014
    gap in the singular values at the numerical rank:
    singular value # 641 / singular value # 642
    5.8156e+013
    calculated condition number3.1467e+031
    condest-2
    nonzeros14,966
    # of blocks from dmperm3
    # strongly connected comp.12
    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
    SJid630
    UFid2,190

    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_8.sms                                  
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU565,487 528,963
    nnz(R) for QR, upper bound nnz(U) for LU512,491 526,198

    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.