• 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_7
  • Description: Differentials of the Voronoi complex of perfect forms
  • download as a MATLAB mat-file, file size: 38 KB. Use SJget(626) or SJget('JGD_SL6/D_7') in MATLAB.
  • download in Matrix Market format, file size: 42 KB.
  • download in Rutherford/Boeing format, file size: 32 KB.

    JGD_SL6/D_7

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

    JGD_SL6/D_7

    dmperm of JGD_SL6/D_7

    scc of JGD_SL6/D_7

    Matrix properties (click for a legend)  
    number of rows1,270
    number of columns971
    structural full rank?no
    structural rank968
    numerical rank 629
    dimension of the numerical null space342
    numerical rank / min(size(A))0.64779
    Euclidean norm of A 58.523
    calculated singular value # 6290.42588
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    9.0239e-012
    calculated singular value # 6301.8609e-014
    gap in the singular values at the numerical rank:
    singular value # 629 / singular value # 630
    2.2885e+013
    calculated condition numberInf
    condest-2
    nonzeros12,714
    # of blocks from dmperm2
    # strongly connected comp.3
    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
    SJid626
    UFid2,189

    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_7.sms                                  
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU544,966 505,258
    nnz(R) for QR, upper bound nnz(U) for LU370,337 384,487

    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.