• 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_9
  • Description: Differentials of the Voronoi complex of perfect forms
  • download as a MATLAB mat-file, file size: 35 KB. Use SJget(622) or SJget('JGD_SL6/D_9') in MATLAB.
  • download in Matrix Market format, file size: 40 KB.
  • download in Rutherford/Boeing format, file size: 29 KB.


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


    dmperm of JGD_SL6/D_9

    scc of JGD_SL6/D_9

    Matrix properties (click for a legend)  
    number of rows815
    number of columns1,133
    structural full rank?no
    structural rank810
    numerical rank 491
    dimension of the numerical null space642
    numerical rank / min(size(A))0.60245
    Euclidean norm of A 30.376
    calculated singular value # 4911.2402
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 4921.4372e-014
    gap in the singular values at the numerical rank:
    singular value # 491 / singular value # 492
    calculated condition number1.2526e+031
    # of blocks from dmperm2
    # strongly connected comp.6
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorP. Elbaz-Vincent
    editorJ.-G. Dumas
    kindcombinatorial problem
    2D/3D problem?no


    Differentials of the Voronoi complex of perfect forms                    
    from Philippe Elbaz-Vincent, Institut Fourier, Grenoble, France.         
    From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,             
    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_9.sms                                  

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU401,180 398,874
    nnz(R) for QR, upper bound nnz(U) for LU253,301 259,640

    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.