Matrix: JGD_GL7d/GL7d13

Description: Differentials of the Voronoi complex of perfect forms of rank 7 mod GL_7(Z)

JGD_GL7d/GL7d13 graph
(bipartite graph drawing)


JGD_GL7d/GL7d13 dmperm of JGD_GL7d/GL7d13
scc of JGD_GL7d/GL7d13

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  • Matrix group: JGD_GL7d
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  • download as a MATLAB mat-file, file size: 1 MB. Use UFget(1986) or UFget('JGD_GL7d/GL7d13') in MATLAB.
  • download in Matrix Market format, file size: 1 MB.
  • download in Rutherford/Boeing format, file size: 1 MB.

    Matrix properties
    number of rows47,271
    number of columns8,899
    nonzeros356,232
    structural full rank?no
    structural rank8,897
    # of blocks from dmperm4
    # strongly connected comp.51
    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

    Notes:

    Differentials of the Voronoi complex of perfect forms of rank 7 mod GL_7(Z)  
    equivalences, (related to the cohomology of GL_7(Z) and the K-theory of Z).  
    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    
                                                                                 
    mtx rank        n       m       ker         rank/min(n,m)   homology         
    10 1            60      1       59                                           
    11 59           1019    60      960         0,98333         0                
    12 960          8899    1019    7939        0,94210         1                
    13 7938         47271   8899    39333       0,89201         1                
    14 39332        171375  47271   132043      0,83205         0                
    15 132043       460261  171375  328218      0,77049         0                
    16 328218       955128  460261  626910      0,71311         0                
    17 626910       1548650 955128  921740      0,65636         0*               
    18 921740*      1955309 1548650 1033569*    0,60*           1/0*             
    19 103356(8/9)* 1911130 1955309 87756(2/1)* 0,54*           0/1*             
    20 877562       1437547 1911130 559985      0,61            0                
    21 559985       822922  1437547 262937      0,68048         0                
    22 262937       349443  822922  86506       0,75245         0                
    23 86505        105054  349443  18549       0,82343         1                
    24 18549        21074   105054  2525        0,88018         0                
    25 2525         2798    21074   273         0,90243         0                
    26 273          305     2798    32          0,89508         0                
                                                                                 
    file    size              elements  rank    SF                               
    GL7d10  1 x 60            8         1       1 (1)                            
    GL7d11  60 x 1019         1513      59      1 (59)                           
    GL7d12  1019 x 8899       37519     960     1 (958), 2 (2)                   
    GL7d13  8899 x 47271      356232    7938    1 (7937), 2 (1)                  
    GL7d14  47271 x 171375    1831183   39332   1 (39300),2 (29),4 (3)           
    GL7d15  171375 x 460261   6080381   132043  1 (131993), 2*??? (46), 6*??? (4)
    GL7d16  955128 x 460261   14488881  328218                                   
    GL7d17  1548650 x 955128  25978098                                           
    GL7d18  1955309 x 1548650 35590540                                           
    GL7d19  1911130 x 1955309 37322725                                           
    GL7d20  1437547 x 1911130 29893084  877562                                   
    GL7d21  822922 x 1437547  18174775  559985                                   
    GL7d22  349443 x 822922   8251000   262937                                   
    GL7d23  105054 x 349443   2695430   86505   1 (86488), 2*??? (12), 6*??? (5) 
    GL7d24  21074 x 105054    593892    18549   1 (18544),2 (4),4 (1)            
    GL7d25  21074 x 2798      81671     2525    1 (2507), 2 (18)                 
    GL7d26  2798 x 305        7412      273     1 (258), 2 (7), 6 (7), 36 (1)    
                                                                                 
    Filename in JGD collection: GL7d/GL7d13.sms                                  
    

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD311,455,722
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD33,885,664

    SVD-based statistics:
    norm(A)15.2321
    min(svd(A))0
    cond(A)Inf
    rank(A)7,938
    sprank(A)-rank(A)959
    null space dimension961
    full numerical rank?no
    singular value gap1.544e+13

    singular values (MAT file):click here
    SVD method used:s = svd (full (R)) ; where [~,R,E] = spqr (A) with droptol of zero
    status:ok

    JGD_GL7d/GL7d13 svd

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.