Matrix: JGD_G5/IG5-14

Description: Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery.

JGD_G5/IG5-14 graph
(bipartite graph drawing)


JGD_G5/IG5-14 dmperm of JGD_G5/IG5-14
scc of JGD_G5/IG5-14

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  • Matrix group: JGD_G5
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  • download as a MATLAB mat-file, file size: 323 KB. Use UFget(1973) or UFget('JGD_G5/IG5-14') in MATLAB.
  • download in Matrix Market format, file size: 460 KB.
  • download in Rutherford/Boeing format, file size: 333 KB.

    Matrix properties
    number of rows6,735
    number of columns7,621
    nonzeros173,337
    structural full rank?no
    structural rank3,906
    # of blocks from dmperm11
    # strongly connected comp.3,716
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typeinteger
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorN. Thiery
    editorJ.-G. Dumas
    date2008
    kindcombinatorial problem
    2D/3D problem?no

    Notes:

    Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery.
    Univ. Paris Sud.                                                               
                                                                                   
    From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,                   
    http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html                      
                                                                                   
    http://www.lapcs.univ-lyon1.fr/~nthiery/LinearAlgebra/                         
                                                                                   
    Linear Algebra for combinatorics                                               
                                                                                   
    Abstract:  Computations in algebraic combinatorics often boils down to         
    sparse linear algebra over some exact field. Such computations are             
    usually done in high level computer algebra systems like MuPAD or              
    Maple, which are reasonnably efficient when the ground field requires          
    symbolic computations. However, when the ground field is, say Q  or            
    Z/pZ, the use of external specialized libraries becomes necessary. This        
    document, geared toward developpers of such libraries, present a brief         
    overview of my needs, which seems to be fairly typical in the                  
    community.                                                                     
                                                                                   
    IG5-6: 30 x 77 : rang = 30  (Iteratif: 0.01 s, Gauss: 0.01 s)                  
    IG5-7: 62 x 150 : rang = 62  (Iteratif: 0.02 s, Gauss: 0.01 s)                 
    IG5-8: 156 x 292 : rang = 154  (Iteratif: 0.08 s, Gauss: 0.01 s)               
    IG5-9: 342 x 540 : rang = 308  (Iteratif: 0.46 s, Gauss: 0.02 s)               
    IG5-10: 652 x 976 : rang = 527  (Iteratif: 2.1 s, Gauss: 0.07 s)               
    IG5-11: 1227 x 1692 : rang = 902  (Iteratif: 7.5 s, Gauss: 0.22 s)             
    IG5-12: 2296 x 2875 : rang = 1578  (Iteratif: 26 s, Gauss: 0.93 s)             
    IG5-13: 3994 x 4731 : rang = 2532  (Iteratif: 80 s, Gauss: 3.35 s)             
    IG5-14: 6727 x 7621 : rang = 3906  (Iteratif: 244 s, Gauss: 10.06 s)           
    IG5-15: 11358 x 11987 : rang = 6146  (Iteratif: s, Gauss: 29.74 s)             
    IG5-16: 18485 x 18829 : rang = 9519  (Iteratif: s, Gauss: 621.97 s)            
    IG5-17: 27944 x 30131 : rang = 14060  (Iteratif: s, Gauss: 1973.8 s)           
                                                                                   
    Filename in JGD collection: G5/IG5-14.txt2                                     
    

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD3,795,130
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD19,020,772

    SVD-based statistics:
    norm(A)124.426
    min(svd(A))1.8723e-17
    cond(A)6.6456e+18
    rank(A)3,906
    sprank(A)-rank(A)0
    null space dimension2,829
    full numerical rank?no
    singular value gap1.16889e+12

    singular values (MAT file):click here
    SVD method used:s = svd (full (A)) ;
    status:ok

    JGD_G5/IG5-14 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.