Matrix: JGD_G5/IG5-12

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

JGD_G5/IG5-12 graph
(bipartite graph drawing)

JGD_G5/IG5-12 dmperm of JGD_G5/IG5-12
scc of JGD_G5/IG5-12

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  • Matrix group: JGD_G5
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  • download as a MATLAB mat-file, file size: 85 KB. Use UFget(1971) or UFget('JGD_G5/IG5-12') in MATLAB.
  • download in Matrix Market format, file size: 121 KB.
  • download in Rutherford/Boeing format, file size: 86 KB.

    Matrix properties
    number of rows2,296
    number of columns2,875
    structural full rank?no
    structural rank1,578
    # of blocks from dmperm2
    # strongly connected comp.1,298
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

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


    Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery.
    Univ. Paris Sud.                                                               
    From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,                                    
    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                  
    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/IG5-12.txt2                                     

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD617,218
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD2,133,365

    SVD-based statistics:
    null space dimension718
    full numerical rank?no
    singular value gap2.49996e+12

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

    JGD_G5/IG5-12 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.