• SJSU Singular Matrix Database
  • Matrix group: JGD_G5
  • Click here for a description of the JGD_G5 group.
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  • Matrix: JGD_G5/IG5-13
  • Description: Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery.
  • download as a MATLAB mat-file, file size: 197 KB. Use SJget(670) or SJget('JGD_G5/IG5-13') in MATLAB.
  • download in Matrix Market format, file size: 242 KB.
  • download in Rutherford/Boeing format, file size: 171 KB.

    JGD_G5/IG5-13

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

    JGD_G5/IG5-13

    dmperm of JGD_G5/IG5-13

    scc of JGD_G5/IG5-13

    Matrix properties (click for a legend)  
    number of rows3,994
    number of columns4,731
    structural full rank?no
    structural rank2,532
    numerical rank 2,532
    dimension of the numerical null space2,199
    numerical rank / min(size(A))0.63395
    Euclidean norm of A 99.755
    calculated singular value # 25320.035171
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    6.7232e-011
    calculated singular value # 25332.4578e-014
    gap in the singular values at the numerical rank:
    singular value # 2532 / singular value # 2533
    1.431e+012
    calculated condition number7.0049e+017
    condest-2
    nonzeros91,209
    # of blocks from dmperm3
    # strongly connected comp.2,200
    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
    SJid670
    UFid1,972

    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/IG5-13.txt2                                     
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU1,535,290 1,227,575
    nnz(R) for QR, upper bound nnz(U) for LU6,529,567 6,514,449

    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.