• 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/IG5-8
  • Description: Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery.
  • download as a MATLAB mat-file, file size: 6 KB. Use SJget(587) or SJget('JGD_G5/IG5-8') in MATLAB.
  • download in Matrix Market format, file size: 6 KB.
  • download in Rutherford/Boeing format, file size: 4 KB.

    JGD_G5/IG5-8

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

    JGD_G5/IG5-8

    scc of JGD_G5/IG5-8

    Matrix properties (click for a legend)  
    number of rows156
    number of columns292
    structural full rank?yes
    structural rank156
    numerical rank 154
    dimension of the numerical null space138
    numerical rank / min(size(A))0.98718
    Euclidean norm of A 44.478
    calculated singular value # 1540.014672
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.0748e-012
    calculated singular value # 1551.1737e-015
    gap in the singular values at the numerical rank:
    singular value # 154 / singular value # 155
    1.2501e+013
    calculated condition number5.4852e+016
    condest-2
    nonzeros1,711
    # of blocks from dmperm1
    # strongly connected comp.135
    entries not in dmperm blocks0
    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
    SJid587
    UFid1,967

    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/IG5-8.txt2                                      
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU6,634 5,690
    nnz(R) for QR, upper bound nnz(U) for LU9,529 9,816

    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.