• SJSU Singular Matrix Database
  • Matrix group: JGD_Kocay
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  • Matrix: JGD_Kocay/Trec13
  • Description: Brute force disjoint product matrices in tree algebra on n nodes, Nicolas Thiery
  • download as a MATLAB mat-file, file size: 1 MB. Use SJget(646) or SJget('JGD_Kocay/Trec13') in MATLAB.
  • download in Matrix Market format, file size: 2 MB.
  • download in Rutherford/Boeing format, file size: 1 MB.

    JGD_Kocay/Trec13

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

    JGD_Kocay/Trec13

    scc of JGD_Kocay/Trec13

    Matrix properties (click for a legend)  
    number of rows1,301
    number of columns6,561
    structural full rank?yes
    structural rank1,301
    numerical rank 1,295
    dimension of the numerical null space5,266
    numerical rank / min(size(A))0.99539
    Euclidean norm of A 2497.6
    calculated singular value # 12950.49166
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.9836e-009
    calculated singular value # 12965.2917e-014
    gap in the singular values at the numerical rank:
    singular value # 1295 / singular value # 1296
    9.2912e+012
    calculated condition number6.5233e+016
    condest-2
    nonzeros654,517
    # of blocks from dmperm1
    # strongly connected comp.2
    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
    SJid646
    UFid2,147

    Notes:

    Brute force disjoint product matrices in tree algebra on n nodes, Nicolas Thiery
    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.                                                                      
                                                                                    
    Filename in JGD collection: Kocay/Trec13.txt2                                   
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU6,121,701 6,510,504
    nnz(R) for QR, upper bound nnz(U) for LU796,184 821,223

    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.