• SJSU Singular Matrix Database
  • Matrix group: JGD_Kocay
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  • Matrix: JGD_Kocay/Trec14
  • Description: Brute force disjoint product matrices in tree algebra on n nodes, Nicolas Thiery
  • download as a MATLAB mat-file, file size: 6 MB. Use SJget(676) or SJget('JGD_Kocay/Trec14') in MATLAB.
  • download in Matrix Market format, file size: 8 MB.
  • download in Rutherford/Boeing format, file size: 5 MB.

    JGD_Kocay/Trec14

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

    JGD_Kocay/Trec14

    scc of JGD_Kocay/Trec14

    Matrix properties (click for a legend)  
    number of rows3,159
    number of columns15,905
    structural full rank?yes
    structural rank3,159
    numerical rank 3,133
    dimension of the numerical null space12,772
    numerical rank / min(size(A))0.99177
    Euclidean norm of A 6088.5
    calculated singular value # 31330.32776
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.4466e-008
    calculated singular value # 31341.1457e-013
    gap in the singular values at the numerical rank:
    singular value # 3133 / singular value # 3134
    2.8607e+012
    calculated condition number1.0253e+017
    condest-2
    nonzeros2,872,265
    # 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
    SJid676
    UFid2,148

    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/Trec14.txt2                                   
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU35,970,189 32,996,897
    nnz(R) for QR, upper bound nnz(U) for LU4,741,823 4,840,721

    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.