Matrix: JGD_Kocay/Trec13

Description: Brute force disjoint product matrices in tree algebra on n nodes, Nicolas Thiery

JGD_Kocay/Trec13 graph
(bipartite graph drawing)

scc of JGD_Kocay/Trec13

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  • download as a MATLAB mat-file, file size: 1 MB. Use UFget(2147) or UFget('JGD_Kocay/Trec13') in MATLAB.
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    Matrix properties
    number of rows1,301
    number of columns6,561
    structural full rank?yes
    structural rank1,301
    # of blocks from dmperm1
    # strongly connected comp.2
    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


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

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD6,121,701
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD796,184

    SVD-based statistics:
    null space dimension6
    full numerical rank?no
    singular value gap8.75095e+12

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

    JGD_Kocay/Trec13 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.