• SJSU Singular Matrix Database
  • Matrix group: JGD_Kocay
  • Click here for a description of the JGD_Kocay group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups

  • 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.


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


    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)) =
    calculated singular value # 12965.2917e-014
    gap in the singular values at the numerical rank:
    singular value # 1295 / singular value # 1296
    calculated condition number6.5233e+016
    # of blocks from dmperm1
    # strongly connected comp.2
    entries not in dmperm blocks0
    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: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.