• SJSU Singular Matrix Database
  • Matrix group: JGD_Homology
  • Click here for a description of the JGD_Homology group.
  • Click here for a list of all matrices
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  • Matrix: JGD_Homology/ch7-6-b3
  • Description: Simplicial complexes from Homology from Volkmar Welker.
  • download as a MATLAB mat-file, file size: 118 KB. Use SJget(681) or SJget('JGD_Homology/ch7-6-b3') in MATLAB.
  • download in Matrix Market format, file size: 158 KB.
  • download in Rutherford/Boeing format, file size: 126 KB.

    JGD_Homology/ch7-6-b3

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

    JGD_Homology/ch7-6-b3

    Matrix properties (click for a legend)  
    number of rows12,600
    number of columns4,200
    structural full rank?yes
    structural rank4,200
    numerical rank 3,611
    dimension of the numerical null space589
    numerical rank / min(size(A))0.85976
    Euclidean norm of A 4.899
    calculated singular value # 36113
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.1191e-011
    calculated singular value # 36122.4259e-014
    gap in the singular values at the numerical rank:
    singular value # 3611 / singular value # 3612
    1.2366e+014
    calculated condition number6.7422e+015
    condest-2
    nonzeros50,400
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typeinteger
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorV. Welker
    editorJ.-G. Dumas
    date2008
    kindcombinatorial problem
    2D/3D problem?no
    SJid681
    UFid2,024

    Notes:

    Simplicial complexes from Homology from Volkmar Welker.     
    From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,
    http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html   
                                                                
    http://www.mathematik.uni-marburg.de/~welker/               
                                                                
    Filename in JGD collection: Homology/ch7-6.b3.12600x4200.sms
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU30,016,346 22,772,579
    nnz(R) for QR, upper bound nnz(U) for LU5,565,695 5,034,643

    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.