• SJSU Singular Matrix Database
  • Matrix group: JGD_Homology
  • Click here for a description of the JGD_Homology group.
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  • Matrix: JGD_Homology/n3c6-b7
  • Description: Simplicial complexes from Homology from Volkmar Welker.
  • download as a MATLAB mat-file, file size: 126 KB. Use SJget(682) or SJget('JGD_Homology/n3c6-b7') in MATLAB.
  • download in Matrix Market format, file size: 169 KB.
  • download in Rutherford/Boeing format, file size: 122 KB.

    JGD_Homology/n3c6-b7

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

    JGD_Homology/n3c6-b7

    Matrix properties (click for a legend)  
    number of rows6,435
    number of columns6,435
    structural full rank?yes
    structural rank6,435
    numerical rank 3,432
    dimension of the numerical null space3,003
    numerical rank / min(size(A))0.53333
    Euclidean norm of A 3.873
    calculated singular value # 34323.873
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.8577e-012
    calculated singular value # 34331.9813e-014
    gap in the singular values at the numerical rank:
    singular value # 3432 / singular value # 3433
    1.9547e+014
    calculated condition number8.6245e+017
    condestInf
    nonzeros51,480
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetry 53%
    typeinteger
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorV. Welker
    editorJ.-G. Dumas
    date2008
    kindcombinatorial problem
    2D/3D problem?no
    SJid682
    UFid2,104

    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/n3c6.b7.6435x6435.sms  
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))4,246,625 4,294,600
    Cholesky flop count7.7e+009 6.6e+009
    nnz(L+U), no partial pivoting8,486,815 8,582,765
    nnz(V) for QR, upper bound nnz(L) for LU12,659,868 6,965,932
    nnz(R) for QR, upper bound nnz(U) for LU14,851,943 11,853,528

    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.