• 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/ch3-3-b1
  • Description: Simplicial complexes from Homology from Volkmar Welker.
  • download as a MATLAB mat-file, file size: 960 bytes. Use SJget(544) or SJget('JGD_Homology/ch3-3-b1') in MATLAB.
  • download in Matrix Market format, file size: 673 bytes.
  • download in Rutherford/Boeing format, file size: 721 bytes.

    JGD_Homology/ch3-3-b1

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

    JGD_Homology/ch3-3-b1

    Matrix properties (click for a legend)  
    number of rows18
    number of columns9
    structural full rank?yes
    structural rank9
    numerical rank 8
    dimension of the numerical null space1
    numerical rank / min(size(A))0.88889
    Euclidean norm of A 2.4495
    calculated singular value # 81.7321
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    7.9936e-015
    calculated singular value # 92.7214e-016
    gap in the singular values at the numerical rank:
    singular value # 8 / singular value # 9
    6.3644e+015
    calculated condition number9.0007e+015
    condest-2
    nonzeros36
    # 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
    SJid544
    UFid2,008

    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/ch3-3.b1.18x9.sms      
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU80 74
    nnz(R) for QR, upper bound nnz(U) for LU36 36

    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.