• 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/ch5-5-b3
  • Description: Simplicial complexes from Homology from Volkmar Welker.
  • download as a MATLAB mat-file, file size: 8 KB. Use SJget(613) or SJget('JGD_Homology/ch5-5-b3') in MATLAB.
  • download in Matrix Market format, file size: 8 KB.
  • download in Rutherford/Boeing format, file size: 7 KB.

    JGD_Homology/ch5-5-b3

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

    JGD_Homology/ch5-5-b3

    Matrix properties (click for a legend)  
    number of rows600
    number of columns600
    structural full rank?yes
    structural rank600
    numerical rank 424
    dimension of the numerical null space176
    numerical rank / min(size(A))0.70667
    Euclidean norm of A 3.1623
    calculated singular value # 4241
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.6645e-013
    calculated singular value # 4254.6315e-015
    gap in the singular values at the numerical rank:
    singular value # 424 / singular value # 425
    2.1592e+014
    calculated condition number3.4788e+017
    condestInf
    nonzeros2,400
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetry 2%
    numeric value symmetry 1%
    typeinteger
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorV. Welker
    editorJ.-G. Dumas
    date2008
    kindcombinatorial problem
    2D/3D problem?no
    SJid613
    UFid2,015

    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/ch5-5.b3.600x600.sms   
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))42,083 45,190
    Cholesky flop count6.5e+006 7.0e+006
    nnz(L+U), no partial pivoting83,566 89,780
    nnz(V) for QR, upper bound nnz(L) for LU37,492 31,612
    nnz(R) for QR, upper bound nnz(U) for LU60,846 55,242

    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.