• 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
  • Click here for a list of all matrix groups

  • Matrix: JGD_Homology/ch6-6-b4
  • Description: Simplicial complexes from Homology from Volkmar Welker.
  • download as a MATLAB mat-file, file size: 59 KB. Use SJget(673) or SJget('JGD_Homology/ch6-6-b4') in MATLAB.
  • download in Matrix Market format, file size: 74 KB.
  • download in Rutherford/Boeing format, file size: 58 KB.


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


    Matrix properties (click for a legend)  
    number of rows4,320
    number of columns5,400
    structural full rank?yes
    structural rank4,320
    numerical rank 3,390
    dimension of the numerical null space2,010
    numerical rank / min(size(A))0.78472
    Euclidean norm of A 3.4641
    calculated singular value # 33901
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 33911.2266e-014
    gap in the singular values at the numerical rank:
    singular value # 3390 / singular value # 3391
    calculated condition number1.1095e+016
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorV. Welker
    editorJ.-G. Dumas
    kindcombinatorial problem
    2D/3D problem?no


    Simplicial complexes from Homology from Volkmar Welker.     
    From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,
    Filename in JGD collection: Homology/ch6-6.b4.4320x5400.sms 

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU6,012,819 4,147,441
    nnz(R) for QR, upper bound nnz(U) for LU3,747,987 3,122,287

    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.