• SJSU Singular Matrix Database
  • Matrix group: JGD_Franz
  • Click here for a description of the JGD_Franz group.
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  • Matrix: JGD_Franz/Franz4
  • Description: Cohomology of various rings, from Matthias Franz, Univ. Konstanz, Germany
  • download as a MATLAB mat-file, file size: 110 KB. Use SJget(680) or SJget('JGD_Franz/Franz4') in MATLAB.
  • download in Matrix Market format, file size: 149 KB.
  • download in Rutherford/Boeing format, file size: 108 KB.

    JGD_Franz/Franz4

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

    JGD_Franz/Franz4

    Matrix properties (click for a legend)  
    number of rows6,784
    number of columns5,252
    structural full rank?yes
    structural rank5,252
    numerical rank 3,297
    dimension of the numerical null space1,955
    numerical rank / min(size(A))0.62776
    Euclidean norm of A 8.6023
    calculated singular value # 32971.7809
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.2051e-011
    calculated singular value # 32987.6398e-014
    gap in the singular values at the numerical rank:
    singular value # 3297 / singular value # 3298
    2.3311e+013
    calculated condition number7.3935e+015
    condest-2
    nonzeros46,528
    # 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

    authorM. Franz
    editorJ.-G. Dumas
    date2008
    kindcombinatorial problem
    2D/3D problem?no
    SJid680
    UFid1,957

    Notes:

    Cohomology of various rings, from Matthias Franz, Univ. Konstanz, Germany
    From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,             
    http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html                
                                                                             
    Filename in JGD collection: Franz/6784x5252                              
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU10,314,022 5,719,870
    nnz(R) for QR, upper bound nnz(U) for LU7,830,856 5,026,783

    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.