• 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/Franz1
  • Description: Cohomology of various rings, from Matthias Franz, Univ. Konstanz, Germany
  • download as a MATLAB mat-file, file size: 15 KB. Use SJget(628) or SJget('JGD_Franz/Franz1') in MATLAB.
  • download in Matrix Market format, file size: 18 KB.
  • download in Rutherford/Boeing format, file size: 15 KB.

    JGD_Franz/Franz1

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

    JGD_Franz/Franz1

    Matrix properties (click for a legend)  
    number of rows2,240
    number of columns768
    structural full rank?yes
    structural rank768
    numerical rank 755
    dimension of the numerical null space13
    numerical rank / min(size(A))0.98307
    Euclidean norm of A 4.179
    calculated singular value # 7550.87403
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.9895e-012
    calculated singular value # 7562.7752e-015
    gap in the singular values at the numerical rank:
    singular value # 755 / singular value # 756
    3.1495e+014
    calculated condition number2.4534e+015
    condest-2
    nonzeros5,120
    # 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
    SJid628
    UFid1,954

    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/big1sparse                             
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU470,398 359,761
    nnz(R) for QR, upper bound nnz(U) for LU78,146 70,144

    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.