• SJSU Singular Matrix Database
  • Matrix group: JGD_SPG
  • Click here for a description of the JGD_SPG group.
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  • Matrix: JGD_SPG/EX2
  • Description: Symmetric powers of graphs from Gordon Royle, Univ Western Australia
  • download as a MATLAB mat-file, file size: 17 KB. Use SJget(609) or SJget('JGD_SPG/EX2') in MATLAB.
  • download in Matrix Market format, file size: 12 KB.
  • download in Rutherford/Boeing format, file size: 9 KB.

    JGD_SPG/EX2

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

    JGD_SPG/EX2

    Matrix properties (click for a legend)  
    number of rows560
    number of columns560
    structural full rank?yes
    structural rank560
    numerical rank 553
    dimension of the numerical null space7
    numerical rank / min(size(A))0.9875
    Euclidean norm of A 15.835
    calculated singular value # 5530.1948
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    9.9476e-013
    calculated singular value # 5541.4704e-015
    gap in the singular values at the numerical rank:
    singular value # 553 / singular value # 554
    1.3248e+014
    calculated condition number1.1973e+017
    condest5.3173e+016
    nonzeros8,736
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typebinary
    structuresymmetric
    Cholesky candidate?yes
    positive definite?unknown

    authorG. Royle
    editorJ.-G. Dumas
    date2008
    kindcombinatorial problem
    2D/3D problem?no
    SJid609
    UFid2,196

    Notes:

    Symmetric powers of graphs from Gordon Royle, Univ Western Australia
    From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,        
    http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html           
                                                                        
    http://www.csse.uwa.edu.au/~gordon/sympower.html                    
                                                                        
    Filename in JGD collection: SPG/EX2.sms                             
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))74,333 71,914
    Cholesky flop count1.6e+007 1.4e+007
    nnz(L+U), no partial pivoting148,106 143,268
    nnz(V) for QR, upper bound nnz(L) for LU110,886 101,155
    nnz(R) for QR, upper bound nnz(U) for LU133,863 139,587

    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.