• 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/EX6
  • Description: Symmetric powers of graphs from Gordon Royle, Univ Western Australia
  • download as a MATLAB mat-file, file size: 534 KB. Use SJget(684) or SJget('JGD_SPG/EX6') in MATLAB.
  • download in Matrix Market format, file size: 369 KB.
  • download in Rutherford/Boeing format, file size: 285 KB.

    JGD_SPG/EX6

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

    JGD_SPG/EX6

    Matrix properties (click for a legend)  
    number of rows6,545
    number of columns6,545
    structural full rank?yes
    structural rank6,545
    numerical rank 4,740
    dimension of the numerical null space1,805
    numerical rank / min(size(A))0.72422
    Euclidean norm of A 45.259
    calculated singular value # 47400.92785
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    4.6505e-011
    calculated singular value # 47412.4761e-013
    gap in the singular values at the numerical rank:
    singular value # 4740 / singular value # 4741
    3.7472e+012
    calculated condition number2.3899e+019
    condest1.0962e+018
    nonzeros295,680
    # 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
    SJid684
    UFid2,200

    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/EX6.sms                             
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))15,203,059 12,890,176
    Cholesky flop count5.5e+010 3.7e+010
    nnz(L+U), no partial pivoting30,399,573 25,773,807
    nnz(V) for QR, upper bound nnz(L) for LU19,253,430 16,792,828
    nnz(R) for QR, upper bound nnz(U) for LU20,660,929 20,822,180

    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.