• SJSU Singular Matrix Database
  • Matrix group: TSOPF
  • Click here for a description of the TSOPF group.
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  • Matrix: TSOPF/TSOPF_FS_b9_c6
  • Description: transient optimal power flow, Reduced-Space. Guangchao Geng, Zhejiang Univ
  • download as a MATLAB mat-file, file size: 216 KB. Use SJget(696) or SJget('TSOPF/TSOPF_FS_b9_c6') in MATLAB.
  • download in Matrix Market format, file size: 297 KB.
  • download in Rutherford/Boeing format, file size: 202 KB.

    TSOPF/TSOPF_FS_b9_c6

    A singular value of A is guaranteed1 to be in the interval pictured by the blue bars around each of the calculated singular values.

    Routine svds_err, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate the 6 largest singular values and associated error bounds.
    Routine spnrank, version 1.0 with opts.tol_eigs = 1e-008, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 14442 to 14447 and associated error bounds.

    TSOPF/TSOPF_FS_b9_c6

    dmperm of TSOPF/TSOPF_FS_b9_c6

    scc of TSOPF/TSOPF_FS_b9_c6

    Matrix properties (click for a legend)  
    number of rows14,454
    number of columns14,454
    structural full rank?yes
    structural rank14,454
    numerical rank 14,444
    dimension of the numerical null space10
    numerical rank / min(size(A))0.99931
    Euclidean norm of A 5306.2
    calculated singular value # 144441.4283e-008
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.3146e-008
    calculated singular value # 144451.1652e-008
    gap in the singular values at the numerical rank:
    singular value # 14444 / singular value # 14445
    1.2258
    calculated condition number-2
    condest2.9617e+012
    nonzeros147,972
    # of blocks from dmperm2
    # strongly connected comp.2
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typereal
    structuresymmetric
    Cholesky candidate?no
    positive definite?no

    authorG. Geng
    editorT. Davis
    date2009
    kindpower network problem
    2D/3D problem?no
    SJid696
    UFid2,231

    Additional fieldssize and type
    bsparse 14454-by-1

    Notes:

    Transient stability-constrained optimal power flow (TSOPF) problems from     
    Guangchao Geng, Institute of Power System, College of Electrical Engineering,
    Zhejiang University, Hangzhou, 310027, China.  (genggc AT gmail DOT com).    
    Matrices in the  Full-Space (FS) group are symmetric indefinite, and are best
    solved with MA57.  Matrices in the the Reduced-Space (RS) group are best     
    solved with KLU, which for these matrices can be 10 times faster than UMFPACK
    or SuperLU.                                                                  
    

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))178,786 211,362 -
    Cholesky flop count2.6e+006 3.8e+006 -
    nnz(L+U), no partial pivoting343,118 408,270 -
    nnz(V) for QR, upper bound nnz(L) for LU17,856,448 8,290,763 17,856,447
    nnz(R) for QR, upper bound nnz(U) for LU26,478,449 28,095,620 26,478,449

    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.