• SJSU Singular Matrix Database
  • Matrix group: QY
  • Click here for a description of the QY group.
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  • Matrix: QY/case9
  • Description: Transient stabilty constrained interior pt. optimal power flow, J. Quanyuan
  • download as a MATLAB mat-file, file size: 10 MB. Use SJget(695) or SJget('QY/case9') in MATLAB.
  • download in Matrix Market format, file size: 10 MB.
  • download in Rutherford/Boeing format, file size: 9 MB.

    QY/case9

    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,rr, 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,spnrank.pdf"> 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.

    QY/case9

    dmperm of QY/case9

    scc of QY/case9

    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
    condest3.1256e+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

    authorJ. Quanyuan
    editorT. Davis
    date2008
    kindpower network problem sequence
    2D/3D problem?no
    SJid695
    UFid2,214

    Additional fieldssize and type
    bsparse 14454-by-1
    Acell 12-by-1
    b1cell 12-by-1
    b2cell 12-by-1

    Notes:

    Transient stabilty constrained interior pt. optimal power flow, J. Quanyuan
    Two problem sets from Dr. Jiang Quanyuan from Zhejiang University,         
    Hangzhou, China, March, 2008, used in an electrical power system.          
    Each matrix A is solved sequentially with two right-hand-sides, b1 and     
    b2, one at a time.  In the UF collection, the sequence of all first        
    and second right-hand-sides is in Problem.aux.b2 and Problem.aux.b1.       
    These matrices are symmetric indefinite (x=A\b uses MA57)                  
    Note that the last matrices in the sequence are ill-conditioned.           
                                                                               
    Transient Stability Constrained Interior Point Optimal Power Flow Program  
          Version 1.0 -- Developed by Dr. Jiang Quanyuan, March 2008           
                                                                               
    case9.m - TSOPF converges after 12 iterations                              
     object    = 3.945939E+03                                                  
     max_equ   = 3.287326E-11                                                  
     low_inequ = None                                                          
     up_inequ  = None                                                          
    

    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.