• SJSU Singular Matrix Database
  • Matrix group: Bai
  • Click here for a description of the Bai group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups


  • Matrix: Bai/qh768
  • Description: QUEBEC HYDRO POWER SYSTEM
  • download as a MATLAB mat-file, file size: 16 KB. Use SJget(211) or SJget('Bai/qh768') in MATLAB.
  • download in Matrix Market format, file size: 14 KB.
  • download in Rutherford/Boeing format, file size: 12 KB.

    Bai/qh768

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

    Bai/qh768

    dmperm of Bai/qh768

    Matrix properties (click for a legend)  
    number of rows768
    number of columns768
    structural full rank?yes
    structural rank768
    numerical rank 644
    dimension of the numerical null space124
    numerical rank / min(size(A))0.83854
    Euclidean norm of A 1.3567e+013
    calculated singular value # 6441.545
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.5
    calculated singular value # 6451.49
    gap in the singular values at the numerical rank:
    singular value # 644 / singular value # 645
    1.0369
    calculated condition number8.64e+016
    condest1.2927e+017
    nonzeros2,934
    # of blocks from dmperm43
    # strongly connected comp.1
    entries not in dmperm blocks78
    explicit zero entries0
    nonzero pattern symmetry 93%
    numeric value symmetry 0%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorD. Ndereyimana
    editorZ. Bai, D. Day, J. Demmel, J. Dongarra
    date1994
    kindpower network problem
    2D/3D problem?no
    SJid211
    UFid1,627

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))2,884 3,374 3,421
    Cholesky flop count1.2e+004 1.9e+004 2.1e+004
    nnz(L+U), no partial pivoting5,000 5,980 6,152
    nnz(V) for QR, upper bound nnz(L) for LU3,205 3,642 3,113
    nnz(R) for QR, upper bound nnz(U) for LU6,409 7,005 5,984

    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.