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

  • Matrix: Bomhof/circuit_4
  • Description: Circuit DAE with BDF method & Newton. W. Bomhof, Univ. Utrecht
  • download as a MATLAB mat-file, file size: 1 MB. Use SJget(436) or SJget('Bomhof/circuit_4') in MATLAB.
  • download in Matrix Market format, file size: 2 MB.
  • download in Rutherford/Boeing format, file size: 2 MB.


    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 (R2008a) to calculate the 6 largest singular values and associated error bounds.
    Routine spnrank, version 1.0, used with Matlab (R2008a) to calculate singular values 80183 to 80188 and associated error bounds.


    dmperm of Bomhof/circuit_4

    scc of Bomhof/circuit_4

    Matrix properties (click for a legend)  
    number of rows80,209
    number of columns80,209
    structural full rank?yes
    structural rank80,209
    numerical rank 80,185
    dimension of the numerical null space24
    numerical rank / min(size(A))0.9997
    Euclidean norm of A 5340.9
    calculated singular value # 801857.8206e-008
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 801867.1919e-008
    gap in the singular values at the numerical rank:
    singular value # 80185 / singular value # 80186
    calculated condition number-2
    # of blocks from dmperm28,005
    # strongly connected comp.27,923
    entries not in dmperm blocks23,846
    explicit zero entries0
    nonzero pattern symmetry 83%
    numeric value symmetry 36%
    Cholesky candidate?no
    positive definite?no

    authorW. Bomhof
    editorT. Davis
    kindcircuit simulation problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 80209-by-1
    xfull 80209-by-1

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))261,650 301,959 241,255
    Cholesky flop count2.8e+006 5.3e+006 2.9e+006
    nnz(L+U), no partial pivoting443,091 523,709 426,147
    nnz(V) for QR, upper bound nnz(L) for LU102,852,606 - 128,047,445
    nnz(R) for QR, upper bound nnz(U) for LU194,371,104 - 179,623,652

    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.