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

  • Matrix: Rajat/rajat23
  • Description: Rajat/rajat23 circuit simulation matrix
  • download as a MATLAB mat-file, file size: 3 MB. Use SJget(445) or SJget('Rajat/rajat23') in MATLAB.
  • download in Matrix Market format, file size: 4 MB.
  • download in Rutherford/Boeing format, file size: 4 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 with opts.tol_eigs = 1e-008, used with Matlab (R2008a) to calculate singular values 109818 to 109823 and associated error bounds.


    dmperm of Rajat/rajat23

    scc of Rajat/rajat23

    Matrix properties (click for a legend)  
    number of rows110,355
    number of columns110,355
    structural full rank?yes
    structural rank110,355
    numerical rank 109,820
    dimension of the numerical null space535
    numerical rank / min(size(A))0.99515
    Euclidean norm of A 8.4473e+005
    calculated singular value # 1098201.3009e-005
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 1098211.284e-005
    gap in the singular values at the numerical rank:
    singular value # 109820 / singular value # 109821
    calculated condition number-2
    # of blocks from dmperm6,052
    # strongly connected comp.1,410
    entries not in dmperm blocks34,461
    explicit zero entries1,497
    nonzero pattern symmetry 99%
    numeric value symmetry 33%
    Cholesky candidate?no
    positive definite?no

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

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))455,569 480,779 638,059
    Cholesky flop count2.8e+006 3.3e+006 7.1e+006
    nnz(L+U), no partial pivoting800,783 851,203 1,200,224
    nnz(V) for QR, upper bound nnz(L) for LU9,552,852 8,728,882 7,575,573
    nnz(R) for QR, upper bound nnz(U) for LU29,899,740 30,661,980 25,441,281

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 1497 explicit zero entries.

    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.