Matrix: Rajat/Raj1

Description: Circuit simulation matrix from Raj

Rajat/Raj1 graph Rajat/Raj1 graph
(bipartite graph drawing) (graph drawing of A+A')

Rajat/Raj1 dmperm of Rajat/Raj1
scc of Rajat/Raj1

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  • Matrix group: Rajat
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  • download as a MATLAB mat-file, file size: 4 MB. Use UFget(1863) or UFget('Rajat/Raj1') in MATLAB.
  • download in Matrix Market format, file size: 7 MB.
  • download in Rutherford/Boeing format, file size: 5 MB.

    Matrix properties
    number of rows263,743
    number of columns263,743
    structural full rank?yes
    structural rank263,743
    # of blocks from dmperm169
    # strongly connected comp.3
    explicit zero entries2,203
    nonzero pattern symmetry 100%
    numeric value symmetry 58%
    Cholesky candidate?no
    positive definite?no

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


    High fill-in with KLU, because the matrix is nearly singular and lots of 
    partial pivoting occurs.  If the pattern of A+A' is considered to be the 
    nonzero pattern of a symmetric positive definite matrix, then nnz(L) has 
    only 3,728,967 nonzeros using p=amd(A) and chol(A(p,p)), where A excludes
    the explicit zeros in Problem.Zeros.  The flop count for the Cholesky    
    factorization is only 340.9 million.  With a pivot tolerance of 2.2e-16, 
    KLU Version 1.0 constructs and LU factorization with about 31 million    
    nonzeros, even though it uses AMD for the diagonal blocks of the BTF for 
    which the expected nnz(L) is only 3.705 million (for the Cholesky factor-
    ization of the large diagonal block).  The BTF form has little impact on 
    the factorization.                                                       

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD3,728,967
    Cholesky flop count3.4e+08
    nnz(L+U), no partial pivoting, with AMD7,194,191
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD6,973,362,829
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD12,971,084,610

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 2203 explicit zero entries.

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.