Matrix: Rajat/Raj1

Description: Circuit simulation matrix from Raj

 (bipartite graph drawing) (graph drawing of A+A')

• Home page of the UF Sparse Matrix Collection
• 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
• 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 rows 263,743 number of columns 263,743 nonzeros 1,300,261 structural full rank? yes structural rank 263,743 # of blocks from dmperm 169 # strongly connected comp. 3 explicit zero entries 2,203 nonzero pattern symmetry 100% numeric value symmetry 58% type real structure unsymmetric Cholesky candidate? no positive definite? no

 author Raj editor T. Davis date 2007 kind circuit simulation problem 2D/3D problem? no

Notes:

```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 AMD 3,728,967 Cholesky flop count 3.4e+08 nnz(L+U), no partial pivoting, with AMD 7,194,191 nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD 6,973,362,829 nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD 12,971,084,610

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.