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.