Matrix properties
number of rows	2,142
number of columns	2,142
nonzeros	45,262
structural full rank?	no
structural rank	2,140
# of blocks from dmperm	92
# strongly connected comp.	183
explicit zero entries	0
nonzero pattern symmetry	95%
numeric value symmetry	4%
type	real
structure	unsymmetric
Cholesky candidate?	no
positive definite?	no

author	P. Quillen
editor	T. Davis
date	2009
kind	counter-example problem
2D/3D problem?	no

Additional fields	size and type
b	sparse 2142-by-1

Notes:

This is a structurally singular matrix that triggers a bug in the   
2-by-2 pivoting strategy in UMFPACK versions 4.1 through 5.3.       
The bug thus exists in MATLAB R2006b through R2009a.  It was        
fixed in UMFPACK 5.4 and MATLAB R2009b.  Contributed by Pat Quillen,
The MathWorks, Inc.  The sprank(A) and rank(A) are 2140.            

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	73,792
Cholesky flop count	2.8e+06
nnz(L+U), no partial pivoting, with AMD	145,442
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	43,575
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	86,695

SVD-based statistics:
norm(A)	443.42
min(svd(A))	1.96114e-15
cond(A)	2.26103e+17
rank(A)	2,140
sprank(A)-rank(A)	0
null space dimension	2
full numerical rank?	no
singular value gap	2.05462e+13

singular values (MAT file):	click here
SVD method used:	s = svd (full (A)) ;
status:	ok

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.