Matrix properties
number of rows	4,326
number of columns	4,326
nonzeros	61,166
structural full rank?	yes
structural rank	4,326
# of blocks from dmperm	1
# strongly connected comp.	1
explicit zero entries	0
nonzero pattern symmetry	74%
numeric value symmetry	0%
type	real
structure	unsymmetric
Cholesky candidate?	no
positive definite?	no

author	A. Quaglino
editor	T. Davis
date	2007
kind	materials problem
2D/3D problem?	yes

Additional fields	size and type
b	full 4326-by-1
C	cell 7-by-1

Notes:

The matrix is in the form [A11 A12 ; A21 A22] where A11 and A22 are diagonal. 
Originally, the matrices in this set were poorly scaled, but this was resolved
by a scale factor of the form [A11 A12*e ; A21/e A4] where the scalar e is    
of magnitude 1e2 but can be 1e6 or 1e7 for a stiff material.  The Problem.A   
matrix is the properly scaled problem.  The Problem.aux.C{1:7} matrices have  
been "unscaled" with a factor e = 10.^(-(1:7)), to give a sequence of matrices
that are well scaled to poorly scaled, and thus well conditioned (C{1}) to    
poorly conditioned (C{7}).  This mimics the original poorly scaled and ill-   
conditioned problem, and may be of interest for those developing algorithms   
for automatic scaling.  From a FEM discretization of a viscoplastic collision 
problem, Alessio Quaglino.                                                    

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	71,771
Cholesky flop count	2.2e+06
nnz(L+U), no partial pivoting, with AMD	139,216
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	705,015
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	1,530,390

SVD-based statistics:
norm(A)	73.8743
min(svd(A))	0.000529054
cond(A)	139635
rank(A)	4,326
sprank(A)-rank(A)	0
null space dimension	0
full numerical rank?	yes

singular values (MAT file):	click here
SVD method used:	s = piro_band_svd (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.