Matrix properties
number of rows	81,920
number of columns	81,920
nonzeros	327,680
structural full rank?	yes
structural rank	81,920
# of blocks from dmperm	1
# strongly connected comp.	1
explicit zero entries	0
nonzero pattern symmetry	symmetric
numeric value symmetry	symmetric
type	real
structure	symmetric
Cholesky candidate?	yes
positive definite?	yes

author	K. Leppkes, U. Naumann
editor	T. Davis
date	2009
kind	computational fluid dynamics problem
2D/3D problem?	yes

Notes:

The two shallow_water* matrices arise from weather shallow water equations   
(see http://www.icon.enes.org), from the Max-Plank Institute of Meteorology. 
The problem gives rise to an automatic differentiation problem.  An iterative
solver is used for the larger problem, but a direct sovler is used for       
finding the adjoints of a linear problem.  The velocity field is integrated  
over a time loop with a semi-implicit method.  The implicit part leads to    
a linear problem A*x=b, whose entries vary with time.  Two of these matrices 
A are in this collection, with shallow_water1 at dtime=100 and shallow_water2
at dtime=200.  The nonzero patterns of the two matrices are the same, but    
shallow_water1 is much slower.  The reason is that many denormals appear     
during factorization, which greatly slows down the BLAS.  This can be solved 
by compiling with gcc -ffast-math, to flush denormals to zero.               

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	2,357,535
Cholesky flop count	5.8e+08
nnz(L+U), no partial pivoting, with AMD	4,633,150
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	5,355,578
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	9,691,968

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.