Matrix properties
number of rows	112,211
number of columns	112,211
nonzeros	748,331
structural full rank?	yes
structural rank	112,211
# of blocks from dmperm	2
# strongly connected comp.	2
explicit zero entries	12,300
nonzero pattern symmetry	symmetric
numeric value symmetry	0%
type	real
structure	unsymmetric
Cholesky candidate?	no
positive definite?	no

author	L. Watson and J. Zhang
editor	T. Davis
date	2007
kind	2D/3D problem
2D/3D problem?	yes

Notes:

The ODE system \frac{dp}{dt}=Qp is what we call a chemical master equation (a 
Kolmogorov's backward/forward equation). Q is a sparse asymmetric matrix,     
whose off-diagonal entries are non-negative and row sum to zero. On each row, 
q_{ij}h gives the probability the system makes a transition from current state
i to some other state j, in small time interval h. By "state", we mean a      
possible combination of number of molecules in each chemical species. Now, h  
is small enough so that only one reaction happens.  In this way q_{ij} is     
nonzero only if there exists a chemical reaction that connects state i and j, 
i.e. j=i+s_k, s_k's are constant state vectors that correspond to every       
reaction.  Say we have M reactions, then there are at most M+1 nonzero        
entries on each row of Q.  On the other hand, the number of possible          
combination of molecules is huge, which means the dimension of Q is huge.     
The linear system we want to solve is (I - Q/lambda)x=b, and we have          
to solve it several times. (Here lambda is a constant).  Problem.A is the Q   
matrix.  This is a medium test problem; the largest has dimension 10^8.       
It has the nonzero pattern of a 11-by-101-by-101 mesh.                        

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	26,112,094
Cholesky flop count	2.7e+10
nnz(L+U), no partial pivoting, with AMD	52,111,977
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	61,376,869
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	110,190,364

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 12300 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.