Matrix properties
number of rows	40,401
number of columns	40,401
nonzeros	201,201
structural full rank?	yes
structural rank	40,401
# of blocks from dmperm	1
# strongly connected comp.	1
explicit zero entries	0
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

Additional fields	size and type
b	full 40401-by-1

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 small test problem; the largest has dimension 10^8.        
It has the nonzero pattern of a 201-by-201 mesh, minus 300 entries on the     
+1 and -1 diagonal.                                                           

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	1,052,209
Cholesky flop count	1.1e+08
nnz(L+U), no partial pivoting, with AMD	2,064,017
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	1,842,081
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	3,377,747

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.