chemical master eqn, aij*h = prob of i->j transition in time h (Markov model)
Name Baumann
Group Watson
Matrix ID 1855
Num Rows 112,211
Num Cols 112,211
Nonzeros 748,331
Pattern Entries 760,631
Kind 2D/3D Problem
Symmetric No
Date 2007
Author L. Watson and J. Zhang
Editor T. Davis
Structural Rank 112,211
Structural Rank Full true
Num Dmperm Blocks 2
Strongly Connect Components 2
Num Explicit Zeros 12,300
Pattern Symmetry 100%
Numeric Symmetry 0%
Cholesky Candidate no
Positive Definite no
Type real
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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.