Watson/chem_master1
chemical master eqn, aij*h = prob of i>j transition in time h (Markov model)
Name 
chem_master1 
Group 
Watson 
Matrix ID 
1854 
Num Rows

40,401 
Num Cols

40,401 
Nonzeros

201,201 
Pattern Entries

201,201 
Kind

2D/3D Problem 
Symmetric

No 
Date

2007 
Author

L. Watson and J. Zhang 
Editor

T. Davis 
Structural Rank 
40,401 
Structural Rank Full 
true 
Num Dmperm Blocks

1 
Strongly Connect Components

1 
Num Explicit Zeros

0 
Pattern Symmetry

100% 
Numeric Symmetry

0% 
Cholesky Candidate

no 
Positive Definite

no 
Type

real 
Download 
MATLAB
Rutherford Boeing
Matrix Market

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 offdiagonal entries are nonnegative 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 201by201 mesh, minus 300 entries on the
+1 and 1 diagonal.
