In the first dimension, the state variable assumes all values from 0 through Nx; in the second dimension the state variable takes on value from 0 through Ny. The state space is then as follows:
This two dimensional Markov chain model allows for transitions from any nonboundary state to adjacent states in the North, South, East, West, North-East, North-West, South-East and South-West directions. The rates (or probabilities) of transition are set in the subroutine instant of the TwoD.f source code file.
In the 2D epidemic model specified in this collection, only transitions to the South, East and North-West are permitted. From any nonboundary state (u,v) , transitions to the South are assigned the value v ; transitions to the East are assigned the value 2025.0; and transitions to the North-West are assigned the value u.
In the data set corresponding to this model, TwoD_in, the values of Nx and Ny are as shown in the table below, along with the size of the matrix generated and the number of nonzeros in the matrix.
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Values of Nx, Ny, n and nz for the 10 datasets:
Nx Ny n nz
10 10 121 441
64 16 1,105 4,257
64 64 4,225 16,641
100 100 10,201 40,401
256 64 16,705 66,177
256 256 66,049 263,169
512 64 33,345 132,225
512 128 66,177 263,425
512 256 131,841 525,825
512 512 263,169 1,050,625
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