Illustration of the main steps in dPDM. (a) Illustration of the linear search to find the interval p such that the global time of firing (initiation) of the next reaction . In this figure, the number of pending reactions Δ = 6. (b) Illustration of the partial-propensity structure and the grouping based on the index of the common factored-out reactant. The group index I of the next reaction is sampled using linear search over the total propensities of the groups, . The element index J within the selected group is found using linear search over the partial propensities stored in group I.
Computational cost of dPDM (squares) and dDM (circles). The average (over 100 independent runs) CPU time Θ per reaction initiation (i.e., the average time to execute steps 2–7 in Table II for dPDM, and Table I for dDM) is shown as a function of the number of species N in the reaction network. (a) Logarithmic plot of Θ(N) for the strongly coupled colloidal aggregation model, considering systems of size up to N = 320. Θ is O(N) for dPDM and for dDM. (b) Linear plot of Θ(N) for the strongly coupled colloidal aggregation model, considering systems of size up to N = 2000 (2 million reactions). While the scaling of the computational cost remains linear for all system sizes tested, the slope increases around N = 1000. This is the system size beyond which the partial-propensity structure does not fit into the computer's cache memory any more. (c) Linear plot of Θ(N) for the weakly coupled cyclic chain model. The solid lines are linear least square fits. Θ is O(N) for both dPDM and dDM, but with a smaller slope for dPDM.
Outline of the algorithm for the delay direct method (dDM) with global times. We only give the main steps and refer to the original publication for the detailed substeps (Ref. 13).
Detailed algorithm for the delay partial-propensity direct method (dPDM), explicitly describing all substeps.
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