# DiffEqJump.jl API

## Core Types

`DiffEqJump.JumpProblem`

— Type`mutable struct JumpProblem{iip, P, A, C, J<:Union{Nothing, DiffEqJump.AbstractJumpAggregator}, J2, J3, J4, R} <: SciMLBase.AbstractJumpProblem{P, J<:Union{Nothing, DiffEqJump.AbstractJumpAggregator}}`

Defines a collection of jump processes to associate with another problem type.

**Constructors**

`JumpProblem`

s can be constructed by first building another problem type to which the jumps will be associated. For example, to simulate a collection of jump processes for which the transition rates are constant *between* jumps (called `ConstantRateJump`

s or `MassActionJump`

s), we must first construct a `DiscreteProblem`

`prob = DiscreteProblem(u0, p, tspan)`

where `u0`

is the initial condition, `p`

the parameters and `tspan`

the time span. If we wanted to have the jumps coupled with a system of ODEs, or have transition rates with explicit time dependence, we would use an `ODEProblem`

instead that defines the ODE portion of the dynamics.

Given `prob`

we define the jumps via

`JumpProblem(prob, aggregator::AbstractAggregatorAlgorithm, jumps::JumpSet ; kwargs...)`

`JumpProblem(prob, aggregator::AbstractAggregatorAlgorithm, jumps...; kwargs...)`

Here `aggregator`

specifies the underlying algorithm for calculating next jump times and types, for example `Direct`

. The collection of different `AbstractJump`

types can then be passed within a single `JumpSet`

or as subsequent sequential arguments.

**Fields**

`prob`

The type of problem to couple the jumps to. For a pure jump process use

`DiscreteProblem`

, to couple to ODEs,`ODEProblem`

, etc.`aggregator`

The aggregator algorithm that determines the next jump times and types for

`ConstantRateJump`

s and`MassActionJump`

s. Examples include`Direct`

.`discrete_jump_aggregation`

The underlying state data associated with the chosen aggregator.

`jump_callback`

`CallBackSet`

with the underlying`ConstantRate`

and`VariableRate`

jumps.`variable_jumps`

The

`VariableRateJump`

s.`regular_jump`

The

`RegularJump`

s.`massaction_jump`

The

`MassActionJump`

s.`rng`

The random number generator to use.

**Keyword Arguments**

`rng`

, the random number generator to use. On 1.7 and up defaults to Julia's builtin generator, below 1.7 uses RandomNumbers.jl's`Xorshifts.Xoroshiro128Star(rand(UInt64))`

.`save_positions=(true,true)`

, specifies whether to save the system's state (before,after) the jump occurs.`spatial_system`

, for spatial problems the underlying spatial structure.`hopping_constants`

, for spatial problems the spatial transition rate coefficients.

Please see the tutorial page in the DifferentialEquations.jl docs for usage examples and commonly asked questions.

`DiffEqJump.SSAStepper`

— Type`struct SSAStepper <: SciMLBase.DEAlgorithm`

Highly efficient integrator for pure jump problems that involve only `ConstantRateJump`

s and/or `MassActionJump`

s.

**Notes**

- Only works with
`JumProblem`

s defined from`DiscreteProblem`

s. - Only works with collections of
`ConstantRateJump`

s and`MassActionJump`

s. - Only supports
`DiscreteCallback`

s for events.

**Examples**

SIR model:

```
using DiffEqJump
β = 0.1 / 1000.0; ν = .01;
p = (β,ν)
rate1(u,p,t) = p[1]*u[1]*u[2] # β*S*I
function affect1!(integrator)
integrator.u[1] -= 1 # S -> S - 1
integrator.u[2] += 1 # I -> I + 1
end
jump = ConstantRateJump(rate1,affect1!)
rate2(u,p,t) = p[2]*u[2] # ν*I
function affect2!(integrator)
integrator.u[2] -= 1 # I -> I - 1
integrator.u[3] += 1 # R -> R + 1
end
jump2 = ConstantRateJump(rate2,affect2!)
u₀ = [999,1,0]
tspan = (0.0,250.0)
prob = DiscreteProblem(u₀, tspan, p)
jump_prob = JumpProblem(prob, Direct(), jump, jump2)
sol = solve(jump_prob, SSAStepper())
```

see the tutorial for details.

`DiffEqJump.reset_aggregated_jumps!`

— Function`reset_aggregated_jumps!(integrator, uprev = nothing; update_jump_params=true)`

Reset the state of jump processes and associated solvers following a change in parameters or such.

Notes - `update_jump_params=true`

will recalculate the rates stored within any MassActionJump that was built from the parameter vector. If the parameter vector is unchanged this can safely be set to false to improve performance.

## Types of Jumps

`DiffEqJump.ConstantRateJump`

— Type`struct ConstantRateJump{F1, F2} <: DiffEqJump.AbstractJump`

Defines a jump process with a rate (i.e. hazard, intensity, or propensity) that does not *explicitly* depend on time. More precisely, one where the rate function is constant *between* the occurrence of jumps. For detailed examples and usage information see the

**Fields**

`rate`

Function

`rate(u,p,t)`

that returns the jump's current rate.`affect!`

Function

`affect(integrator)`

that updates the state for one occurrence of the jump.

**Examples**

Suppose `u[1]`

gives the amount of particles and `p[1]`

the probability per time each particle can decay away. A corresponding `ConstantRateJump`

for this jump process is

```
rate(u,p,t) = p[1]*u[1]
affect!(integrator) = integrator.u[1] -= 1
crj = ConstantRateJump(rate, affect!)
```

Notice, here that `rate`

changes in time, but is constant between the occurrence of jumps (when `u[1]`

will decrease).

`DiffEqJump.MassActionJump`

— Type`struct MassActionJump{T, S, U, V} <: DiffEqJump.AbstractMassActionJump`

Optimized representation for `ConstantRateJump`

s that can be represented in mass action form, offering improved performance within jump algorithms compared to `ConstantRateJump`

. For detailed examples and usage information see the

**Constructors**

`MassActionJump(reactant_stoich, net_stoich; scale_rates=true, param_idxs=nothing)`

Here `reactant_stoich`

denotes the reactant stoichiometry for each reaction and `net_stoich`

the net stoichiometry for each reaction.

**Fields**

`scaled_rates`

The (scaled) reaction rate constants.

`reactant_stoch`

The reactant stoichiometry vectors.

`net_stoch`

The net stoichiometry vectors.

`param_mapper`

Parameter mapping functor to identify reaction rate constants with parameters in

`p`

vectors.

**Keyword Arguments**

`scale_rates=true`

, whether to rescale the reaction rate constants according to the stoichiometry.`nocopy=false`

, whether the`MassActionJump`

can alias the`scaled_rates`

and`reactant_stoch`

from the input. Note, if`scale_rates=true`

this will potentially modify both of these.`param_idxs=nothing`

, indexes in the parameter vector,`JumpProblem.prob.p`

, that correspond to each reaction's rate.

See the tutorial and main docs for details.

**Examples**

An SIR model with `S + I --> 2I`

at rate β as the first reaction and `I --> R`

at rate ν as the second reaction can be encoded by

```
p = (β=1e-4, ν=.01)
u0 = [999, 1, 0] # (S,I,R)
tspan = (0.0, 250.0)
rateidxs = [1, 2] # i.e. [β,ν]
reactant_stoich =
[
[1 => 1, 2 => 1], # 1*S and 1*I
[2 => 1] # 1*I
]
net_stoich =
[
[1 => -1, 2 => 1], # -1*S and 1*I
[2 => -1, 3 => 1] # -1*I and 1*R
]
maj = MassActionJump(reactant_stoich, net_stoich; param_idxs=rateidxs)
prob = DiscreteProblem(u0, tspan, p)
jprob = JumpProblem(prob, Direct(), maj)
```

**Notes**

`DiffEqJump.VariableRateJump`

— Type`struct VariableRateJump{R, F, I, T, T2} <: DiffEqJump.AbstractJump`

Defines a jump process with a rate (i.e. hazard, intensity, or propensity) that may explicitly depend on time. More precisely, one where the rate function is allowed to change *between* the occurrence of jumps. For detailed examples and usage information see the

**Fields**

`rate`

Function

`rate(u,p,t)`

that returns the jump's current rate.`affect!`

Function

`affect(integrator)`

that updates the state for one occurrence of the jump.`idxs`

`rootfind`

`interp_points`

`save_positions`

`abstol`

`reltol`

**Examples**

Suppose `u[1]`

gives the amount of particles and `t*p[1]`

the probability per time each particle can decay away. A corresponding `VariableRateJump`

for this jump process is

```
rate(u,p,t) = t*p[1]*u[1]
affect!(integrator) = integrator.u[1] -= 1
crj = VariableRateJump(rate, affect!)
```

**Notes**

See`VariableRateJump`

s result in`integrator`

s storing an effective state type that wraps the main state vector.`ExtendedJumpArray`

for details on using this object. Note that the presence of*any*`VariableRateJump`

s will result in all`ConstantRateJump`

,`VariableRateJump`

and callback`affect!`

functions receiving an integrator with`integrator.u`

an`ExtendedJumpArray`

.- Must be used with
`ODEProblem`

s or`SDEProblem`

s to be correctly simulated (i.e. can not currently be used with`DiscreteProblem`

s). - Salis H., Kaznessis Y., Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions, Journal of Chemical Physics, 122 (5), DOI:10.1063/1.1835951 is used for calculating jump times with
`VariableRateJump`

s within ODE/SDE integrators.

`DiffEqJump.JumpSet`

— Type`struct JumpSet{T1, T2, T3, T4} <: DiffEqJump.AbstractJump`

Defines a collection of jumps that should collectively be included in a simulation.

**Fields**

`variable_jumps`

Collection of

`VariableRateJump`

s`constant_jumps`

Collection of

`ConstantRateJump`

s`regular_jump`

Collection of

`RegularJump`

s`massaction_jump`

Collection of

`MassActionJump`

s

**Examples**

Here we construct two jumps, store them in a `JumpSet`

, and then simulate the resulting process.

```
using DiffEqJump, OrdinaryDiffEq
rate1(u,p,t) = p[1]
affect1!(integrator) = (integrator.u[1] += 1)
crj = ConstantRateJump(rate1, affect1!)
rate2(u,p,t) = (t/(1+t))*p[2]*u[1]
affect2!(integrator) = (integrator.u[1] -= 1)
vrj = VariableRateJump(rate2, affect2!)
jset = JumpSet(crj, vrj)
f!(du,u,p,t) = (du .= 0)
u0 = [0.0]
p = (20.0, 2.0)
tspan = (0.0, 200.0)
oprob = ODEProblem(f!, u0, tspan, p)
jprob = JumpProblem(oprob, Direct(), jset)
sol = solve(jprob, Tsit5())
```

## Aggregators

Aggregators are the underlying algorithms used for sampling `MassActionJump`

s and `ConstantRateJump`

s.

`DiffEqJump.Direct`

— TypeGillespie's Direct method. `ConstantRateJump`

rates and affects are stored in tuples. Fastest for a small (total) number of `ConstantRateJump`

s or `MassActionJump`

s (~10). For larger numbers of possible jumps use other methods.

Gillespie, Daniel T. (1976). A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions. Journal of Computational Physics. 22 (4): 403–434. doi:10.1016/0021-9991(76)90041-3.

`DiffEqJump.DirectCR`

— TypeThe Composition-Rejection Direct method. Performs best relative to other methods for systems with large numbers of jumps with special structure (for example a linear chain of reactions, or jumps corresponding to particles hopping on a grid or graph).

A. Slepoy, A.P. Thompson and S.J. Plimpton, A constant-time kinetic Monte Carlo algorithm for simulation of large biochemical reaction networks, Journal of Chemical Physics, 128 (20), 205101 (2008). doi:10.1063/1.2919546

S. Mauch and M. Stalzer, Efficient formulations for exact stochastic simulation of chemical systems, ACM Transactions on Computational Biology and Bioinformatics, 8 (1), 27-35 (2010). doi:10.1109/TCBB.2009.47

`DiffEqJump.FRM`

— TypeGillespie's First Reaction Method. Should not be used for practical applications due to slow performance relative to all other methods.

Gillespie, Daniel T. (1976). A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions. Journal of Computational Physics. 22 (4): 403–434. doi:10.1016/0021-9991(76)90041-3.

`DiffEqJump.NRM`

— TypeThe Next Reaction Method. Can significantly outperform Direct for systems with large numbers of jumps and sparse dependency graphs, but is usually slower than one of `DirectCR`

, `RSSA`

, or `RSSACR`

for such systems.

M. A. Gibson and J. Bruck, Efficient exact stochastic simulation of chemical systems with many species and many channels, Journal of Physical Chemistry A, 104 (9), 1876-1889 (2000). doi:10.1021/jp993732q

`DiffEqJump.RDirect`

— TypeA rejection-based direct method.

`DiffEqJump.RSSA`

— TypeThe Rejection SSA method. One of the best methods for systems with hundreds to many thousands of jumps (along with `RSSACR`

) and sparse dependency graphs.

V. H. Thanh, C. Priami and R. Zunino, Efficient rejection-based simulation of biochemical reactions with stochastic noise and delays, Journal of Chemical Physics, 141 (13), 134116 (2014). doi:10.1063/1.4896985

V. H. Thanh, R. Zunino and C. Priami, On the rejection-based algorithm for simulation and analysis of large-scale reaction networks, Journal of Chemical Physics, 142 (24), 244106 (2015). doi:10.1063/1.4922923

`DiffEqJump.RSSACR`

— TypeThe Rejection SSA Composition-Rejection method. Often the best performer for systems with tens of thousands of jumps and sparse depedency graphs.

V. H. Thanh, R. Zunino, and C. Priami, Efficient Constant-Time Complexity Algorithm for Stochastic Simulation of Large Reaction Networks, IEEE/ACM Transactions on Computational Biology and Bioinformatics, Vol. 14, No. 3, 657-667 (2017).

`DiffEqJump.SortingDirect`

— TypeThe Sorting Direct method. Often the fastest algorithm for smaller to moderate sized systems (tens of jumps), or systems where a few jumps occur much more frequently than others.

J. M. McCollum, G. D. Peterson, C. D. Cox, M. L. Simpson and N. F. Samatova, The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior, Computational Biology and Chemistry, 30 (1), 39049 (2006). doi:10.1016/j.compbiolchem.2005.10.007

# Private API Functions

`DiffEqJump.ExtendedJumpArray`

— Type`struct ExtendedJumpArray{T3<:Number, T1, T<:AbstractArray{T3<:Number, T1}, T2} <: AbstractArray{T3<:Number, 1}`

Extended state definition used within integrators when there are `VariableRateJump`

s in a system. For detailed examples and usage information see the

**Fields**

`u`

The current state.

`jump_u`

The current rate (i.e. hazard, intensity, or propensity) values for the

`VariableRateJump`

s.

**Examples**

```
using DiffEqJump, OrdinaryDiffEq
f(du,u,p,t) = du .= 0
rate(u,p,t) = (1+t)*u[1]*u[2]
# suppose we wish to decrease each of the two variables by one
# when a jump occurs
function affect!(integrator)
# Method 1, direct indexing works like normal
integrator.u[1] -= 1
integrator.u[2] -= 1
# Method 2, if we want to broadcast or use array operations we need
# to access integrator.u.u which is the actual state object.
# So equivalently to above we could have said:
# integrator.u.u .-= 1
end
u0 = [10.0, 10.0]
vrj = VariableRateJump(rate, affect!)
oprob = ODEProblem(f, u0, (0.0,2.0))
jprob = JumpProblem(oprob, Direct(), vrj)
sol = solve(jprob,Tsit5())
```

**Notes**

If

`ueja isa ExtendedJumpArray`

with`ueja.u`

of size`N`

and`ueja.jump_u`

of size`num_variableratejumps`

then`# for 1 <= i <= N ueja[i] == ueja.u[i] # for N < i <= (N+num_variableratejumps) ueja[i] == ueja.jump_u[i]`

In a system with

`VariableRateJump`

s all callback,`ConstantRateJump`

, and`VariableRateJump`

`affect!`

functions will receive integrators with`integrator.u`

an`ExtendedJumpArray`

.As such,

`affect!`

functions that wish to modify the state via vector operations should use`ueja.u.u`

to obtain the aliased state object.

`DiffEqJump.SSAIntegrator`

— Type`mutable struct SSAIntegrator{F, uType, tType, tdirType, P, S, CB, SA, OPT, TS} <: SciMLBase.DEIntegrator{SSAStepper, Nothing, uType, tType}`

Solution objects for pure jump problems solved via `SSAStepper`

.

**Fields**

`f`

The underlying

`prob.f`

function. Not currently used.`u`

The current solution values.

`t`

The current solution time.

`tprev`

The previous time a jump occured.

`tdir`

The direction time is changing in (must be positive indicating time is increasing)

`p`

The current parameters.

`sol`

The current solution object.

`i`

`tstop`

The next jump time.

`cb`

The jump aggregator callback.

`saveat`

Times to save the solution at.

`save_everystep`

Whether to save everytime a jump occurs.

`save_end`

Whether to save at the final step.

`cur_saveat`

Index of the next

`saveat`

time.`opts`

Tuple storing callbacks.

`tstops`

User supplied times to step to, useful with callbacks.

`tstops_idx`

`u_modified`

`keep_stepping`