SDESystem
System Constructors
ModelingToolkit.SDESystem
— Typestruct SDESystem <: ModelingToolkit.AbstractODESystem
A system of stochastic differential equations.
Fields
eqs
The expressions defining the drift term.
noiseeqs
The expressions defining the diffusion term.
iv
Independent variable.
states
Dependent (state) variables.
ps
Parameter variables.
observed
tgrad
Time-derivative matrix. Note: this field will not be defined until
calculate_tgrad
is called on the system.
jac
Jacobian matrix. Note: this field will not be defined until
calculate_jacobian
is called on the system.
Wfact
Wfact
matrix. Note: this field will not be defined untilgenerate_factorized_W
is called on the system.
Wfact_t
Wfact_t
matrix. Note: this field will not be defined untilgenerate_factorized_W
is called on the system.
name
Name: the name of the system
systems
Systems: the internal systems
defaults
defaults: The default values to use when initial conditions and/or parameters are not supplied in
ODEProblem
.
Example
using ModelingToolkit
@parameters t σ ρ β
@variables x(t) y(t) z(t)
D = Differential(t)
eqs = [D(x) ~ σ*(y-x),
D(y) ~ x*(ρ-z)-y,
D(z) ~ x*y - β*z]
noiseeqs = [0.1*x,
0.1*y,
0.1*z]
de = SDESystem(eqs,noiseeqs,t,[x,y,z],[σ,ρ,β])
Composition and Accessor Functions
get_eqs(sys)
orequations(sys)
: The equations that define the SDE.get_states(sys)
orstates(sys)
: The set of states in the SDE.get_ps(sys)s
orparameters(sys)
: The parameters of the SDE.independent_variable(sys)
: The independent variable of the SDE.
Transformations
Missing docstring for structural_simplify
. Check Documenter's build log for details.
Missing docstring for alias_elimination
. Check Documenter's build log for details.
Analyses
Applicable Calculation and Generation Functions
calculate_jacobian
calculate_tgrad
calculate_factorized_W
generate_jacobian
generate_tgrad
generate_factorized_W
jacobian_sparsity
Problem Constructors
SciMLBase.SDEFunction
— Typefunction DiffEqBase.SDEFunction{iip}(sys::SDESystem, dvs = sys.states, ps = sys.ps;
version = nothing, tgrad=false, sparse = false,
jac = false, Wfact = false, kwargs...) where {iip}
Create an SDEFunction
from the SDESystem
. The arguments dvs
and ps
are used to set the order of the dependent variable and parameter vectors, respectively.
SciMLBase.SDEProblem
— Typefunction DiffEqBase.SDEProblem{iip}(sys::SDESystem,u0map,tspan,p=parammap;
version = nothing, tgrad=false,
jac = false, Wfact = false,
checkbounds = false, sparse = false,
sparsenoise = sparse,
skipzeros = true, fillzeros = true,
linenumbers = true, parallel=SerialForm(),
kwargs...)
Generates an SDEProblem from an SDESystem and allows for automatically symbolically calculating numerical enhancements.