NonlinearSystem

struct NonlinearSystem <: AbstractTimeIndependentSystem

A nonlinear system of equations.

Fields

• eqs

  Vector of equations defining the system.

• states

  Unknown variables.

• ps

  Parameters.

• var_to_name

  Array variables.

• observed

• jac

  Jacobian matrix. Note: this field will not be defined until calculate_jacobian is called on the system.

• name

  Name: the name of the system. These are required to have unique names.

• systems

  systems: The internal systems

• defaults

  defaults: The default values to use when initial conditions and/or parameters are not supplied in ODEProblem.

• connector_type

  type: type of the system

• metadata

  metadata: metadata for the system, to be used by downstream packages.

• tearing_state

  tearing_state: cache for intermediate tearing state

• substitutions

  substitutions: substitutions generated by tearing.

Examples

@variables x y z
@parameters σ ρ β

eqs = [0 ~ σ*(y-x),
       0 ~ x*(ρ-z)-y,
       0 ~ x*y - β*z]
@named ns = NonlinearSystem(eqs, [x,y,z],[σ,ρ,β])

tearing(sys; simplify=false)

Tear the nonlinear equations in system. When simplify=true, we simplify the new residual residual equations after tearing. End users are encouraged to call structural_simplify instead, which calls this function internally.

function SciMLBase.NonlinearFunction{iip}(sys::NonlinearSystem, dvs = states(sys),
                                     ps = parameters(sys);
                                     version = nothing,
                                     jac = false,
                                     sparse = false,
                                     kwargs...) where {iip}

Create an NonlinearFunction from the NonlinearSystem. The arguments dvs and ps are used to set the order of the dependent variable and parameter vectors, respectively.

function DiffEqBase.NonlinearProblem{iip}(sys::NonlinearSystem,u0map,
                                          parammap=DiffEqBase.NullParameters();
                                          jac = false, sparse=false,
                                          checkbounds = false,
                                          linenumbers = true, parallel=nothing,
                                          kwargs...) where iip

Generates an NonlinearProblem from a NonlinearSystem and allows for automatically symbolically calculating numerical enhancements.

function SciMLBase.NonlinearFunctionExpr{iip}(sys::NonlinearSystem, dvs = states(sys),
                                     ps = parameters(sys);
                                     version = nothing,
                                     jac = false,
                                     sparse = false,
                                     kwargs...) where {iip}

Create a Julia expression for an ODEFunction from the ODESystem. The arguments dvs and ps are used to set the order of the dependent variable and parameter vectors, respectively.

function DiffEqBase.NonlinearProblemExpr{iip}(sys::NonlinearSystem,u0map,
                                          parammap=DiffEqBase.NullParameters();
                                          jac = false, sparse=false,
                                          checkbounds = false,
                                          linenumbers = true, parallel=nothing,
                                          kwargs...) where iip

Generates a Julia expression for a NonlinearProblem from a NonlinearSystem and allows for automatically symbolically calculating numerical enhancements.