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NonlinearSystem

System Constructors

ModelingToolkit.NonlinearSystem — Type
struct NonlinearSystem <: AbstractTimeIndependentSystem

A nonlinear system of equations.

Fields

  • tag: tag: a tag for the system. If two systems have the same tag, then they are structurally identical.

  • 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.
  • gui_metadata: gui_metadata: metadata for MTK GUI.
  • tearing_state: tearing_state: cache for intermediate tearing state
  • substitutions: substitutions: substitutions generated by tearing.
  • complete: complete: if a model sys is complete, then sys.x no longer performs namespacing.

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])
source

Composition and Accessor Functions

  • get_eqs(sys) or equations(sys): The equations that define the nonlinear system.
  • get_states(sys) or states(sys): The set of states in the nonlinear system.
  • get_ps(sys) or parameters(sys): The parameters of the nonlinear system.
  • get_u0_p(sys, u0map, parammap) Numeric arrays for the initial condition and parameters given var => value maps.

Transformations

Missing docstring.

Missing docstring for structural_simplify. Check Documenter's build log for details.

Missing docstring.

Missing docstring for alias_elimination. Check Documenter's build log for details.

Analyses

Missing docstring.

Missing docstring for ModelingToolkit.isaffine. Check Documenter's build log for details.

Missing docstring.

Missing docstring for ModelingToolkit.islinear. Check Documenter's build log for details.

Applicable Calculation and Generation Functions

calculate_jacobian
generate_jacobian
jacobian_sparsity

Problem Constructors

SciMLBase.NonlinearFunction — Method
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.

source
SciMLBase.NonlinearProblem — Method
DiffEqBase.NonlinearProblem{iip}(sys::NonlinearSystem, u0map,
                                 parammap = DiffEqBase.NullParameters();
                                 jac = false, sparse = false,
                                 checkbounds = false,
                                 linenumbers = true, parallel = SerialForm(),
                                 kwargs...) where {iip}

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

source

Torn Problem Constructors

Missing docstring.

Missing docstring for BlockNonlinearProblem. Check Documenter's build log for details.

Expression Constructors

ModelingToolkit.NonlinearFunctionExpr — Type
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.

source
ModelingToolkit.NonlinearProblemExpr — Type
DiffEqBase.NonlinearProblemExpr{iip}(sys::NonlinearSystem, u0map,
                                     parammap = DiffEqBase.NullParameters();
                                     jac = false, sparse = false,
                                     checkbounds = false,
                                     linenumbers = true, parallel = SerialForm(),
                                     kwargs...) where {iip}

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

source