Solution

CTModels.Components.state Function

Return the state model (on a CTModels.Models.Model) or the state trajectory function (on a CTModels.Solutions.Solution).

CTModels.Components.control Function

Return the control model (on a CTModels.Models.Model) or the control trajectory function (on a CTModels.Solutions.Solution).

CTModels.Components.costate Function

Return the costate trajectory function from a CTModels.Solutions.Solution.

CTModels.Components.variable Function

Return the variable model (on a CTModels.Models.Model) or the variable value (on a CTModels.Solutions.Solution).

CTModels.Components.time_grid Function

Return the time grid for a component from a CTModels.Solutions.Solution.

CTModels.Components.objective Function

Return the objective model (on a CTModels.Models.Model) or the objective value (on a CTModels.Solutions.Solution).

CTModels.Solutions.status Function

julia

status(sol::CTModels.Solutions.Solution) -> Any

Return the status criterion (a Symbol).

julia

status(r::AbstractIntegrationResult) -> Any

Return the termination status of the integration result, as a Symbol.

This generic is owned by CTModels.Solutions; CTSolvers.Integrators contributes the methods for AbstractIntegrationResult subtypes so that a single status works uniformly on OCP solutions and on integration results.

Arguments

r::AbstractIntegrationResult: The integration result.

Throws

CTBase.Exceptions.NotImplemented: If not implemented by the concrete type.

julia

status(
    sol::CTFlows.Trajectories.VectorFieldTrajectory
) -> Any

Return the termination status of the solution by delegating to the integration result.

Arguments

sol::VectorFieldTrajectory: The vector field solution.

Returns

The termination status (a Symbol) from the integration result.

julia

status(
    sol::CTFlows.Trajectories.HamiltonianVectorFieldTrajectory
) -> Any

Return the termination status of the solution by delegating to the integration result.

Arguments

sol::HamiltonianVectorFieldTrajectory: The Hamiltonian vector field solution.

Returns

The termination status (a Symbol) from the integration result.

julia

status(sol::CTFlows.Trajectories.StateFlowTrajectory) -> Any

Return the termination status of a StateFlowTrajectory, delegating to the underlying state trajectory.

julia

status(
    r::CTSolversSciMLIntegrator.SciMLIntegrationResult
) -> Any

Return the termination status of the SciML ODE solution, as a Symbol derived from its retcode (e.g. :Success, :MaxIters).

CTModels.Solutions.message Function

julia

message(sol::CTModels.Solutions.Solution) -> Any

Return the message associated to the status criterion.

CTModels.Solutions.successful Function

julia

successful(sol::CTModels.Solutions.Solution) -> Bool

Return the successful status.

julia

successful(r::AbstractIntegrationResult) -> Any

Return whether the integration terminated successfully.

This generic is owned by CTModels.Solutions; CTSolvers.Integrators contributes the methods for AbstractIntegrationResult subtypes so that a single successful works uniformly on OCP solutions and on integration results.

Arguments

r::AbstractIntegrationResult: The integration result.

Throws

CTBase.Exceptions.NotImplemented: If not implemented by the concrete type.

julia

successful(
    sol::CTFlows.Trajectories.VectorFieldTrajectory
) -> Any

Return whether the solution terminated successfully by delegating to the integration result.

Arguments

sol::VectorFieldTrajectory: The vector field solution.

Returns

Whether the integration succeeded.

julia

successful(
    sol::CTFlows.Trajectories.HamiltonianVectorFieldTrajectory
) -> Any

Return whether the solution terminated successfully by delegating to the integration result.

Arguments

sol::HamiltonianVectorFieldTrajectory: The Hamiltonian vector field solution.

Returns

Whether the integration succeeded.

julia

successful(
    sol::CTFlows.Trajectories.StateFlowTrajectory
) -> Any

Return whether a StateFlowTrajectory terminated successfully, delegating to the underlying state trajectory.

julia

successful(
    r::CTSolversSciMLIntegrator.SciMLIntegrationResult
) -> Any

Return whether the SciML ODE solution terminated successfully, per SciMLBase.successful_retcode.

CTModels.Solutions.iterations Function

julia

iterations(sol::CTModels.Solutions.Solution) -> Any

Return the number of iterations (if solved by an iterative method).

CTModels.Solutions.constraints_violation Function

julia

constraints_violation(
    sol::CTModels.Solutions.Solution
) -> Any

Return the constraints violation.

CTModels.Solutions.infos Function

julia

infos(sol::CTModels.Solutions.Solution) -> Dict{Symbol, Any}

Return a dictionary of additional infos depending on the solver or nothing.

CTModels.Solutions.model Function

julia

model(
    sol::CTModels.Solutions.Solution{<:CTModels.Solutions.AbstractTimeGridModel, <:CTModels.Components.AbstractTimesModel, <:CTModels.Components.AbstractStateModel, <:CTModels.Components.AbstractControlModel, <:CTModels.Components.AbstractVariableModel, M<:CTModels.Models.AbstractModel}
) -> CTModels.Models.AbstractModel

Return the model of the optimal control problem.

CTModels.Solutions.is_empty Function

julia

is_empty(
    model::CTModels.Solutions.EmptyTimeGridModel
) -> Bool

Return true if the time grid model is empty.

Arguments

model::EmptyTimeGridModel: An empty time grid model

Returns

Bool: Always true for empty time grid models

Example

julia

julia> etg = CTModels.EmptyTimeGridModel()
julia> CTModels.is_empty(etg)
true

julia

is_empty(
    model::CTModels.Solutions.AbstractTimeGridModel
) -> Bool

Return false for non-empty time grid models.

Arguments

model::AbstractTimeGridModel: Any non-empty time grid model

Returns

Bool: Always false for non-empty time grid models

Example

julia

julia> T = LinRange(0, 1, 101)
julia> utg = CTModels.UnifiedTimeGridModel(T)
julia> CTModels.is_empty(utg)
false

CTModels.Solutions.is_empty_time_grid Function

julia

is_empty_time_grid(sol::CTModels.Solutions.Solution) -> Bool

Check if the time grid is empty from the solution.

CTModels.Solutions.dual Function

julia

dual(
    sol::CTModels.Solutions.Solution,
    model::CTModels.Models.Model,
    label::Symbol
) -> Any

Return the dual variable associated with a constraint identified by its label.

Searches through all constraint types (path, boundary, state, control, and variable constraints) defined in the model and returns the corresponding dual value from the solution.

Arguments

sol::Solution: Solution object containing dual variables.
model::Model: Model containing constraint definitions.
label::Symbol: Symbol corresponding to a constraint label.

Returns

A function of time t for time-dependent constraints, or a scalar/vector for time-invariant duals. If the label is not found, throws an IncorrectArgument exception.

Notes

For path/boundary constraints, duals are indexed per declaration (one column per row of the stacked nonlinear constraint vector).
For box constraints (state/control/variable), the dual matrices/vectors stored in the Solution are indexed by primal component (i.e. state_dimension(model) columns for state, etc.), following the CTDirect convention. For a label targeting component indices rg, this function returns duals_lb[:, rg] - duals_ub[:, rg] (or the time-independent analogue for variables). Components never constrained carry a zero multiplier.
If several labels target the same component, dual(sol, model, :label) returns the (same) per-component multiplier for each: CTModels does not track which declaration "owns" the multiplier, because the solver only sees the effective (intersected) bound.

CTModels.Solutions.path_constraints_dual Function

julia

path_constraints_dual(
    model::CTModels.Solutions.DualModel{PC_Dual<:Union{Nothing, Function}}
) -> Union{Nothing, Function}

Return the dual function associated with the nonlinear path constraints.

Arguments

model::DualModel: A model including dual variables for path constraints.

Returns

PC_Dual: A function mapping time t to the vector of dual values, or nothing if not set.

julia

path_constraints_dual(_::CTModels.Solutions.EmptyDualModel)

Return nothing for an empty dual model: the path constraints dual is absent.

julia

path_constraints_dual(
    sol::CTModels.Solutions.Solution
) -> Union{Nothing, Function}

Return the dual of the path constraints.

CTModels.Solutions.boundary_constraints_dual Function

julia

boundary_constraints_dual(
    model::CTModels.Solutions.DualModel{<:Union{Nothing, Function}, BC_Dual<:Union{Nothing, AbstractVector{<:Real}}}
) -> Union{Nothing, AbstractVector{<:Real}}

Return the dual vector associated with the boundary constraints.

Arguments

model::DualModel: A model including dual variables for boundary constraints.

Returns

BC_Dual: A vector of dual values, or nothing if not set.

julia

boundary_constraints_dual(
    _::CTModels.Solutions.EmptyDualModel
)

Return nothing for an empty dual model: the boundary constraints dual is absent.

julia

boundary_constraints_dual(
    sol::CTModels.Solutions.Solution
) -> Union{Nothing, AbstractVector{<:Real}}

Return the dual of the boundary constraints.

CTModels.Solutions.state_constraints_lb_dual Function

julia

state_constraints_lb_dual(
    model::CTModels.Solutions.DualModel{<:Union{Nothing, Function}, <:Union{Nothing, AbstractVector{<:Real}}, SC_LB_Dual<:Union{Nothing, Function}}
) -> Union{Nothing, Function}

Return the dual function associated with the lower bounds of state constraints.

Arguments

model::DualModel: A model including dual variables for state lower bounds.

Returns

SC_LB_Dual: A function mapping time t to a vector of dual values, or nothing if not set.

julia

state_constraints_lb_dual(
    _::CTModels.Solutions.EmptyDualModel
)

Return nothing for an empty dual model: the state lower-bound dual is absent.

julia

state_constraints_lb_dual(
    sol::CTModels.Solutions.Solution
) -> Union{Nothing, Function}

Return the lower bound dual of the state constraints.

CTModels.Solutions.state_constraints_ub_dual Function

julia

state_constraints_ub_dual(
    model::CTModels.Solutions.DualModel{<:Union{Nothing, Function}, <:Union{Nothing, AbstractVector{<:Real}}, <:Union{Nothing, Function}, SC_UB_Dual<:Union{Nothing, Function}}
) -> Union{Nothing, Function}

Return the dual function associated with the upper bounds of state constraints.

Arguments

model::DualModel: A model including dual variables for state upper bounds.

Returns

SC_UB_Dual: A function mapping time t to a vector of dual values, or nothing if not set.

julia

state_constraints_ub_dual(
    _::CTModels.Solutions.EmptyDualModel
)

Return nothing for an empty dual model: the state upper-bound dual is absent.

julia

state_constraints_ub_dual(
    sol::CTModels.Solutions.Solution
) -> Union{Nothing, Function}

Return the upper bound dual of the state constraints.

CTModels.Solutions.control_constraints_lb_dual Function

julia

control_constraints_lb_dual(
    model::CTModels.Solutions.DualModel{<:Union{Nothing, Function}, <:Union{Nothing, AbstractVector{<:Real}}, <:Union{Nothing, Function}, <:Union{Nothing, Function}, CC_LB_Dual<:Union{Nothing, Function}}
) -> Union{Nothing, Function}

Return the dual function associated with the lower bounds of control constraints.

Arguments

model::DualModel: A model including dual variables for control lower bounds.

Returns

CC_LB_Dual: A function mapping time t to a vector of dual values, or nothing if not set.

julia

control_constraints_lb_dual(
    _::CTModels.Solutions.EmptyDualModel
)

Return nothing for an empty dual model: the control lower-bound dual is absent.

julia

control_constraints_lb_dual(
    sol::CTModels.Solutions.Solution
) -> Union{Nothing, Function}

Return the lower bound dual of the control constraints.

CTModels.Solutions.control_constraints_ub_dual Function

julia

control_constraints_ub_dual(
    model::CTModels.Solutions.DualModel{<:Union{Nothing, Function}, <:Union{Nothing, AbstractVector{<:Real}}, <:Union{Nothing, Function}, <:Union{Nothing, Function}, <:Union{Nothing, Function}, CC_UB_Dual<:Union{Nothing, Function}}
) -> Union{Nothing, Function}

Return the dual function associated with the upper bounds of control constraints.

Arguments

model::DualModel: A model including dual variables for control upper bounds.

Returns

CC_UB_Dual: A function mapping time t to a vector of dual values, or nothing if not set.

julia

control_constraints_ub_dual(
    _::CTModels.Solutions.EmptyDualModel
)

Return nothing for an empty dual model: the control upper-bound dual is absent.

julia

control_constraints_ub_dual(
    sol::CTModels.Solutions.Solution
) -> Union{Nothing, Function}

Return the upper bound dual of the control constraints.

CTModels.Solutions.variable_constraints_lb_dual Function

julia

variable_constraints_lb_dual(
    model::CTModels.Solutions.DualModel{<:Union{Nothing, Function}, <:Union{Nothing, AbstractVector{<:Real}}, <:Union{Nothing, Function}, <:Union{Nothing, Function}, <:Union{Nothing, Function}, <:Union{Nothing, Function}, VC_LB_Dual<:Union{Nothing, AbstractVector{<:Real}}}
) -> Union{Nothing, AbstractVector{<:Real}}

Return the dual vector associated with the lower bounds of variable constraints.

Arguments

model::DualModel: A model including dual variables for variable lower bounds.

Returns

VC_LB_Dual: A vector of dual values, or nothing if not set.

julia

variable_constraints_lb_dual(
    _::CTModels.Solutions.EmptyDualModel
)

Return nothing for an empty dual model: the variable lower-bound dual is absent.

julia

variable_constraints_lb_dual(
    sol::CTModels.Solutions.Solution
) -> Union{Nothing, AbstractVector{<:Real}}

Return the lower bound dual of the variable constraints.

CTModels.Solutions.variable_constraints_ub_dual Function

julia

variable_constraints_ub_dual(
    model::CTModels.Solutions.DualModel{<:Union{Nothing, Function}, <:Union{Nothing, AbstractVector{<:Real}}, <:Union{Nothing, Function}, <:Union{Nothing, Function}, <:Union{Nothing, Function}, <:Union{Nothing, Function}, <:Union{Nothing, AbstractVector{<:Real}}, VC_UB_Dual<:Union{Nothing, AbstractVector{<:Real}}}
) -> Union{Nothing, AbstractVector{<:Real}}

Return the dual vector associated with the upper bounds of variable constraints.

Arguments

model::DualModel: A model including dual variables for variable upper bounds.

Returns

VC_UB_Dual: A vector of dual values, or nothing if not set.

julia

variable_constraints_ub_dual(
    _::CTModels.Solutions.EmptyDualModel
)

Return nothing for an empty dual model: the variable upper-bound dual is absent.

julia

variable_constraints_ub_dual(
    sol::CTModels.Solutions.Solution
) -> Union{Nothing, AbstractVector{<:Real}}

Return the upper bound dual of the variable constraints.

CTModels.Solutions.dim_dual_state_constraints_box Function

julia

dim_dual_state_constraints_box(
    sol::CTModels.Solutions.Solution
) -> Int64

Return the dimension of the box constraints duals on state.

Arguments

sol::Solution: The optimal control solution.

Returns

Dimension: The state box constraints duals dimension.

CTModels.Solutions.dim_dual_control_constraints_box Function

julia

dim_dual_control_constraints_box(
    sol::CTModels.Solutions.Solution
) -> Int64

Return the dimension of the box constraints duals on control.

Arguments

sol::Solution: The optimal control solution.

Returns

Dimension: The control box constraints duals dimension.

CTModels.Solutions.dim_dual_variable_constraints_box Function

julia

dim_dual_variable_constraints_box(
    sol::CTModels.Solutions.Solution
) -> Int64

Return the dimension of the variable box constraints duals.

Arguments

sol::Solution: The optimal control solution.

Returns

Dimension: The variable box constraints duals dimension.

Solution ​

Solution