GeometricBase

AbstractScalarVariable{T} is a wrapper around a zero-dimensional AbstractArray{T,0} that provides context for the nature of the variable, e.g., time.

AbstractSolverState

The state is used in solvers and optimizers to translate information about previous solver/optimization steps to successive iterations.

AbstractStateVariable{T,N,AT} is a wrapper around a AT <: AbstractArray{T,N} that provides context for the nature of the variable, e.g., a state or a vector field.

AbstractVariable{T,N} is a wrapper around a AbstractArray{T,N} that provides context for the nature of the variable.

GeometricData is a wrapper for different types of data sets such as the solution of a Lagrangian or Hamiltonian system.

NullInvariants is an empty struct that is used to indicate than an equation does not have invariants.

NullParameters is an empty struct that is used to indicate than an equation does not have parameters.

NullPeriodicity is an empty struct that is used to indicate than an equation does not have periodic solution components.

NullSolverState is an empty struct that is used to indicate than a solver does not store a state.

Holds the solution of a geometric equation at a single time step.

It stores all the information that is required to uniquely determine the state of a systen, in particular all state variables and their corresponding vector fields.

StateVariable{T,N,AT,RT,PT} is a wrapper around a AT <: AbstractArray{T,N} that holds one of the variables consituting the state of a dynamical system.

The value field holds the actual data, the range field holds the range of valid values, and the periodic field holds a bitmask indicating which dimensions are periodic.

StateVector{DT,VT} is a vector of StateVariables, where DT is the datatype of the state and VT is the type of the vector.

initialize!(st::State, ics::NamedTuple)

Copy the values from a NamedTuple ics to the State st.

The keys of ics must be the same as the solution keys of the state.

Arguments

• st: the state to copy into
• ics: the named tuple containing the initial values to copy

copy!(dst::State, src::State)

Copy the values from one State src to another State dst.

The keys of src and dst must identical.

Arguments

• src: the state to copy into
• dst: the state containing the solution values to copy

getindex(st::State, args...)

Passes getindex on to the state in State.

keys(st::State)

Return the keys of all the state variables in the State.

HistoryState(st::State)

Constructs a state whose symbols are decorated by a bar to indicate a previous value of the state.

SolverState(::Union{<:AbstractSolver,<:SolverMethod}, args...; kwargs...)

This method returns a subtype of AbstractSolverState according to the AbstractSolver or SolverMethod that is passed to it. By default, i.e., if no such method is defined for a given solver, it returns NullSolverState.

integrate(problem, method; kwargs...)

Integrate a problem with method and return the solution.

Solve one time step:

integrate!(integrator)

The vectorfield function returns a datastructure that stores the vectorfield for an AbstractStateVariable s that holds the state of a system. By default it returns a VectorfieldVariable that wraps zero(parent(s)), i.e., the same kind of array as the state variable, but custom methods can be implemented in order to account for more specific use cases, e.g., when s also contains constant fields that should not be present in the vector field.

zerovector(X::StateVector) returns a new StateVector with zero applied all elements of X.