# DiffEqCallbacks.jl

This is a library of callbacks for extending the solvers of DifferentialEquations.jl.

## Usage

To use the callbacks provided in this library with DifferentialEquations.jl solvers,
just pass it to the solver via the `callback`

keyword argument:

`sol = solve(prob,alg;callback=cb)`

For more information on using callbacks, see the manual page.

## ManifoldProjection

This projects the solution to a manifold, conserving a property while conserving the order.

`ManifoldProjection(g;nlsolve=NLSOLVEJL_SETUP(),save=true)`

`g`

: The residual function for the manifold:`g(resid,u)`

. This is an inplace function which writes to the residual the difference from the manifold components.`nlsolve`

: A nonlinear solver as defined in the nlsolve format`save`

: Whether to do the standard saving (applied after the callback)

## AutoAbstol

Many problem solving environments such as MATLAB
provide a way to automatically adapt the absolute tolerance to the problem. This
helps the solvers automatically "learn" what appropriate limits are. Via the
callback interface, DiffEqCallbacks.jl implements a callback `AutoAbstol`

which
has the same behavior as the MATLAB implementation, that is the absolute tolerance
starts at `init_curmax`

(default `1-e6`

), and at each iteration it is set
to the maximum value that the state has thus far reached times the relative tolerance.

To generate the callback, use the constructor:

`AutoAbstol(save=true;init_curmax=1e-6)`

`save`

determines whether this callback has saving enabled, and `init_curmax`

is
the initial `abstol`

. If this callback is used in isolation, `save=true`

is required
for normal saving behavior. Otherwise, `save=false`

should be set to ensure
extra saves do not occur.

## Domain Controls

The domain controls are efficient methods for preserving a domain relation for
the solution value `u`

. Unlike the `isoutofdomain`

method, these methods use
interpolations and extrapolations to more efficiently choose stepsizes, but
require that the solution is well defined slightly outside of the domain.

### PositiveDomain

`PositiveDomain(u=nothing; save=true, abstol=nothing, scalefactor=nothing)`

### GeneralDomain

```
GeneralDomain(g, u=nothing; nlsolve=NLSOLVEJL_SETUP(), save=true,
abstol=nothing, scalefactor=nothing, autonomous=numargs(g)==2,
nlopts=Dict(:ftol => 10*eps()))
```

## StepsizeLimiter

The stepsize limiter lets you define a function `dtFE(u,p,t)`

which changes the
allowed maximal stepsize throughout the computation. The constructor is:

`StepsizeLimiter(dtFE;safety_factor=9//10,max_step=false,cached_dtcache=0.0)`

`dtFE`

is the maximal timestep and is calculated using the previous `t`

and `u`

.
`safety_factor`

is the factor below the true maximum that will be stepped to
which defaults to `9//10`

. `max_step=true`

makes every step equal to
`safety_factor*dtFE(u,p,t)`

when the solver is set to `adaptive=false`

. `cached_dtcache`

should be set to match the type for time when not using Float64 values.

## FunctionCallingCallback

The function calling callback lets you define a function `func(u,t,integrator)`

which gets calls at the time points of interest. The constructor is:

```
FunctionCallingCallback(func;
funcat=Vector{Float64}(),
func_everystep=isempty(funcat),
func_start = true
tdir=1)
```

`func(t, u, integrator)`

is the function to be called.`funcat`

values that the function is sure to be evaluated at.`func_everystep`

whether to call the function after each integrator step.`func_start`

whether the function is called the initial condition.`tdir`

should be`sign(tspan[end]-tspan[1])`

. It defaults to`1`

and should be adapted if`tspan[1] > tspan[end]`

.

## SavingCallback

The saving callback lets you define a function `save_func(u, t, integrator)`

which
returns quantities of interest that shall be saved. The constructor is:

```
SavingCallback(save_func, saved_values::SavedValues;
saveat=Vector{eltype(saved_values.t)}(),
save_everystep=isempty(saveat),
save_start = true,
tdir=1)
```

`save_func(u, t, integrator)`

returns the quantities which shall be saved. Note that this should allocate the output (not as a view to`u`

).`saved_values::SavedValues`

is the types that`save_func`

will return, i.e.`save_func(t, u, integrator)::savevalType`

. It's specified via`SavedValues(typeof(t),savevalType)`

, i.e. give the type for time and the type that`save_func`

will output (or higher compatible type).`saveat`

mimics`saveat`

in`solve`

from`solve`

.`save_everystep`

mimics`save_everystep`

from`solve`

.`save_start`

mimics`save_start`

from`solve`

.`tdir`

should be`sign(tspan[end]-tspan[1])`

. It defaults to`1`

and should be adapted if`tspan[1] > tspan[end]`

.

The outputted values are saved into `saved_values`

. Time points are found via
`saved_values.t`

and the values are `saved_values.saveval`

.

## PresetTimeCallback

`PresetTimeCallback`

is a callback that adds callback `affect!`

calls at preset
times. No playing around with `tstops`

or anything is required: this callback
adds the triggers for you to make it automatic.

```
PresetTimeCallback(tstops,user_affect!;
initialize = DiffEqBase.INITIALIZE_DEFAULT,
filter_tstops = true,
kwargs...)
```

`tstops`

: the times for the`affect!`

to trigger at.`user_affect!`

: an`affect!(integrator)`

function to use at the time points.`filter_tstops`

: Whether to filter out tstops beyond the end of the integration timespan. Defaults to true. If false, then tstops can extend the interval of integration.

## IterativeCallback

`IterativeCallback`

is a callback to be used to iteratively apply some affect.
For example, if given the first effect at `tโ`

, you can define `tโ`

to apply
the next effect.

A `IterativeCallback`

is constructed as follows:

```
function IterativeCallback(time_choice, user_affect!,tType = Float64;
initial_affect = false, kwargs...)
```

where `time_choice(integrator)`

determines the time of the next callback and
`user_affect!`

is the effect applied to the integrator at the stopping points.
If `nothing`

is returned for the time choice then the iterator ends. `initial_affect`

is whether to apply the affect at `t=0`

which defaults to `false`

## PeriodicCallback

`PeriodicCallback`

can be used when a function should be called periodically in terms of integration time (as opposed to wall time), i.e. at `t = tspan[1]`

, `t = tspan[1] + ฮt`

, `t = tspan[1] + 2ฮt`

, and so on. This callback can, for example, be used to model a discrete-time controller for a continuous-time system, running at a fixed rate.

A `PeriodicCallback`

can be constructed as follows:

`PeriodicCallback(f, ฮt::Number; initial_affect = true, kwargs...)`

where `f`

is the function to be called periodically, `ฮt`

is the period, `initial_affect`

is whether to apply
the affect at `t=0`

which defaults to `false`

, and `kwargs`

are keyword arguments accepted by the `DiscreteCallback`

constructor.

## TerminateSteadyState

`TerminateSteadyState`

can be used to solve the problem for the steady-state
by running the solver until the derivatives of the problem converge to 0 or
`tspan[2]`

is reached. This is an alternative approach to root finding (see
the Steady State Solvers section). The constructor of this callback is:

`TerminateSteadyState(abstol = 1e-8, reltol = 1e-6, test = allDerivPass)`

where `abstol`

and `reltol`

are the absolute and relative tolerance, respectively.
These tolerances may be specified as scalars or as arrays of the same length
as the states of the problem. `test`

represents the function that evaluates the
condition for termination. The default condition is that all derivatives should
become smaller than `abstol`

and the states times `reltol`

. The user
can pass any other function to implement a different termination condition. Such
function should take four arguments: `integrator`

(see Integrator Interface
for details), `abstol`

and `reltol`

.