package scipy

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package scipy
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type tag = [
  1. | `RK45
]
type t = [ `Object | `RK45 ] Obj.t
val of_pyobject : Py.Object.t -> t
val to_pyobject : [> tag ] Obj.t -> Py.Object.t
val create : ?max_step:float -> ?rtol:Py.Object.t -> ?atol:Py.Object.t -> ?vectorized:bool -> ?first_step:float -> ?extraneous:(string * Py.Object.t) list -> fun_:Py.Object.t -> t0:float -> y0:[> `Ndarray ] Np.Obj.t -> t_bound:float -> unit -> t

Explicit Runge-Kutta method of order 5(4).

This uses the Dormand-Prince pair of formulas 1_. The error is controlled assuming accuracy of the fourth-order method accuracy, but steps are taken using the fifth-order accurate formula (local extrapolation is done). A quartic interpolation polynomial is used for the dense output 2_.

Can be applied in the complex domain.

Parameters ---------- fun : callable Right-hand side of the system. The calling signature is ``fun(t, y)``. Here ``t`` is a scalar, and there are two options for the ndarray ``y``: It can either have shape (n,); then ``fun`` must return array_like with shape (n,). Alternatively it can have shape (n, k); then ``fun`` must return an array_like with shape (n, k), i.e., each column corresponds to a single column in ``y``. The choice between the two options is determined by `vectorized` argument (see below). t0 : float Initial time. y0 : array_like, shape (n,) Initial state. t_bound : float Boundary time - the integration won't continue beyond it. It also determines the direction of the integration. first_step : float or None, optional Initial step size. Default is ``None`` which means that the algorithm should choose. max_step : float, optional Maximum allowed step size. Default is np.inf, i.e., the step size is not bounded and determined solely by the solver. rtol, atol : float and array_like, optional Relative and absolute tolerances. The solver keeps the local error estimates less than ``atol + rtol * abs(y)``. Here `rtol` controls a relative accuracy (number of correct digits). But if a component of `y` is approximately below `atol`, the error only needs to fall within the same `atol` threshold, and the number of correct digits is not guaranteed. If components of y have different scales, it might be beneficial to set different `atol` values for different components by passing array_like with shape (n,) for `atol`. Default values are 1e-3 for `rtol` and 1e-6 for `atol`. vectorized : bool, optional Whether `fun` is implemented in a vectorized fashion. Default is False.

Attributes ---------- n : int Number of equations. status : string Current status of the solver: 'running', 'finished' or 'failed'. t_bound : float Boundary time. direction : float Integration direction: +1 or -1. t : float Current time. y : ndarray Current state. t_old : float Previous time. None if no steps were made yet. step_size : float Size of the last successful step. None if no steps were made yet. nfev : int Number evaluations of the system's right-hand side. njev : int Number of evaluations of the Jacobian. Is always 0 for this solver as it does not use the Jacobian. nlu : int Number of LU decompositions. Is always 0 for this solver.

References ---------- .. 1 J. R. Dormand, P. J. Prince, 'A family of embedded Runge-Kutta formulae', Journal of Computational and Applied Mathematics, Vol. 6, No. 1, pp. 19-26, 1980. .. 2 L. W. Shampine, 'Some Practical Runge-Kutta Formulas', Mathematics of Computation,, Vol. 46, No. 173, pp. 135-150, 1986.

val dense_output : [> tag ] Obj.t -> Py.Object.t

Compute a local interpolant over the last successful step.

Returns ------- sol : `DenseOutput` Local interpolant over the last successful step.

val step : [> tag ] Obj.t -> string option

Perform one integration step.

Returns ------- message : string or None Report from the solver. Typically a reason for a failure if `self.status` is 'failed' after the step was taken or None otherwise.

val n : t -> int

Attribute n: get value or raise Not_found if None.

val n_opt : t -> int option

Attribute n: get value as an option.

val status : t -> string

Attribute status: get value or raise Not_found if None.

val status_opt : t -> string option

Attribute status: get value as an option.

val t_bound : t -> float

Attribute t_bound: get value or raise Not_found if None.

val t_bound_opt : t -> float option

Attribute t_bound: get value as an option.

val direction : t -> float

Attribute direction: get value or raise Not_found if None.

val direction_opt : t -> float option

Attribute direction: get value as an option.

val t : t -> float

Attribute t: get value or raise Not_found if None.

val t_opt : t -> float option

Attribute t: get value as an option.

val y : t -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Attribute y: get value or raise Not_found if None.

val y_opt : t -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t option

Attribute y: get value as an option.

val t_old : t -> float

Attribute t_old: get value or raise Not_found if None.

val t_old_opt : t -> float option

Attribute t_old: get value as an option.

val step_size : t -> float

Attribute step_size: get value or raise Not_found if None.

val step_size_opt : t -> float option

Attribute step_size: get value as an option.

val nfev : t -> int

Attribute nfev: get value or raise Not_found if None.

val nfev_opt : t -> int option

Attribute nfev: get value as an option.

val njev : t -> int

Attribute njev: get value or raise Not_found if None.

val njev_opt : t -> int option

Attribute njev: get value as an option.

val nlu : t -> int

Attribute nlu: get value or raise Not_found if None.

val nlu_opt : t -> int option

Attribute nlu: get value as an option.

val to_string : t -> string

Print the object to a human-readable representation.

val show : t -> string

Print the object to a human-readable representation.

val pp : Stdlib.Format.formatter -> t -> unit

Pretty-print the object to a formatter.