ostk.mathematics.solver.NumericalSolver

class NumericalSolver(

self: ostk.mathematics.solver.NumericalSolver,

log_type: ostk::mathematics::solver::NumericalSolver::LogType,

stepper_type: ostk::mathematics::solver::NumericalSolver::StepperType,

time_step: ostk.core.type.Real,

relative_tolerance: ostk.core.type.Real,

absolute_tolerance: ostk.core.type.Real,

)

Bases: pybind11_object

Create a numerical solver with specified parameters.

Parameters:

• log_type (NumericalSolver.LogType) -- The logging type for the solver.

• stepper_type (NumericalSolver.StepperType) -- The stepper algorithm to use.

• time_step (float) -- The time step for integration.

• relative_tolerance (float) -- The relative tolerance for adaptive steppers.

• absolute_tolerance (float) -- The absolute tolerance for adaptive steppers.

Example

>>> solver = NumericalSolver(
...     NumericalSolver.LogType.NoLog,
...     NumericalSolver.StepperType.RungeKutta4,
...     1.0, 1e-12, 1e-12
... )

Methods

default	Create a default numerical solver.
get_absolute_tolerance	Get the absolute tolerance of the solver.
get_log_type	Get the log type of the solver.
get_observed_state_vectors	Get the observed state vectors from the last integration.
get_relative_tolerance	Get the relative tolerance of the solver.
get_stepper_type	Get the stepper type of the solver.
get_time_step	Get the time step of the solver.
integrate_duration	Overloaded function.
integrate_time	Overloaded function.
is_defined	Check if the numerical solver is defined.
string_from_log_type	Get string representation of a log type.
string_from_stepper_type	Get string representation of a stepper type.
undefined	Create an undefined numerical solver.

class LogType(

self: ostk.mathematics.solver.NumericalSolver.LogType,

value: int,

)

Bases: pybind11_object

Members:

NoLog

LogConstant

LogAdaptive

property name

class StepperType(

self: ostk.mathematics.solver.NumericalSolver.StepperType,

value: int,

)

Bases: pybind11_object

Members:

RungeKutta4

RungeKuttaCashKarp54

RungeKuttaFehlberg78

RungeKuttaDopri5

property name

static default() → ostk.mathematics.solver.NumericalSolver

Create a default numerical solver.

Returns:

A solver with default settings.

Return type:

NumericalSolver

Example

>>> solver = NumericalSolver.default()
>>> solver.is_defined()  # True

get_absolute_tolerance(

self: ostk.mathematics.solver.NumericalSolver,

) → ostk.core.type.Real

Get the absolute tolerance of the solver.

Returns:

The absolute tolerance value.

Return type:

float

Example

>>> solver = NumericalSolver.default()
>>> abs_tol = solver.get_absolute_tolerance()

get_log_type(

self: ostk.mathematics.solver.NumericalSolver,

) → ostk::mathematics::solver::NumericalSolver::LogType

Get the log type of the solver.

Returns:

The log type.

Return type:

NumericalSolver.LogType

Example

>>> solver = NumericalSolver.default()
>>> log_type = solver.get_log_type()

get_observed_state_vectors(

self: ostk.mathematics.solver.NumericalSolver,

) → list[tuple[numpy.ndarray[numpy.float64[m, 1]], float]]

Get the observed state vectors from the last integration.

Returns:

List of observed state vectors during integration.

Return type:

list

Example

>>> solver = NumericalSolver.default()
>>> # After performing integration...
>>> states = solver.get_observed_state_vectors()

get_relative_tolerance(

self: ostk.mathematics.solver.NumericalSolver,

) → ostk.core.type.Real

Get the relative tolerance of the solver.

Returns:

The relative tolerance value.

Return type:

float

Example

>>> solver = NumericalSolver.default()
>>> rel_tol = solver.get_relative_tolerance()

get_stepper_type(

self: ostk.mathematics.solver.NumericalSolver,

) → ostk::mathematics::solver::NumericalSolver::StepperType

Get the stepper type of the solver.

Returns:

The stepper type.

Return type:

NumericalSolver.StepperType

Example

>>> solver = NumericalSolver.default()
>>> stepper_type = solver.get_stepper_type()

get_time_step(

self: ostk.mathematics.solver.NumericalSolver,

) → ostk.core.type.Real

Get the time step of the solver.

Returns:

The time step value.

Return type:

float

Example

>>> solver = NumericalSolver.default()
>>> time_step = solver.get_time_step()

integrate_duration(*args, **kwargs)

Overloaded function.

1. integrate_duration(self: ostk.mathematics.solver.NumericalSolver, arg0: numpy.ndarray[numpy.float64[m, 1]], arg1: ostk.core.type.Real, arg2: object) -> tuple[numpy.ndarray[numpy.float64[m, 1]], float]

   Integrate a system of differential equations for a specified duration.

   Args:

   state_vector (StateVector): Initial state vector. duration_in_seconds (float): Integration duration in seconds. system_of_equations (callable): Function defining the system of ODEs.

   Signature: f(x, dxdt, t) -> StateVector

   Returns:

   StateVector: Final state vector after integration.

   Example:

   >>> def equations(x, dxdt, t):
   ...     dxdt[0] = x[1]  # dx/dt = v
   ...     dxdt[1] = -x[0]  # dv/dt = -x (harmonic oscillator)
   ...     return dxdt
   >>> solver = NumericalSolver.default()
   >>> initial_state = [1.0, 0.0]  # x=1, v=0
   >>> final_state = solver.integrate_duration(initial_state, 1.0, equations)
   

2. integrate_duration(self: ostk.mathematics.solver.NumericalSolver, arg0: numpy.ndarray[numpy.float64[m, 1]], arg1: list[ostk.core.type.Real], arg2: object) -> list[tuple[numpy.ndarray[numpy.float64[m, 1]], float]]

   Integrate a system of differential equations at multiple duration points.

   Args:

   state_vector (StateVector): Initial state vector. duration_array (list): Array of duration values in seconds. system_of_equations (callable): Function defining the system of ODEs.

   Signature: f(x, dxdt, t) -> StateVector

   Returns:

   list: State vectors at each duration point.

   Example:

   >>> def equations(x, dxdt, t):
   ...     dxdt[0] = x[1]  # dx/dt = v
   ...     dxdt[1] = -x[0]  # dv/dt = -x (harmonic oscillator)
   ...     return dxdt
   >>> solver = NumericalSolver.default()
   >>> initial_state = [1.0, 0.0]
   >>> durations = [0.5, 1.0, 1.5]
   >>> states = solver.integrate_duration(initial_state, durations, equations)
   

integrate_time(*args, **kwargs)

Overloaded function.

1. integrate_time(self: ostk.mathematics.solver.NumericalSolver, arg0: numpy.ndarray[numpy.float64[m, 1]], arg1: ostk.core.type.Real, arg2: ostk.core.type.Real, arg3: object) -> tuple[numpy.ndarray[numpy.float64[m, 1]], float]

   Integrate a system of differential equations from start to end time.

   Args:

   state_vector (StateVector): Initial state vector. start_time (float): Integration start time. end_time (float): Integration end time. system_of_equations (callable): Function defining the system of ODEs.

   Signature: f(x, dxdt, t) -> StateVector

   Returns:

   StateVector: Final state vector at end time.

   Example:

   >>> def equations(x, dxdt, t):
   ...     dxdt[0] = x[1]  # dx/dt = v
   ...     dxdt[1] = -x[0]  # dv/dt = -x (harmonic oscillator)
   ...     return dxdt
   >>> solver = NumericalSolver.default()
   >>> initial_state = [1.0, 0.0]
   >>> final_state = solver.integrate_time(initial_state, 0.0, 2.0, equations)
   

2. integrate_time(self: ostk.mathematics.solver.NumericalSolver, arg0: numpy.ndarray[numpy.float64[m, 1]], arg1: ostk.core.type.Real, arg2: list[ostk.core.type.Real], arg3: object) -> list[tuple[numpy.ndarray[numpy.float64[m, 1]], float]]

   Integrate a system of differential equations at specified time points.

   Args:

   state_vector (StateVector): Initial state vector. start_time (float): Integration start time. time_array (list): Array of time points to evaluate at. system_of_equations (callable): Function defining the system of ODEs.

   Signature: f(x, dxdt, t) -> StateVector

   Returns:

   list: State vectors at each time point.

   Example:

   >>> def equations(x, dxdt, t):
   ...     dxdt[0] = x[1]  # dx/dt = v
   ...     dxdt[1] = -x[0]  # dv/dt = -x (harmonic oscillator)
   ...     return dxdt
   >>> solver = NumericalSolver.default()
   >>> initial_state = [1.0, 0.0]
   >>> times = [0.5, 1.0, 1.5, 2.0]
   >>> states = solver.integrate_time(initial_state, 0.0, times, equations)
   

is_defined(self: ostk.mathematics.solver.NumericalSolver) → bool

Check if the numerical solver is defined.

Returns:

True if the solver is defined, False otherwise.

Return type:

bool

Example

>>> solver = NumericalSolver.default()
>>> solver.is_defined()  # True

static string_from_log_type(

log_type: ostk::mathematics::solver::NumericalSolver::LogType,

) → ostk.core.type.String

Get string representation of a log type.

Parameters:

log_type (NumericalSolver.LogType) -- The log type.

Returns:

String representation of the log type.

Return type:

str

Example

>>> NumericalSolver.string_from_log_type(NumericalSolver.LogType.NoLog)

static string_from_stepper_type(

stepper_type: ostk::mathematics::solver::NumericalSolver::StepperType,

) → ostk.core.type.String

Get string representation of a stepper type.

Parameters:

stepper_type (NumericalSolver.StepperType) -- The stepper type.

Returns:

String representation of the stepper type.

Return type:

str

Example

>>> NumericalSolver.string_from_stepper_type(NumericalSolver.StepperType.RungeKutta4)

static undefined() → ostk.mathematics.solver.NumericalSolver

Create an undefined numerical solver.

Returns:

An undefined solver.

Return type:

NumericalSolver

Example

>>> solver = NumericalSolver.undefined()
>>> solver.is_defined()  # False