OpenGoddard.optimize

OpenGoddard.optimize - Optimal Trajectories module with PseudoSpectral Method

クラス

名前	説明
Condition	Accumulate dimensionless equality or inequality residuals.
Dynamics	Scaled state derivatives at a section's collocation nodes.
Guess	Construct physical initial guesses on a supplied time grid.
Problem	Define a physical optimal-control problem and solve its LGL discretization.

Conditionクラス#

再エクスポート元 OpenGoddard._helpersソースを表示

class Condition(length=0, *, backend=np)

Accumulate dimensionless equality or inequality residuals.

Equality residuals must be zero; inequality residuals must be nonnegative. Scalar and one-dimensional inputs follow NumPy broadcasting rules. A positive reference unit scales each residual. Prefer problem.condition() inside callbacks so automatic differentiation selects the correct backend.

パラメーター

名前	型	デフォルト	説明
length	int	0	Number of initial zero residuals, normally zero.
backend	module	np	NumPy-compatible module, supplied by the callback view.

例

>>> result = Condition()
>>> result.equal(5, 5)
>>> result()
array([0.])

For physical bounds 0 <= x <= 100 in an inequality callback, call result.lower_bound(x, 0) and result.upper_bound(x, 100).

addメソッド#

ソースを表示

def add(arg, unit=1.0)

Append scalar or one-dimensional residuals using a positive scale.

change_valueメソッド#

ソースを表示

def change_value(index, value)

Replace an existing dimensionless residual by its flattened index.

equalメソッド#

ソースを表示

def equal(arg1, arg2, unit=1.0)

Append (arg1 - arg2)/unit; enforces arg1 = arg2 in an equality callback.

パラメーター

名前	型	デフォルト	説明
arg1	float or array_like	必須	Left side of the equation.
arg2	float or array_like	必須	Right side of the equation.
unit	float	1.0	Positive reference unit for the residual.

lower_boundメソッド#

ソースを表示

def lower_bound(arg1, arg2, unit=1.0)

Append (arg1 - arg2)/unit; enforces arg1 >= arg2 in inequalities.

パラメーター

名前	型	デフォルト	説明
arg1	float or array_like	必須	Physical values to constrain.
arg2	float or array_like	必須	Physical lower bounds.
unit	float	1.0	Positive reference unit for the residual.

upper_boundメソッド#

ソースを表示

def upper_bound(arg1, arg2, unit=1.0)

Append (arg2 - arg1)/unit; enforces arg1 <= arg2 in inequalities.

パラメーター

名前	型	デフォルト	説明
arg1	float or array_like	必須	Physical values to constrain.
arg2	float or array_like	必須	Physical upper bounds.
unit	float	1.0	Positive reference unit for the residual.

Dynamicsクラス#

再エクスポート元 OpenGoddard._helpersソースを表示

class Dynamics(prob, section=0)

Scaled state derivatives at a section’s collocation nodes.

Assign physical dx/dt values with dx[state] = values. Calling dx() converts them to d(x/unit_states)/d(t/unit_time), flattened in state order for the LGL residual. Scalars are broadcast to every node. Unassigned states have zero derivative. For pointwise models that also support independent-grid error checks and structured derivatives, use DynamicsModel.

例

Dynamics class must be used in dynamics function. It is an example of the equation of motion of thrust and free fall. Thrust is controllable.

$$\dot{x} = v, \qquad \dot{v} = T/m - g$$

>>> def dynamics(prob, obj, section):
>>>     x = prob.states(0, section)
>>>     v = prob.states(1, section)
>>>     T = prob.controls(0, section)
>>>     g = 9.8
>>>     m = 1.0
>>>     dx = Dynamics(prob, section)
>>>     dx[0] = v
>>>     dx[1] = T / m - g
>>>     return dx()

number_of_state属性インスタンス属性#

ソースを表示

number_of_state = prob.number_of_states[self.section]

section属性インスタンス属性#

ソースを表示

section = index(section, prob.number_of_section, 'section')

unit_states属性インスタンス属性#

ソースを表示

unit_states = prob.unit_states

unit_time属性インスタンス属性#

ソースを表示

unit_time = prob.unit_time

Guessクラス#

再エクスポート元 OpenGoddard._helpersソースを表示

class Guess

Construct physical initial guesses on a supplied time grid.

constantメソッドclassmethod#

ソースを表示

def constant(time, const: float) -> NDArray[np.float64]

Return one constant physical value per time node.

パラメーター

名前	型	説明
time	array_like	Time nodes; only their count is used.
const	float	Constant physical value.

戻り値

ndarrayNDArray[np.float64]

Values of shape (N,).

cubicメソッドclassmethod#

ソースを表示

def cubic(time, y0: float, yprime0: float, yf: float, yprimef: float) -> NDArray[np.float64]

Interpolate endpoint values and physical-time slopes with a cubic.

パラメーター

名前	型	説明
time	array_like	Finite, nondecreasing physical times with a positive span. Repeated interface times are supported.
y0	float	Physical value at the first time.
yprime0	float	Physical dy/dt at the first time.
yf	float	Physical value at the last time.
yprimef	float	Physical dy/dt at the last time.

戻り値

ndarrayNDArray[np.float64]

Values of shape (N,).

linearメソッドclassmethod#

ソースを表示

def linear(time, y0: float, yf: float) -> NDArray[np.float64]

Interpolate physical endpoint values linearly in time.

パラメーター

名前	型	説明
time	array_like	Finite, nondecreasing physical times with a positive span. Repeated interface times are supported.
y0	float	Physical value at the first time.
yf	float	Physical value at the last time.

戻り値

ndarrayNDArray[np.float64]

Values of shape (N,).

plotメソッドclassmethod#

ソースを表示

def plot(x, y, title='', xlabel='', ylabel='')

Plot physical initial-guess values against time.

パラメーター

名前	型	デフォルト	説明
x	array_like	必須	array on the horizontal axis of the plot
y	array_like	必須	array on the vertical axis of the plot
title	str	''	title
xlabel	str	''	xlabel
ylabel	str	''	ylabel

zerosメソッドclassmethod#

ソースを表示

def zeros(time) -> NDArray[np.float64]

Return one zero per time node.

パラメーター

名前	型	説明
time	array_like	Time nodes; only their count is used.

戻り値

ndarrayNDArray[np.float64]

Values of shape (N,).

Problemクラス#

ソースを表示

class Problem(time_init, nodes, number_of_states, number_of_controls, maxIterator=100, method='LGL', *, mesh=None)

Define a physical optimal-control problem and solve its LGL discretization.

パラメーター

名前	型	デフォルト	説明
time_init	sequence of float	必須	Strictly increasing physical phase times.
nodes	sequence of int	必須	LGL node counts, at least two per phase.
number_of_states	sequence of int	必須	Positive state counts per phase.
number_of_controls	sequence of int	必須	Nonnegative control counts per phase.
maxIterator	int	100	Maximum solver attempts, including the first attempt. Another attempt is made only after an iteration-limit status. solve(maxiter=...) limits iterations within each attempt.
method	str	'LGL'	Only "LGL" is supported for optimal control.
mesh	optional	None	Per-section lists of (left, right, nodes) elements partitioning the phase coordinate [-1, 1]. Logical section numbers do not change. Node counts include both sides of internal interfaces.

All state, control and time getters and setters use physical units. Only p and bounds use scaled units. Setters for units preserve physical guesses and bounds. Node, state, control and section indices follow Python’s negative indexing convention and raise IndexError outside their range.

属性

名前	型	説明
nodes	list[int]	Node counts per phase, including duplicated interfaces.
number_of_states	list[int]	State counts per phase.
number_of_controls	list[int]	Control counts per phase.
number_of_section	int	Number of logical phases.
number_of_param	ndarray	State plus control counts per phase.
number_of_variables	int	Length of p, including phase end times.
div	list[list[int]]	Exclusive ends of state/control blocks in p.
tau	list[ndarray]	LGL phase coordinates in [-1, 1].
w	list[ndarray]	Quadrature weights in phase coordinates.
D	list[ndarray]	Differentiation matrices in phase coordinates.
time	list[ndarray]	Physical node times, derived from current p.
time_all_section	ndarray	Times concatenated in phase order.
unit_states	list[list[float]]	State reference units per phase.
unit_controls	list[list[float]]	Control reference units per phase.
unit_time	float	Time reference unit.
p	ndarray	Scaled states, controls and phase end times, shape (N,).
bounds	list[tuple]	Scaled lower/upper bounds for every entry of p.
dynamics	list[Callable]	One scaled-derivative callback per phase, called as dynamics(problem, obj, section). Use Dynamics to assemble physical derivatives, or DynamicsModel for a pointwise physical model supporting derivatives and error estimation.
knot_states_smooth	list[bool]	Enforce continuity at phase knots with equal state counts. Disable it when supplying jump conditions.
cost	Callable | None	Terminal cost, called as cost(problem, obj).
running_cost	Callable | None	Physical-time integrand, shape (sum(nodes),), called as running_cost(problem, obj).
cost_derivative	function	Complete objective gradient in p.
equality	Callable | None	One-dimensional residuals equal to zero.
inequality	Callable | None	One-dimensional residuals >= 0.
array_module		NumPy; differentiable callback views supply autograd.numpy.
metadata	dict	User metadata, shallow-copied on refine/remesh.
result	OptimizeResult | None	Latest solver result, or None before solve.
result_history	list[OptimizeResult]	Attempts of the latest solve.

Callback views share states/controls (including all-section getters), time_start/time_final, time_knots, time/time_all_section, dimensions, units, array_module and condition(). Use this reading interface for portable callbacks; mutations and direct p indices do not support path sampling. Use unit setters and refine/remesh rather than editing configuration lists. Construct a new Problem to change state/control counts. Refine/remesh create a new mesh and reset solver results.

D属性インスタンス属性#

ソースを表示

D = [rule[2] for rule in rules]

array_module属性クラス属性インスタンス属性#

ソースを表示

array_module = np

bounds属性インスタンス属性#

ソースを表示

bounds = [(None, None)] * self.number_of_variables

cost属性インスタンス属性#

ソースを表示

cost: Callable[[Problem, Any], float] | None = None

cost_derivative属性インスタンス属性#

ソースを表示

cost_derivative: Callable[[Problem, Any], NDArray[np.float64]] | None = None

div属性インスタンス属性#

ソースを表示

div = [list(phase) for phase in self._layout.divisions]

dynamics属性インスタンス属性#

ソースを表示

dynamics: list[Callable[[Problem, Any, int], NDArray[np.float64]] | None] = [None] * self.number_of_section

equality属性インスタンス属性#

ソースを表示

equality: Callable[[Problem, Any], NDArray[np.float64]] | None = None

inequality属性インスタンス属性#

ソースを表示

inequality: Callable[[Problem, Any], NDArray[np.float64]] | None = None

iterator属性インスタンス属性#

ソースを表示

iterator = 0

knot_states_smooth属性インスタンス属性#

ソースを表示

knot_states_smooth = [True] * self.number_of_section - 1

maxIterator属性インスタンス属性#

ソースを表示

maxIterator = integer(maxIterator, 'maxIterator', 1)

mesh属性インスタンス属性#

ソースを表示

mesh = normalize_mesh(self.nodes, mesh)

metadata属性インスタンス属性#

ソースを表示

metadata: dict[str, Any] = {}

method属性インスタンス属性#

ソースを表示

method = method

nodes属性インスタンス属性#

ソースを表示

nodes = [integer(n, 'nodes', 2) for n in nodes]

number_of_controls属性インスタンス属性#

ソースを表示

number_of_controls = [integer(n, 'number_of_controls') for n in number_of_controls]

number_of_param属性インスタンス属性#

ソースを表示

number_of_param = np.array(self.number_of_states) + self.number_of_controls

number_of_section属性インスタンス属性#

ソースを表示

number_of_section = len(self.nodes)

number_of_states属性インスタンス属性#

ソースを表示

number_of_states = [integer(n, 'number_of_states', 1) for n in number_of_states]

number_of_variables属性インスタンス属性#

ソースを表示

number_of_variables = self._layout.size

p属性インスタンス属性#

ソースを表示

p = np.zeros(self.number_of_variables)

result属性インスタンス属性#

ソースを表示

result: optimize.OptimizeResult | None = None

result_history属性インスタンス属性#

ソースを表示

result_history: list[optimize.OptimizeResult] = []

running_cost属性インスタンス属性#

ソースを表示

running_cost: Callable[[Problem, Any], NDArray[np.float64]] | None = None

t0属性インスタンス属性#

ソースを表示

t0 = float(times[0])

tau属性インスタンス属性#

ソースを表示

tau = [rule[0] for rule in rules]

time_init属性インスタンス属性#

ソースを表示

time_init = times.tolist()

unit_controls属性インスタンス属性#

ソースを表示

unit_controls = [[1.0] * n for n in self.number_of_controls]

unit_states属性インスタンス属性#

ソースを表示

unit_states = [[1.0] * n for n in self.number_of_states]

unit_time属性インスタンス属性#

ソースを表示

unit_time = 1.0

w属性インスタンス属性#

ソースを表示

w = [rule[1] for rule in rules]

timeプロパティ#

ソースを表示

time: list[NDArray[np.float64]]

Physical node times per phase, derived from the current p.

Returned arrays are independent values. Change phase end times with set_time_final(); editing these arrays does not change the problem. Both sides of phase and element interfaces are included.

time_all_sectionプロパティ#

ソースを表示

time_all_section: NDArray[np.float64]

Physical node times concatenated in phase order, including interfaces.

conditionメソッド#

ソースを表示

def condition(length: int = 0) -> Condition

Build equality or inequality residuals in this view’s array backend.

パラメーター

名前	型	デフォルト	説明
length	int	0	Number of initial zero residuals, normally zero.

戻り値

ConditionCondition

A residual builder. Use equal() for equality callbacks; lower_bound()/upper_bound() produce nonnegative feasible residuals.

controlsメソッド#

ソースを表示

def controls(control: int, section: int) -> NDArray[np.float64]

Return one control’s physical values in a phase.

パラメーター

名前	型	説明
control	int	Variable index, supporting negative indices.
section	int	Phase index, supporting negative indices.

戻り値

ndarrayNDArray[np.float64]

Independent array of shape (nodes[section],). Both sides of internal element interfaces are present. Use set_controls() to edit.

controls_all_sectionメソッド#

ソースを表示

def controls_all_section(control: int) -> NDArray[np.float64]

Return a control’s physical values concatenated in phase order.

パラメーター

名前	型	説明
control	int	Variable index, which must exist in every phase.

戻り値

ndarrayNDArray[np.float64]

Shape (sum(nodes),), including duplicated interface nodes.

estimate_errorメソッド#

ソースを表示

def estimate_error(obj: Any = None, check_factor: int = 2) -> dict[str, Any]

Estimate dimensionless residuals between the LGL nodes.

パラメーター

名前	型	デフォルト	説明
obj	Any	None	User data passed to the model and inequality callback.
check_factor	int	2	Integer >= 2. Check each element at check_factor * element.nodes + 1 Gauss points.

戻り値

dictdict[str, Any]

section_errors (per-phase ODE indicators), max_error (their maximum), path_violation (scaled inequality/box-bound violation), and elements (per-element error, smoothness, overshoot and split point). Indicators are residual estimates, not rigorous state-error bounds. Nonlinear path constraints are checked by sampling, not certified.

発生する例外

ValueError

A phase lacks DynamicsModel, has nonpositive duration, or uses varying nodal box bounds.

index_controlsメソッド#

ソースを表示

def index_controls(control: int, section: int, index: int | None = None) -> int

Return the index of a control node in the scaled vector p.

パラメーター

名前	型	デフォルト	説明
control	int	必須	Variable index, supporting negative indices.
section	int	必須	Phase index, supporting negative indices.
index	int | None	None	Local node index, supporting negative indices; None selects the first node.

戻り値

intint

Index into p, whose values use reference-unit scaling.

index_statesメソッド#

ソースを表示

def index_states(state: int, section: int, index: int | None = None) -> int

Return the index of a state node in the scaled vector p.

パラメーター

名前	型	デフォルト	説明
state	int	必須	Variable index, supporting negative indices.
section	int	必須	Phase index, supporting negative indices.
index	int | None	None	Local node index, supporting negative indices; None selects the first node.

戻り値

intint

Index into p, whose values use reference-unit scaling.

index_time_finalメソッド#

ソースを表示

def index_time_final(section: int) -> int

Return the index of a phase end time in the scaled vector p.

method_LGメソッド#

ソースを表示

def method_LG(n) -> tuple[NDArray[np.float64], ...]

Legendre-Gauss Pseudospectral method Gauss nodes are roots of $P_n(x)$.

パラメーター

名前	型	説明
n	int	number of nodes

戻り値

tuple[NDArray[np.float64], ...]

tuple[ndarray, ndarray, ndarray]: Nodes (n,), weights (n,), and D (n, n).

method_LGLメソッド#

ソースを表示

def method_LGL(n) -> tuple[NDArray[np.float64], ...]

Legendre-Gauss-Lobatto Pseudospectral method Gauss-Lobatto nodes are roots of $P'_{n-1}(x)$, plus -1 and 1.

パラメーター

名前	型	説明
n	int	number of nodes

戻り値

tuple[NDArray[np.float64], ...]

tuple[ndarray, ndarray, ndarray]: Nodes (n,), weights (n,), and D (n, n).

References

Fariba Fahroo and I. Michael Ross. “Advances in Pseudospectral Methods for Optimal Control”, AIAA Guidance, Navigation and Control Conference and Exhibit, Guidance, Navigation, and Control and Co-located Conferences http://dx.doi.org/10.2514/6.2008-7309

method_LGRメソッド#

ソースを表示

def method_LGR(n) -> tuple[NDArray[np.float64], ...]

Legendre-Gauss-Radau Pseudospectral method Gauss-Radau nodes are roots of $P_n(x) + P_{n-1}(x)$.

パラメーター

名前	型	説明
n	int	number of nodes

戻り値

tuple[NDArray[np.float64], ...]

tuple[ndarray, ndarray, ndarray]: Nodes (n,), weights (n,), and D (n, n).

plotメソッド#

ソースを表示

def plot(title_comment='')

plot inner variables that to be optimized

パラメーター

名前	型	デフォルト	説明
title_comment	str	''	string for title

refineメソッド#

ソースを表示

def refine(nodes) -> Problem

Return a new problem with interpolated guesses and new node counts.

パラメーター

名前	型	説明
nodes	sequence of int	Total node counts per phase, including duplicated interfaces. At least two nodes per element are required.

戻り値

ProblemProblem

A new problem preserving element boundaries, physical units, constant box bounds and callbacks. Solver results are reset. Metadata containers are shallow-copied; nested objects remain shared.

発生する例外

ValueError

Counts are invalid or box bounds vary between nodes.

remeshメソッド#

ソースを表示

def remesh(mesh) -> Problem

Return a warm start on per-phase lists of (left, right, nodes) elements.

Element endpoints are phase coordinates in [-1, 1]. Logical section indices remain unchanged. States are continuous at internal interfaces; controls have independent left and right limits.

パラメーター

名前	型	説明
mesh	sequence	Per-phase lists of (left, right, nodes) elements partitioning [-1, 1]. Each element includes both endpoints.

戻り値

ProblemProblem

A new problem with interpolated guesses, preserved physical units, constant bounds and callbacks, and reset solver results. Metadata containers are shallow-copied. Private extension caches are not copied.

発生する例外

ValueError

The mesh is invalid or box bounds vary between nodes.

set_controlsメソッド#

ソースを表示

def set_controls(control: int, section: int, value: ArrayLike) -> None

Set one control’s initial guess in physical units.

パラメーター

名前	型	説明
control	int	Variable index, supporting negative indices.
section	int	Phase index, supporting negative indices.
value	ArrayLike	Finite one-dimensional values of shape (nodes[section],).

発生する例外

ValueError

Values have the wrong shape or are not finite.

set_controls_all_sectionメソッド#

ソースを表示

def set_controls_all_section(control: int, value_all_section: ArrayLike) -> None

Set a control’s physical initial guess across all phases.

パラメーター

名前	型	説明
control	int	Variable index, which must exist in every phase.
value_all_section	ArrayLike	Finite values of shape (sum(nodes),), in phase order and including duplicated interface nodes.

set_controls_boundsメソッド#

ソースを表示

def set_controls_bounds(control: int, section: int, lb: float | None, ub: float | None) -> None

Set constant physical box bounds at every node of a phase.

パラメーター

名前	型	説明
control	int	Variable index, supporting negative indices.
section	int	Phase index, supporting negative indices.
lb	float | None	Physical lower bound, or None for no lower bound.
ub	float | None	Physical upper bound, or None for no upper bound.

Notes

Bounds constrain mesh nodes. Use solve_adaptive() with a supported model to check for violations between nodes.

set_controls_bounds_all_sectionメソッド#

ソースを表示

def set_controls_bounds_all_section(control: int, lb: float | None, ub: float | None) -> None

set value to bounds of control at all sections

パラメーター

名前	型	説明
control	int	control
lb	float or None	lower bound
ub	float or None	upper bound

set_statesメソッド#

ソースを表示

def set_states(state: int, section: int, value: ArrayLike) -> None

Set one state’s initial guess in physical units.

パラメーター

名前	型	説明
state	int	Variable index, supporting negative indices.
section	int	Phase index, supporting negative indices.
value	ArrayLike	Finite one-dimensional values of shape (nodes[section],).

発生する例外

ValueError

Values have the wrong shape or are not finite.

set_states_all_sectionメソッド#

ソースを表示

def set_states_all_section(state: int, value_all_section: ArrayLike) -> None

Set a state’s physical initial guess across all phases.

パラメーター

名前	型	説明
state	int	Variable index, which must exist in every phase.
value_all_section	ArrayLike	Finite values of shape (sum(nodes),), in phase order and including duplicated interface nodes.

set_states_boundsメソッド#

ソースを表示

def set_states_bounds(state: int, section: int, lb: float | None, ub: float | None) -> None

Set constant physical box bounds at every node of a phase.

パラメーター

名前	型	説明
state	int	Variable index, supporting negative indices.
section	int	Phase index, supporting negative indices.
lb	float | None	Physical lower bound, or None for no lower bound.
ub	float | None	Physical upper bound, or None for no upper bound.

Notes

Bounds constrain mesh nodes. Use solve_adaptive() with a supported model to check for violations between nodes.

set_states_bounds_all_sectionメソッド#

ソースを表示

def set_states_bounds_all_section(state: int, lb: float | None, ub: float | None) -> None

set value to bounds of state at all sections

パラメーター

名前	型	説明
state	int	state
lb	float or None	lower bound
ub	float or None	upper bound

set_time_finalメソッド#

ソースを表示

def set_time_final(section: int, value: float) -> None

Set a phase’s end-time guess in physical units.

パラメーター

名前	型	説明
section	int	Phase index, supporting negative indices.
value	float	Finite physical end time. Times are immediately reflected in time and time_all_section. Forward ordering is enforced at solve.

発生する例外

ValueError

The end time is not finite.

set_time_final_boundsメソッド#

ソースを表示

def set_time_final_bounds(section: int, lb: float | None, ub: float | None) -> None

set value to bounds of time_final at specific section

パラメーター

名前	型	説明
section	int	section
lb	float or None	lower bound
ub	float or None	upper bound

set_unit_controlsメソッド#

ソースを表示

def set_unit_controls(control: int, section: int, value: float) -> None

Change a control’s reference unit, preserving physical values and bounds.

パラメーター

名前	型	説明
control	int	Variable index, supporting negative indices.
section	int	Phase index, supporting negative indices.
value	float	Finite, strictly positive reference unit.

set_unit_controls_all_sectionメソッド#

ソースを表示

def set_unit_controls_all_section(control: int, value: float) -> None

set a canonical unit value to the control at all sections

パラメーター

名前	型	説明
control	int	control
value	float	value

set_unit_statesメソッド#

ソースを表示

def set_unit_states(state: int, section: int, value: float) -> None

Change a state’s reference unit, preserving physical values and bounds.

パラメーター

名前	型	説明
state	int	Variable index, supporting negative indices.
section	int	Phase index, supporting negative indices.
value	float	Finite, strictly positive reference unit.

set_unit_states_all_sectionメソッド#

ソースを表示

def set_unit_states_all_section(state: int, value: float) -> None

set a canonical unit value to the state at all sections

パラメーター

名前	型	説明
state	int	state
value	float	value

set_unit_timeメソッド#

ソースを表示

def set_unit_time(value: float) -> None

set a canonical unit value to the time

パラメーター

名前	型	説明
value	float	value

solveメソッド#

ソースを表示

def solve(obj: Any = None, display_func: Callable[[], None] = _dummy_func, *, solver: str = 'SLSQP', derivatives: str = 'finite-difference', **options: Any) -> optimize.OptimizeResult

Solve the LGL transcription and return a SciPy OptimizeResult.

solver selects SLSQP (default) or sparse trust-constr. derivatives='finite-difference' preserves arbitrary legacy callbacks. 'structured' assembles exact spectral blocks and local central differences, and 'autograd' uses optional automatic differentiation. Both structured modes require DynamicsModel in every section. AD callbacks use view.array_module and view.condition(); they must not mutate arrays or coerce traced values to Python floats. With trust-constr, AD also supplies matrix-free Hessian-vector products.

dynamics must contain a callable for each section; equality and inequality may be None. running_cost returns one integrand value per node, concatenated in section order, in physical time. The solver applies each section’s (tf - ti) / 2 quadrature factor.

cost_derivative, when set, must differentiate the complete objective (including running cost) with respect to the scaled vector p. All SLSQP options, including ftol, maxiter, eps and disp, are forwarded. Concurrent workers are unsupported because callbacks share this mutable Problem instance.

Solver-specific options are forwarded: SLSQP accepts ftol/eps; trust-constr accepts gtol/xtol/barrier_tol. They are not interchangeable. cost_derivative is used in finite-difference and structured modes; autograd differentiates the complete objective itself.

maxIterator limits total attempts, including the first. A restart occurs only after an iteration limit (SLSQP status 9, trust-constr status 0). Other failures stop immediately and emit RuntimeWarning. Each call resets the restart counter. The final result is also saved in result and every attempt in result_history. display_func is called without arguments after each attempt, as in the legacy API. time and time_all_section always reflect the current parameters.

パラメーター

名前	型	デフォルト	説明
obj	Any	None	User data passed unchanged to every model/cost/constraint callback.
display_func	Callable[[], None]	_dummy_func	Called without arguments after each solver attempt.
solver	str	'SLSQP'	“SLSQP” or “trust-constr”.
derivatives	str	'finite-difference'	“finite-difference”, “structured”, or “autograd”.
**options	Any	{}	SciPy solver options, e.g. maxiter, ftol (SLSQP) or gtol (trust-constr).

戻り値

OptimizeResultoptimize.OptimizeResult

SciPy result with solver, derivatives and scaled equality_violation/inequality_violation diagnostics. The solution also replaces this problem’s p. Failure returns success=False and emits RuntimeWarning; it does not raise a convergence exception.

solve_adaptiveメソッド#

ソースを表示

def solve_adaptive(obj: Any = None, *, tolerance: float = 1e-05, max_refinements: int = 4, max_nodes: int = 100, growth: float = 1.5, strategy: str = 'p', max_elements: int = 24, min_element_nodes: int = 6, max_order: int = 14, path_check_factor: int = 4, **solve_options: Any) -> optimize.OptimizeResult

Solve and adapt the mesh, updating this problem to the final mesh.

Requires DynamicsModel in every phase. Callbacks must use physical getters and work with changing node counts. For h/hp path sampling, avoid direct p indices and mesh-dependent global reductions.

パラメーター

名前	型	デフォルト	説明
obj	Any	None	User data passed to all callbacks.
tolerance	float	1e-05	Positive tolerance for ODE and scaled path residuals.
max_refinements	int	4	Maximum changes after the initial solve.
max_nodes	int	100	Maximum total nodes per phase, including interfaces.
growth	float	1.5	Node growth factor > 1 for p refinement.
strategy	str	'p'	“p” increases orders; “h” splits elements; “hp” chooses between increasing orders and splitting using error indicators.
max_elements	int	24	Maximum elements per phase for h/hp.
min_element_nodes	int	6	Minimum child node count for hp, at least four.
max_order	int	14	Node threshold for choosing h instead of p in hp.
path_check_factor	int	4	Sampling density for h/hp path constraints, at least two. Not used by the p strategy.
**solve_options	Any	{}	Options forwarded to solve(), including solver, derivatives and SciPy tolerances.

戻り値

OptimizeResultoptimize.OptimizeResult

Final solver result. success reports optimizer convergence; mesh_converged separately reports meeting the mesh tolerance. mesh_history records every solve and residual estimate. h/hp also supply mesh_strategy and mesh_stop_reason. Stopping at a limit emits RuntimeWarning when the mesh has not converged.

statesメソッド#

ソースを表示

def states(state: int, section: int) -> NDArray[np.float64]

Return one state’s physical values in a phase.

パラメーター

名前	型	説明
state	int	Variable index, supporting negative indices.
section	int	Phase index, supporting negative indices.

戻り値

ndarrayNDArray[np.float64]

Independent array of shape (nodes[section],). Both sides of internal element interfaces are present. Use set_states() to edit.

states_all_sectionメソッド#

ソースを表示

def states_all_section(state: int) -> NDArray[np.float64]

Return a state’s physical values concatenated in phase order.

パラメーター

名前	型	説明
state	int	Variable index, which must exist in every phase.

戻り値

ndarrayNDArray[np.float64]

Shape (sum(nodes),), including duplicated interface nodes.

time_finalメソッド#

ソースを表示

def time_final(section: int) -> float

Return a phase’s physical end time from the current scaled p.

パラメーター

名前	型	説明
section	int	Phase index; negative indices count from the last phase.

戻り値

float

Physical time, equal to p[index_time_final(section)] * unit_time.

time_final_all_sectionメソッド#

ソースを表示

def time_final_all_section() -> list[float]

Return physical phase end times in phase order.

time_knotsメソッド#

ソースを表示

def time_knots() -> list[float]

Return physical phase boundaries [t0, tf0, tf1, …].

time_startメソッド#

ソースを表示

def time_start(section: int) -> float

Return a phase’s physical start time.

パラメーター

名前	型	説明
section	int	Phase index; negative indices count from the last phase.

戻り値

float

Physical time. The first phase starts at the fixed t0; later phases start at the preceding phase’s current end time.

time_to_tauメソッド#

ソースを表示

def time_to_tau(time)

Map a finite, nonconstant time vector to [-1, 1].

time_updateメソッド#

ソースを表示

def time_update() -> NDArray[np.float64]

Return current physical node times concatenated in phase order.

Kept for compatibility. Times are derived from p on access, so explicit refreshes are unnecessary even after direct changes to p.

to_csvメソッド#

ソースを表示

def to_csv(filename='OpenGoddard_output.csv', delimiter: str = ',') -> None

Write physical times, states and controls in phase/node order.

パラメーター

名前	型	デフォルト	説明
filename	str or PathLike	'OpenGoddard_output.csv'	Output path. Missing components in phases with fewer states or controls are written as NaN.
delimiter	str	','	Column separator; a comma by default.