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from typing import (
Any,
Callable,
Literal,
Optional,
overload,
)
import numpy as np
_IntegerType = int | np.integer
_FloatingType = float | np.floating
_PointsAndWeights = tuple[np.ndarray, np.ndarray]
_PointsAndWeightsAndMu = tuple[np.ndarray, np.ndarray, float]
_ArrayLike0D = bool | int | float | complex | str | bytes | np.generic
__all__ = [
'legendre',
'chebyt',
'chebyu',
'chebyc',
'chebys',
'jacobi',
'laguerre',
'genlaguerre',
'hermite',
'hermitenorm',
'gegenbauer',
'sh_legendre',
'sh_chebyt',
'sh_chebyu',
'sh_jacobi',
'roots_legendre',
'roots_chebyt',
'roots_chebyu',
'roots_chebyc',
'roots_chebys',
'roots_jacobi',
'roots_laguerre',
'roots_genlaguerre',
'roots_hermite',
'roots_hermitenorm',
'roots_gegenbauer',
'roots_sh_legendre',
'roots_sh_chebyt',
'roots_sh_chebyu',
'roots_sh_jacobi',
]
@overload
def roots_jacobi(
n: _IntegerType,
alpha: _FloatingType,
beta: _FloatingType,
) -> _PointsAndWeights: ...
@overload
def roots_jacobi(
n: _IntegerType,
alpha: _FloatingType,
beta: _FloatingType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_jacobi(
n: _IntegerType,
alpha: _FloatingType,
beta: _FloatingType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_sh_jacobi(
n: _IntegerType,
p1: _FloatingType,
q1: _FloatingType,
) -> _PointsAndWeights: ...
@overload
def roots_sh_jacobi(
n: _IntegerType,
p1: _FloatingType,
q1: _FloatingType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_sh_jacobi(
n: _IntegerType,
p1: _FloatingType,
q1: _FloatingType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_genlaguerre(
n: _IntegerType,
alpha: _FloatingType,
) -> _PointsAndWeights: ...
@overload
def roots_genlaguerre(
n: _IntegerType,
alpha: _FloatingType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_genlaguerre(
n: _IntegerType,
alpha: _FloatingType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_laguerre(n: _IntegerType) -> _PointsAndWeights: ...
@overload
def roots_laguerre(
n: _IntegerType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_laguerre(
n: _IntegerType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_hermite(n: _IntegerType) -> _PointsAndWeights: ...
@overload
def roots_hermite(
n: _IntegerType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_hermite(
n: _IntegerType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_hermitenorm(n: _IntegerType) -> _PointsAndWeights: ...
@overload
def roots_hermitenorm(
n: _IntegerType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_hermitenorm(
n: _IntegerType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_gegenbauer(
n: _IntegerType,
alpha: _FloatingType,
) -> _PointsAndWeights: ...
@overload
def roots_gegenbauer(
n: _IntegerType,
alpha: _FloatingType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_gegenbauer(
n: _IntegerType,
alpha: _FloatingType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_chebyt(n: _IntegerType) -> _PointsAndWeights: ...
@overload
def roots_chebyt(
n: _IntegerType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_chebyt(
n: _IntegerType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_chebyu(n: _IntegerType) -> _PointsAndWeights: ...
@overload
def roots_chebyu(
n: _IntegerType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_chebyu(
n: _IntegerType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_chebyc(n: _IntegerType) -> _PointsAndWeights: ...
@overload
def roots_chebyc(
n: _IntegerType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_chebyc(
n: _IntegerType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_chebys(n: _IntegerType) -> _PointsAndWeights: ...
@overload
def roots_chebys(
n: _IntegerType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_chebys(
n: _IntegerType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_sh_chebyt(n: _IntegerType) -> _PointsAndWeights: ...
@overload
def roots_sh_chebyt(
n: _IntegerType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_sh_chebyt(
n: _IntegerType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_sh_chebyu(n: _IntegerType) -> _PointsAndWeights: ...
@overload
def roots_sh_chebyu(
n: _IntegerType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_sh_chebyu(
n: _IntegerType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_legendre(n: _IntegerType) -> _PointsAndWeights: ...
@overload
def roots_legendre(
n: _IntegerType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_legendre(
n: _IntegerType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
@overload
def roots_sh_legendre(n: _IntegerType) -> _PointsAndWeights: ...
@overload
def roots_sh_legendre(
n: _IntegerType,
mu: Literal[False],
) -> _PointsAndWeights: ...
@overload
def roots_sh_legendre(
n: _IntegerType,
mu: Literal[True],
) -> _PointsAndWeightsAndMu: ...
class orthopoly1d(np.poly1d):
def __init__(
self,
roots: np.typing.ArrayLike,
weights: np.typing.ArrayLike | None,
hn: float = ...,
kn: float = ...,
wfunc = Optional[Callable[[float], float]], # noqa: UP007
limits = tuple[float, float] | None,
monic: bool = ...,
eval_func: np.ufunc = ...,
) -> None: ...
@property
def limits(self) -> tuple[float, float]: ...
def weight_func(self, x: float) -> float: ...
@overload
def __call__(self, x: _ArrayLike0D) -> Any: ...
@overload
def __call__(self, x: np.poly1d) -> np.poly1d: ... # type: ignore[overload-overlap]
@overload
def __call__(self, x: np.typing.ArrayLike) -> np.ndarray: ...
def legendre(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
def chebyt(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
def chebyu(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
def chebyc(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
def chebys(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
def jacobi(
n: _IntegerType,
alpha: _FloatingType,
beta: _FloatingType,
monic: bool = ...,
) -> orthopoly1d: ...
def laguerre(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
def genlaguerre(
n: _IntegerType,
alpha: _FloatingType,
monic: bool = ...,
) -> orthopoly1d: ...
def hermite(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
def hermitenorm(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
def gegenbauer(
n: _IntegerType,
alpha: _FloatingType,
monic: bool = ...,
) -> orthopoly1d: ...
def sh_legendre(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
def sh_chebyt(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
def sh_chebyu(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
def sh_jacobi(
n: _IntegerType,
p: _FloatingType,
q: _FloatingType,
monic: bool = ...,
) -> orthopoly1d: ...
# These functions are not public, but still need stubs because they
# get checked in the tests.
def _roots_hermite_asy(n: _IntegerType) -> _PointsAndWeights: ...
|