from collections.abc import Sequence from typing import ( Any, Literal, NoReturn, Protocol, Self, SupportsIndex, SupportsInt, overload, type_check_only, ) import numpy as np import numpy.typing as npt from numpy._typing import ( _ArrayLikeComplex_co, _ArrayLikeFloat_co, _ArrayLikeNumber_co, _ComplexLike_co, _FloatLike_co, _IntLike_co, _NestedSequence, _NumberLike_co, _SupportsArray, ) # compatible with e.g. int, float, complex, Decimal, Fraction, and ABCPolyBase @type_check_only class _SupportsCoefOps[T](Protocol): def __eq__(self, x: object, /) -> bool: ... def __ne__(self, x: object, /) -> bool: ... def __neg__(self, /) -> Self: ... def __pos__(self, /) -> Self: ... def __add__(self, x: T, /) -> Self: ... def __sub__(self, x: T, /) -> Self: ... def __mul__(self, x: T, /) -> Self: ... def __pow__(self, x: T, /) -> Self | float: ... def __radd__(self, x: T, /) -> Self: ... def __rsub__(self, x: T, /) -> Self: ... def __rmul__(self, x: T, /) -> Self: ... type _PolyScalar = np.bool | np.number | np.object_ type _Series[ScalarT: _PolyScalar] = np.ndarray[tuple[int], np.dtype[ScalarT]] type _FloatSeries = _Series[np.floating] type _ComplexSeries = _Series[np.complexfloating] type _ObjectSeries = _Series[np.object_] type _CoefSeries = _Series[np.inexact | np.object_] type _FloatArray = npt.NDArray[np.floating] type _ComplexArray = npt.NDArray[np.complexfloating] type _ObjectArray = npt.NDArray[np.object_] type _CoefArray = npt.NDArray[np.inexact | np.object_] type _Tuple2[_T] = tuple[_T, _T] type _Array1[ScalarT: _PolyScalar] = np.ndarray[tuple[Literal[1]], np.dtype[ScalarT]] type _Array2[ScalarT: _PolyScalar] = np.ndarray[tuple[Literal[2]], np.dtype[ScalarT]] type _AnyInt = SupportsInt | SupportsIndex type _CoefObjectLike_co = np.object_ | _SupportsCoefOps[Any] type _CoefLike_co = _NumberLike_co | _CoefObjectLike_co # The term "series" is used here to refer to 1-d arrays of numeric scalars. type _SeriesLikeBool_co = _SupportsArray[np.dtype[np.bool]] | Sequence[bool | np.bool] type _SeriesLikeInt_co = _SupportsArray[np.dtype[np.integer | np.bool]] | Sequence[_IntLike_co] type _SeriesLikeFloat_co = _SupportsArray[np.dtype[np.floating | np.integer | np.bool]] | Sequence[_FloatLike_co] type _SeriesLikeComplex_co = _SupportsArray[np.dtype[np.number | np.bool]] | Sequence[_ComplexLike_co] type _SeriesLikeObject_co = _SupportsArray[np.dtype[np.object_]] | Sequence[_CoefObjectLike_co] type _SeriesLikeCoef_co = _SupportsArray[np.dtype[_PolyScalar]] | Sequence[_CoefLike_co] type _ArrayLikeCoefObject_co = _CoefObjectLike_co | _SeriesLikeObject_co | _NestedSequence[_SeriesLikeObject_co] type _ArrayLikeCoef_co = npt.NDArray[_PolyScalar] | _ArrayLikeNumber_co | _ArrayLikeCoefObject_co type _Line[ScalarT: _PolyScalar] = np.ndarray[tuple[int], np.dtype[ScalarT]] type _Companion[ScalarT: _PolyScalar] = np.ndarray[tuple[int, int], np.dtype[ScalarT]] type _AnyDegrees = Sequence[SupportsIndex] type _FullFitResult = Sequence[np.inexact | np.int32] @type_check_only class _FuncLine(Protocol): @overload def __call__[ScalarT: _PolyScalar](self, /, off: ScalarT, scl: ScalarT) -> _Line[ScalarT]: ... @overload def __call__(self, /, off: int, scl: int) -> _Line[np.int_]: ... @overload def __call__(self, /, off: float, scl: float) -> _Line[np.float64]: ... @overload def __call__(self, /, off: complex, scl: complex) -> _Line[np.complex128]: ... @overload def __call__(self, /, off: _SupportsCoefOps[Any], scl: _SupportsCoefOps[Any]) -> _Line[np.object_]: ... @type_check_only class _FuncFromRoots(Protocol): @overload def __call__(self, /, roots: _SeriesLikeFloat_co) -> _FloatSeries: ... @overload def __call__(self, /, roots: _SeriesLikeComplex_co) -> _ComplexSeries: ... @overload def __call__(self, /, roots: _SeriesLikeCoef_co) -> _ObjectSeries: ... @type_check_only class _FuncBinOp(Protocol): @overload def __call__(self, /, c1: _SeriesLikeBool_co, c2: _SeriesLikeBool_co) -> NoReturn: ... @overload def __call__(self, /, c1: _SeriesLikeFloat_co, c2: _SeriesLikeFloat_co) -> _FloatSeries: ... @overload def __call__(self, /, c1: _SeriesLikeComplex_co, c2: _SeriesLikeComplex_co) -> _ComplexSeries: ... @overload def __call__(self, /, c1: _SeriesLikeCoef_co, c2: _SeriesLikeCoef_co) -> _ObjectSeries: ... @type_check_only class _FuncUnOp(Protocol): @overload def __call__(self, /, c: _SeriesLikeFloat_co) -> _FloatSeries: ... @overload def __call__(self, /, c: _SeriesLikeComplex_co) -> _ComplexSeries: ... @overload def __call__(self, /, c: _SeriesLikeCoef_co) -> _ObjectSeries: ... @type_check_only class _FuncPoly2Ortho(Protocol): @overload def __call__(self, /, pol: _SeriesLikeFloat_co) -> _FloatSeries: ... @overload def __call__(self, /, pol: _SeriesLikeComplex_co) -> _ComplexSeries: ... @overload def __call__(self, /, pol: _SeriesLikeCoef_co) -> _ObjectSeries: ... @type_check_only class _FuncPow(Protocol): @overload def __call__(self, /, c: _SeriesLikeFloat_co, pow: _IntLike_co, maxpower: _IntLike_co | None = ...) -> _FloatSeries: ... @overload def __call__(self, /, c: _SeriesLikeComplex_co, pow: _IntLike_co, maxpower: _IntLike_co | None = ...) -> _ComplexSeries: ... @overload def __call__(self, /, c: _SeriesLikeCoef_co, pow: _IntLike_co, maxpower: _IntLike_co | None = ...) -> _ObjectSeries: ... @type_check_only class _FuncDer(Protocol): @overload def __call__( self, /, c: _ArrayLikeFloat_co, m: SupportsIndex = 1, scl: _FloatLike_co = 1, axis: SupportsIndex = 0, ) -> _FloatArray: ... @overload def __call__( self, /, c: _ArrayLikeComplex_co, m: SupportsIndex = 1, scl: _ComplexLike_co = 1, axis: SupportsIndex = 0, ) -> _ComplexArray: ... @overload def __call__( self, /, c: _ArrayLikeCoef_co, m: SupportsIndex = 1, scl: _CoefLike_co = 1, axis: SupportsIndex = 0, ) -> _ObjectArray: ... @type_check_only class _FuncInteg(Protocol): @overload def __call__( self, /, c: _ArrayLikeFloat_co, m: SupportsIndex = 1, k: _FloatLike_co | _SeriesLikeFloat_co = [], lbnd: _FloatLike_co = 0, scl: _FloatLike_co = 1, axis: SupportsIndex = 0, ) -> _FloatArray: ... @overload def __call__( self, /, c: _ArrayLikeComplex_co, m: SupportsIndex = 1, k: _ComplexLike_co | _SeriesLikeComplex_co = [], lbnd: _ComplexLike_co = 0, scl: _ComplexLike_co = 1, axis: SupportsIndex = 0, ) -> _ComplexArray: ... @overload def __call__( self, /, c: _ArrayLikeCoef_co, m: SupportsIndex = 1, k: _CoefLike_co | _SeriesLikeCoef_co = [], lbnd: _CoefLike_co = 0, scl: _CoefLike_co = 1, axis: SupportsIndex = 0, ) -> _ObjectArray: ... @type_check_only class _FuncVal(Protocol): @overload def __call__(self, /, x: _FloatLike_co, c: _SeriesLikeFloat_co, tensor: bool = True) -> np.floating: ... @overload def __call__(self, /, x: _NumberLike_co, c: _SeriesLikeComplex_co, tensor: bool = True) -> np.complexfloating: ... @overload def __call__(self, /, x: _ArrayLikeFloat_co, c: _ArrayLikeFloat_co, tensor: bool = True) -> _FloatArray: ... @overload def __call__(self, /, x: _ArrayLikeComplex_co, c: _ArrayLikeComplex_co, tensor: bool = True) -> _ComplexArray: ... @overload def __call__(self, /, x: _ArrayLikeCoef_co, c: _ArrayLikeCoef_co, tensor: bool = True) -> _ObjectArray: ... @overload def __call__(self, /, x: _CoefLike_co, c: _SeriesLikeObject_co, tensor: bool = True) -> _SupportsCoefOps[Any]: ... @type_check_only class _FuncVal2D(Protocol): @overload def __call__(self, /, x: _FloatLike_co, y: _FloatLike_co, c: _SeriesLikeFloat_co) -> np.floating: ... @overload def __call__(self, /, x: _NumberLike_co, y: _NumberLike_co, c: _SeriesLikeComplex_co) -> np.complexfloating: ... @overload def __call__(self, /, x: _ArrayLikeFloat_co, y: _ArrayLikeFloat_co, c: _ArrayLikeFloat_co) -> _FloatArray: ... @overload def __call__(self, /, x: _ArrayLikeComplex_co, y: _ArrayLikeComplex_co, c: _ArrayLikeComplex_co) -> _ComplexArray: ... @overload def __call__(self, /, x: _ArrayLikeCoef_co, y: _ArrayLikeCoef_co, c: _ArrayLikeCoef_co) -> _ObjectArray: ... @overload def __call__(self, /, x: _CoefLike_co, y: _CoefLike_co, c: _SeriesLikeCoef_co) -> _SupportsCoefOps[Any]: ... @type_check_only class _FuncVal3D(Protocol): @overload def __call__( self, /, x: _FloatLike_co, y: _FloatLike_co, z: _FloatLike_co, c: _SeriesLikeFloat_co, ) -> np.floating: ... @overload def __call__( self, /, x: _NumberLike_co, y: _NumberLike_co, z: _NumberLike_co, c: _SeriesLikeComplex_co, ) -> np.complexfloating: ... @overload def __call__( self, /, x: _ArrayLikeFloat_co, y: _ArrayLikeFloat_co, z: _ArrayLikeFloat_co, c: _ArrayLikeFloat_co, ) -> _FloatArray: ... @overload def __call__( self, /, x: _ArrayLikeComplex_co, y: _ArrayLikeComplex_co, z: _ArrayLikeComplex_co, c: _ArrayLikeComplex_co, ) -> _ComplexArray: ... @overload def __call__( self, /, x: _ArrayLikeCoef_co, y: _ArrayLikeCoef_co, z: _ArrayLikeCoef_co, c: _ArrayLikeCoef_co, ) -> _ObjectArray: ... @overload def __call__( self, /, x: _CoefLike_co, y: _CoefLike_co, z: _CoefLike_co, c: _SeriesLikeCoef_co, ) -> _SupportsCoefOps[Any]: ... @type_check_only class _FuncValND(Protocol): @overload def __call__( self, /, pts: Sequence[_FloatLike_co], c: _SeriesLikeFloat_co, ) -> np.floating: ... @overload def __call__( self, /, pts: Sequence[_NumberLike_co], c: _SeriesLikeComplex_co, ) -> np.complexfloating: ... @overload def __call__( self, /, pts: Sequence[_ArrayLikeFloat_co], c: _ArrayLikeFloat_co, ) -> _FloatArray: ... @overload def __call__( self, /, pts: Sequence[_ArrayLikeComplex_co], c: _ArrayLikeComplex_co, ) -> _ComplexArray: ... @overload def __call__( self, /, pts: Sequence[_ArrayLikeCoef_co], c: _ArrayLikeCoef_co, ) -> _ObjectArray: ... @overload def __call__( self, /, pts: Sequence[_CoefLike_co], c: _SeriesLikeCoef_co, ) -> _SupportsCoefOps[Any]: ... @type_check_only class _FuncVander(Protocol): @overload def __call__(self, /, x: _ArrayLikeFloat_co, deg: SupportsIndex) -> _FloatArray: ... @overload def __call__(self, /, x: _ArrayLikeComplex_co, deg: SupportsIndex) -> _ComplexArray: ... @overload def __call__(self, /, x: _ArrayLikeCoef_co, deg: SupportsIndex) -> _ObjectArray: ... @overload def __call__(self, /, x: npt.ArrayLike, deg: SupportsIndex) -> _CoefArray: ... @type_check_only class _FuncVander2D(Protocol): @overload def __call__(self, /, x: _ArrayLikeFloat_co, y: _ArrayLikeFloat_co, deg: _AnyDegrees) -> _FloatArray: ... @overload def __call__(self, /, x: _ArrayLikeComplex_co, y: _ArrayLikeComplex_co, deg: _AnyDegrees) -> _ComplexArray: ... @overload def __call__(self, /, x: _ArrayLikeCoef_co, y: _ArrayLikeCoef_co, deg: _AnyDegrees) -> _ObjectArray: ... @overload def __call__(self, /, x: npt.ArrayLike, y: npt.ArrayLike, deg: _AnyDegrees) -> _CoefArray: ... @type_check_only class _FuncVander3D(Protocol): @overload def __call__( self, /, x: _ArrayLikeFloat_co, y: _ArrayLikeFloat_co, z: _ArrayLikeFloat_co, deg: _AnyDegrees, ) -> _FloatArray: ... @overload def __call__( self, /, x: _ArrayLikeComplex_co, y: _ArrayLikeComplex_co, z: _ArrayLikeComplex_co, deg: _AnyDegrees, ) -> _ComplexArray: ... @overload def __call__( self, /, x: _ArrayLikeCoef_co, y: _ArrayLikeCoef_co, z: _ArrayLikeCoef_co, deg: _AnyDegrees, ) -> _ObjectArray: ... @overload def __call__( self, /, x: npt.ArrayLike, y: npt.ArrayLike, z: npt.ArrayLike, deg: _AnyDegrees, ) -> _CoefArray: ... @type_check_only class _FuncFit(Protocol): @overload def __call__( self, /, x: _SeriesLikeFloat_co, y: _ArrayLikeFloat_co, deg: int | _SeriesLikeInt_co, rcond: float | None = ..., full: Literal[False] = False, w: _SeriesLikeFloat_co | None = ..., ) -> _FloatArray: ... @overload def __call__( self, x: _SeriesLikeFloat_co, y: _ArrayLikeFloat_co, deg: int | _SeriesLikeInt_co, rcond: float | None, full: Literal[True], /, w: _SeriesLikeFloat_co | None = ..., ) -> tuple[_FloatArray, _FullFitResult]: ... @overload def __call__( self, /, x: _SeriesLikeFloat_co, y: _ArrayLikeFloat_co, deg: int | _SeriesLikeInt_co, rcond: float | None = ..., *, full: Literal[True], w: _SeriesLikeFloat_co | None = ..., ) -> tuple[_FloatArray, _FullFitResult]: ... @overload def __call__( self, /, x: _SeriesLikeComplex_co, y: _ArrayLikeComplex_co, deg: int | _SeriesLikeInt_co, rcond: float | None = ..., full: Literal[False] = False, w: _SeriesLikeFloat_co | None = ..., ) -> _ComplexArray: ... @overload def __call__( self, x: _SeriesLikeComplex_co, y: _ArrayLikeComplex_co, deg: int | _SeriesLikeInt_co, rcond: float | None, full: Literal[True], /, w: _SeriesLikeFloat_co | None = ..., ) -> tuple[_ComplexArray, _FullFitResult]: ... @overload def __call__( self, /, x: _SeriesLikeComplex_co, y: _ArrayLikeComplex_co, deg: int | _SeriesLikeInt_co, rcond: float | None = ..., *, full: Literal[True], w: _SeriesLikeFloat_co | None = ..., ) -> tuple[_ComplexArray, _FullFitResult]: ... @overload def __call__( self, /, x: _SeriesLikeComplex_co, y: _ArrayLikeCoef_co, deg: int | _SeriesLikeInt_co, rcond: float | None = ..., full: Literal[False] = False, w: _SeriesLikeFloat_co | None = ..., ) -> _ObjectArray: ... @overload def __call__( self, x: _SeriesLikeComplex_co, y: _ArrayLikeCoef_co, deg: int | _SeriesLikeInt_co, rcond: float | None, full: Literal[True], /, w: _SeriesLikeFloat_co | None = ..., ) -> tuple[_ObjectArray, _FullFitResult]: ... @overload def __call__( self, /, x: _SeriesLikeComplex_co, y: _ArrayLikeCoef_co, deg: int | _SeriesLikeInt_co, rcond: float | None = ..., *, full: Literal[True], w: _SeriesLikeFloat_co | None = ..., ) -> tuple[_ObjectArray, _FullFitResult]: ... @type_check_only class _FuncRoots(Protocol): @overload def __call__(self, /, c: _SeriesLikeFloat_co) -> _Series[np.float64]: ... @overload def __call__(self, /, c: _SeriesLikeComplex_co) -> _Series[np.complex128]: ... @overload def __call__(self, /, c: _SeriesLikeCoef_co) -> _ObjectSeries: ... @type_check_only class _FuncCompanion(Protocol): @overload def __call__(self, /, c: _SeriesLikeFloat_co) -> _Companion[np.float64]: ... @overload def __call__(self, /, c: _SeriesLikeComplex_co) -> _Companion[np.complex128]: ... @overload def __call__(self, /, c: _SeriesLikeCoef_co) -> _Companion[np.object_]: ... @type_check_only class _FuncGauss(Protocol): def __call__(self, /, deg: SupportsIndex) -> _Tuple2[_Series[np.float64]]: ... @type_check_only class _FuncWeight(Protocol): @overload def __call__(self, /, x: _ArrayLikeFloat_co) -> npt.NDArray[np.float64]: ... @overload def __call__(self, /, x: _ArrayLikeComplex_co) -> npt.NDArray[np.complex128]: ... @overload def __call__(self, /, x: _ArrayLikeCoef_co) -> _ObjectArray: ...