11from collections .abc import Sequence
22from typing import Literal as L , TypeAlias
33
4+ import _numtype as _nt
45import numpy as np
56import numpy .typing as npt
67from numpy ._typing import _ArrayLikeNumber_co
@@ -26,101 +27,101 @@ _NormKind: TypeAlias = L["backward", "ortho", "forward"] | None
2627
2728def fft (
2829 a : npt .ArrayLike ,
29- n : int | None = ... ,
30- axis : int = ... ,
31- norm : _NormKind = ... ,
32- out : npt . NDArray [np .complex128 ] | None = ... ,
33- ) -> npt . NDArray [np .complex128 ]: ...
30+ n : int | None = None ,
31+ axis : int = - 1 ,
32+ norm : _NormKind = None ,
33+ out : _nt . Array [np .complex128 ] | None = None ,
34+ ) -> _nt . Array [np .complex128 ]: ...
3435def ifft (
3536 a : npt .ArrayLike ,
36- n : int | None = ... ,
37- axis : int = ... ,
38- norm : _NormKind = ... ,
39- out : npt . NDArray [np .complex128 ] | None = ... ,
40- ) -> npt . NDArray [np .complex128 ]: ...
37+ n : int | None = None ,
38+ axis : int = - 1 ,
39+ norm : _NormKind = None ,
40+ out : _nt . Array [np .complex128 ] | None = None ,
41+ ) -> _nt . Array [np .complex128 ]: ...
4142def rfft (
4243 a : npt .ArrayLike ,
43- n : int | None = ... ,
44- axis : int = ... ,
45- norm : _NormKind = ... ,
46- out : npt . NDArray [np .complex128 ] | None = ... ,
47- ) -> npt . NDArray [np .complex128 ]: ...
44+ n : int | None = None ,
45+ axis : int = - 1 ,
46+ norm : _NormKind = None ,
47+ out : _nt . Array [np .complex128 ] | None = None ,
48+ ) -> _nt . Array [np .complex128 ]: ...
4849def irfft (
4950 a : npt .ArrayLike ,
50- n : int | None = ... ,
51- axis : int = ... ,
52- norm : _NormKind = ... ,
53- out : npt . NDArray [np .float64 ] | None = ... ,
54- ) -> npt . NDArray [np .float64 ]: ...
51+ n : int | None = None ,
52+ axis : int = - 1 ,
53+ norm : _NormKind = None ,
54+ out : _nt . Array [np .float64 ] | None = None ,
55+ ) -> _nt . Array [np .float64 ]: ...
5556
5657# Input array must be compatible with `np.conjugate`
5758def hfft (
5859 a : _ArrayLikeNumber_co ,
59- n : int | None = ... ,
60- axis : int = ... ,
61- norm : _NormKind = ... ,
62- out : npt . NDArray [np .float64 ] | None = ... ,
63- ) -> npt . NDArray [np .float64 ]: ...
60+ n : int | None = None ,
61+ axis : int = - 1 ,
62+ norm : _NormKind = None ,
63+ out : _nt . Array [np .float64 ] | None = None ,
64+ ) -> _nt . Array [np .float64 ]: ...
6465def ihfft (
6566 a : npt .ArrayLike ,
66- n : int | None = ... ,
67- axis : int = ... ,
68- norm : _NormKind = ... ,
69- out : npt . NDArray [np .complex128 ] | None = ... ,
70- ) -> npt . NDArray [np .complex128 ]: ...
67+ n : int | None = None ,
68+ axis : int = - 1 ,
69+ norm : _NormKind = None ,
70+ out : _nt . Array [np .complex128 ] | None = None ,
71+ ) -> _nt . Array [np .complex128 ]: ...
7172def fftn (
7273 a : npt .ArrayLike ,
73- s : Sequence [int ] | None = ... ,
74- axes : Sequence [int ] | None = ... ,
75- norm : _NormKind = ... ,
76- out : npt . NDArray [np .complex128 ] | None = ... ,
77- ) -> npt . NDArray [np .complex128 ]: ...
74+ s : Sequence [int ] | None = None ,
75+ axes : Sequence [int ] | None = None ,
76+ norm : _NormKind = None ,
77+ out : _nt . Array [np .complex128 ] | None = None ,
78+ ) -> _nt . Array [np .complex128 ]: ...
7879def ifftn (
7980 a : npt .ArrayLike ,
80- s : Sequence [int ] | None = ... ,
81- axes : Sequence [int ] | None = ... ,
82- norm : _NormKind = ... ,
83- out : npt . NDArray [np .complex128 ] | None = ... ,
84- ) -> npt . NDArray [np .complex128 ]: ...
81+ s : Sequence [int ] | None = None ,
82+ axes : Sequence [int ] | None = None ,
83+ norm : _NormKind = None ,
84+ out : _nt . Array [np .complex128 ] | None = None ,
85+ ) -> _nt . Array [np .complex128 ]: ...
8586def rfftn (
8687 a : npt .ArrayLike ,
87- s : Sequence [int ] | None = ... ,
88- axes : Sequence [int ] | None = ... ,
89- norm : _NormKind = ... ,
90- out : npt . NDArray [np .complex128 ] | None = ... ,
91- ) -> npt . NDArray [np .complex128 ]: ...
88+ s : Sequence [int ] | None = None ,
89+ axes : Sequence [int ] | None = None ,
90+ norm : _NormKind = None ,
91+ out : _nt . Array [np .complex128 ] | None = None ,
92+ ) -> _nt . Array [np .complex128 ]: ...
9293def irfftn (
9394 a : npt .ArrayLike ,
94- s : Sequence [int ] | None = ... ,
95- axes : Sequence [int ] | None = ... ,
96- norm : _NormKind = ... ,
97- out : npt . NDArray [np .float64 ] | None = ... ,
98- ) -> npt . NDArray [np .float64 ]: ...
95+ s : Sequence [int ] | None = None ,
96+ axes : Sequence [int ] | None = None ,
97+ norm : _NormKind = None ,
98+ out : _nt . Array [np .float64 ] | None = None ,
99+ ) -> _nt . Array [np .float64 ]: ...
99100def fft2 (
100101 a : npt .ArrayLike ,
101- s : Sequence [int ] | None = ... ,
102- axes : Sequence [int ] | None = ... ,
103- norm : _NormKind = ... ,
104- out : npt . NDArray [np .complex128 ] | None = ... ,
105- ) -> npt . NDArray [np .complex128 ]: ...
102+ s : Sequence [int ] | None = None ,
103+ axes : Sequence [int ] | None = None ,
104+ norm : _NormKind = None ,
105+ out : _nt . Array [np .complex128 ] | None = None ,
106+ ) -> _nt . Array [np .complex128 ]: ...
106107def ifft2 (
107108 a : npt .ArrayLike ,
108- s : Sequence [int ] | None = ... ,
109- axes : Sequence [int ] | None = ... ,
110- norm : _NormKind = ... ,
111- out : npt . NDArray [np .complex128 ] | None = ... ,
112- ) -> npt . NDArray [np .complex128 ]: ...
109+ s : Sequence [int ] | None = None ,
110+ axes : Sequence [int ] | None = None ,
111+ norm : _NormKind = None ,
112+ out : _nt . Array [np .complex128 ] | None = None ,
113+ ) -> _nt . Array [np .complex128 ]: ...
113114def rfft2 (
114115 a : npt .ArrayLike ,
115- s : Sequence [int ] | None = ... ,
116- axes : Sequence [int ] | None = ... ,
117- norm : _NormKind = ... ,
118- out : npt . NDArray [np .complex128 ] | None = ... ,
119- ) -> npt . NDArray [np .complex128 ]: ...
116+ s : Sequence [int ] | None = None ,
117+ axes : Sequence [int ] | None = None ,
118+ norm : _NormKind = None ,
119+ out : _nt . Array [np .complex128 ] | None = None ,
120+ ) -> _nt . Array [np .complex128 ]: ...
120121def irfft2 (
121122 a : npt .ArrayLike ,
122- s : Sequence [int ] | None = ... ,
123- axes : Sequence [int ] | None = ... ,
124- norm : _NormKind = ... ,
125- out : npt . NDArray [np .float64 ] | None = ... ,
126- ) -> npt . NDArray [np .float64 ]: ...
123+ s : Sequence [int ] | None = None ,
124+ axes : Sequence [int ] | None = None ,
125+ norm : _NormKind = None ,
126+ out : _nt . Array [np .float64 ] | None = None ,
127+ ) -> _nt . Array [np .float64 ]: ...
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