✨ integrate: improve the odeint signature

scipy-stubs/integrate/_odepack.pyi

@@ -1,29 +1,77 @@
-from _typeshed import Incomplete
+# defined in scipy/integrate/_odepackmodule.c
+
 from collections.abc import Callable
+from typing import Literal, TypedDict, overload, type_check_only
 
+import numpy as np
 import optype.numpy as onp
 
 class error(Exception): ...
 
+@type_check_only
+class _InfoDict(TypedDict):
+    hu: onp.Array1D[np.float64]
+    tcur: onp.Array1D[np.float64]
+    tolsf: onp.Array1D[np.float64]
+    tsw: onp.Array1D[np.float64]
+    nst: onp.Array1D[np.int32]
+    nfe: onp.Array1D[np.int32]
+    nje: onp.Array1D[np.int32]
+    nqu: onp.Array1D[np.int32]
+    imxer: int
+    lenrw: int
+    leniw: int
+    mused: onp.Array1D[np.int32]
+
+###
+
+# NOTE: This (private) `odeint` differs from the one in `_odepack_py` because it
+# doesn't have a `printmessg` kwarg, and has a different return type.
+@overload
 def odeint(
-    fun: Callable[..., Incomplete],
-    y0: onp.ToFloat | onp.ToFloatND,
-    t: float,
+    fun: Callable[..., onp.ToFloat1D | float],
+    y0: onp.ToFloatND | float,
+    t: onp.ToFloat1D,
     args: tuple[object, ...] = (),
-    Dfun: Callable[..., Incomplete] | None = None,
-    col_deriv: int = 0,
-    ml: int = ...,
-    mu: int = ...,
-    full_output: onp.ToBool = 0,
-    rtol: float = ...,
-    atol: float = ...,
-    tcrit: float = ...,
+    Dfun: Callable[..., onp.ToFloat2D] | None = None,
+    col_deriv: onp.ToBool = 0,
+    ml: int = -1,
+    mu: int = -1,
+    full_output: Literal[0, False] = 0,
+    rtol: float | None = None,
+    atol: float | None = None,
+    tcrit: onp.ToFloat1D | None = None,
+    h0: float = 0.0,
+    hmax: float = 0.0,
+    hmin: float = 0.0,
+    ixpr: onp.ToBool = 0,
+    mxstep: int = 0,
+    mxhnil: int = 0,
+    mxordn: int = 12,
+    mxords: int = 5,
+    tfirst: int = 0,
+) -> tuple[onp.Array2D[np.float64], int]: ...
+@overload
+def odeint(
+    fun: Callable[..., onp.ToFloat1D | float],
+    y0: onp.ToFloatND | float,
+    t: onp.ToFloat1D,
+    args: tuple[object, ...],
+    Dfun: Callable[..., onp.ToFloat2D] | None,
+    col_deriv: onp.ToBool,
+    ml: int,
+    mu: int,
+    full_output: Literal[True, 1],
+    rtol: float | None = None,
+    atol: float | None = None,
+    tcrit: onp.ToFloat1D | None = None,
     h0: float = 0.0,
     hmax: float = 0.0,
     hmin: float = 0.0,
-    ixpr: float = 0.0,
-    mxstep: float = 0.0,
+    ixpr: onp.ToBool = 0,
+    mxstep: int = 0,
     mxhnil: int = 0,
-    mxordn: int = 0,
-    mxords: int = 0,
-) -> tuple[Incomplete, ...]: ...
+    mxordn: int = 12,
+    mxords: int = 5,
+    tfirst: int = 0,
+) -> tuple[onp.Array2D[np.float64], _InfoDict, int]: ...