From 6285933ba90c4d9dc70350d12ad0bec5c23550ce Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Wed, 5 Aug 2026 22:09:01 +0200
Subject: [PATCH 1/8] FEAT: accept array-valued parameters in estimators

Parameter values passed to ChiSquared and UnbinnedNLL may now be
one-dimensional arrays of shape (p,), which are broadcast against the
event axis so that the estimator returns one value per parameter point,
all in a single backend-parallelized call. This makes it cheap to e.g.
propagate fit uncertainties over bootstrapped parameter samples, as done
in ComPWA/polarimetry. Behavior for scalar parameter values is unchanged.

Closes #571
---
 .cspell.json                         |  1 +
 benchmarks/unbinned_nll.py           |  6 ++--
 src/tensorwaves/estimator.py         | 50 ++++++++++++++++++----------
 src/tensorwaves/function/__init__.py | 20 +++++------
 src/tensorwaves/interface.py         | 27 +++++++++++----
 src/tensorwaves/optimizer/minuit.py  |  2 +-
 src/tensorwaves/optimizer/scipy.py   |  4 +--
 tests/optimizer/__init__.py          |  6 ++--
 tests/test_estimator.py              | 42 +++++++++++++++++++++++
 9 files changed, 115 insertions(+), 43 deletions(-)

diff --git a/.cspell.json b/.cspell.json
index af5fdd97..0fa9a858 100644
--- a/.cspell.json
+++ b/.cspell.json
@@ -242,6 +242,7 @@
     "vectorize",
     "venv",
     "vmap",
+    "vmapped",
     "weisskopf",
     "wirtinger",
     "xcode",
diff --git a/benchmarks/unbinned_nll.py b/benchmarks/unbinned_nll.py
index c5ed4906..2b632222 100644
--- a/benchmarks/unbinned_nll.py
+++ b/benchmarks/unbinned_nll.py
@@ -277,16 +277,16 @@ def _compute_estimator_reference(
 
 
 def _benchmark_estimator_numpy(
-    benchmark: Callable[[Callable[[], float]], float],
+    benchmark: Callable[[Callable[[], float | np.ndarray]], float | np.ndarray],
     backend: str,
     data: dict[str, np.ndarray],
     phsp: dict[str, np.ndarray],
     parameters: dict[str, float],
-) -> float:
+) -> float | np.ndarray:
     estimator = _create_estimator(backend, data, phsp)
     estimator(parameters)
 
-    def run() -> float:
+    def run() -> float | np.ndarray:
         return estimator(parameters)
 
     return benchmark(run)
diff --git a/src/tensorwaves/estimator.py b/src/tensorwaves/estimator.py
index 07470c3d..d1d08a76 100644
--- a/src/tensorwaves/estimator.py
+++ b/src/tensorwaves/estimator.py
@@ -15,6 +15,7 @@
     DataSample,
     DataTransformer,
     Estimator,
+    ParameterType,
     ParameterValue,
     ParametrizedFunction,
 )
@@ -85,14 +86,23 @@ def _determine_backend(function: ParametrizedFunction, backend: str | None) -> s
 
 
 def _coerce_parameter_types(
-    parameters: Mapping[str, ParameterValue],
-) -> dict[str, ParameterValue]:
-    # normalize to float/complex so that JIT compilers see stable input types
-    # (an int value would otherwise trigger a re-trace once it becomes a float)
-    return {
-        name: complex(value) if isinstance(value, complex) else float(value)
-        for name, value in parameters.items()
-    }
+    parameters: Mapping[str, ParameterType],
+) -> dict[str, ParameterType]:
+    return {name: _coerce_parameter_value(value) for name, value in parameters.items()}
+
+
+def _coerce_parameter_value(value: ParameterType) -> ParameterType:
+    # normalize scalars to float/complex so that JIT compilers see stable input
+    # types (an int value would otherwise trigger a re-trace once it becomes a
+    # float) and give parameter arrays a new trailing axis, so that they
+    # broadcast against the event axis of the data samples
+    if isinstance(value, complex):
+        return complex(value)
+    if isinstance(value, (int, float)):
+        return float(value)
+    if getattr(value, "ndim", 0) >= 1:
+        return value[..., None]
+    return value
 
 
 def _import_jax():  # ruff: ignore[missing-return-type-private-function]
@@ -220,19 +230,19 @@ def __init__(
         sum_function = find_function("sum", backend)
 
         def estimator(
-            parameters: Mapping[str, ParameterValue],
+            parameters: Mapping[str, ParameterType],
             domain: DataSample,
             observed_values: np.ndarray,
             weights: np.ndarray,
         ) -> float:
             computed_values = function(domain, parameters)
             chi_squared = weights * (computed_values - observed_values) ** 2
-            return sum_function(chi_squared)
+            return sum_function(chi_squared, axis=-1)
 
         self.__estimator = _jit_estimator_core(estimator, backend)
         self.__gradient = _create_core_gradient(estimator, backend)
 
-    def __call__(self, parameters: Mapping[str, ParameterValue]) -> float:
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarray:
         return self.__estimator(*self.__estimator_args(parameters))
 
     def gradient(
@@ -240,7 +250,7 @@ def gradient(
     ) -> dict[str, ParameterValue]:
         return self.__gradient(*self.__estimator_args(parameters))
 
-    def __estimator_args(self, parameters: Mapping[str, ParameterValue]) -> tuple:
+    def __estimator_args(self, parameters: Mapping[str, ParameterType]) -> tuple:
         return (
             _coerce_parameter_types(parameters),
             self.__domain,
@@ -306,7 +316,7 @@ def __init__(
         log_function = find_function("log", backend)
 
         def estimator(
-            parameters: Mapping[str, ParameterValue],
+            parameters: Mapping[str, ParameterType],
             data: DataSample,
             phsp: DataSample,
             phsp_weights: np.ndarray | None,
@@ -315,16 +325,20 @@ def estimator(
             phsp_intensities = function(phsp, parameters)
             if phsp_weights is not None:
                 phsp_intensities *= phsp_weights
-            normalization_integral = phsp_volume * mean_function(phsp_intensities)
-            log_normalization = len(bare_intensities) * log_function(
+            normalization_integral = phsp_volume * mean_function(
+                phsp_intensities, axis=-1
+            )
+            log_normalization = bare_intensities.shape[-1] * log_function(
                 normalization_integral
             )
-            return log_normalization - sum_function(log_function(bare_intensities))
+            return log_normalization - sum_function(
+                log_function(bare_intensities), axis=-1
+            )
 
         self.__estimator = _jit_estimator_core(estimator, backend)
         self.__gradient = _create_core_gradient(estimator, backend)
 
-    def __call__(self, parameters: Mapping[str, ParameterValue]) -> float:
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarray:
         return self.__estimator(*self.__estimator_args(parameters))
 
     def gradient(
@@ -332,7 +346,7 @@ def gradient(
     ) -> dict[str, ParameterValue]:
         return self.__gradient(*self.__estimator_args(parameters))
 
-    def __estimator_args(self, parameters: Mapping[str, ParameterValue]) -> tuple:
+    def __estimator_args(self, parameters: Mapping[str, ParameterType]) -> tuple:
         return (
             _coerce_parameter_types(parameters),
             self.__data,
diff --git a/src/tensorwaves/function/__init__.py b/src/tensorwaves/function/__init__.py
index e8f1ad9b..cd2ef0d8 100644
--- a/src/tensorwaves/function/__init__.py
+++ b/src/tensorwaves/function/__init__.py
@@ -12,6 +12,7 @@
 from tensorwaves.interface import (
     DataSample,
     Function,
+    ParameterType,
     ParameterValue,
     ParametrizedFunction,
 )
@@ -146,10 +147,13 @@ def __init__(
     def __call__(
         self,
         data: DataSample,
-        parameters: Mapping[str, ParameterValue] | None = None,
+        parameters: Mapping[str, ParameterType] | None = None,
     ) -> np.ndarray:
-        extended_data = {**data, **self.__merge_parameters(parameters)}
-        return self.__function(extended_data)  # ty:ignore[invalid-argument-type]
+        extended_data: dict = {**data, **self.__parameters}
+        if parameters is not None:
+            self.__validate_parameters(parameters)
+            extended_data.update(parameters)
+        return self.__function(extended_data)
 
     @property
     def function(self) -> Callable[..., np.ndarray]:
@@ -170,18 +174,15 @@ def parameters(self) -> dict[str, ParameterValue]:
     def with_parameters(
         self, parameters: Mapping[str, ParameterValue]
     ) -> ParametrizedBackendFunction:
+        self.__validate_parameters(parameters)
         return ParametrizedBackendFunction(
             function=self.function,
             argument_order=self.argument_order,
-            parameters=self.__merge_parameters(parameters),
+            parameters={**self.__parameters, **parameters},
             backend=self.backend,
         )
 
-    def __merge_parameters(
-        self, parameters: Mapping[str, ParameterValue] | None
-    ) -> dict[str, ParameterValue]:
-        if parameters is None:
-            return self.__parameters
+    def __validate_parameters(self, parameters: Mapping[str, ParameterType]) -> None:
         over_defined = set(parameters) - set(self.__parameters)
         if over_defined:
             sep = "\n    "
@@ -191,7 +192,6 @@ def __merge_parameters(
                 f" Expecting one of:{sep}{parameter_listing}"
             )
             raise ValueError(msg)
-        return {**self.__parameters, **parameters}
 
 
 def get_source_code(function: Function) -> str:
diff --git a/src/tensorwaves/interface.py b/src/tensorwaves/interface.py
index 85c5e740..9db00655 100644
--- a/src/tensorwaves/interface.py
+++ b/src/tensorwaves/interface.py
@@ -39,7 +39,16 @@ def __call__(self, data: InputType) -> OutputType: ...
 DataSample = dict[str, np.ndarray]
 """Mapping of variable names to a sequence of data points, used by `Function`."""
 ParameterValue = complex | float
-"""Allowed types for parameter values."""
+"""Allowed types for scalar parameter values."""
+ParameterType = ParameterValue | np.ndarray
+"""Types for parameter values in an evaluation, including arrays of values.
+
+An array of parameter values represents several parameter points that are evaluated in
+one call through `broadcasting
+<https://numpy.org/doc/stable/user/basics.broadcasting.html>`_ against the event axis
+of a `.DataSample`. This can be used to propagate fit uncertainties by evaluating over
+e.g. bootstrapped parameter samples in a single, backend-parallelized call.
+"""
 
 
 class ParametrizedFunction(Function[InputType, OutputType]):
@@ -62,12 +71,13 @@ class ParametrizedFunction(Function[InputType, OutputType]):
     def __call__(
         self,
         data: InputType,
-        parameters: Mapping[str, ParameterValue] | None = None,
+        parameters: Mapping[str, ParameterType] | None = None,
     ) -> OutputType:
         """Evaluate the function over :code:`data` for these parameter values.
 
         Given parameter values are merged with the defaults in :attr:`parameters` for
-        this evaluation only.
+        this evaluation only. Parameter values may be arrays, as long as they
+        broadcast against the event arrays in :code:`data` (see `.ParameterType`).
         """
 
     @property
@@ -90,7 +100,7 @@ class DataTransformer(Function[DataSample, DataSample]):
     """
 
 
-class Estimator(Function[Mapping[str, ParameterValue], float]):
+class Estimator(Function[Mapping[str, ParameterType], float | np.ndarray]):
     """Estimator for discrepancy model and data.
 
     See the :mod:`.estimator` module for different implementations of this interface.
@@ -99,8 +109,13 @@ class Estimator(Function[Mapping[str, ParameterValue], float]):
     """
 
     @abstractmethod
-    def __call__(self, parameters: Mapping[str, ParameterValue]) -> float:  # ty:ignore[invalid-method-override]
-        """Compute estimator value for this combination of parameter values."""
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarray:  # ty:ignore[invalid-method-override]
+        """Compute estimator value for this combination of parameter values.
+
+        Parameter values may be one-dimensional arrays of shape :code:`(p,)`, in which
+        case the estimator returns an array of :code:`p` estimator values, one for
+        each parameter point (see `.ParameterType`).
+        """
 
     @abstractmethod
     def gradient(
diff --git a/src/tensorwaves/optimizer/minuit.py b/src/tensorwaves/optimizer/minuit.py
index 9bb01cd8..41a27c33 100644
--- a/src/tensorwaves/optimizer/minuit.py
+++ b/src/tensorwaves/optimizer/minuit.py
@@ -70,7 +70,7 @@ def optimize(
                 logs=_create_log(
                     optimizer=type(self),
                     estimator_type=type(estimator),
-                    estimator_value=estimator(parameters),
+                    estimator_value=float(estimator(parameters)),
                     function_call=n_function_calls,
                     parameters=parameters,
                 )
diff --git a/src/tensorwaves/optimizer/scipy.py b/src/tensorwaves/optimizer/scipy.py
index 915ea2b2..a546f536 100644
--- a/src/tensorwaves/optimizer/scipy.py
+++ b/src/tensorwaves/optimizer/scipy.py
@@ -62,7 +62,7 @@ def optimize(  # ruff:ignore[complex-structure]
                 logs=_create_log(
                     optimizer=type(self),
                     estimator_type=type(estimator),
-                    estimator_value=estimator(parameters),
+                    estimator_value=float(estimator(parameters)),
                     function_call=n_function_calls,
                     parameters=parameters,
                 )
@@ -91,7 +91,7 @@ def wrapped_function(pars: list) -> float:
                     logs=_create_log(
                         optimizer=type(self),
                         estimator_type=type(estimator),
-                        estimator_value=estimator(parameters),
+                        estimator_value=float(estimator(parameters)),
                         function_call=n_function_calls,
                         parameters=parameters,
                     ),
diff --git a/tests/optimizer/__init__.py b/tests/optimizer/__init__.py
index 03aae18b..5ff3f1d2 100644
--- a/tests/optimizer/__init__.py
+++ b/tests/optimizer/__init__.py
@@ -3,7 +3,7 @@
 from enum import Enum
 from typing import TYPE_CHECKING, Any
 
-from tensorwaves.interface import Estimator, ParameterValue
+from tensorwaves.interface import Estimator, ParameterType, ParameterValue
 from tensorwaves.optimizer.callbacks import Callback
 
 if TYPE_CHECKING:
@@ -60,7 +60,7 @@ class Polynomial1DMinimaEstimator(Estimator):
     def __init__(self, polynomial: Callable) -> None:
         self.__polynomial = polynomial
 
-    def __call__(self, parameters: Mapping[str, ParameterValue]) -> float:
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float:
         x = parameters["x"]
         return self.__polynomial(x)
 
@@ -74,7 +74,7 @@ class Polynomial2DMinimaEstimator(Estimator):
     def __init__(self, polynomial: Callable) -> None:
         self.__polynomial = polynomial
 
-    def __call__(self, parameters: Mapping[str, ParameterValue]) -> float:
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float:
         x = parameters["x"]
         y = parameters["y"]
         return self.__polynomial(x, y)
diff --git a/tests/test_estimator.py b/tests/test_estimator.py
index c915c0f7..aa78bf8a 100644
--- a/tests/test_estimator.py
+++ b/tests/test_estimator.py
@@ -109,6 +109,11 @@ def it_scales_the_residuals_with_the_weights(backend: str, linear_function):
         )
         assert estimator({"a": 0, "b": 2}) == 2.5
 
+    def it_broadcasts_array_valued_parameters(linear_function):
+        estimator = ChiSquared(linear_function, x_data, y_data)
+        b_values = np.array([1.0, 2.0])
+        np.testing.assert_allclose(estimator({"b": b_values}), [0.0, 5.0])
+
     def it_traces_the_jax_function_only_once():
         trace_count = 0
 
@@ -315,3 +320,40 @@ def it_recovers_the_parameters_that_generated_the_data(
             assert isinstance(par_error, float)
             assert abs(par_values[par_name] - par_value) < 4.0 * par_error
             assert par_value == pytest.approx(par_values[par_name], rel=0.1)
+
+    @pytest.mark.parametrize("backend", ["jax", "numba", "numpy", "tf"])
+    def it_broadcasts_array_valued_parameters(backend: str):
+        x, mu, sigma = sp.symbols("x mu sigma")
+        function = create_parametrized_function(
+            expression=sp.exp(-(((x - mu) / sigma) ** 2) / 2),
+            parameters={mu: 0.5, sigma: 0.1},
+            backend=backend,
+        )
+        rng = np.random.default_rng(seed=0)
+        data = {"x": rng.normal(0.5, 0.1, size=2_000)}
+        phsp = {"x": rng.uniform(-2.0, 5.0, size=5_000)}
+        estimator = UnbinnedNLL(function, data, phsp, phsp_volume=7.0)
+        mu_values = np.array([0.4, 0.5, 0.6])
+        batched_output = np.asarray(estimator({"mu": mu_values}))
+        scalar_outputs = [float(estimator({"mu": value})) for value in mu_values]
+        assert batched_output.shape == mu_values.shape
+        np.testing.assert_allclose(batched_output, scalar_outputs, rtol=1e-8)
+
+    def it_matches_jax_vmap_for_batched_evaluation():
+        jax = pytest.importorskip("jax")
+        x, mu, sigma = sp.symbols("x mu sigma")
+        function = create_parametrized_function(
+            expression=sp.exp(-(((x - mu) / sigma) ** 2) / 2),
+            parameters={mu: 0.5, sigma: 0.1},
+            backend="jax",
+        )
+        rng = np.random.default_rng(seed=0)
+        data = {"x": rng.normal(0.5, 0.1, size=2_000)}
+        phsp = {"x": rng.uniform(-2.0, 5.0, size=5_000)}
+        estimator = UnbinnedNLL(function, data, phsp, phsp_volume=7.0)
+        mu_values = np.array([0.4, 0.5, 0.6])
+        batched_output = np.asarray(estimator({"mu": mu_values}))
+        vmapped_output = jax.vmap(lambda value: estimator({"mu": value}))(mu_values)
+        np.testing.assert_allclose(
+            batched_output, np.asarray(vmapped_output), rtol=1e-8
+        )

From d0163bcaeed0af5b46ea42fcda7f6006df867b00 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Tue, 1 Sep 2026 11:38:14 +0200
Subject: [PATCH 2/8] MAINT: minor formatting improvements

---
 src/tensorwaves/estimator.py | 10 ++++++----
 src/tensorwaves/interface.py | 14 +++++++-------
 2 files changed, 13 insertions(+), 11 deletions(-)

diff --git a/src/tensorwaves/estimator.py b/src/tensorwaves/estimator.py
index d1d08a76..894e3f8c 100644
--- a/src/tensorwaves/estimator.py
+++ b/src/tensorwaves/estimator.py
@@ -92,10 +92,12 @@ def _coerce_parameter_types(
 
 
 def _coerce_parameter_value(value: ParameterType) -> ParameterType:
-    # normalize scalars to float/complex so that JIT compilers see stable input
-    # types (an int value would otherwise trigger a re-trace once it becomes a
-    # float) and give parameter arrays a new trailing axis, so that they
-    # broadcast against the event axis of the data samples
+    """Normalize values for stable JIT inputs and event-axis broadcasting.
+
+    Scalars are converted to ``float`` or ``complex`` so that a change from an integer
+    value does not trigger retracing. Parameter arrays receive a new trailing axis so
+    that they broadcast against the data samples' event axis.
+    """
     if isinstance(value, complex):
         return complex(value)
     if isinstance(value, (int, float)):
diff --git a/src/tensorwaves/interface.py b/src/tensorwaves/interface.py
index 9db00655..7b5a77e8 100644
--- a/src/tensorwaves/interface.py
+++ b/src/tensorwaves/interface.py
@@ -45,9 +45,9 @@ def __call__(self, data: InputType) -> OutputType: ...
 
 An array of parameter values represents several parameter points that are evaluated in
 one call through `broadcasting
-<https://numpy.org/doc/stable/user/basics.broadcasting.html>`_ against the event axis
-of a `.DataSample`. This can be used to propagate fit uncertainties by evaluating over
-e.g. bootstrapped parameter samples in a single, backend-parallelized call.
+<https://numpy.org/doc/stable/user/basics.broadcasting.html>`_ against the event axis of
+a `.DataSample`. This can be used to propagate fit uncertainties by evaluating over e.g.
+bootstrapped parameter samples in a single, backend-parallelized call.
 """
 
 
@@ -76,8 +76,8 @@ def __call__(
         """Evaluate the function over :code:`data` for these parameter values.
 
         Given parameter values are merged with the defaults in :attr:`parameters` for
-        this evaluation only. Parameter values may be arrays, as long as they
-        broadcast against the event arrays in :code:`data` (see `.ParameterType`).
+        this evaluation only. Parameter values may be arrays, as long as they broadcast
+        against the event arrays in :code:`data` (see `.ParameterType`).
         """
 
     @property
@@ -113,8 +113,8 @@ def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarra
         """Compute estimator value for this combination of parameter values.
 
         Parameter values may be one-dimensional arrays of shape :code:`(p,)`, in which
-        case the estimator returns an array of :code:`p` estimator values, one for
-        each parameter point (see `.ParameterType`).
+        case the estimator returns an array of :code:`p` estimator values, one for each
+        parameter point (see `.ParameterType`).
         """
 
     @abstractmethod

From 1108ab9665c0d89c6aca9edc31f57a861ff9bce1 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Tue, 1 Sep 2026 11:51:17 +0200
Subject: [PATCH 3/8] ENH: use `@overload` for estimator calls

---
 src/tensorwaves/estimator.py | 18 +++++++++++++++++-
 src/tensorwaves/interface.py | 10 +++++++++-
 tests/optimizer/__init__.py  | 24 +++++++++++++++++++++---
 3 files changed, 47 insertions(+), 5 deletions(-)

diff --git a/src/tensorwaves/estimator.py b/src/tensorwaves/estimator.py
index 894e3f8c..1e35012e 100644
--- a/src/tensorwaves/estimator.py
+++ b/src/tensorwaves/estimator.py
@@ -5,7 +5,7 @@
 
 from __future__ import annotations
 
-from typing import TYPE_CHECKING
+from typing import TYPE_CHECKING, overload
 
 from tensorwaves.config import _initialize_jax
 from tensorwaves.data.transform import SympyDataTransformer
@@ -244,6 +244,14 @@ def estimator(
         self.__estimator = _jit_estimator_core(estimator, backend)
         self.__gradient = _create_core_gradient(estimator, backend)
 
+    @overload
+    def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
+    @overload
+    def __call__(self, parameters: Mapping[str, np.ndarray]) -> np.ndarray: ...
+    @overload
+    def __call__(
+        self, parameters: Mapping[str, ParameterType]
+    ) -> float | np.ndarray: ...
     def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarray:
         return self.__estimator(*self.__estimator_args(parameters))
 
@@ -340,6 +348,14 @@ def estimator(
         self.__estimator = _jit_estimator_core(estimator, backend)
         self.__gradient = _create_core_gradient(estimator, backend)
 
+    @overload
+    def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
+    @overload
+    def __call__(self, parameters: Mapping[str, np.ndarray]) -> np.ndarray: ...
+    @overload
+    def __call__(
+        self, parameters: Mapping[str, ParameterType]
+    ) -> float | np.ndarray: ...
     def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarray:
         return self.__estimator(*self.__estimator_args(parameters))
 
diff --git a/src/tensorwaves/interface.py b/src/tensorwaves/interface.py
index 7b5a77e8..caf254c6 100644
--- a/src/tensorwaves/interface.py
+++ b/src/tensorwaves/interface.py
@@ -4,7 +4,7 @@
 
 from abc import ABC, abstractmethod
 from collections.abc import Mapping
-from typing import TYPE_CHECKING, Any, Generic, TypeVar
+from typing import TYPE_CHECKING, Any, Generic, TypeVar, overload
 
 import attrs
 import numpy as np
@@ -108,6 +108,14 @@ class Estimator(Function[Mapping[str, ParameterType], float | np.ndarray]):
     .. automethod:: __call__
     """
 
+    @overload
+    def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
+    @overload
+    def __call__(self, parameters: Mapping[str, np.ndarray]) -> np.ndarray: ...
+    @overload
+    def __call__(
+        self, parameters: Mapping[str, ParameterType]
+    ) -> float | np.ndarray: ...
     @abstractmethod
     def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarray:  # ty:ignore[invalid-method-override]
         """Compute estimator value for this combination of parameter values.
diff --git a/tests/optimizer/__init__.py b/tests/optimizer/__init__.py
index 5ff3f1d2..966ee5ba 100644
--- a/tests/optimizer/__init__.py
+++ b/tests/optimizer/__init__.py
@@ -1,7 +1,7 @@
 from __future__ import annotations
 
 from enum import Enum
-from typing import TYPE_CHECKING, Any
+from typing import TYPE_CHECKING, Any, overload
 
 from tensorwaves.interface import Estimator, ParameterType, ParameterValue
 from tensorwaves.optimizer.callbacks import Callback
@@ -10,6 +10,8 @@
     from collections.abc import Callable, Mapping
     from unittest.mock import MagicMock
 
+    import numpy as np
+
 
 class CallbackType(Enum):
     ON_OPTIMIZE_START = "on_optimize_start"
@@ -60,7 +62,15 @@ class Polynomial1DMinimaEstimator(Estimator):
     def __init__(self, polynomial: Callable) -> None:
         self.__polynomial = polynomial
 
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float:
+    @overload
+    def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
+    @overload
+    def __call__(self, parameters: Mapping[str, np.ndarray]) -> np.ndarray: ...
+    @overload
+    def __call__(
+        self, parameters: Mapping[str, ParameterType]
+    ) -> float | np.ndarray: ...
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarray:
         x = parameters["x"]
         return self.__polynomial(x)
 
@@ -74,7 +84,15 @@ class Polynomial2DMinimaEstimator(Estimator):
     def __init__(self, polynomial: Callable) -> None:
         self.__polynomial = polynomial
 
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float:
+    @overload
+    def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
+    @overload
+    def __call__(self, parameters: Mapping[str, np.ndarray]) -> np.ndarray: ...
+    @overload
+    def __call__(
+        self, parameters: Mapping[str, ParameterType]
+    ) -> float | np.ndarray: ...
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarray:
         x = parameters["x"]
         y = parameters["y"]
         return self.__polynomial(x, y)

From 6bbb240250c17bcc4b4dbb70273f9b0933768d29 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Tue, 1 Sep 2026 12:16:56 +0200
Subject: [PATCH 4/8] ENH: implement `Array` type alias

---
 benchmarks/ampform.py                    |  5 ++--
 benchmarks/expression.py                 |  4 +--
 benchmarks/unbinned_nll.py               | 24 ++++++++-------
 docs/conf.py                             |  3 ++
 src/tensorwaves/data/__init__.py         |  3 +-
 src/tensorwaves/data/_data_sample.py     |  6 ++--
 src/tensorwaves/data/rng.py              |  6 ++--
 src/tensorwaves/data/transform.py        |  9 ++----
 src/tensorwaves/estimator.py             | 38 +++++++++++-------------
 src/tensorwaves/function/__init__.py     | 18 +++++------
 src/tensorwaves/interface.py             | 20 ++++++-------
 tests/data/test_data.py                  |  5 ++--
 tests/optimizer/__init__.py              | 20 +++++--------
 tests/optimizer/test_fit_simple_model.py |  4 +--
 14 files changed, 80 insertions(+), 85 deletions(-)

diff --git a/benchmarks/ampform.py b/benchmarks/ampform.py
index d6b64149..91eb3c1b 100644
--- a/benchmarks/ampform.py
+++ b/benchmarks/ampform.py
@@ -24,6 +24,7 @@
 
     from tensorwaves.function import ParametrizedBackendFunction
     from tensorwaves.interface import (
+        Array,
         DataSample,
         FitResult,
         Function,
@@ -72,7 +73,7 @@ def create_function(
 
 def generate_data(
     model: HelicityModel,
-    function: Function[DataSample, np.ndarray],
+    function: Function[DataSample, Array],
     data_sample_size: int,
     phsp_sample_size: int,
     backend: str,
@@ -109,7 +110,7 @@ def generate_data(
 def fit(
     data: DataSample,
     phsp: DataSample,
-    function: ParametrizedFunction[DataSample, np.ndarray],
+    function: ParametrizedFunction[DataSample, Array],
     initial_parameters: Mapping[str, ParameterValue],
     backend: str,
 ) -> FitResult:
diff --git a/benchmarks/expression.py b/benchmarks/expression.py
index 796b9c9a..f8a9606d 100644
--- a/benchmarks/expression.py
+++ b/benchmarks/expression.py
@@ -12,7 +12,7 @@
 from tensorwaves.optimizer.scipy import ScipyMinimizer
 
 if TYPE_CHECKING:
-    from tensorwaves.interface import DataSample, Function
+    from tensorwaves.interface import Array, DataSample, Function
 
 
 def gaussian(x: sp.Symbol, mu: sp.Symbol, sigma: sp.Symbol) -> sp.Expr:
@@ -64,7 +64,7 @@ def _generate_domain(
 
 def _generate_data(
     size: int,
-    function: Function[DataSample, np.ndarray],
+    function: Function[DataSample, Array],
     rng: np.random.Generator,
     bunch_size: int = 10_000,
 ) -> DataSample:
diff --git a/benchmarks/unbinned_nll.py b/benchmarks/unbinned_nll.py
index 2b632222..c7bd1a82 100644
--- a/benchmarks/unbinned_nll.py
+++ b/benchmarks/unbinned_nll.py
@@ -18,6 +18,8 @@
 if TYPE_CHECKING:
     from collections.abc import Callable
 
+    from tensorwaves.interface import Array, DataSample
+
     def prange(stop: int) -> range: ...
 
 else:
@@ -193,7 +195,7 @@ def intensities() -> tuple[np.ndarray, np.ndarray]:
 
 
 @pytest.fixture(scope="module")
-def estimator_samples() -> tuple[dict[str, np.ndarray], dict[str, np.ndarray]]:
+def estimator_samples() -> tuple[DataSample, DataSample]:
     rng = np.random.default_rng(seed=0)
     data = {"x": rng.uniform(low=-2.0, high=2.0, size=1_000_000)}
     phsp = {"x": rng.uniform(low=-2.0, high=2.0, size=1_000_000)}
@@ -221,7 +223,7 @@ def tensorflow_intensities(
 
 @pytest.fixture(scope="module")
 def jax_estimator_samples(
-    estimator_samples: tuple[dict[str, np.ndarray], dict[str, np.ndarray]],
+    estimator_samples: tuple[DataSample, DataSample],
 ) -> tuple[dict[str, jax.Array], dict[str, jax.Array]]:
     configure(jax_precision="float64")
     data, phsp = estimator_samples
@@ -233,7 +235,7 @@ def jax_estimator_samples(
 
 @pytest.fixture(scope="module")
 def tensorflow_estimator_samples(
-    estimator_samples: tuple[dict[str, np.ndarray], dict[str, np.ndarray]],
+    estimator_samples: tuple[DataSample, DataSample],
 ) -> tuple[dict[str, tf.Tensor], dict[str, tf.Tensor]]:
     data, phsp = estimator_samples
     return {"x": tnp.asarray(data["x"])}, {"x": tnp.asarray(phsp["x"])}
@@ -267,8 +269,8 @@ def _create_estimator(
 
 
 def _compute_estimator_reference(
-    data: dict[str, np.ndarray],
-    phsp: dict[str, np.ndarray],
+    data: DataSample,
+    phsp: DataSample,
     center: float,
 ) -> float:
     data_intensities = _numpy_intensity(data["x"], center)
@@ -277,16 +279,16 @@ def _compute_estimator_reference(
 
 
 def _benchmark_estimator_numpy(
-    benchmark: Callable[[Callable[[], float | np.ndarray]], float | np.ndarray],
+    benchmark: Callable[[Callable[[], float | Array]], float | Array],
     backend: str,
-    data: dict[str, np.ndarray],
-    phsp: dict[str, np.ndarray],
+    data: DataSample,
+    phsp: DataSample,
     parameters: dict[str, float],
-) -> float | np.ndarray:
+) -> float | Array:
     estimator = _create_estimator(backend, data, phsp)
     estimator(parameters)
 
-    def run() -> float | np.ndarray:
+    def run() -> float | Array:
         return estimator(parameters)
 
     return benchmark(run)
@@ -413,7 +415,7 @@ def test_unbinned_nll_normalization_formula(
 def test_unbinned_nll_estimator(
     benchmark,
     backend: str,
-    estimator_samples: tuple[dict[str, np.ndarray], dict[str, np.ndarray]],
+    estimator_samples: tuple[DataSample, DataSample],
     request: pytest.FixtureRequest,
 ) -> None:
     data, phsp = estimator_samples
diff --git a/docs/conf.py b/docs/conf.py
index 38984f42..6f870356 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -53,6 +53,7 @@ def get_tensorflow_url() -> str:
 add_module_names = False
 api_github_repo = f"{ORGANIZATION}/{REPO_NAME}"
 api_target_substitutions: dict[str, str | tuple[str, str]] = {
+    "Array": "tensorwaves.interface.Array",
     "DataSample": "tensorwaves.interface.DataSample",
     "np.ndarray": "numpy.ndarray",
     "ParameterValue": "tensorwaves.interface.ParameterValue",
@@ -64,6 +65,7 @@ def get_tensorflow_url() -> str:
     "TypeAliasForwardRef": "typing.TypeAlias",
 }
 api_target_types: dict[str, str | tuple[str, str]] = {
+    "tensorwaves.interface.Array": "obj",
     "tensorwaves.interface.DataSample": "obj",
     "tensorwaves.interface.InputType": "obj",
     "tensorwaves.interface.OutputType": "obj",
@@ -77,6 +79,7 @@ def get_tensorflow_url() -> str:
 }
 autodoc_member_order = "bysource"
 autodoc_type_aliases = {
+    "Array": "tensorwaves.interface.Array",
     "DataSample": "tensorwaves.interface.DataSample",
     "InputType": "tensorwaves.interface.InputType",
     "OutputType": "tensorwaves.interface.OutputType",
diff --git a/src/tensorwaves/data/__init__.py b/src/tensorwaves/data/__init__.py
index fb6622a5..8983fc03 100644
--- a/src/tensorwaves/data/__init__.py
+++ b/src/tensorwaves/data/__init__.py
@@ -8,6 +8,7 @@
 from tqdm.auto import tqdm
 
 from tensorwaves.interface import (
+    Array,
     DataGenerator,
     DataSample,
     DataTransformer,
@@ -69,7 +70,7 @@ class IntensityDistributionGenerator(DataGenerator):
     def __init__(
         self,
         domain_generator: DataGenerator,
-        function: Function[DataSample, np.ndarray],
+        function: Function[DataSample, Array],
         domain_transformer: DataTransformer | None = None,
         bunch_size: int = 50_000,
     ) -> None:
diff --git a/src/tensorwaves/data/_data_sample.py b/src/tensorwaves/data/_data_sample.py
index bbb35dee..34f937d5 100644
--- a/src/tensorwaves/data/_data_sample.py
+++ b/src/tensorwaves/data/_data_sample.py
@@ -12,7 +12,7 @@
 
     from tqdm.auto import tqdm
 
-    from tensorwaves.interface import DataSample
+    from tensorwaves.interface import Array, DataSample
 
 
 def get_number_of_events(four_momenta: DataSample) -> int:
@@ -28,7 +28,7 @@ def merge_events(sample1: DataSample, sample2: DataSample) -> DataSample:
 
 def _determine_merge_method(
     sample: DataSample,
-) -> Callable[[tuple[np.ndarray, np.ndarray]], np.ndarray]:
+) -> Callable[[tuple[Array, Array]], Array]:
     if len(sample) == 0:
         return operator.itemgetter(1)
     some_array = next(iter(sample.values()))
@@ -44,7 +44,7 @@ def _determine_merge_method(
 def _merge_events(
     sample1: DataSample,
     sample2: DataSample,
-    merge_method: Callable[[tuple[np.ndarray, np.ndarray]], np.ndarray],
+    merge_method: Callable[[tuple[Array, Array]], Array],
 ) -> DataSample:
     if len(sample1) and len(sample2) and set(sample1) != set(sample2):
         msg = "Keys of data sets are not matching"
diff --git a/src/tensorwaves/data/rng.py b/src/tensorwaves/data/rng.py
index 3054ef71..68b8d6df 100644
--- a/src/tensorwaves/data/rng.py
+++ b/src/tensorwaves/data/rng.py
@@ -8,7 +8,7 @@
 
 from tensorwaves.config import _tensorflow_precision
 from tensorwaves.function._backend import raise_missing_module_error
-from tensorwaves.interface import RealNumberGenerator
+from tensorwaves.interface import Array, RealNumberGenerator
 
 if TYPE_CHECKING:  # pragma: no cover
     import tensorflow as tf
@@ -24,7 +24,7 @@ def __init__(self, seed: int | None = None) -> None:
 
     def __call__(
         self, size: int, min_value: float = 0.0, max_value: float = 1.0
-    ) -> np.ndarray:
+    ) -> Array:
         return self.generator.uniform(size=size, low=min_value, high=max_value)
 
     @property
@@ -50,7 +50,7 @@ def __init__(self, seed: int | None = None) -> None:
 
     def __call__(
         self, size: int, min_value: float = 0.0, max_value: float = 1.0
-    ) -> np.ndarray:
+    ) -> Array:
         return self.generator.uniform(
             shape=[size],
             minval=min_value,
diff --git a/src/tensorwaves/data/transform.py b/src/tensorwaves/data/transform.py
index af244716..05e1d97c 100644
--- a/src/tensorwaves/data/transform.py
+++ b/src/tensorwaves/data/transform.py
@@ -8,14 +8,13 @@
 
 from tensorwaves.function import PositionalArgumentFunction
 from tensorwaves.function.sympy import _get_free_symbols, _lambdify_normal_or_fast
-from tensorwaves.interface import DataSample, DataTransformer, Function
+from tensorwaves.interface import Array, DataSample, DataTransformer, Function
 
 from ._attrs import to_tuple
 
 if TYPE_CHECKING:  # pragma: no cover
     from collections.abc import Mapping
 
-    import numpy as np
     import sympy as sp
 
 
@@ -55,9 +54,7 @@ def __call__(self, data: DataSample) -> DataSample:
 class SympyDataTransformer(DataTransformer):
     """Implementation of a `.DataTransformer`."""
 
-    def __init__(
-        self, functions: Mapping[str, Function[DataSample, np.ndarray]]
-    ) -> None:
+    def __init__(self, functions: Mapping[str, Function[DataSample, Array]]) -> None:
         if any(not isinstance(f, Function) for f in functions.values()):
             msg = (
                 f"Not all values in the mapping are an instance of {Function.__name__}"
@@ -66,7 +63,7 @@ def __init__(
         self.__functions = dict(functions)
 
     @property
-    def functions(self) -> dict[str, Function[DataSample, np.ndarray]]:
+    def functions(self) -> dict[str, Function[DataSample, Array]]:
         """Read-only access to the internal mapping of functions."""
         return dict(self.__functions)
 
diff --git a/src/tensorwaves/estimator.py b/src/tensorwaves/estimator.py
index 1e35012e..2df5df0f 100644
--- a/src/tensorwaves/estimator.py
+++ b/src/tensorwaves/estimator.py
@@ -12,6 +12,7 @@
 from tensorwaves.function._backend import find_function, raise_missing_module_error
 from tensorwaves.function.sympy import create_parametrized_function, prepare_caching
 from tensorwaves.interface import (
+    Array,
     DataSample,
     DataTransformer,
     Estimator,
@@ -23,7 +24,6 @@
 if TYPE_CHECKING:
     from collections.abc import Callable, Iterable, Mapping
 
-    import numpy as np
     import sympy as sp
 
 
@@ -34,7 +34,7 @@ def create_cached_function(
     free_parameters: Iterable[sp.Basic],
     *,
     use_cse: bool = True,
-) -> tuple[ParametrizedFunction[DataSample, np.ndarray], DataTransformer]:
+) -> tuple[ParametrizedFunction[DataSample, Array], DataTransformer]:
     """Create a function and data transformer for cached computations.
 
     Once it is known which parameters in an expression are to be optimized, this
@@ -171,7 +171,7 @@ def _create_core_gradient(core: Callable, backend: str) -> Callable:
 
         def gradient(
             parameters: Mapping[str, ParameterValue],
-            *data_args: DataSample | np.ndarray | None,
+            *data_args: DataSample | Array | None,
         ) -> dict[str, ParameterValue]:
             return _conjugate_complex_gradient(raw_gradient(parameters, *data_args))
 
@@ -179,7 +179,7 @@ def gradient(
 
     def raise_gradient_not_implemented(
         parameters: Mapping[str, ParameterValue],
-        *data_args: DataSample | np.ndarray | None,
+        *data_args: DataSample | Array | None,
     ) -> dict[str, ParameterValue]:
         msg = f"Gradient not implemented for back-end {backend}."
         raise NotImplementedError(msg)
@@ -213,10 +213,10 @@ class ChiSquared(Estimator):
 
     def __init__(
         self,
-        function: ParametrizedFunction[DataSample, np.ndarray],
+        function: ParametrizedFunction[DataSample, Array],
         domain: DataSample,
-        observed_values: np.ndarray,
-        weights: np.ndarray | None = None,
+        observed_values: Array,
+        weights: Array | None = None,
         backend: str | None = None,
     ) -> None:
         backend = _determine_backend(function, backend)
@@ -234,8 +234,8 @@ def __init__(
         def estimator(
             parameters: Mapping[str, ParameterType],
             domain: DataSample,
-            observed_values: np.ndarray,
-            weights: np.ndarray,
+            observed_values: Array,
+            weights: Array,
         ) -> float:
             computed_values = function(domain, parameters)
             chi_squared = weights * (computed_values - observed_values) ** 2
@@ -247,12 +247,10 @@ def estimator(
     @overload
     def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
     @overload
-    def __call__(self, parameters: Mapping[str, np.ndarray]) -> np.ndarray: ...
+    def __call__(self, parameters: Mapping[str, Array]) -> Array: ...
     @overload
-    def __call__(
-        self, parameters: Mapping[str, ParameterType]
-    ) -> float | np.ndarray: ...
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarray:
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array: ...
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array:
         return self.__estimator(*self.__estimator_args(parameters))
 
     def gradient(
@@ -310,7 +308,7 @@ class UnbinnedNLL(Estimator):
 
     def __init__(
         self,
-        function: ParametrizedFunction[DataSample, np.ndarray],
+        function: ParametrizedFunction[DataSample, Array],
         data: DataSample,
         phsp: DataSample,
         phsp_volume: float = 1.0,
@@ -329,7 +327,7 @@ def estimator(
             parameters: Mapping[str, ParameterType],
             data: DataSample,
             phsp: DataSample,
-            phsp_weights: np.ndarray | None,
+            phsp_weights: Array | None,
         ) -> float:
             bare_intensities = function(data, parameters)
             phsp_intensities = function(phsp, parameters)
@@ -351,12 +349,10 @@ def estimator(
     @overload
     def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
     @overload
-    def __call__(self, parameters: Mapping[str, np.ndarray]) -> np.ndarray: ...
+    def __call__(self, parameters: Mapping[str, Array]) -> Array: ...
     @overload
-    def __call__(
-        self, parameters: Mapping[str, ParameterType]
-    ) -> float | np.ndarray: ...
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarray:
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array: ...
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array:
         return self.__estimator(*self.__estimator_args(parameters))
 
     def gradient(
diff --git a/src/tensorwaves/function/__init__.py b/src/tensorwaves/function/__init__.py
index cd2ef0d8..07350cf7 100644
--- a/src/tensorwaves/function/__init__.py
+++ b/src/tensorwaves/function/__init__.py
@@ -6,10 +6,10 @@
 from typing import TYPE_CHECKING, Protocol, runtime_checkable
 
 import attrs
-import numpy as np
 from attrs import field, frozen
 
 from tensorwaves.interface import (
+    Array,
     DataSample,
     Function,
     ParameterType,
@@ -43,7 +43,7 @@ class BackendFunction(Protocol):
     """
 
     @property
-    def function(self) -> Callable[..., np.ndarray]:
+    def function(self) -> Callable[..., Array]:
         """Backend-native function that takes positional arguments only."""
 
     @property
@@ -102,7 +102,7 @@ def _to_tuple(argument_order: Iterable[str]) -> tuple[str, ...]:
 
 
 @frozen
-class PositionalArgumentFunction(Function[DataSample, np.ndarray]):
+class PositionalArgumentFunction(Function[DataSample, Array]):
     """Wrapper around a function with positional arguments.
 
     This class provides a :meth:`~.Function.__call__` that can take a `.DataSample` for
@@ -114,7 +114,7 @@ class PositionalArgumentFunction(Function[DataSample, np.ndarray]):
     .. seealso:: :func:`.create_function`
     """
 
-    function: Callable[..., np.ndarray] = field(validator=_validate_arguments)
+    function: Callable[..., Array] = field(validator=_validate_arguments)
     """A function with positional arguments only."""
     argument_order: tuple[str, ...] = field(
         converter=_to_tuple, validator=[_all_str, _all_unique]
@@ -123,12 +123,12 @@ class PositionalArgumentFunction(Function[DataSample, np.ndarray]):
     backend: str | None = None
     """Name of the computational backend that :attr:`function` was compiled for."""
 
-    def __call__(self, data: DataSample) -> np.ndarray:
+    def __call__(self, data: DataSample) -> Array:
         args = [data[var_name] for var_name in self.argument_order]
         return self.function(*args)
 
 
-class ParametrizedBackendFunction(ParametrizedFunction[DataSample, np.ndarray]):
+class ParametrizedBackendFunction(ParametrizedFunction[DataSample, Array]):
     """Implements `.ParametrizedFunction` for a specific computational back-end.
 
     .. seealso:: :func:`.create_parametrized_function`
@@ -136,7 +136,7 @@ class ParametrizedBackendFunction(ParametrizedFunction[DataSample, np.ndarray]):
 
     def __init__(
         self,
-        function: Callable[..., np.ndarray],
+        function: Callable[..., Array],
         argument_order: Iterable[str],
         parameters: Mapping[str, ParameterValue],
         backend: str | None = None,
@@ -148,7 +148,7 @@ def __call__(
         self,
         data: DataSample,
         parameters: Mapping[str, ParameterType] | None = None,
-    ) -> np.ndarray:
+    ) -> Array:
         extended_data: dict = {**data, **self.__parameters}
         if parameters is not None:
             self.__validate_parameters(parameters)
@@ -156,7 +156,7 @@ def __call__(
         return self.__function(extended_data)
 
     @property
-    def function(self) -> Callable[..., np.ndarray]:
+    def function(self) -> Callable[..., Array]:
         return self.__function.function
 
     @property
diff --git a/src/tensorwaves/interface.py b/src/tensorwaves/interface.py
index caf254c6..584c23a3 100644
--- a/src/tensorwaves/interface.py
+++ b/src/tensorwaves/interface.py
@@ -4,7 +4,7 @@
 
 from abc import ABC, abstractmethod
 from collections.abc import Mapping
-from typing import TYPE_CHECKING, Any, Generic, TypeVar, overload
+from typing import TYPE_CHECKING, Any, Generic, TypeAlias, TypeVar, overload
 
 import attrs
 import numpy as np
@@ -36,11 +36,13 @@ class Function(ABC, Generic[InputType, OutputType]):
     def __call__(self, data: InputType) -> OutputType: ...
 
 
-DataSample = dict[str, np.ndarray]
+Array: TypeAlias = np.ndarray[Any, np.dtype[Any]]
+"""Type representing numerical arrays."""
+DataSample = dict[str, Array]
 """Mapping of variable names to a sequence of data points, used by `Function`."""
 ParameterValue = complex | float
 """Allowed types for scalar parameter values."""
-ParameterType = ParameterValue | np.ndarray
+ParameterType = ParameterValue | Array
 """Types for parameter values in an evaluation, including arrays of values.
 
 An array of parameter values represents several parameter points that are evaluated in
@@ -100,7 +102,7 @@ class DataTransformer(Function[DataSample, DataSample]):
     """
 
 
-class Estimator(Function[Mapping[str, ParameterType], float | np.ndarray]):
+class Estimator(Function[Mapping[str, ParameterType], float | Array]):
     """Estimator for discrepancy model and data.
 
     See the :mod:`.estimator` module for different implementations of this interface.
@@ -111,13 +113,11 @@ class Estimator(Function[Mapping[str, ParameterType], float | np.ndarray]):
     @overload
     def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
     @overload
-    def __call__(self, parameters: Mapping[str, np.ndarray]) -> np.ndarray: ...
+    def __call__(self, parameters: Mapping[str, Array]) -> Array: ...
     @overload
-    def __call__(
-        self, parameters: Mapping[str, ParameterType]
-    ) -> float | np.ndarray: ...
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array: ...
     @abstractmethod
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarray:  # ty:ignore[invalid-method-override]
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array:  # ty:ignore[invalid-method-override]
         """Compute estimator value for this combination of parameter values.
 
         Parameter values may be one-dimensional arrays of shape :code:`(p,)`, in which
@@ -247,7 +247,7 @@ class RealNumberGenerator(ABC):
     @abstractmethod
     def __call__(
         self, size: int, min_value: float = 0.0, max_value: float = 1.0
-    ) -> np.ndarray:
+    ) -> Array:
         """Generate random floats in the range [min_value, max_value)."""
 
     @property
diff --git a/tests/data/test_data.py b/tests/data/test_data.py
index ee2f694a..0bbdf5a9 100644
--- a/tests/data/test_data.py
+++ b/tests/data/test_data.py
@@ -17,6 +17,7 @@
 )
 from tensorwaves.function.sympy import create_function
 from tensorwaves.interface import (
+    Array,
     DataGenerator,
     DataSample,
     Function,
@@ -27,8 +28,8 @@
     from _pytest.capture import CaptureFixture
 
 
-class FlatDistribution(Function[DataSample, np.ndarray]):
-    def __call__(self, data: DataSample) -> np.ndarray:
+class FlatDistribution(Function[DataSample, Array]):
+    def __call__(self, data: DataSample) -> Array:
         some_key = next(iter(data))
         sample_size = len(data[some_key])
         return np.ones(sample_size)
diff --git a/tests/optimizer/__init__.py b/tests/optimizer/__init__.py
index 966ee5ba..1e228bd9 100644
--- a/tests/optimizer/__init__.py
+++ b/tests/optimizer/__init__.py
@@ -3,15 +3,13 @@
 from enum import Enum
 from typing import TYPE_CHECKING, Any, overload
 
-from tensorwaves.interface import Estimator, ParameterType, ParameterValue
+from tensorwaves.interface import Array, Estimator, ParameterType, ParameterValue
 from tensorwaves.optimizer.callbacks import Callback
 
 if TYPE_CHECKING:
     from collections.abc import Callable, Mapping
     from unittest.mock import MagicMock
 
-    import numpy as np
-
 
 class CallbackType(Enum):
     ON_OPTIMIZE_START = "on_optimize_start"
@@ -65,12 +63,10 @@ def __init__(self, polynomial: Callable) -> None:
     @overload
     def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
     @overload
-    def __call__(self, parameters: Mapping[str, np.ndarray]) -> np.ndarray: ...
+    def __call__(self, parameters: Mapping[str, Array]) -> Array: ...
     @overload
-    def __call__(
-        self, parameters: Mapping[str, ParameterType]
-    ) -> float | np.ndarray: ...
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarray:
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array: ...
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array:
         x = parameters["x"]
         return self.__polynomial(x)
 
@@ -87,12 +83,10 @@ def __init__(self, polynomial: Callable) -> None:
     @overload
     def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
     @overload
-    def __call__(self, parameters: Mapping[str, np.ndarray]) -> np.ndarray: ...
+    def __call__(self, parameters: Mapping[str, Array]) -> Array: ...
     @overload
-    def __call__(
-        self, parameters: Mapping[str, ParameterType]
-    ) -> float | np.ndarray: ...
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | np.ndarray:
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array: ...
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array:
         x = parameters["x"]
         y = parameters["y"]
         return self.__polynomial(x, y)
diff --git a/tests/optimizer/test_fit_simple_model.py b/tests/optimizer/test_fit_simple_model.py
index afb576fd..fcc3eb05 100644
--- a/tests/optimizer/test_fit_simple_model.py
+++ b/tests/optimizer/test_fit_simple_model.py
@@ -23,7 +23,7 @@
 
     import iminuit
 
-    from tensorwaves.interface import DataSample, Function
+    from tensorwaves.interface import Array, DataSample, Function
 
 
 def generate_domain(
@@ -40,7 +40,7 @@ def generate_domain(
 def generate_data(
     size: int,
     boundaries: dict[str, tuple[float, float]],
-    function: Function[DataSample, np.ndarray],
+    function: Function[DataSample, Array],
     rng: np.random.Generator,
     bunch_size: int = 10_000,
 ) -> DataSample:

From a64f925aaca8703775d3ee29b235f5dc7f3575dc Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Tue, 1 Sep 2026 14:50:31 +0200
Subject: [PATCH 5/8] ENH: parametrize `Array` type alias by scalar type

---
 docs/conf.py                 |   7 ++
 pyproject.toml               |   1 +
 src/tensorwaves/estimator.py |  17 ++--
 src/tensorwaves/interface.py |  30 +++++--
 tests/optimizer/__init__.py  |  24 ++++--
 tests/test_estimator.py      |  10 +--
 uv.lock                      | 146 ++++++++++++++++++-----------------
 7 files changed, 137 insertions(+), 98 deletions(-)

diff --git a/docs/conf.py b/docs/conf.py
index 6f870356..7a3f7fa7 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -55,10 +55,13 @@ def get_tensorflow_url() -> str:
 api_target_substitutions: dict[str, str | tuple[str, str]] = {
     "Array": "tensorwaves.interface.Array",
     "DataSample": "tensorwaves.interface.DataSample",
+    "FloatArray": "tensorwaves.interface.FloatArray",
+    "np.floating": "numpy.floating",
     "np.ndarray": "numpy.ndarray",
     "ParameterValue": "tensorwaves.interface.ParameterValue",
     "Path": "pathlib.Path",
     "ProgressColumn": "rich.progress.ProgressColumn",
+    "ScalarT": "tensorwaves.interface.ScalarT",
     "sp.Basic": "sympy.core.basic.Basic",
     "sp.Expr": "sympy.core.expr.Expr",
     "sp.Symbol": "sympy.core.symbol.Symbol",
@@ -67,9 +70,11 @@ def get_tensorflow_url() -> str:
 api_target_types: dict[str, str | tuple[str, str]] = {
     "tensorwaves.interface.Array": "obj",
     "tensorwaves.interface.DataSample": "obj",
+    "tensorwaves.interface.FloatArray": "obj",
     "tensorwaves.interface.InputType": "obj",
     "tensorwaves.interface.OutputType": "obj",
     "tensorwaves.interface.ParameterValue": "obj",
+    "tensorwaves.interface.ScalarT": "obj",
 }
 author = ""
 autodoc_default_options = {
@@ -81,9 +86,11 @@ def get_tensorflow_url() -> str:
 autodoc_type_aliases = {
     "Array": "tensorwaves.interface.Array",
     "DataSample": "tensorwaves.interface.DataSample",
+    "FloatArray": "tensorwaves.interface.FloatArray",
     "InputType": "tensorwaves.interface.InputType",
     "OutputType": "tensorwaves.interface.OutputType",
     "ParameterValue": "tensorwaves.interface.ParameterValue",
+    "ScalarT": "tensorwaves.interface.ScalarT",
 }
 autodoc_typehints_format = "short"
 autosectionlabel_prefix_document = True
diff --git a/pyproject.toml b/pyproject.toml
index aecde89f..a74e4e44 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -39,6 +39,7 @@ dependencies = [
     "rich",
     "sympy >=1.9",  # lambdify cse
     "tqdm >=4.24.0",  # autonotebook
+    "typing-extensions >=4.4.0; python_version <'3.13.0'",  # TypeVar defaults
 ]
 dynamic = ["version"]
 
diff --git a/src/tensorwaves/estimator.py b/src/tensorwaves/estimator.py
index 2df5df0f..b127d3c8 100644
--- a/src/tensorwaves/estimator.py
+++ b/src/tensorwaves/estimator.py
@@ -16,6 +16,7 @@
     DataSample,
     DataTransformer,
     Estimator,
+    FloatArray,
     ParameterType,
     ParameterValue,
     ParametrizedFunction,
@@ -247,10 +248,12 @@ def estimator(
     @overload
     def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
     @overload
-    def __call__(self, parameters: Mapping[str, Array]) -> Array: ...
+    def __call__(self, parameters: Mapping[str, Array]) -> FloatArray: ...
     @overload
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array: ...
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array:
+    def __call__(
+        self, parameters: Mapping[str, ParameterType]
+    ) -> float | FloatArray: ...
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | FloatArray:
         return self.__estimator(*self.__estimator_args(parameters))
 
     def gradient(
@@ -349,10 +352,12 @@ def estimator(
     @overload
     def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
     @overload
-    def __call__(self, parameters: Mapping[str, Array]) -> Array: ...
+    def __call__(self, parameters: Mapping[str, Array]) -> FloatArray: ...
     @overload
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array: ...
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array:
+    def __call__(
+        self, parameters: Mapping[str, ParameterType]
+    ) -> float | FloatArray: ...
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | FloatArray:
         return self.__estimator(*self.__estimator_args(parameters))
 
     def gradient(
diff --git a/src/tensorwaves/interface.py b/src/tensorwaves/interface.py
index 584c23a3..69733b5c 100644
--- a/src/tensorwaves/interface.py
+++ b/src/tensorwaves/interface.py
@@ -2,15 +2,21 @@
 
 from __future__ import annotations
 
+import sys
 from abc import ABC, abstractmethod
 from collections.abc import Mapping
-from typing import TYPE_CHECKING, Any, Generic, TypeAlias, TypeVar, overload
+from typing import TYPE_CHECKING, Any, Generic, TypeAlias, overload
 
 import attrs
 import numpy as np
 from attrs import field, frozen
 from attrs.validators import instance_of, optional
 
+if sys.version_info >= (3, 13):
+    from typing import TypeVar
+else:
+    from typing_extensions import TypeVar  # https://peps.python.org/pep-0696
+
 if TYPE_CHECKING:  # pragma: no cover
     from IPython.lib.pretty import PrettyPrinter
 
@@ -36,8 +42,16 @@ class Function(ABC, Generic[InputType, OutputType]):
     def __call__(self, data: InputType) -> OutputType: ...
 
 
-Array: TypeAlias = np.ndarray[Any, np.dtype[Any]]
-"""Type representing numerical arrays."""
+ScalarT = TypeVar("ScalarT", bound=np.generic, default=Any)
+"""The scalar type (dtype) of an `Array`."""
+Array: TypeAlias = np.ndarray[Any, np.dtype[ScalarT]]
+"""Type representing numerical arrays.
+
+The alias is generic in its scalar type, so `Array` is dtype-agnostic, while
+`FloatArray` narrows to an array of floats.
+"""
+FloatArray: TypeAlias = Array[np.floating]
+"""An `Array` of real-valued numbers."""
 DataSample = dict[str, Array]
 """Mapping of variable names to a sequence of data points, used by `Function`."""
 ParameterValue = complex | float
@@ -102,7 +116,7 @@ class DataTransformer(Function[DataSample, DataSample]):
     """
 
 
-class Estimator(Function[Mapping[str, ParameterType], float | Array]):
+class Estimator(Function[Mapping[str, ParameterType], float | FloatArray]):
     """Estimator for discrepancy model and data.
 
     See the :mod:`.estimator` module for different implementations of this interface.
@@ -113,11 +127,13 @@ class Estimator(Function[Mapping[str, ParameterType], float | Array]):
     @overload
     def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
     @overload
-    def __call__(self, parameters: Mapping[str, Array]) -> Array: ...
+    def __call__(self, parameters: Mapping[str, Array]) -> FloatArray: ...
     @overload
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array: ...
+    def __call__(
+        self, parameters: Mapping[str, ParameterType]
+    ) -> float | FloatArray: ...
     @abstractmethod
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array:  # ty:ignore[invalid-method-override]
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | FloatArray:  # ty:ignore[invalid-method-override]
         """Compute estimator value for this combination of parameter values.
 
         Parameter values may be one-dimensional arrays of shape :code:`(p,)`, in which
diff --git a/tests/optimizer/__init__.py b/tests/optimizer/__init__.py
index 1e228bd9..e32b034c 100644
--- a/tests/optimizer/__init__.py
+++ b/tests/optimizer/__init__.py
@@ -3,7 +3,13 @@
 from enum import Enum
 from typing import TYPE_CHECKING, Any, overload
 
-from tensorwaves.interface import Array, Estimator, ParameterType, ParameterValue
+from tensorwaves.interface import (
+    Array,
+    Estimator,
+    FloatArray,
+    ParameterType,
+    ParameterValue,
+)
 from tensorwaves.optimizer.callbacks import Callback
 
 if TYPE_CHECKING:
@@ -63,10 +69,12 @@ def __init__(self, polynomial: Callable) -> None:
     @overload
     def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
     @overload
-    def __call__(self, parameters: Mapping[str, Array]) -> Array: ...
+    def __call__(self, parameters: Mapping[str, Array]) -> FloatArray: ...
     @overload
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array: ...
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array:
+    def __call__(
+        self, parameters: Mapping[str, ParameterType]
+    ) -> float | FloatArray: ...
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | FloatArray:
         x = parameters["x"]
         return self.__polynomial(x)
 
@@ -83,10 +91,12 @@ def __init__(self, polynomial: Callable) -> None:
     @overload
     def __call__(self, parameters: Mapping[str, ParameterValue]) -> float: ...
     @overload
-    def __call__(self, parameters: Mapping[str, Array]) -> Array: ...
+    def __call__(self, parameters: Mapping[str, Array]) -> FloatArray: ...
     @overload
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array: ...
-    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | Array:
+    def __call__(
+        self, parameters: Mapping[str, ParameterType]
+    ) -> float | FloatArray: ...
+    def __call__(self, parameters: Mapping[str, ParameterType]) -> float | FloatArray:
         x = parameters["x"]
         y = parameters["y"]
         return self.__polynomial(x, y)
diff --git a/tests/test_estimator.py b/tests/test_estimator.py
index aa78bf8a..9c0d713a 100644
--- a/tests/test_estimator.py
+++ b/tests/test_estimator.py
@@ -334,8 +334,8 @@ def it_broadcasts_array_valued_parameters(backend: str):
         phsp = {"x": rng.uniform(-2.0, 5.0, size=5_000)}
         estimator = UnbinnedNLL(function, data, phsp, phsp_volume=7.0)
         mu_values = np.array([0.4, 0.5, 0.6])
-        batched_output = np.asarray(estimator({"mu": mu_values}))
-        scalar_outputs = [float(estimator({"mu": value})) for value in mu_values]
+        batched_output = estimator({"mu": mu_values})
+        scalar_outputs = [estimator({"mu": value}) for value in mu_values]
         assert batched_output.shape == mu_values.shape
         np.testing.assert_allclose(batched_output, scalar_outputs, rtol=1e-8)
 
@@ -352,8 +352,6 @@ def it_matches_jax_vmap_for_batched_evaluation():
         phsp = {"x": rng.uniform(-2.0, 5.0, size=5_000)}
         estimator = UnbinnedNLL(function, data, phsp, phsp_volume=7.0)
         mu_values = np.array([0.4, 0.5, 0.6])
-        batched_output = np.asarray(estimator({"mu": mu_values}))
+        batched_output = estimator({"mu": mu_values})
         vmapped_output = jax.vmap(lambda value: estimator({"mu": value}))(mu_values)
-        np.testing.assert_allclose(
-            batched_output, np.asarray(vmapped_output), rtol=1e-8
-        )
+        np.testing.assert_allclose(batched_output, vmapped_output, rtol=1e-8)
diff --git a/uv.lock b/uv.lock
index 31a03f07..1165430a 100644
--- a/uv.lock
+++ b/uv.lock
@@ -3,16 +3,16 @@ revision = 3
 requires-python = ">=3.10"
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -703,16 +703,16 @@ version = "1.3.3"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -1059,16 +1059,16 @@ version = "0.22.4"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -1683,16 +1683,16 @@ version = "9.17.1"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -1803,16 +1803,16 @@ version = "0.11.1"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
 ]
 dependencies = [
@@ -1905,16 +1905,16 @@ version = "0.11.1"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
 ]
 dependencies = [
@@ -2339,16 +2339,16 @@ version = "3.15.1"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -2620,16 +2620,16 @@ version = "4.2.0"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -2810,16 +2810,16 @@ version = "3.11.1"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -3053,16 +3053,16 @@ version = "5.1.0"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -3380,16 +3380,16 @@ version = "2.5.3"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
 ]
 sdist = { url = "https://files.pythonhosted.org/packages/13/01/11703282db468b85f6f7b8c7f22d058de5970d5c7e60a3a8aaa313c3de36/numpy-2.5.3.tar.gz", hash = "sha256:df2d5874ff183595a4ba404edd04f6bd9b5505c1d7708573f6a6c17489a67563", size = 20791231, upload-time = "2026-09-06T16:27:47.073Z" }
@@ -3681,16 +3681,16 @@ version = "3.0.5"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -4108,16 +4108,16 @@ version = "0.20.0"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -4843,16 +4843,16 @@ version = "2026.6.3"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -5143,16 +5143,16 @@ version = "1.18.1"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
 ]
 dependencies = [
@@ -5346,16 +5346,16 @@ version = "9.1.0"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
 ]
 dependencies = [
@@ -5421,16 +5421,16 @@ version = "1.4.0"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -5516,16 +5516,16 @@ version = "0.7.0"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version == '3.14.*' and sys_platform == 'win32'",
     "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.12.*' and sys_platform == 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -5852,6 +5852,7 @@ dependencies = [
     { name = "rich" },
     { name = "sympy" },
     { name = "tqdm" },
+    { name = "typing-extensions", marker = "python_full_version < '3.13'" },
 ]
 
 [package.optional-dependencies]
@@ -6074,6 +6075,7 @@ requires-dist = [
     { name = "tensorwaves", extras = ["phsp"], marker = "extra == 'pwa'" },
     { name = "tensorwaves", extras = ["tf"], marker = "extra == 'phsp'" },
     { name = "tqdm", specifier = ">=4.24.0" },
+    { name = "typing-extensions", marker = "python_full_version < '3.13'", specifier = ">=4.4.0" },
 ]
 provides-extras = ["jax", "numba", "phsp", "pwa", "scipy", "tf"]
 

From 3e62f806257017775a64a1d8ab19f72c221e6939 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Tue, 1 Sep 2026 14:54:39 +0200
Subject: [PATCH 6/8] MAINT: upgrade lock files

---
 uv.lock | 144 ++++++++++++++++++++++++++++----------------------------
 1 file changed, 72 insertions(+), 72 deletions(-)

diff --git a/uv.lock b/uv.lock
index 1165430a..5a23886c 100644
--- a/uv.lock
+++ b/uv.lock
@@ -3,16 +3,16 @@ revision = 3
 requires-python = ">=3.10"
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -703,16 +703,16 @@ version = "1.3.3"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -1059,16 +1059,16 @@ version = "0.22.4"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -1683,16 +1683,16 @@ version = "9.17.1"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -1803,16 +1803,16 @@ version = "0.11.1"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
 ]
 dependencies = [
@@ -1905,16 +1905,16 @@ version = "0.11.1"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
 ]
 dependencies = [
@@ -2339,16 +2339,16 @@ version = "3.15.1"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -2620,16 +2620,16 @@ version = "4.2.0"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -2810,16 +2810,16 @@ version = "3.11.1"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -3053,16 +3053,16 @@ version = "5.1.0"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -3380,16 +3380,16 @@ version = "2.5.3"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
 ]
 sdist = { url = "https://files.pythonhosted.org/packages/13/01/11703282db468b85f6f7b8c7f22d058de5970d5c7e60a3a8aaa313c3de36/numpy-2.5.3.tar.gz", hash = "sha256:df2d5874ff183595a4ba404edd04f6bd9b5505c1d7708573f6a6c17489a67563", size = 20791231, upload-time = "2026-09-06T16:27:47.073Z" }
@@ -3681,16 +3681,16 @@ version = "3.0.5"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -4108,16 +4108,16 @@ version = "0.20.0"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -4843,16 +4843,16 @@ version = "2026.6.3"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -5143,16 +5143,16 @@ version = "1.18.1"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
 ]
 dependencies = [
@@ -5346,16 +5346,16 @@ version = "9.1.0"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
 ]
 dependencies = [
@@ -5421,16 +5421,16 @@ version = "1.4.0"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",
@@ -5516,16 +5516,16 @@ version = "0.7.0"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.15' and sys_platform == 'win32'",
-    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
-    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform == 'win32'",
+    "python_full_version >= '3.15' and sys_platform == 'emscripten'",
     "python_full_version == '3.14.*' and sys_platform == 'emscripten'",
+    "python_full_version >= '3.15' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.14.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.13.*' and sys_platform == 'win32'",
-    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
-    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform == 'win32'",
+    "python_full_version == '3.13.*' and sys_platform == 'emscripten'",
     "python_full_version == '3.12.*' and sys_platform == 'emscripten'",
+    "python_full_version == '3.13.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.12.*' and sys_platform != 'emscripten' and sys_platform != 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'win32'",
     "python_full_version == '3.11.*' and sys_platform == 'emscripten'",

From db5d0666627a0fb1f4784cb0e0d6e174a9237022 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Tue, 1 Sep 2026 14:57:35 +0200
Subject: [PATCH 7/8] ENH: narrow intensity function types to `FloatArray`

---
 benchmarks/ampform.py            | 6 +++---
 src/tensorwaves/data/__init__.py | 6 +++---
 src/tensorwaves/estimator.py     | 4 ++--
 3 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/benchmarks/ampform.py b/benchmarks/ampform.py
index 91eb3c1b..5cf3f151 100644
--- a/benchmarks/ampform.py
+++ b/benchmarks/ampform.py
@@ -24,9 +24,9 @@
 
     from tensorwaves.function import ParametrizedBackendFunction
     from tensorwaves.interface import (
-        Array,
         DataSample,
         FitResult,
+        FloatArray,
         Function,
         ParameterValue,
         ParametrizedFunction,
@@ -73,7 +73,7 @@ def create_function(
 
 def generate_data(
     model: HelicityModel,
-    function: Function[DataSample, Array],
+    function: Function[DataSample, FloatArray],
     data_sample_size: int,
     phsp_sample_size: int,
     backend: str,
@@ -110,7 +110,7 @@ def generate_data(
 def fit(
     data: DataSample,
     phsp: DataSample,
-    function: ParametrizedFunction[DataSample, Array],
+    function: ParametrizedFunction[DataSample, FloatArray],
     initial_parameters: Mapping[str, ParameterValue],
     backend: str,
 ) -> FitResult:
diff --git a/src/tensorwaves/data/__init__.py b/src/tensorwaves/data/__init__.py
index 8983fc03..54ec2178 100644
--- a/src/tensorwaves/data/__init__.py
+++ b/src/tensorwaves/data/__init__.py
@@ -8,10 +8,10 @@
 from tqdm.auto import tqdm
 
 from tensorwaves.interface import (
-    Array,
     DataGenerator,
     DataSample,
     DataTransformer,
+    FloatArray,
     Function,
     RealNumberGenerator,
 )
@@ -70,7 +70,7 @@ class IntensityDistributionGenerator(DataGenerator):
     def __init__(
         self,
         domain_generator: DataGenerator,
-        function: Function[DataSample, Array],
+        function: Function[DataSample, FloatArray],
         domain_transformer: DataTransformer | None = None,
         bunch_size: int = 50_000,
     ) -> None:
@@ -118,7 +118,7 @@ def _generate_bunch(self, rng: RealNumberGenerator) -> tuple[DataSample, float]:
         )
         transformed_domain = self.__domain_transformer(domain)
         computed_intensities = self.__function(transformed_domain)
-        max_intensity: float = np.max(computed_intensities)
+        max_intensity = float(np.max(computed_intensities))
         random_intensities = rng(size=self.__bunch_size, max_value=max_intensity)
         weights = domain.get("weights", 1)
         hit_and_miss_sample = select_events(
diff --git a/src/tensorwaves/estimator.py b/src/tensorwaves/estimator.py
index b127d3c8..0a10ba9a 100644
--- a/src/tensorwaves/estimator.py
+++ b/src/tensorwaves/estimator.py
@@ -214,7 +214,7 @@ class ChiSquared(Estimator):
 
     def __init__(
         self,
-        function: ParametrizedFunction[DataSample, Array],
+        function: ParametrizedFunction[DataSample, FloatArray],
         domain: DataSample,
         observed_values: Array,
         weights: Array | None = None,
@@ -311,7 +311,7 @@ class UnbinnedNLL(Estimator):
 
     def __init__(
         self,
-        function: ParametrizedFunction[DataSample, Array],
+        function: ParametrizedFunction[DataSample, FloatArray],
         data: DataSample,
         phsp: DataSample,
         phsp_volume: float = 1.0,

From 0add2733f71611d4f01158044626e05977f23e3c Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Tue, 1 Sep 2026 15:07:03 +0200
Subject: [PATCH 8/8] MAINT: remove redundant estimator value casts

---
 src/tensorwaves/optimizer/minuit.py | 2 +-
 src/tensorwaves/optimizer/scipy.py  | 6 +++---
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/tensorwaves/optimizer/minuit.py b/src/tensorwaves/optimizer/minuit.py
index 41a27c33..9bb01cd8 100644
--- a/src/tensorwaves/optimizer/minuit.py
+++ b/src/tensorwaves/optimizer/minuit.py
@@ -70,7 +70,7 @@ def optimize(
                 logs=_create_log(
                     optimizer=type(self),
                     estimator_type=type(estimator),
-                    estimator_value=float(estimator(parameters)),
+                    estimator_value=estimator(parameters),
                     function_call=n_function_calls,
                     parameters=parameters,
                 )
diff --git a/src/tensorwaves/optimizer/scipy.py b/src/tensorwaves/optimizer/scipy.py
index a546f536..7e033dfd 100644
--- a/src/tensorwaves/optimizer/scipy.py
+++ b/src/tensorwaves/optimizer/scipy.py
@@ -62,7 +62,7 @@ def optimize(  # ruff:ignore[complex-structure]
                 logs=_create_log(
                     optimizer=type(self),
                     estimator_type=type(estimator),
-                    estimator_value=float(estimator(parameters)),
+                    estimator_value=estimator(parameters),
                     function_call=n_function_calls,
                     parameters=parameters,
                 )
@@ -91,7 +91,7 @@ def wrapped_function(pars: list) -> float:
                     logs=_create_log(
                         optimizer=type(self),
                         estimator_type=type(estimator),
-                        estimator_value=float(estimator(parameters)),
+                        estimator_value=estimator_value,
                         function_call=n_function_calls,
                         parameters=parameters,
                     ),
@@ -113,7 +113,7 @@ def wrapped_callback(pars: Iterable[float]) -> None:
                     logs=_create_log(
                         optimizer=type(self),
                         estimator_type=type(estimator),
-                        estimator_value=float(estimator_value),
+                        estimator_value=estimator_value,
                         function_call=n_function_calls,
                         parameters=create_parameter_dict(pars),
                     ),