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venv/lib/python3.12/site-packages/jax/_src/scipy/integrate.py

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+# Copyright 2023 The JAX Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from __future__ import annotations
+
+from jax._src.api import jit
+from jax._src.numpy import lax_numpy
+from jax._src.typing import Array, ArrayLike
+
+
+@jit(static_argnames=('axis',))
+def trapezoid(y: ArrayLike, x: ArrayLike | None = None, dx: ArrayLike = 1.0,
+              axis: int = -1) -> Array:
+  r"""
+  Integrate along the given axis using the composite trapezoidal rule.
+
+  JAX implementation of :func:`scipy.integrate.trapezoid`
+
+  The trapezoidal rule approximates the integral under a curve by summing the
+  areas of trapezoids formed between adjacent data points.
+
+  Args:
+    y: array of data to integrate.
+    x: optional array of sample points corresponding to the ``y`` values. If not
+       provided, ``x`` defaults to equally spaced with spacing given by ``dx``.
+    dx: The spacing between sample points when `x` is None (default: 1.0).
+    axis: The axis along which to integrate (default: -1)
+
+  Returns:
+    The definite integral approximated by the trapezoidal rule.
+
+  See also:
+    :func:`jax.numpy.trapezoid`: NumPy-style API for trapezoidal integration
+
+  Examples:
+    Integrate over a regular grid, with spacing 1.0:
+
+    >>> y = jnp.array([1, 2, 3, 2, 3, 2, 1])
+    >>> jax.scipy.integrate.trapezoid(y, dx=1.0)
+    Array(13., dtype=float32)
+
+    Integrate over an irregular grid:
+
+    >>> x = jnp.array([0, 2, 5, 7, 10, 15, 20])
+    >>> jax.scipy.integrate.trapezoid(y, x)
+    Array(43., dtype=float32)
+
+    Approximate :math:`\int_0^{2\pi} \sin^2(x)dx`, which equals :math:`\pi`:
+
+    >>> x = jnp.linspace(0, 2 * jnp.pi, 1000)
+    >>> y = jnp.sin(x) ** 2
+    >>> result = jax.scipy.integrate.trapezoid(y, x)
+    >>> jnp.allclose(result, jnp.pi)
+    Array(True, dtype=bool)
+  """
+  return lax_numpy.trapezoid(y, x, dx, axis)