2025-08-11 12:24:21 +08:00

70 lines
2.3 KiB
Python

# 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 functools import partial
from jax import jit
from jax._src.typing import Array, ArrayLike
import jax.numpy as jnp
@partial(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 jnp.trapezoid(y, x, dx, axis)