uki dddlmZddlmZddlmZddlmZmZed d d dZ y) ) annotations)jit) lax_numpy)Array ArrayLike)axis)static_argnamesNc2tj||||S)aw 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) )r trapezoid)yxdxrs S/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/jax/_src/scipy/integrate.pyr r sZ   Q2t ,,)Ng?) r rr zArrayLike | Nonerrrintreturnr) __future__r jax._src.apirjax._src.numpyrjax._src.typingrrr rrrsB#$,YHK,-,-!&,- ,-r