`scipy.integrate._quadrature:simpson`

source: build-install/usr/lib/python3.14/site-packages/scipy/integrate/_quadrature.py:392

Signature

def simpson(y, x = None, *, dx = 1.0, axis = -1)

Summary

Integrate y(x) using samples along the given axis and the composite Simpson's rule. If x is None, spacing of dx is assumed.

Parameters

y : array_like: Array to be integrated.
x : array_like, optional: If given, the points at which y is sampled.
dx : float, optional: Spacing of integration points along axis of x. Only used when x is None. Default is 1.
axis : int, optional: Axis along which to integrate. Default is the last axis.

Returns

: float: The estimated integral computed with the composite Simpson's rule.

Notes

For an odd number of samples that are equally spaced the result is exact if the function is a polynomial of order 3 or less. If the samples are not equally spaced, then the result is exact only if the function is a polynomial of order 2 or less.

Examples

from scipy import integrate
import numpy as np
x = np.arange(0, 10)
y = np.arange(0, 10)

✓

integrate.simpson(y, x=x)

✗

np.float64(40.5)

y = np.power(x, 3)

✓

integrate.simpson(y, x=x)

✗

np.float64(1640.5)

integrate.quad(lambda x: x**3, 0, 9)[0]

✓

1640.25

Aliases

scipy.integrate.simpson