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bundles / scipy latest / scipy / integrate / _quadrature / simpson

function

scipy.integrate._quadrature:simpson

source: /scipy/integrate/_quadrature.py :389

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.

Array API Standard Support

simpson has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ⛔                     ⛔                   
JAX                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

from scipy import integrate
import numpy as np
x = np.arange(0, 10)
y = np.arange(0, 10)
✓
integrate.simpson(y, x=x)
✗
y = np.power(x, 3)
✓
integrate.simpson(y, x=x)
✗
integrate.quad(lambda x: x**3, 0, 9)[0]
✓

See also

cumulative_simpson

cumulative integration using Simpson's 1/3 rule

cumulative_trapezoid

cumulative integration for sampled data

dblquad

double integrals

fixed_quad

fixed-order Gaussian quadrature

quad

adaptive quadrature using QUADPACK

romb

integrators for sampled data

tplquad

triple integrals

Aliases

  • scipy.integrate.simpson

Referenced by

This package