`scipy.integrate._quadrature:fixed_quad`

source: /scipy/integrate/_quadrature.py:183

Signature

def fixed_quad(func, a, b, args = (), n = 5)

Summary

Compute a definite integral using fixed-order Gaussian quadrature.

Extended Summary

Integrate func from a to b using Gaussian quadrature of order n.

Parameters

func : callable: A Python function or method to integrate (must accept vector inputs). If integrating a vector-valued function, the returned array must have shape (..., len(x)).
a : float: Lower limit of integration.
b : float: Upper limit of integration.
args : tuple, optional: Extra arguments to pass to function, if any.
n : int, optional: Order of quadrature integration. Default is 5.

Returns

val : float: Gaussian quadrature approximation to the integral
none : None: Statically returned value of None

Notes

Array API Standard Support

fixed_quad 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
f = lambda x: x**8

✓

integrate.fixed_quad(f, 0.0, 1.0, n=4)
integrate.fixed_quad(f, 0.0, 1.0, n=5)

✗

(np.float64(0.11111111111111102), None)

print(1/9.0)  # analytical result

✓

0.1111111111111111

integrate.fixed_quad(np.cos, 0.0, np.pi/2, n=4)
integrate.fixed_quad(np.cos, 0.0, np.pi/2, n=5)
np.sin(np.pi/2)-np.sin(0)  # analytical result

✗

np.float64(1.0)

Aliases

scipy.integrate.fixed_quad