scipy.integrate.

fixed_quad#

scipy.integrate.fixed_quad(func, a, b, args=(), n=5)[source]#

Compute a definite integral using fixed-order Gaussian quadrature.

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

Parameters:

funccallable: 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)).
afloat: Lower limit of integration.
bfloat: Upper limit of integration.
argstuple, optional: Extra arguments to pass to function, if any.
nint, optional: Order of quadrature integration. Default is 5.

Returns:

valfloat: Gaussian quadrature approximation to the integral
noneNone: Statically returned value of None

See also

quad: adaptive quadrature using QUADPACK
dblquad: double integrals
tplquad: triple integrals
romb: integrators for sampled data
simpson: integrators for sampled data
cumulative_trapezoid: cumulative integration for sampled data

Notes

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 Support for the array API standard 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)
(0.1110884353741496, None)
>>> integrate.fixed_quad(f, 0.0, 1.0, n=5)
(0.11111111111111102, None)
>>> print(1/9.0)  # analytical result
0.1111111111111111

>>> integrate.fixed_quad(np.cos, 0.0, np.pi/2, n=4)
(0.9999999771971152, None)
>>> integrate.fixed_quad(np.cos, 0.0, np.pi/2, n=5)
(1.000000000039565, None)
>>> np.sin(np.pi/2)-np.sin(0)  # analytical result
1.0