scipy.integrate.quadrature#

scipy.integrate.quadrature(func, a, b, args=(), tol=1.49e-08, rtol=1.49e-08, maxiter=50, vec_func=True, miniter=1)[source]#

Compute a definite integral using fixed-tolerance Gaussian quadrature.

Deprecated since version 1.12.0: This function is deprecated as of SciPy 1.12.0 and will be removed in SciPy 1.15.0. Please use scipy.integrate.quad instead.

Integrate func from a to b using Gaussian quadrature with absolute tolerance tol.

Parameters:

funcfunction: A Python function or method to integrate.
afloat: Lower limit of integration.
bfloat: Upper limit of integration.
argstuple, optional: Extra arguments to pass to function.
tol, rtolfloat, optional: Iteration stops when error between last two iterates is less than tol OR the relative change is less than rtol.
maxiterint, optional: Maximum order of Gaussian quadrature.
vec_funcbool, optional: True or False if func handles arrays as arguments (is a “vector” function). Default is True.
miniterint, optional: Minimum order of Gaussian quadrature.

Returns:

valfloat: Gaussian quadrature approximation (within tolerance) to integral.
errfloat: Difference between last two estimates of the integral.

See also

romberg: adaptive Romberg quadrature
fixed_quad: fixed-order Gaussian quadrature
quad: adaptive quadrature using QUADPACK
dblquad: double integrals
tplquad: triple integrals
romb: integrator for sampled data
simpson: integrator for sampled data
cumulative_trapezoid: cumulative integration for sampled data
ode: ODE integrator
odeint: ODE integrator

Examples

>>> from scipy import integrate
>>> import numpy as np
>>> f = lambda x: x**8
>>> integrate.quadrature(f, 0.0, 1.0)
(0.11111111111111106, 4.163336342344337e-17)
>>> print(1/9.0)  # analytical result
0.1111111111111111

>>> integrate.quadrature(np.cos, 0.0, np.pi/2)
(0.9999999999999536, 3.9611425250996035e-11)
>>> np.sin(np.pi/2)-np.sin(0)  # analytical result
1.0