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.

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

Parameters:

Parameters:	func : function A Python function or method to integrate. a : float Lower limit of integration. b : float Upper limit of integration. args : tuple, optional Extra arguments to pass to function. tol, rol : float, optional Iteration stops when error between last two iterates is less than tol OR the relative change is less than rtol. maxiter : int, optional Maximum order of Gaussian quadrature. vec_func : bool, optional True or False if func handles arrays as arguments (is a “vector” function). Default is True. miniter : int, optional Minimum order of Gaussian quadrature.
Returns:	val : float Gaussian quadrature approximation (within tolerance) to integral. err : float Difference between last two estimates of the integral.

func : function

A Python function or method to integrate.

a : float

Lower limit of integration.

b : float

Upper limit of integration.

args : tuple, optional

Extra arguments to pass to function.

tol, rol : float, optional

Iteration stops when error between last two iterates is less than tol OR the relative change is less than rtol.

maxiter : int, optional

Maximum order of Gaussian quadrature.

vec_func : bool, optional

True or False if func handles arrays as arguments (is a “vector” function). Default is True.

miniter : int, optional

Minimum order of Gaussian quadrature.

Returns:

val : float

Gaussian quadrature approximation (within tolerance) to integral.

err : float

Difference between last two estimates of the integral.