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The scipy.integrate.quadrature()
method in Python computes a definite integral using the numerical integration method of the fixed-tolerance Gaussian quadrature. The method takes a Python function, limits of integration, and absolute tolerance value as arguments and calculates the definite integral using the Gaussian quadrature.
The function prototype is as follows:
scipy.integrate.quadrature(func, a, b, args = (),tol = 1.49e-08,rtol = 1.49e-08,maxiter = 50,vec_func = True,miniter = 1)
func
: This is the Python function or the method that is being integrated.
a
: This is a float value that specifies the lower limit of integration.
args
: This is an optional tuple
parameter. It specifies the extra arguments to be passed to the func
function.
tol, rtol
: This is an optional float value that defines the absolute tolerance.
Note: Iteration stops when the error between the last two iterates is less than
tol
or the relative change is less thanrtol
. Its default value is1.49e-08
.
maxiter
: This is an optional int value that specifies the maximum order of the Gaussian quadrature.
miniter
: This is an optional int value that specifies the minimum order of the Gaussian quadrature.
vec_func
: This is an optional bool value that specifies True
or False
, if func
handles arrays as arguments. The default value is True
.
val
: This float value computes the Gaussian quadrature approximation to the integral within the absolute tolerance.
err
: This float value tells the difference between the last two estimates of the integral.
from scipy import integrateimport numpy as npprint(integrate.quadrature(np.sin, 0.0, np.pi/4))
Line 1–2: We import the required libraries.
Line 4: We use the sine function, np.sin
, from the NumPy library and pass it to the integrate.quadrature
method. The method integrates it using the Gaussian quadrature method with integration limits from $0$ to $\pi/4$.
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Grokking Modern System Design Interview for Engineers & Managers
Ace your System Design Interview and take your career to the next level. Learn to handle the design of applications like Netflix, Quora, Facebook, Uber, and many more in a 45-min interview. Learn the RESHADED framework for architecting web-scale applications by determining requirements, constraints, and assumptions before diving into a step-by-step design process.