Python | Numpy np.leggauss() method

np.leggauss() Computes the sample points and weights for Gauss-legendre quadrature. These sample points and weights will correctly integrate polynomials of degree 2*deg - 1 or less over the interval [-1, 1] with the weight function f(x) = 1

Syntax : np.leggauss(deg)
Parameters:
deg :[int] Number of sample points and weights. It must be >= 1.

Return : 1.[ndarray] 1-D ndarray containing the sample points.
2.[ndarray] 1-D ndarray containing the weights.

Code #1 :

# Python program explaining
# numpy.leggauss() method

# importing numpy as np
# and numpy.polynomial.legendre module as geek
import numpy as np
import numpy.polynomial.legendre as geek

# Input degree = 2

degree = 2

# using np.leggauss() method
res = geek.leggauss(degree)

# Resulting array of sample point and weight
print (res)

Output:

(array([-0.57735027,  0.57735027]), array([ 1.,  1.]))

Code #2 :

# Python program explaining
# numpy.leggauss() method

# importing numpy as np
# and numpy.polynomial.legendre module as geek
import numpy as np
import numpy.polynomial.legendre as geek

# Input degree
degree = 3

# using np.leggauss() method
res = geek.leggauss(degree)

# Resulting array of sample point and weight
print (res)

Output:

(array([-0.77459667,  0.,  0.77459667]), array([ 0.55555556,  0.88888889,  0.55555556]))