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Newton’s method is an old numerical approximation technique that could be used to find the roots of complex polynomials and any differentiable function.
Newton's method
Author: Daniel Homola
Licence: BSD 3-clause
from scipy.optimize import newton
from sklearn.utils.testing import assert_almost_equal
def f(x):
return 6*x**5-5*x**4-4*x**3+3*x**2
def df(x):
return 30*x**4-20*x**3-12*x**2+6*x
def dx(f, x):
return abs(0-f(x))
def newtons_method(f, df, x0, e, print_res=False):
delta = dx(f, x0)
while delta > e:
x0 = x0 - f(x0)/df(x0)
delta = dx(f, x0)
if print_res:
print 'Root is at: ', x0
print 'f(x) at root is: ', f(x0)
return x0
def test_with_scipy(f, df, x0s, e):
for x0 in x0s:
my_newton = newtons_method(f, df, x0, e)
scipy_newton = newton(f, x0, df, tol=e)
assert_almost_equal(my_newton, scipy_newton, decimal=5)
print 'Tests passed.'
if __name__ == '__main__':
# run test
x0s= [0, .5, 1]
test_with_scipy(f, df, x0s, 1e-5)
for x0 in x0s:
newtons_method(f, df, x0, 1e-10, True)
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