def test_newton():
f = poly1d([1,0,0,-1])
df = [f.deriv(k) for k in range(1,f.order+1)]
r = f.r
eps = 1e-6j
xi = r[0]
x = smale_newton(f, xi, df=df)
assert abs(xi - x) < 1e-8
xi = r[1]
x = smale_newton(f, xi+eps, df=df)
assert abs(xi - x) < 1e-8
xi = r[2]
x = smale_newton(f, xi+eps, df=df)
assert abs(xi - x) < 1e-8
def test_warning_alpha_condition():
# test warning due to poor newton guess
f = poly1d([1,0,0,-1])
df = [f.deriv(k) for k in range(1,f.order+1)]
with warnings.catch_warnings(True) as w:
_ = smale_newton(f, 10.0, df=df)
print 'w =', w
assert len(w) > 0
def test_function_arguments():
# test warning due to poor newton guess
f = lambda x,a: x**3 - a
df = [
lambda x,a: 3*x**2,
lambda x,a: 6*x,
lambda x,a: 6
]
x = smale_newton(f, 1.1, df=df, args=(1,))
xi = 1.
assert abs(xi - x) < 1e-8
def test_warning_not_enough_derivatives():
# test warning when not enough derivatives are provided
f = poly1d([1,0,0,-1])
with warnings.catch_warnings(True) as w:
_ = smale_newton(f, 10.0)
assert len(w) > 0