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from __future__ import division, print_function, absolute_import
from math import sqrt, exp, sin, cos
from numpy.testing import (assert_warns, assert_,
assert_allclose,
assert_equal)
from numpy import finfo
from scipy.optimize import zeros as cc
from scipy.optimize import zeros
# Import testing parameters
from scipy.optimize._tstutils import functions, fstrings
class TestBasic(object):
def run_check(self, method, name):
a = .5
b = sqrt(3)
xtol = 4*finfo(float).eps
rtol = 4*finfo(float).eps
for function, fname in zip(functions, fstrings):
zero, r = method(function, a, b, xtol=xtol, rtol=rtol,
full_output=True)
assert_(r.converged)
assert_allclose(zero, 1.0, atol=xtol, rtol=rtol,
err_msg='method %s, function %s' % (name, fname))
def test_bisect(self):
self.run_check(cc.bisect, 'bisect')
def test_ridder(self):
self.run_check(cc.ridder, 'ridder')
def test_brentq(self):
self.run_check(cc.brentq, 'brentq')
def test_brenth(self):
self.run_check(cc.brenth, 'brenth')
def test_newton(self):
f1 = lambda x: x**2 - 2*x - 1
f1_1 = lambda x: 2*x - 2
f1_2 = lambda x: 2.0 + 0*x
f2 = lambda x: exp(x) - cos(x)
f2_1 = lambda x: exp(x) + sin(x)
f2_2 = lambda x: exp(x) + cos(x)
for f, f_1, f_2 in [(f1, f1_1, f1_2), (f2, f2_1, f2_2)]:
x = zeros.newton(f, 3, tol=1e-6)
assert_allclose(f(x), 0, atol=1e-6)
x = zeros.newton(f, 3, fprime=f_1, tol=1e-6)
assert_allclose(f(x), 0, atol=1e-6)
x = zeros.newton(f, 3, fprime=f_1, fprime2=f_2, tol=1e-6)
assert_allclose(f(x), 0, atol=1e-6)
def test_deriv_zero_warning(self):
func = lambda x: x**2
dfunc = lambda x: 2*x
assert_warns(RuntimeWarning, cc.newton, func, 0.0, dfunc)
def test_gh_5555():
root = 0.1
def f(x):
return x - root
methods = [cc.bisect, cc.ridder]
xtol = 4*finfo(float).eps
rtol = 4*finfo(float).eps
for method in methods:
res = method(f, -1e8, 1e7, xtol=xtol, rtol=rtol)
assert_allclose(root, res, atol=xtol, rtol=rtol,
err_msg='method %s' % method.__name__)
def test_gh_5557():
# Show that without the changes in 5557 brentq and brenth might
# only achieve a tolerance of 2*(xtol + rtol*|res|).
# f linearly interpolates (0, -0.1), (0.5, -0.1), and (1,
# 0.4). The important parts are that |f(0)| < |f(1)| (so that
# brent takes 0 as the initial guess), |f(0)| < atol (so that
# brent accepts 0 as the root), and that the exact root of f lies
# more than atol away from 0 (so that brent doesn't achieve the
# desired tolerance).
def f(x):
if x < 0.5:
return -0.1
else:
return x - 0.6
atol = 0.51
rtol = 4*finfo(float).eps
methods = [cc.brentq, cc.brenth]
for method in methods:
res = method(f, 0, 1, xtol=atol, rtol=rtol)
assert_allclose(0.6, res, atol=atol, rtol=rtol)
class TestRootResults:
def test_repr(self):
r = zeros.RootResults(root=1.0,
iterations=44,
function_calls=46,
flag=0)
expected_repr = (" converged: True\n flag: 'converged'"
"\n function_calls: 46\n iterations: 44\n"
" root: 1.0")
assert_equal(repr(r), expected_repr)
def test_complex_halley():
"""Test Halley's works with complex roots"""
def f(x, *a):
return a[0] * x**2 + a[1] * x + a[2]
def f_1(x, *a):
return 2 * a[0] * x + a[1]
def f_2(x, *a):
return 2 * a[0]
z = complex(1.0, 2.0)
coeffs = (2.0, 3.0, 4.0)
y = zeros.newton(f, z, args=coeffs, fprime=f_1, fprime2=f_2, tol=1e-6)
# (-0.75000000000000078+1.1989578808281789j)
assert_allclose(f(y, *coeffs), 0, atol=1e-6)
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