def test_scalar_basic2(self):
# f(x) = x**0.5; x0=1.05; fixed point should be x=1
def func(x):
return x**0.5
x0 = 1.05
x = fixed_point(func, x0)
assert_almost_equal(x, 1.0)
def test_array_trivial(self):
def func(x):
return 2.0 * x
x0 = [0.3, 0.15]
with np.errstate(all='ignore'):
x = fixed_point(func, x0)
assert_almost_equal(x, [0.0, 0.0])
def test_scalar_trivial(self):
# f(x) = 2x; fixed point should be x=0
def func(x):
return 2.0 * x
x0 = 1.0
x = fixed_point(func, x0)
assert_almost_equal(x, 0.0)
def test_lambertw(self):
# python-list/2010-December/594592.html
xxroot = fixed_point(lambda xx: np.exp(-2.0 * xx) / 2.0,
1.0,
args=(),
xtol=1e-12,
maxiter=500)
assert_allclose(xxroot, np.exp(-2.0 * xxroot) / 2.0)
assert_allclose(xxroot, lambertw(1) / 2)
def test_array_basic2(self):
# f(x) = c * x**0.5; fixed point should be x=c**2
def func(x, c):
return c * x**0.5
c = array([0.75, 1.0, 1.25])
x0 = [0.8, 1.1, 1.1]
x = fixed_point(func, x0, args=(c, ))
assert_almost_equal(x, c**2)
def test_array_basic1(self):
# f(x) = c * x**2; fixed point should be x=1/c
def func(x, c):
return c * x**2
c = array([0.75, 1.0, 1.25])
x0 = [1.1, 1.15, 0.9]
with np.errstate(all='ignore'):
x = fixed_point(func, x0, args=(c, ))
assert_almost_equal(x, 1.0 / c)
def test_no_acceleration(self):
# github issue 5460
ks = 2
kl = 6
m = 1.3
n0 = 1.001
i0 = ((m - 1) / m) * (kl / ks / m)**(1 / (m - 1))
def func(n):
return np.log(kl / ks / n) / np.log((i0 * n / (n - 1))) + 1
n = fixed_point(func, n0, method='iteration')
assert_allclose(n, m)