def test_adfd():
# Test delay.adfd()
# Embed a straight line.
a, b = 1.0 + np.random.random(2)
t = np.arange(1000)
x = a + b * t
# Sum of squares of first n natural numbers.
sqsum = lambda n: n * (n + 1) * (2 * n + 1) / 6.0
dim, maxtau = 7, 25
desired = np.sqrt(sqsum(dim - 1)) * b * np.arange(maxtau)
assert_allclose(delay.adfd(x, dim=dim, maxtau=maxtau), desired)
from nolitsa import data, delay
sample = 0.25
x = data.mackey_glass(length=2500,
a=0.2,
b=0.1,
c=10.0,
tau=17.0,
discard=500,
sample=sample)
dim = 7
maxtau = 50
tau = np.arange(maxtau)
disp = delay.adfd(x, dim=dim, maxtau=maxtau)
ddisp = np.diff(disp)
forty = np.argmax(ddisp < 0.4 * ddisp[1])
print(r'Time delay %d' % forty)
fig, ax1 = plt.subplots()
ax1.set_xlabel(r'Time ($\tau\Delta t$)')
ax1.set_ylabel(r'$\mathrm{ADFD}$')
ax1.plot(tau[1:] * sample, disp[1:])
ax2 = ax1.twinx()
ax2.plot(tau[1:] * sample, ddisp, 'g--')
ax2.plot(tau[forty + 1] * sample, ddisp[forty], 'o')
ax2.set_ylabel(r'$\frac{d}{d\tau}(\mathrm{ADFD}$)')