def optimal_test():
def fx(x):
return .1 * x**2 + 3 * x - 4
g, h, k = optimal_noise_smoothing(.2)
f = GHKFilter(-4, 0, 0, 1, g, h, k)
ys = []
zs = []
for i in range(100):
z = fx(i) + randn() * 10
f.update(z)
ys.append(f.x)
zs.append(z)
plt.plot(ys)
plt.plot(zs)
def test_ghk_formulation():
beta = .6
g = 1 - beta**3
h = 1.5 * (1 + beta) * (1 - beta)**2
k = 0.5 * (1 - beta)**3
f1 = GHKFilter(0, 0, 0, 1, g, h, k)
f2 = FadingMemoryFilter(x0=0, dt=1, order=2, beta=beta)
def fx(x):
return .02 * x**2 + 2 * x - 3
for i in range(1, 100):
z = fx(i)
f1.update(z)
f2.update(z)
assert abs(f1.x - f2.x[0]) < 1.e-80