def test_simple_polynomial(self):
T = symengine.Symbol("T")
poly = 2 * T**3 - 3 * T**2 - 36 * T + 17
arg_extremes = [-2, 3]
arrify = lambda expr, t: np.atleast_1d(float(expr.subs({T: t})))
spline = CubicHermiteSpline(
1, [(t, arrify(poly, t), arrify(poly.diff(T), t))
for t in arg_extremes])
result = extrema_from_anchors(spline)
assert_allclose(result.minima, arrify(poly, arg_extremes[1]))
assert_allclose(result.maxima, arrify(poly, arg_extremes[0]))
assert_allclose(result.arg_min, arg_extremes[1])
assert_allclose(result.arg_max, arg_extremes[0])
def test_given_extrema(self):
n = 100
positions = sorted(np.random.random(2))
state = np.random.random(n)
spline = CubicHermiteSpline(n, [
(positions[0], state, np.zeros(n)),
(positions[1], state + np.random.uniform(0, 5), np.zeros(n)),
])
result = extrema_from_anchors(spline)
assert_allclose(result.arg_min, spline[0].time)
assert_allclose(result.arg_max, spline[1].time)
assert_allclose(result.minima, spline[0][1])
assert_allclose(result.maxima, spline[1][1])
def test_arbitrary_anchors(self):
n = 100
spline = CubicHermiteSpline(
n, [(time, np.random.normal(0, 1, n), np.random.normal(0, 0.1, n))
for time in sorted(np.random.uniform(-10, 10, 2))])
times = np.linspace(spline[0].time, spline[1].time, 10000)
values = np.vstack([spline.get_recent_state(time) for time in times])
result = extrema_from_anchors(spline[-2:])
assert_allclose(result.minima, np.min(values, axis=0), atol=1e-3)
assert_allclose(result.maxima, np.max(values, axis=0), atol=1e-3)
assert_allclose(result.arg_min,
times[np.argmin(values, axis=0)],
atol=1e-3)
assert_allclose(result.arg_max,
times[np.argmax(values, axis=0)],
atol=1e-3)
def extrema_in_last_step(self):
extrema = extrema_from_anchors(self[-2:])
return extrema.minima, extrema.maxima