def test_eval_points_scaling(Simulator, sample, radius, seed, rng, scale):
eval_points = UniformHypersphere()
if sample:
eval_points = eval_points.sample(500, 3, rng=rng)
model = nengo.Network(seed=seed)
with model:
a = nengo.Ensemble(
1,
3,
encoders=np.ones((1, 3)),
intercepts=nengo.dists.Choice([-1]),
radius=radius,
)
b = nengo.Ensemble(1, 3)
con = nengo.Connection(a,
b,
eval_points=eval_points,
scale_eval_points=scale)
with Simulator(model) as sim:
dists = npext.norm(sim.data[con].eval_points, axis=1)
limit = radius if scale else 1.0
assert np.all(dists <= limit)
assert np.any(dists >= 0.9 * limit)
def test_hypersphere_surface(dimensions, rng):
n = 150 * dimensions
dist = UniformHypersphere(surface=True)
samples = dist.sample(n, dimensions, rng=rng)
assert samples.shape == (n, dimensions)
assert np.allclose(npext.norm(samples, axis=1), 1)
assert np.allclose(np.mean(samples, axis=0), 0, atol=0.25 / dimensions)
def test_hypersphere_volume(min_magnitude, d, rng):
n = 150 * d
dist = UniformHypersphere(min_magnitude=min_magnitude)
samples = dist.sample(n, d, rng=rng)
assert samples.shape == (n, d)
assert np.allclose(np.mean(samples, axis=0), 0, atol=0.1)
assert np.all(npext.norm(samples, axis=1) >= min_magnitude)
def sample(self):
unif_dist = UniformHypersphere()
pt = unif_dist.sample(1, self.nbasis) * (
self.bounds[:, 1] - self.bounds[:, 0]) + self.bounds[:, 0]
sample = spa.SemanticPointer(data=np.fft.ifft(
np.fft.fft(self.basis[0], axis=0)**pt[0, 0], axis=0).real)
for i in np.arange(1, self.nbasis):
nextS = spa.SemanticPointer(data=np.fft.ifft(
np.fft.fft(self.basis[i], axis=0)**pt[0, i], axis=0).real)
sample = sample * nextS
return sample.v
def test_eval_points_scaling(Simulator, sample, radius, seed, rng):
eval_points = UniformHypersphere()
if sample:
eval_points = eval_points.sample(500, 3, rng=rng)
model = nengo.Network(seed=seed)
with model:
a = nengo.Ensemble(1, 3, eval_points=eval_points, radius=radius)
sim = Simulator(model)
dists = np.linalg.norm(sim.data[a].eval_points, axis=1)
assert np.all(dists <= radius)
assert np.any(dists >= 0.9 * radius)
def test_eval_points_scaling(Simulator, sample, radius, seed, rng):
eval_points = UniformHypersphere()
if sample:
eval_points = eval_points.sample(500, 3, rng=rng)
model = nengo.Network(seed=seed)
with model:
a = nengo.Ensemble(1, 3, eval_points=eval_points, radius=radius)
with Simulator(model) as sim:
dists = npext.norm(sim.data[a].eval_points, axis=1)
assert np.all(dists <= radius)
assert np.any(dists >= 0.9 * radius)
def test_cosine_intercept(d, p, rng, allclose):
"""Tests CosineSimilarity inverse cdf for finding intercepts."""
pytest.importorskip("scipy") # betaincinv
num_samples = 500
exp_dist = UniformHypersphere(surface=True)
act_dist = CosineSimilarity(d)
dots = exp_dist.sample(num_samples, d, rng=rng)[:, 0]
# Find the desired intercept so that dots >= c with probability p
c = act_dist.ppf(1 - p)
assert allclose(np.sum(dots >= c) / float(num_samples), p, atol=0.05)
def samples(self, n):
unif_dist = UniformHypersphere()
pt = unif_dist.sample(n, self.nbasis) * (
self.bounds[:, 1] - self.bounds[:, 0]) + self.bounds[:, 0]
samples = np.zeros((n, self.dim))
for j in np.arange(n):
sample = spa.SemanticPointer(data=np.fft.ifft(
np.fft.fft(self.basis[0], axis=0)**pt[j, 0], axis=0).real)
for i in np.arange(1, self.nbasis):
nextS = spa.SemanticPointer(data=np.fft.ifft(
np.fft.fft(self.basis[i], axis=0)**pt[j, i], axis=0).real)
sample = sample * nextS
samples[j, :] = sample.v
return samples
def sample(self, n, d=None, rng=np.random):
unif_dist = UniformHypersphere()
xy = unif_dist.sample(n, 2)
samples = np.zeros((n, d))
for i in np.arange(n):
samples[i, :] = ssp(self.X,
self.Y,
xy[i, 0],
xy[i, 1],
alg=self.alg).v.real
return samples.real * self.radius
def test_cosine_similarity(d, rng):
"""Tests CosineSimilarity sampling."""
num_samples = 2500
num_bins = 8
# Check that it gives a single dimension from UniformHypersphere
exp_dist = UniformHypersphere(surface=True)
act_dist = CosineSimilarity(d)
exp = exp_dist.sample(num_samples, d, rng=rng)[:, 0]
act = act_dist.sample(num_samples, rng=rng)
exp_hist, _ = np.histogram(exp, bins=num_bins)
act_hist, _ = np.histogram(act, bins=num_bins)
assert np.all(np.abs(np.asfarray(exp_hist - act_hist) / num_samples) < 0.15)
def test_eval_points_scaling(Simulator, sample, radius, seed, rng, scale):
eval_points = UniformHypersphere()
if sample:
eval_points = eval_points.sample(500, 3, rng=rng)
model = nengo.Network(seed=seed)
with model:
a = nengo.Ensemble(1, 3, radius=radius)
b = nengo.Ensemble(1, 3)
con = nengo.Connection(a, b, eval_points=eval_points,
scale_eval_points=scale)
sim = Simulator(model)
dists = npext.norm(sim.data[con].eval_points, axis=1)
limit = radius if scale else 1.0
assert np.all(dists <= limit)
assert np.any(dists >= 0.9 * limit)
def test_eval_points_scaling(Simulator, sample, radius, seed, rng, scale):
eval_points = UniformHypersphere()
if sample:
eval_points = eval_points.sample(500, 3, rng=rng)
model = nengo.Network(seed=seed)
with model:
a = nengo.Ensemble(1, 3, radius=radius)
b = nengo.Ensemble(1, 3)
con = nengo.Connection(a,
b,
eval_points=eval_points,
scale_eval_points=scale)
sim = Simulator(model)
dists = np.linalg.norm(sim.data[con].eval_points, axis=1)
limit = radius if scale else 1.0
assert np.all(dists <= limit)
assert np.any(dists >= 0.9 * limit)
