def test_sampling():
for radius in [2.3, 42, 0.001, 10]:
for centroid in [
np.array([-5, 2]),
np.array([600, -3]),
np.array([0.1, 80])
]:
hs = HyperSphere(centroid, radius)
samples = hs.sample(100)
assert (np.all(
np.abs(np.linalg.norm(samples - centroid, axis=1) -
radius) < eps))
def hypersphere(self):
"""Handles details of parameterization of the correlation matrix.
DO NOT cache this object, clone_with_theta() will not
update it properly with new zeta values."""
return HyperSphere(self.dim, self.zeta)
def unrestrictive_correlation(self):
"""Calculate parameters to initialize UnrestrictiveCorrelation kernel.
Assume all zeta values are positive, which will be true if produced by
MultiplicativeCorrelation model."""
t = np.array(self.zeta, dtype=np.float64)
t = np.exp(-t)
t = np.atleast_2d(t)
T = t.T.dot(t)
return HyperSphere.zeta(T)
def hypersphere(self):
return HyperSphere(self.dim, self.zeta)
def is_stationary(self):
"""Returns whether the kernel is stationary. """
return self.kernel.is_stationary()
if __name__ == "__main__":
X = np.array([[1,2,3,0],[2,1,3,0],[2,2,3,1],[1,4,3,2]])
# note only two dimensions are being retained by the projection
rbf = RBF(length_scale=np.ones(2))
fubar = Projection(rbf, [2,3], "proj")
K = fubar(X)
print("Projection Kernel:\n", K)
print("Diagonal:\n", fubar.diag(X))
lt = HyperSphere(2)
print("2-parameter, lower triangular\n", lt._lower_triangular())
lt1 = HyperSphere(3, [pi, pi/3, pi/6])
print("3-parameter, lower triangular\n", lt1._lower_triangular())
ltz = HyperSphere(5) #, [0.0]*10)
print("5-parameter, lower triangular\n", ltz._lower_triangular())
ltk = UnrestrictiveCorrelation(3, [0.5,0.5,0.5])
print("Factor Kernel\n", ltk)
print("Factor Kernel\n", ltk(X[:,[0,1,2]]))
#C5 = np.array([0,0,1,1,1,2,2,2,3,3]).reshape((-1,1))
C = [0,0,1,1,1,2,2,2,3,3]
e = [[1,0,0,0], [0,1,0,0], [0,0,1,0], [0,0,0,1]]
def sampling_density_experiments():
from scipy.spatial.distance import pdist
import matplotlib.pyplot as plt
max_iters = 1000
n_tries = 15
n_dimss = np.arange(2, 61)
samples_needed = np.zeros_like(n_dimss)
for i, n_dims in enumerate(n_dimss):
# Unit hypersphere around origin
hs = HyperSphere(np.zeros(n_dims), 1)
n_samples = 2
iters = 0
dense_enough = False
while iters < max_iters:
iters += 1
dense_enough = True
for _ in range(n_tries):
samples = hs.sample(n_samples)
pdists = pdist(samples)
if pdists.min() > 1:
dense_enough = False
break
if dense_enough:
break
n_samples += 2
if dense_enough:
print('{}d hypersphere dense enough with {} samples.'.format(
n_dims, n_samples))
samples_needed[i] = n_samples
plt.figure(1)
plt.semilogy(n_dimss, samples_needed)
plt.xlabel('Dimensionality of unit hypersphere')
plt.ylabel('Samples needed')
plt.grid(True)
n_dims = 6
radii = np.linspace(1, 10, num=30)
samples_needed = np.zeros_like(radii)
for i, radius in enumerate(radii):
hs = HyperSphere(np.zeros(n_dims), radius)
n_samples = 2
iters = 0
dense_enough = False
while iters < max_iters:
iters += 1
dense_enough = True
for _ in range(n_tries):
samples = hs.sample(n_samples)
pdists = pdist(samples)
if pdists.min() > 1:
dense_enough = False
break
if dense_enough:
break
n_samples += 1
if dense_enough:
print(
'{}d hypersphere with radius {} dense enough with {} samples.'.
format(n_dims, radius, n_samples))
samples_needed[i] = n_samples
plt.figure(2)
plt.semilogy(radii, samples_needed)
plt.xlabel('Radius of {}-d hypersphere'.format(n_dims))
plt.ylabel('Samples needed')
plt.grid(True)
plt.show()
assert (False)
def test_contains():
hs = HyperSphere([3, 4], 1.5)
assert ([3, 4] in hs)
hs2 = HyperSphere([3, 4.5], 0.9)
hs3 = HyperSphere([3, 4.5], 1.1)
assert (hs2 in hs)
assert (hs3 not in hs)
points = np.array([[4.25, 5.25], [3.75, 4.75], [3, 1], [2.5, 3]])
assert (np.all(
hs.contains(points) == np.array([False, True, False, True])))
for radius in [2.3, 42, 0.001, 10]:
for centroid in [
np.array([-5, 2]),
np.array([600, -3]),
np.array([0.1, 80])
]:
hs = HyperSphere(centroid, radius)
assert (np.all(
hs.contains((hs.sample(100) - hs.centroid()) * 0.99 +
hs.centroid())))
assert (not np.any(
hs.contains((hs.sample(100) - hs.centroid()) * 1.01 +
hs.centroid())))