def sample(self, num, d=1, rng=np.random, ntm=Sobol()):
if d == 1:
return super(ScatteredHypersphere, self).sample(num, d, rng)
if self.surface:
cube = ntm.sample(num, d-1)
radius = 1.0
else:
dcube = ntm.sample(num, d)
cube, radius = dcube[:, :-1], dcube[:, -1:] ** (1.0 / d)
# inverse transform method (section 1.5.2)
for j in range(d-1):
cube[:, j] = SphericalCoords(d-1-j).ppf(cube[:, j])
# spherical coordinate transform
mapped = np.ones((num, d))
i = np.ones(d-1)
i[-1] = 2.0
s = np.sin(i[None, :] * np.pi * cube)
c = np.cos(i[None, :] * np.pi * cube)
mapped[:, 1:] = np.cumprod(s, axis=1)
mapped[:, :-1] *= c
# radius adjustment for ball versus sphere, and rotate
rotation = random_orthogonal(d, rng=rng)
return np.dot(mapped * radius, rotation)
