def make_case(name, nb_diracs, dim):
# default domain
if name == "random":
positions = np.random.rand(nb_diracs, dim)
elif name == "grid":
positions = make_grid(nb_diracs, dim)
elif name == "grid_with_rand":
positions = make_grid(nb_diracs, dim, rand_val=1)
elif name == "faces":
# voronoi with 100 points
pd = PowerDiagram(np.random.rand(5, dim))
# quantization
lot = OptimalTransport(positions=make_grid(nb_diracs, dim))
lot.obj_max_dw = 1e-5
lot.verbosity = 1
for ratio in [1 - 0.85**n for n in range(50)]:
# density
img_size = 1000
img_points = []
items = [range(img_size) for i in range(dim)]
for i in itertools.product(*items):
img_points.append(i)
img = pd.distances_from_boundaries(
np.array(img_points) / img_size).reshape((img_size, img_size))
img = (1 - ratio) + ratio * np.exp(-(100 * img)**2)
lot.set_domain(ScaledImage([0, 0], [1, 1], img / np.mean(img)))
# opt
for _ in range(10):
lot.adjust_weights()
B = lot.get_centroids()
lot.set_positions(lot.get_positions() + 0.3 *
(B - lot.get_positions()))
positions = lot.get_positions()
plt.plot(positions[:, 0], positions[:, 1], ".")
plt.show()
np.save("/data/{}_n{}_d{}_voro.npy".format(name, nb_diracs, dim),
(positions[:, 0], positions[:, 1]))
# solve
if nb_diracs < 32000000:
ot = OptimalTransport(positions)
# ot.verbosity = 1
# solve
ot.adjust_weights()
# display
# ot.display_vtk( "results/pd.vtk" )
np.save("/data/{}_n{}_d{}.npy".format(name, nb_diracs, dim),
(positions[:, 0], positions[:, 1], ot.get_weights()))
for y in range(n):
for x in range(n):
positions.append([(y + 0.25 + 0.5 * np.random.rand()) / n,
(x + 0.25 + 0.5 * np.random.rand()) / n])
ot = OptimalTransport(np.array(positions))
ot.verbosity = 1
# solve
for l in [2, 4, 8]:
t = np.linspace(-1, 1, 100)
x, y = np.meshgrid(t, t)
img = np.exp(-l * (x**2 + y**2))
img /= np.mean(img)
# domain
ot.set_domain(ScaledImage([0, 0], [1, 1], img))
quantization(ot, 0.1, 10)
# display
# ot.pd.display_vtk( "results/pd.vtk", centroids=True )
# optimal transport with a simple [0,1]^2 domain
ot = OptimalTransport(ot.get_positions())
ot.adjust_weights()
img = ot.pd.image_integrals([0, 0], [1, 1], [100, 100])
for d in range(2):
plt.subplot(1, 2, d + 1)
plt.imshow(img[:, :, d] / img[:, :, 2])
plt.colorbar()
