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()))
def proj_noncongested(points,
domain,
center=None,
mass=None,
radial_func=RadialFuncInBall(),
verbose=None):
nb_points = len(points)
assert (nb_points != 0)
if mass is None:
mass = np.ones(nb_points) / nb_points
laguerre = OptimalTransport(positions=points,
weights=None,
masses=mass,
domain=domain,
radial_func=radial_func,
linear_solver="CuPyx")
if not center is None:
initialize_weights(power_diagram=laguerre.pd,
center=center,
verbose=verbose)
laguerre.adjust_weights(relax=1)
if np.linalg.norm(laguerre.pd.integrals() - mass) > 1e-5:
print("The Newton algorithm did not converge!")
laguerre.display_vtk("debug_file/bad_Newton.vtk", points=True)
laguerre.get_domain().display_boundaries_vtk(
"debug_file/bad_Newton_domain.vtk")
np.save("debug_file/bad_positions", laguerre.get_positions())
np.save("debug_file/integrals", laguerre.pd.integrals())
np.save("debug_file/bad_weights", laguerre.get_weights())
assert (False)
return laguerre.pd
def optimal_transport(density, Y, masses, psi0 = None, err=1e-8):
center = (density.min_position() + density.max_position())/2
halfsides = (density.max_position() - density.min_position())/2
ratio = 1/np.max(np.abs((Y-center)/halfsides))
psi = (1-ratio)*np.sum((Y-center)**2, axis=-1)
ot = OptimalTransport(Y, psi, density, radial_func=RadialFuncUnit(), obj_max_dw=err)
ot.set_masses(masses)
ot.adjust_weights()
return ot.pd
def run(n, base_filename, l=0.5):
# domain
domain = ConvexPolyhedraAssembly()
domain.add_box([0, 0], [1, 1])
# initial positions, weights and masses
positions = []
if n == 1:
radius = 0.3
mass = 3.14159 * radius**2
positions.append([0.5, radius])
else:
radius = l / (2 * (n - 1))
mass = l**2 / n**2
for y in np.linspace(radius, l - radius, n):
for x in np.linspace(0.5 - l / 2 + radius, 0.5 + l / 2 - radius,
n):
nx = x + 0.0 * radius * (np.random.rand() - 0.5)
ny = y + 0.0 * radius * (np.random.rand() - 0.5) + 0.5 * radius
positions.append([nx, ny])
positions = np.array(positions)
nb_diracs = positions.shape[0]
# dim = positions.shape[ 1 ]
# OptimalTransport
ot = OptimalTransport(domain, RadialFuncInBall())
ot.set_weights(np.ones(nb_diracs) * radius**2)
ot.set_masses(np.ones(nb_diracs) * mass)
ot.set_positions(positions)
ot.max_iter = 100
ot.adjust_weights()
ot.display_vtk(base_filename + "0.vtk", points=True, centroids=True)
# history of centroids
ce = ot.get_centroids()
ce[:, 1] += radius / 10
bh = [ce]
dt = 1.0
for num_iter in range(200):
print("num_iter", num_iter)
bh.append(ot.get_centroids())
fit_positions(ot, bh, dt)
# display
n1 = int(num_iter / 1) + 1
ot.display_vtk(base_filename + "{}.vtk".format(n1),
points=True,
centroids=True)
def run(n, base_filename, l=0.5):
# domain
domain = ConvexPolyhedraAssembly()
domain.add_box([0, 0], [1, 1])
# initial positions, weights and masses
positions = []
if n == 1:
radius = 0.3
mass = 3.14159 * radius**2
positions.append([0.5, radius])
else:
radius = l / (2 * (n - 1))
mass = l**2 / n**2
for y in np.linspace(radius, l - radius, n):
for x in np.linspace(radius, l - radius, n):
nx = x # + 0.2 * radius * (np.random.rand() - 0.5)
ny = y # + 0.2 * radius * (np.random.rand() - 0.5)
positions.append([nx, ny])
positions = np.array(positions)
nb_diracs = positions.shape[0]
dim = positions.shape[1]
# OptimalTransport
ot = OptimalTransport(domain, RadialFuncInBall())
ot.set_weights(np.ones(nb_diracs) * radius**2)
ot.set_masses(np.ones(nb_diracs) * mass)
ot.set_positions(positions)
ot.adjust_weights()
ot.display_vtk(base_filename + "0.vtk", points=True)
g = np.zeros((nb_diracs, dim))
g[:, 1] = -0.001
bh = [ot.get_centroids()] # history of centroids
for num_iter in range(50):
bh.append(ot.get_centroids())
print("num_iter", num_iter)
# proposition for centroids
bn = 2 * bh[-1] - bh[-2] + g
# find a new set of diracs parameters (position and weight)
# to be as close to the new centroids as possible
update_positions_to_get_centroids(ot, bn)
# display
n1 = num_iter + 1
ot.display_vtk(base_filename + "{}.vtk".format(n1), points=True)
def test_base_ot(self, nb_diracs=1000):
for _ in range(10):
ot = OptimalTransport(self.domain)
# diracs
ot.set_positions(np.random.rand(nb_diracs, 2))
ot.set_weights(np.ones(nb_diracs))
# optimal weights
ot.adjust_weights()
# integrals
areas = ot.pd.integrals()
self.assertAlmostEqual(np.min(areas), 1.0 / nb_diracs, places=6)
self.assertAlmostEqual(np.max(areas), 1.0 / nb_diracs, places=6)
def __init__( self, domain, positions, velocities, masses, base_filename ):
self.ot = OptimalTransport(domain, RadialFuncInBall())
self.ot.set_positions(np.array(positions))
self.ot.set_weights(np.array(masses)/np.pi)
self.ot.set_masses(np.array(masses))
self.base_filename = base_filename
self.cpt_display = 0
self.max_iter = 200
self.time = 0
# initial centroid positions and velocities
self.ot.adjust_weights()
self.centroids = self.ot.get_centroids()
self.velocities = np.array(velocities)
self.coeff_centroid_force = 1e-4
def run(n, base_filename):
domain = ConvexPolyhedraAssembly()
domain.add_box([0, 0], [1, 1])
domain.add_box([0.2, -0.5], [0.8, 0])
positions = []
radius = 0.5 / (2 * (n - 1))
for y in np.linspace(radius, 0.5 + radius, n):
for x in np.linspace(radius, 0.5 + radius, n):
positions.append([x, y])
nb_diracs = len(positions)
#
ot = OptimalTransport(domain, RadialFuncInBall())
ot.set_masses(np.ones(nb_diracs) * 0.8 * 0.5**2 / nb_diracs)
ot.set_weights(np.ones(nb_diracs) * radius**2)
ot.set_positions(np.array(positions))
b_old = ot.pd.centroids()
ot.adjust_weights()
ot.display_vtk(base_filename + "0.vtk")
nb_timesteps = int(20 / radius)
v = np.zeros((nb_diracs, 2))
dt = 0.003 * radius
for i in range(nb_timesteps):
print(i, "/", nb_timesteps)
# first trial
v[:, 1] -= 1
p_old = ot.get_positions()
p_tst = p_old + dt * v
ot.set_positions(p_tst)
ot.adjust_weights()
# display
d = int(n / 5)
if i % d == 0:
ot.display_vtk(base_filename + "{:03}.vtk".format(1 + int(i / d)))
# corrections
b_new = ot.pd.centroids()
v = (b_new - b_old) / dt
ot.set_positions(b_new)
b_old = b_new
def test_ball_cut(self, nb_diracs=100):
for _ in range(10):
ot = OptimalTransport(self.domain, RadialFuncInBall())
positions = np.random.rand(nb_diracs, 2)
positions[:, 1] *= 0.5
radius = 0.25 / nb_diracs**0.5
mass = np.pi * radius**2
# diracs
ot.set_positions(positions)
ot.set_weights(np.ones(nb_diracs) * radius**2)
ot.set_masses(np.ones(nb_diracs) * mass)
# optimal weights
ot.adjust_weights()
# integrals
areas = ot.pd.integrals()
self.assertAlmostEqual(np.min(areas), mass, places=6)
self.assertAlmostEqual(np.max(areas), mass, places=6)
from pysdot import OptimalTransport
from matplotlib import pyplot
import numpy as np
positions = []
ss = 1e-3
for x in np.linspace(0, 1 - ss, 20):
positions.append([x, 0.5])
positions.append([x + ss, 0.5])
ot = OptimalTransport(np.array(positions))
ot.verbosity = 1
ot.adjust_weights()
pyplot.plot(ot.get_positions()[:, 0], ot.get_weights(), '+')
pyplot.show()
def run(n, base_filename, l=0.5):
# domain
domain = ConvexPolyhedraAssembly()
# domain.add_box([0, 0], [1, 1])
domain.add_convex_polyhedron([
# x y Nx Ny (ext)
[0, 0, -1, -0.2],
[0, 0, -0.2, -1],
[1, 1, +1, 0],
[1, 1, 0, +1],
])
# initial positions, weights and masses
positions = []
if n == 1:
radius = 0.2
else:
radius = l / (2 * (n - 1))
for y in np.linspace(radius, l - radius, n):
for x in np.linspace(radius, l - radius, n):
nx = x + 0.2 * radius * (np.random.rand() - 0.5)
ny = y + 0.2 * radius * (np.random.rand() - 0.5)
positions.append([nx, ny])
positions = np.array(positions)
nb_diracs = positions.shape[0]
# OptimalTransport
ot = OptimalTransport(domain, RadialFuncInBall())
ot.set_weights(np.ones(nb_diracs) * radius**2)
ot.set_masses(np.ones(nb_diracs) * l**2 / nb_diracs)
ot.set_positions(positions)
ot.adjust_weights()
ot.display_vtk(base_filename + "0.vtk")
ot.set_positions(ot.get_centroids())
velocity = 0.0 * positions
for num_iter in range(200):
print("num_iter", num_iter)
# barycenters at the beginning
ot.adjust_weights()
b_o = ot.get_centroids()
# trial for the new barycenters
velocity[:, 0] -= 0.05 * radius * 0.707
velocity[:, 1] -= 0.05 * radius * 0.707
b_n = b_o + velocity
# optimisation of positions to go to the target barycenters
ropt = scipy.optimize.minimize(obj,
b_n.flatten(), (ot, b_n),
tol=1e-4,
method='BFGS',
options={'eps': 1e-4 * radius})
positions = ropt.x.reshape((-1, 2))
ot.set_positions(positions)
ot.adjust_weights()
# new barycenters, corrected (minimize have update the weights)
b_n = ot.get_centroids()
velocity = b_n - b_o
print(positions, velocity)
# display
ot.pd.display_vtk_points(base_filename +
"pts_{}.vtk".format(num_iter + 1))
ot.display_vtk(base_filename + "{}.vtk".format(num_iter + 1))
dws = 5
img = imageio.imread("clay.jpg")
img = img[:, :, 1]
beg = int(img.shape[1] / 2 - img.shape[0] / 2)
end = beg + img.shape[0]
img = img[:, beg:end]
img = downscale_local_mean(img, (dws, dws))
img = np.max(img) * 1.05 - img
img /= np.sum(img)
# plt.imshow( img )
# plt.show()
# domain
domain = ConvexPolyhedraAssembly()
domain.add_img([0, 0], [1, 1], img)
# diracs
nd = 100000
ot = OptimalTransport(domain)
ot.set_positions(np.random.rand(nd, 2))
ot.set_weights(np.ones(nd) / nd)
ot.obj_max_dw = 1e-5
ot.verbosity = True
# solve
ot.adjust_weights(relax=1.0)
# display
ot.pd.display_vtk("results/pd.vtk", centroids=True)
[+2, -1, 1, -1], [-1, +2, 0, +1]])
domain.display_boundaries_vtk(directory + "/bounds.vtk")
#
positions = []
for y in np.linspace(0, 1, n):
for x in np.linspace(0, 1, n):
positions.append([x, y])
positions = np.array(positions)
# iterations
max_w = -1
min_w = 0
ot = OptimalTransport(domain, RadialFuncEntropy(eps))
ot.set_masses(np.ones(positions.shape[0]))
weights = np.zeros(positions.shape[0])
for i in range(101):
# optimal weights
ot.set_positions(positions)
ot.adjust_weights()
weights = ot.get_weights()
min_w = np.min(weights)
max_w = np.max(weights)
# display
if i % 10 == 0:
ot.display_asy(directory + "/we_{:03}.asy".format(int(i / 10)),
def run(n, base_filename, l=0.5):
# domain
domain = ConvexPolyhedraAssembly()
domain.add_box([0, 0], [1, 1])
# initial positions, weights and masses
positions = []
radius = l / (2 * (n - 1))
mass = l**2 / n**2
for y in np.linspace(radius, l - radius, n):
for x in np.linspace(0.5 - l / 2 + radius, 0.5 + l / 2 - radius, n):
nx = x + 0.0 * radius * (np.random.rand() - 0.5)
ny = y + 0.0 * radius * (np.random.rand() - 0.5)
positions.append([nx, ny])
positions = np.array(positions)
nb_diracs = positions.shape[0]
dim = positions.shape[1]
# OptimalTransport
ot = OptimalTransport(domain, RadialFuncInBall())
ot.set_weights(np.ones(nb_diracs) * radius**2)
ot.set_masses(np.ones(nb_diracs) * mass)
ot.set_positions(positions)
ot.max_iter = 100
ot.adjust_weights()
ot.display_vtk(base_filename + "0.vtk", points=True, centroids=True)
# gravity
G = np.zeros((nb_diracs, dim))
G[:, 1] = -9.81
#
eps = 0.5
dt = radius * 0.1
V = np.zeros((nb_diracs, dim))
M = np.stack([ot.get_masses() for d in range(dim)]).transpose()
for num_iter in range(500):
print("num_iter:", num_iter, "dt:", dt)
C = ot.get_centroids()
X = ot.get_positions()
A = G + (C - ot.get_positions()) / (M * eps**2)
while True:
dV = dt * A
dX = dt * (V + dV)
if np.max(np.linalg.norm(dX, axis=1, ord=2)) < 0.2 * radius:
dt *= 1.05
V += dV
X += dX
break
dt *= 0.5
ot.set_positions(X)
ot.adjust_weights()
# display
n1 = int(num_iter / 1) + 1
ot.display_vtk(base_filename + "{}.vtk".format(n1),
points=True,
centroids=True)
from pysdot.domain_types import ConvexPolyhedraAssembly
from pysdot import OptimalTransport
import numpy as np
positions = np.random.rand(200, 2)
# diracs
ot = OptimalTransport()
ot.set_positions(np.array(positions))
ot.set_weights(np.ones(ot.get_positions().shape[0]))
ot.verbosity = 1
# solve
ot.adjust_weights()
# display
ot.display_vtk("results/pd.vtk")
# print( ot.pd.display_html() )
])
num_dirac += 1
# plt.plot( res[ :, 0 ], res[ :, 1 ], "x" )
# plt.show()
return res
for dist_name in ["uniform"]: # , "voro_50"
for dim in [3]:
for nb_diracs in map(
int, [1e5 / 8, 1e5 / 4, 1e5 / 2]): # 1e5, 2e5, 4e5, 8e5, 16e5
positions = make_positions(dist_name, nb_diracs, dim)
# diracs
ot = OptimalTransport(positions=positions)
ot.verbosity = 1
# solve
print(dim, nb_diracs)
ot.adjust_weights()
# display, save
if nb_diracs <= 1e6:
ot.display_vtk("vtk/pd.vtk", points=True)
pw = np.zeros([dim + 1, nb_diracs])
for d in range(dim):
pw[d, :] = positions[:, d]
np.save(
"/data/sdot/{}_{}_{}D_equalw.npy".format(
ot.set_weights(np.array(masses) / np.pi * 0.25)
ot.set_masses(np.array(masses))
ot.max_iter = 100
ot.adjust_weights(relax=0.5)
ot.display_vtk("lc_{}.vtk".format(cpt))
return ot.pd.der_boundary_integral()
domain = ConvexPolyhedraAssembly()
domain.add_box([0, 0], [10, 10])
crb = {}
for n in range(30, 31):
ot = OptimalTransport(domain, RadialFuncInBall())
k = "{}".format(n)
crb[k] = []
cpt = 0
for coeff_r in [0.9875]: # np.linspace( 0.9875, 0.4, 120 ):
e = test_discr(ot, n, coeff_r, cpt)
print(e)
# crb[ k ].append( [ coeff_r, e ] )
# cpt += 1
# for key, val in crb.items():
# val = np.array( val )
# plt.plot( val[ :, 0 ], val[ :, 1 ] )
# plt.show()
def quantization(ot, tau=.3, niter=10):
for _ in range(niter):
ot.adjust_weights()
B = ot.get_centroids()
ot.set_positions(ot.get_positions() + tau * (B - ot.get_positions()))
ot.adjust_weights()
# initial positions
n = 40
positions = []
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 )