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 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
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() )
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()
class FluidSystem:
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 display( self ):
fn = "{}{}.vtk".format( self.base_filename, self.cpt_display )
self.ot.display_vtk( fn, points=True, centroids=True )
self.cpt_display += 1
def make_step( self ):
ratio_dt = 1.0
while self.try_step( ratio_dt ) == False:
ratio_dt *= 0.5
print( " dt ratio:", ratio_dt )
def try_step( self, ratio_dt ):
old_p = self.ot.get_positions()
# find dt
radii_ap = ( np.array( self.ot.get_masses() ) / np.pi ) ** 0.5
vn2 = np.linalg.norm( self.velocities, axis=1, ord=2 )
dt = ratio_dt * 0.2 / np.max( np.abs( vn2 / radii_ap ) )
adv = dt * self.velocities
# target centroid positions + initial guess for the dirac positions
target_centroids = self.centroids + adv
self.ot.set_positions( old_p + adv )
# stuff to extract centroids, masses, ...
d = self.ot.dim()
n = self.ot.nb_diracs()
rd = np.arange( d * n, dtype=np.int )
b0 = ( d + 1 ) * np.floor_divide( rd, d )
l0 = b0 + rd % d # l1 = (d + 1) * np.arange(n, dtype=np.int) + d
# find positions to fit the target centroid positions
ratio = 1.0
for num_iter in range( self.max_iter + 1 ):
if num_iter == self.max_iter:
self.ot.set_positions( old_p )
return False
# search dir
mvs = self.ot.pd.der_centroids_and_integrals_wrt_weight_and_positions()
if mvs.error:
self.ot.set_positions( old_p )
ratio *= 0.5
if ratio < 1e-2:
return False
print( " solve X ratio:", ratio )
continue
M = csr_matrix( ( mvs.m_values, mvs.m_columns, mvs.m_offsets ) )[ l0, : ][ :, l0 ]
V = mvs.v_values[ l0 ] - target_centroids.flatten()
c = self.coeff_centroid_force * np.max( M )
V += c * ( self.ot.get_positions() - target_centroids ).flatten()
M += c * diag( 2 * n )
X = spsolve( M, V ).reshape( ( -1, d ) )
# if np.linalg.norm( X, ord=np.inf ) > self.max_disp_at_each_sub_iter:
# X *= self.max_disp_at_each_sub_iter / np.linalg.norm( X, ord=np.inf )
self.ot.set_positions( self.ot.get_positions() - ratio * X )
e = np.linalg.norm( X )
# print( " e", e )
if e < 1e-6:
break
# projection
# self.ot.verbosity = 1
self.ot.adjust_weights( relax=0.75 )
# update centroid pos and speed
self.time += dt
old_centroids = self.centroids
self.centroids = self.ot.get_centroids()
self.velocities = ( self.centroids - old_centroids ) / dt
return 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 = []
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)
# 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()
plt.show()
plt.plot(img[50, :, 0] / img[50, :, 2], '+')
plt.show()