positions = np.hstack( ( x.reshape( ( -1, 1 ) ), y.reshape( ( -1, 1 ) ) ) )
limx = pos_door + 1.2 / opened_width
#
pon = []
for i in range( 16 ):
a = 2 * np.pi * i / 16
pon.append( [ 1.5 + obstacle_radius * np.cos( a ), 0.5 + obstacle_radius * np.sin( a ), np.cos( a ), np.sin( a ) ] )
# domain
domain = ConvexPolyhedraAssembly()
domain.add_box( [ 0, 0 ], [ 2, 1 ] )
domain.add_box( [ pos_door, 0.5 - opened_width / 2 ], [ limx, 0.5 + opened_width / 2 ] )
if obstacle_radius:
domain.add_convex_polyhedron( np.array( pon ), -1.0 )
domain.display_boundaries_vtk( directory + "/bound.vtk" )
# domain_asy = "draw((0,0)--(3,0)--(3,1)--(4,1)--(4,0)--(7,0)--(7,3)--(4,3)--(4,2)--(3,2)--(3,3)--(0,3)--cycle);\n"
s = 0.5 * target_radius
g = GradGrid( domain, [ [ limx - 2 * s, 0.5 ] ], s )
# iterations
color_values = positions[ :, 1 ]
color_values = ( color_values - np.min( color_values ) ) / np.ptp( color_values )
ot = OptimalTransport(domain, RadialFuncInBall())
ot.set_weights( np.ones( positions.shape[ 0 ] ) * target_radius ** 2 )
ot.set_masses( np.ones( positions.shape[ 0 ] ) * np.pi * target_radius ** 2 )
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))
R2 = positions[:, 0]**2 + positions[:, 1]**2
positions = positions[R2 <= 4]
positions = positions[positions[:, 0] + positions[:, 1] > 1.0 / n]
positions = positions[-positions[:, 0] + positions[:, 1] > 1.0 / n]
N = positions.shape[0]
rho0 = 1 / np.pi
mass = 0.25 * rho0 * np.pi * 4 / N
target_radius = (mass / np.pi)**0.5
# iterations
weights = np.ones(positions.shape[0]) * target_radius**2
domain = ConvexPolyhedraAssembly()
domain.add_convex_polyhedron([
[0, 0, +1, -1],
[9, 9, 0, +1],
[-9, 9, -1, -1],
])
domain.display_boundaries_vtk(directory + "/bounds.vtk")
color_values = 0.5 * np.linalg.norm(
positions, axis=1, keepdims=True, ord=2)
color_values = (color_values - np.min(color_values)) / (
np.max(color_values) - np.min(color_values))
ot = OptimalTransport(domain, RadialFuncInBall())
ot.set_weights(weights)
ot.set_masses(np.ones(positions.shape[0]) * mass)
nb_timesteps = int(3 / target_radius)
for i in range(nb_timesteps):
from pysdot.domain_types import ConvexPolyhedraAssembly
from pysdot.radial_funcs import RadialFuncEntropy
from pysdot import OptimalTransport
import numpy as np
# constants
for n in [10]:
directory = "results/diffusion_{}".format(n)
# constants
eps = n**-0.5
# domain
domain = ConvexPolyhedraAssembly()
domain.add_convex_polyhedron([[-1, -1, -1, 0], [-1, -1, 0, -1],
[+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))
