def run(n, base_filename, l=0.5):
os.system("rm {}*.vtk".format(base_filename))
# initial conditions
domain = ConvexPolyhedraAssembly()
domain.add_box([0, 0], [1, 1])
positions = []
velocities = []
radius = 0.5 * l / n
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 * radius * (np.random.rand() - 0.5)
ny = y + 0 * radius + 0 * radius * (np.random.rand() - 0.5)
if (nx - 0.5)**2 + (ny - 0.5 * l)**2 < (0.5 * l)**2:
velocities.append([0, -radius / 5])
positions.append([nx, ny])
masses = np.ones(len(positions)) * l**2 / n**2
# simulation
fs = FluidSystem(domain, positions, velocities, masses, base_filename)
fs.coeff_centroid_force = 1e-5
fs.display()
for num_iter in range(500):
print("num_iter:", num_iter, "time:", fs.time)
fs.make_step()
fs.display()
def make_square(box=[0, 0, 1, 1]):
"""
Constructs a square domain with uniform measure (source measure 'rho').
To be passed to the 'newton_ot' and 'PowerDiagram' functions.
Args:
box (list): coordinates of the bottom-left and top-right corners
Returns:
domain (pysdot.domain_types): domain
"""
domain = ConvexPolyhedraAssembly()
domain.add_box([box[0], box[1]], [box[2], box[3]])
return domain
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 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 setUp(self):
rf = RadialFuncArfd(
lambda r: ((1 - r * r) * (r < 1))**2.5, # value
lambda w: 1 / w**0.5, # input scaling
lambda w: w**2.5, # output scaling
lambda r: 2.5 * ((1 - r * r) *
(r < 1))**1.5, # value for the der wrt weight
lambda w: 1 / w**0.5, # input scaling for the der wrt weight
lambda w: w**1.5, # output scaling for the der wrt weight
[1], # stops (radii values where we may have discontinuities)
1e-8 # precision
)
# set up a domain, with only 1 dirac
domain = ConvexPolyhedraAssembly()
domain.add_box([0.0, 0.0], [2.0, 1.0])
self.pd = PowerDiagram(domain=domain, radial_func=rf)
def setUp(self):
rf = RadialFuncArfd(
lambda r: (1 - r * r) * (r < 1), # value
lambda w: 1 / w**0.5, # input (radius) scaling
lambda w: w, # output scaling
lambda r: r < 1, # value for the der wrt weight
lambda w: 1 / w**0.5, # input scaling for the der wrt weight
lambda w: 1, # output scaling for the der wrt weight
[1] # stops (radii value where we may have discontinuities)
)
# should use only 2 polynomials
self.assertEqual(rf.nb_polynomials(), 2)
# set up a domain, with only 1 dirac
domain = ConvexPolyhedraAssembly()
domain.add_box([0.0, 0.0], [2.0, 1.0])
self.pd = PowerDiagram(domain=domain, radial_func=rf)
positions.append([r * np.cos(a), r * np.sin(a)])
ot.set_positions(np.array(positions))
if cpt == 0:
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():
def setUp(self):
self.domain = ConvexPolyhedraAssembly()
self.domain.add_box([0.0, 0.0], [10.0, 10.0])
self.solver = Scipy.Solver()
def make_square(box=[0, 0, 1, 1]):
density = ConvexPolyhedraAssembly()
density.add_box([box[0], box[1]], [box[2], box[3]])
return density
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))
def setUp(self):
self.domain = ConvexPolyhedraAssembly()
self.domain.add_box([0, 0], [1, 1])
def test_measure(self):
domain = ConvexPolyhedraAssembly()
domain.add_box([0, 0], [2, 1])
self.assertAlmostEqual(domain.measure(), 2.0)
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)