def charged_nucleation_in_2D(writer,
args,
R=30,
D=25,
weights=(0, -10, -8, 8)):
dx = 2 * R / args.height
x = (np.arange(args.width) - args.width // 2) * dx
y = (np.arange(args.height) - args.height // 2) * dx
x, y = np.meshgrid(x, y, indexing='ij')
def source_G(t):
amount = np.exp(-0.5 * (t - 5)**2)
return (np.exp(-0.5 *
((x - D)**2 + y * y)) * weights[0] + np.exp(-0.5 * (
(x + D)**2 + y * y)) * weights[1]) * amount
def source_X(t):
amount = np.exp(-0.5 * (t - 5)**2)
return (np.exp(-0.5 *
((x - D)**2 + y * y)) * weights[2] + np.exp(-0.5 * (
(x + D)**2 + y * y)) * weights[3]) * amount
source_functions = {
'G': source_G,
'X': source_X,
}
noise_scale = 1e-4
model_g = ModelG(
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
dx,
dt=args.dt,
params=args.model_params,
source_functions=source_functions,
)
print("Rendering 'Charged nucleation in 2D'")
print("Lattice constant dx = {}, time step dt = {}".format(
model_g.dx, model_g.dt))
min_G = -4.672736908320116
max_G = 0.028719261862332906
min_X = -3.8935243721220334
max_X = 1.2854028081816122
min_Y = -0.7454193158963579
max_Y = 4.20524950766914
for n in progressbar.progressbar(range(args.num_frames)):
model_g.step()
if n % args.oversampling == 0:
rgb = [
6 * (-model_g.G + max_G) / (max_G - min_G),
5 * (model_g.Y - min_Y) / (max_Y - min_Y),
0.7 * (model_g.X - min_X) / (max_X - min_X),
]
zero_line = 1 - tf.exp(-600 * model_g.Y**2)
frame = make_video_frame([c * zero_line for c in rgb])
writer.append_data(frame)
def soliton_in_g_well_2D(writer, args, R=25, D=15):
dx = 2 * R / args.height
x = (np.arange(args.width) - args.width // 2) * dx
y = (np.arange(args.height) - args.height // 2) * dx
x, y = np.meshgrid(x, y, indexing='ij')
def source_G(t):
nucleator = -np.exp(-0.5 * (t - 5)**2)
#potential = 0.015 * (np.tanh(t-25) + 1)
#potential = 0.0003 * (np.tanh(t-25) + 1) # gradient = (1+np.tanh(t-30)) * 0.0003 # see above
#u = x / R
#u = x/10 - 5 # see: "soliton_in_g_well_2D___1_seed__gradient_1__2a.mp4"
#u = x/15 # see: "soliton_in_g_well_2D___1_seed__gradient_2__2b.mp4"
#u = x/25
return (
#np.exp(-0.5*((x-D)**2+y*y)) * nucleator +
#(u*u - 1) * potential
np.exp(-0.5 * ((x)**2 + y * y)) * nucleator #+ (x+8) * potential
#(u*u - 1) * potential #+ (x+8) * gradient
)
source_functions = {
'G': source_G,
}
noise_scale = 1e-4
model_g = ModelG(
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
dx,
dt=args.dt,
params=args.model_params,
source_functions=source_functions,
)
print("Rendering 'Soliton in G-well in 2D'")
print("Lattice constant dx = {}, time step dt = {}".format(
model_g.dx, model_g.dt))
G_scale = 0.02
X_scale = 0.25
Y_scale = 0.5
for n in progressbar.progressbar(range(args.num_frames)):
model_g.step()
if n % args.oversampling == 0:
rgb = [
(G_scale * 0.5 - model_g.G) / G_scale,
(model_g.Y - Y_scale * 0.5) / Y_scale,
(model_g.X - X_scale * 0.5) / X_scale,
]
zero_line = 1 - tf.exp(-600 * model_g.Y**2)
frame = make_video_frame([c * zero_line for c in rgb])
writer.append_data(frame)
def random_1D_fields():
x = linspace(-20, 20, 512)
dx = x[1] - x[0]
noise_scale = 1.0
fig, axs = subplots(2, 3)
for ax_ in axs:
for ax in ax_:
while True:
params = {
"A": rand() * 20,
"B": rand() * 20,
"k2": rand() * 2,
"k-2": rand() * 2,
"k5": rand() * 2,
"Dx": rand() * 4,
"Dy": rand() * 4,
}
model_g = ModelG(bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
dx,
params=params)
while model_g.t < 20:
model_g.step()
if rand() < 0.05:
G, X, Y = model_g.numpy()
if abs(X).max() >= 100:
break
G, X, Y = model_g.numpy()
if abs(X).max() < 100:
break
print("Rejected", params)
print("Done", params)
G /= abs(G).max()
X /= abs(X).max()
Y /= abs(Y).max()
ax.plot(x, G)
ax.plot(x, X)
ax.plot(x, Y)
show()
def nucleation_3D(writer, args, R=20):
raise NotImplementedError("Needs some work")
params = {
"A": 3.4,
"B": 13.5,
"k2": 1.0,
"k-2": 0.1,
"k5": 0.9,
"D_G": 1.0,
"D_X": 1.0,
"D_Y": 1.95,
"density_G": 1.0,
"density_X": 0.0002,
"density_Y": 0.043,
"base-density": 9.0,
"viscosity": 0.3,
"speed-of-sound": 1.0,
}
dx = 2 * R / args.height
x = (np.arange(args.width) - args.width // 2) * dx
y = (np.arange(args.height) - args.height // 2) * dx
z = y
x, y, z = np.meshgrid(x, y, z, indexing='ij')
def source_G(t):
center = np.exp(-0.3 * (t - 6)**2) * 10
return -np.exp(-0.5 * (x * x + y * y + z * z)) * center
source_functions = {
'G': source_G,
}
# We need some noise to break spherical symmetry
noise_scale = 1e-4
G = bl_noise(x.shape) * noise_scale
X = bl_noise(x.shape) * noise_scale
Y = bl_noise(x.shape) * noise_scale
flow = [
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale
]
fluid_model_g = FluidModelG(
G,
X,
Y,
flow,
dx,
dt=args.dt,
params=params,
source_functions=source_functions,
)
flow_particle_origins = []
for _ in range(1000):
flow_particle_origins.append([np.random.rand() * s for s in x.shape])
flow_particles = tf.constant(flow_particle_origins, dtype='float64')
flow_streaks = 0 * x[:, :, 0]
print("Rendering 'Nucleation and Motion in G gradient in 3D'")
print("Lattice constant dx = {}, time step dt = {}".format(
fluid_model_g.dx, fluid_model_g.dt))
for n in progressbar.progressbar(range(args.num_frames)):
fluid_model_g.step()
for _ in range(20):
indices = tf.cast(flow_particles, 'int32')
for index in indices.numpy():
flow_streaks[index[0], index[1]] += 0.15 / args.oversampling
dx = tf.gather_nd(fluid_model_g.u, indices)
dy = tf.gather_nd(fluid_model_g.v, indices)
dz = tf.gather_nd(fluid_model_g.w, indices)
flow_particles = (flow_particles +
tf.stack([dx, dy, dz], axis=1) * 400) % x.shape
if n % args.oversampling == 0:
rgb = [
tf.reduce_mean(
(7 * fluid_model_g.G)**2, axis=2) + flow_streaks,
tf.reduce_mean((4 * fluid_model_g.Y)**2, axis=2),
tf.reduce_mean((2 * fluid_model_g.X)**2, axis=2),
]
frame = make_video_frame(rgb)
writer.append_data(frame)
flow_streaks *= 0
flow_particles = tf.constant(flow_particle_origins,
dtype='float64')
def nucleation_3D(animated=False, N=128, R=20):
params = {
"A": 3.4,
"B": 13.5,
"k2": 1.0,
"k-2": 0.1,
"k5": 0.9,
"D_G": 1.0,
"D_X": 1.0,
"D_Y": 1.95,
"density_G": 1.0,
"density_X": 0.0002,
"density_Y": 0.043,
"base-density": 20.0,
"viscosity": 0.4,
"speed-of-sound": 1.0,
}
x = np.linspace(-R, R, N)
dx = x[1] - x[0]
x, y, z = np.meshgrid(x, x, x, indexing='ij')
def source_G(t):
center = np.exp(-0.5 * (t - 5)**2) * 10
return -np.exp(-0.5 * (x * x + y * y + z * z)) * center
source_functions = {
'G': source_G,
}
# We need some noise to break spherical symmetry
noise_scale = 1e-4
G = bl_noise(x.shape) * noise_scale
X = bl_noise(x.shape) * noise_scale
Y = bl_noise(x.shape) * noise_scale
flow = [
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale
]
dt = 0.2 * dx
fluid_model_g = FluidModelG(
G,
X,
Y,
flow,
dx,
dt=dt,
params=params,
source_functions=source_functions,
)
if animated:
def get_data():
G, X, Y, (u, v, w) = fluid_model_g.numpy()
x_scale = 0.1
y_scale = 0.1
return (
G[N // 2, N // 2],
X[N // 2, N // 2] * x_scale,
Y[N // 2, N // 2] * y_scale,
u[N // 2, N // 2],
v[N // 2, N // 2],
w[N // 2, N // 2],
)
G, X, Y, u, v, w = get_data()
plots = []
plots.extend(pylab.plot(z[0, 0], G))
plots.extend(pylab.plot(z[0, 0], X))
plots.extend(pylab.plot(z[0, 0], Y))
plots.extend(pylab.plot(z[0, 0], u))
plots.extend(pylab.plot(z[0, 0], v))
pylab.ylim(-0.1, 0.1)
def update(frame):
fluid_model_g.step()
G, X, Y, u, v, w = get_data()
print(fluid_model_g.t, abs(G).max(), abs(u).max())
plots[0].set_ydata(G)
plots[1].set_ydata(X)
plots[2].set_ydata(Y)
plots[3].set_ydata(u)
plots[4].set_ydata(v)
plots[4].set_ydata(w)
return plots
FuncAnimation(pylab.gcf(),
update,
frames=range(100),
init_func=lambda: plots,
blit=True,
repeat=True,
interval=20)
pylab.show()
else:
from datetime import datetime
from pathlib import Path
start = datetime.now()
num_steps = int(1.0 / dt)
print("Starting simulation {} steps at a time".format(num_steps))
path = Path("/tmp/model_g")
path.mkdir(exist_ok=True)
while True:
for _ in range(num_steps):
fluid_model_g.step()
print("Saving a snapshot into {}".format(path))
G, X, Y, (u, v, w) = fluid_model_g.numpy()
np.save(path / 'G.npy', G)
np.save(path / 'X.npy', X)
np.save(path / 'Y.npy', Y)
np.save(path / 'u.npy', u)
np.save(path / 'v.npy', v)
np.save(path / 'w.npy', w)
print("Saved everything")
wall_clock_time = (datetime.now() - start).total_seconds()
print("t={}, wall clock time={} s, efficiency={}".format(
fluid_model_g.t, wall_clock_time,
fluid_model_g.t / wall_clock_time))
print("max|G|={}, max|u|={}".format(abs(G).max(), abs(u).max()))
def nucleation_3D(writer, args, R=12):
# raise NotImplementedError("Needs some work")
params = {
"A": 3.4,
"B": 13.5,
"k2": 1.0,
"k-2": 0.1,
"k5": 0.9,
"D_G": 1.0,
"D_X": 1.0,
"D_Y": 1.95,
"density_G": 1.0,
"density_X": 0.0002,
"density_Y": 0.043,
"base-density": 9.0,
"viscosity": 0.3,
"speed-of-sound": 1.0,
}
c1 = 0 # BJD added this on 22.4.2021
dx = 2 * R / args.height
x = (np.arange(args.width) - args.width // 2) * dx
y = (np.arange(args.height) - args.height // 2) * dx
z = y
x, y, z = np.meshgrid(x, y, z, indexing='ij')
def source_G(t):
center = np.exp(-0.3 * (t - 6)**2) * 10
return -np.exp(-0.5 * (x * x + y * y + z * z)) * center
source_functions = {
'G': source_G,
}
# We need some noise to break spherical symmetry
noise_scale = 1e-4
G = bl_noise(x.shape) * noise_scale
X = bl_noise(x.shape) * noise_scale
Y = bl_noise(x.shape) * noise_scale
flow = [
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale
]
fluid_model_g = FluidModelG(
G,
X,
Y,
flow,
dx,
dt=args.dt,
params=params,
source_functions=source_functions,
)
flow_particle_origins = []
for _ in range(1000):
flow_particle_origins.append([np.random.rand() * s for s in x.shape])
flow_particles = tf.constant(flow_particle_origins, dtype='float64')
flow_streaks = 0 * x[:, :, 0]
print("Rendering 'Nucleation and Motion in G gradient in 3D'")
print("Lattice constant dx = {}, time step dt = {}".format(
fluid_model_g.dx, fluid_model_g.dt))
for n in progressbar.progressbar(range(args.num_frames)):
fluid_model_g.step()
for _ in range(20):
indices = tf.cast(flow_particles, 'int32')
for index in indices.numpy():
flow_streaks[index[0], index[1]] += 0.15 / args.oversampling
dx = tf.gather_nd(fluid_model_g.u, indices)
dy = tf.gather_nd(fluid_model_g.v, indices)
dz = tf.gather_nd(fluid_model_g.w, indices)
flow_particles = (flow_particles +
tf.stack([dx, dy, dz], axis=1) * 400) % x.shape
if n % args.oversampling == 0:
rgb = [
tf.reduce_mean(
(7 * fluid_model_g.G)**2, axis=2) + flow_streaks,
tf.reduce_mean((4 * fluid_model_g.Y)**2, axis=2),
tf.reduce_mean((2 * fluid_model_g.X)**2, axis=2),
]
frame = make_video_frame(rgb)
writer.append_data(frame)
flow_streaks *= 0
flow_particles = tf.constant(flow_particle_origins,
dtype='float64')
#=====================BJD 20.4.2021==========================================
#-------------------------BJD 22.4.2021----rough code at present-----------------------------------------
if n == 200:
print("n = ", n)
break
#c1 = c1 + 1
print("H E L L O")
#y1 = np.loadtxt("/home/brendan/software/tf2-model-g/arrays/quiver_array14/u.txt") #, delimiter=" :-) ", usecols=(120)) # (426, 240)
#y2 = np.loadtxt("/home/brendan/software/tf2-model-g/arrays/quiver_array14/v.txt") #, delimiter=" :-) ", usecols=(120)) # (426, 240)
c1 = c1 + 1
# Set up grid and test data
#nx, ny = 256, 1024
nx, ny, nz = 240, 426, 426
#nx, ny = 426, 240 # changed round to check!
#(426,240)
x1 = range(nx)
y1 = range(ny)
z1 = range(nz)
#data = numpy.random.random((nx, ny))
U = np.loadtxt(
"/home/brendan/software/tf2-model-g/arrays/quiver3D_array31/u.txt"
) #, delimiter=" :-) ", usecols=(120)) # (426, 240)
V = np.loadtxt(
"/home/brendan/software/tf2-model-g/arrays/quiver3D_array31/v.txt"
) #, delimiter=" :-) ", usecols=(120)) # (426, 240)
W = np.loadtxt(
"/home/brendan/software/tf2-model-g/arrays/quiver3D_array31/w.txt"
) #, delimiter=" :-) ", usecols=(120)) # (426, 240)
# BJD 28.1.2021: u and v are saved as arrays in fluid_model_g.py as fllows:
# np.savetxt("/home/brendan/software/tf2-model-g/arrays/quiver_array18/u.txt", self.u)
# np.savetxt("/home/brendan/software/tf2-model-g/arrays/quiver_array18/v.txt", self.v)
#data = np.loadtxt("/home/brendan/software/tf2-model-g/arrays/array12/Y.txt")
#hf = plt.figure(figsize=(10,10))
#ha = hf.add_subplot(111, projection='3d')
#ha = hf.add_subplot(111, projection='2d')
X1, Y1, Z1 = np.meshgrid(
x1, y1, z1) # `plot_surface` expects `x` and `y` data to be 2D
#x, y, z = np.meshgrid(np.arange(-0.8, 1, 0.2),
# np.arange(-0.8, 1, 0.2),
# np.arange(-0.8, 1, 0.8))
#ha.plot_surface(X, Y, data)
#ha.plot_surface(X, Y, data, rstride=1, cstride=1, cmap=cm.coolwarm,
# linewidth=0, antialiased=False)
#ha.plot_surface(X.T, Y.T, data)
#surf = ha.plot_surface(X1, Y1, data, rstride=1, cstride=1, cmap=cm.coolwarm,
# linewidth=0, antialiased=False)
#ha.set_zlim(-1, 3)
#hf.colorbar(surf, shrink=0.5, aspect=10)
#hf = plt.figure(figsize=(10,10))
"""
fig, hf = plt.subplots(figsize=(10,10))
#ax3.set_title("pivot='tip'; scales with x view")
hf.set_title("pivot='tip'; scales with x view" + str(c1))
M = np.hypot(U, V)
Q = hf.quiver(X1, Y1, U, V, M, units='x', pivot='tip', width=0.022,
scale=1 / 0.15)
qk = hf.quiverkey(Q, 0.9, 0.9, 1, r'$1 \frac{m}{s}$', labelpos='E',
coordinates='figure')
hf.scatter(X1, Y1, color='0.5', s=1)
# Below, from Color_Quiver_Plot.py 17.4.2021 - BJD
color = np.sqrt(((dx-n)/2)*2 + ((dy-n)/2)*2)
ax2.quiver(X, Y, dx, dy, color)
ax2.xaxis.set_ticks([])
ax2.yaxis.set_ticks([])
ax2.set_aspect('equal')
ax2.set_title('gradient')
plt.tight_layout()
plt.show()
#also arrow head 17.4.2021 BJD:
Q = hf.quiver(X1[::10, ::10], Y1[::10, ::10], U[::10, ::10], V[::10, ::10], units='width',
pivot='mid', scale=0.005)#pivot='mid', units='inches')#, scale=1)#, scale=5)
"""
#fig, hf = plt.subplots(figsize=(10,10))
fig = plt.figure(figsize=(10, 10))
ax = fig.gca(projection='3d')
ax.set_title(
"pivot='mid'; every 10th arrow; units='velocity vector' time="
+ str(c1))
#Q = ax.quiver(X1[::10, ::10], Y1[::10, ::10], Z1[::10, ::10], U[::10, ::10],
# V[::10, ::10], W[::10, ::10], pivot='mid', units='inches')
Q = ax.quiver(X1[::10, ::10, ::10],
Y1[::10, ::10, ::10],
Z1[::10, ::10, ::10],
U[::10, ::10, ::10],
V[::10, ::10, ::10],
W[::10, ::10, ::10],
pivot='mid',
units='inches')
#hf.set_title("pivot='mid'; every 10th arrow; units='velocity vector' time=" + str(c1))
#Q = hf.quiver(X1[::10, ::10], Y1[::10, ::10], U[::10, ::10], V[::10, ::10], pivot='mid',
#units='inches')
#q = ax.quiver(x, y, z, u, v, w, length=0.1, cmap='Reds', lw=2)
#q.set_array(np.random.rand(np.prod(x.shape)))
Q.set_array(np.random.rand(np.prod(
x.shape))) # may need this? BJD 22.4.2021
#plt.show()
#qk = ax.quiverkey(Q, 0.9, 0.9, 5, r'$1 \frac{m}{s}$', labelpos='E',
#coordinates='figure')
#Q = hf.quiver(X1[::10, ::10], Y1[::10, ::10], U[::10, ::10], V[::10, ::10], units='width',
#pivot='mid', scale=0.1, headwidth=7)
#ax1.quiver(X, Y, u, v, color, alpha = 0.8) # from Color_Quiver_Plot.py
#qk = hf.quiverkey(Q, 0.9, 0.9, 5, r'$1 \frac{m}{s}$', labelpos='E',
#coordinates='figure')
#hf.scatter(X1[::10, ::10], Y1[::10, ::10], color='r', s=5)
#hf.scatter(X1[::10, ::10], Y1[::10, ::10], color='c', alpha = 0.8)
#hf.scatter(X1[::10, ::10], Y1[::10, ::10], color='c', s=0)
#ax.scatter(X1[::10, ::10], Y1[::10, ::10], Z1[::10, ::10], color='c', s=0)
ax.scatter(X1[::10, ::10, ::10],
Y1[::10, ::10, ::10],
Z1[::10, ::10, ::10],
color='c',
s=0)
plt.tight_layout()
plt.savefig(
'/home/brendan/software/tf2-model-g/plots/3D_video37/3D_video_velocity_'
+ str(c1) + '.png')
def self_stabilizing_soliton_2D():
params = {
"A": 4.2,
"B": 18,
"k2": 1.0,
"k-2": 0.2,
"k5": 0.9,
"D_G": 1.0,
"D_X": 1.0,
"D_Y": 2.0,
}
x = np.linspace(-16, 16, 256)
dx = x[1] - x[0]
x, y = np.meshgrid(x, x)
r2 = x * x + y * y
model_g = ModelG(
-np.exp(-0.1 * r2) * 1.0,
np.exp(-r2) * 0.01,
np.exp(-r2) * 0.01 + bl_noise(x.shape) * 0.02,
dx,
0.1 * dx,
params,
)
def get_data():
G, X, Y = model_g.numpy()
x_scale = 0.2
y_scale = 0.1
return (
G[64],
X[64] * x_scale,
Y[64] * y_scale,
)
G, X, Y = get_data()
plots = []
plots.extend(pylab.plot(x[0], G))
plots.extend(pylab.plot(x[0], X))
plots.extend(pylab.plot(x[0], Y))
pylab.ylim(-0.03, 0.03)
def update(frame):
for _ in range(5):
model_g.step()
G, X, Y = get_data()
plots[0].set_ydata(G)
plots[1].set_ydata(X)
plots[2].set_ydata(Y)
return plots
FuncAnimation(pylab.gcf(),
update,
frames=range(100),
init_func=lambda: plots,
blit=True,
repeat=True,
interval=20)
pylab.show()
G, X, Y = model_g.numpy()
pylab.imshow(Y)
pylab.show()
def random_3D():
r = np.random.randn
params = {
"A": 2 + r() * 0.1,
"B": 10 + r(),
"k2": 1.0 + 0.1 * r(),
"k-2": 0.1 + 0.01 * r(),
"k5": 0.9 + 0.1 * r(),
"D_G": 1.0,
"D_X": 1.0 + 0.1 * r(),
"D_Y": 2.0 + 0.1 * r(),
}
print(params)
x = np.linspace(-16, 16, 128)
dx = x[1] - x[0]
x, y, z = np.meshgrid(x, x, x)
def source_G(t):
center = np.exp(-0.5 * (t - 20)**2) * 10
gradient = (1 + np.tanh(t - 40)) * 0.0005
print("t = {}\tcenter potential = {}\tx-gradient = {}".format(
t, center, gradient))
return -np.exp(-0.5 * (x * x + y * y + z * z)) * center + x * gradient
source_functions = {
'G': source_G,
}
model_g = ModelG(
bl_noise(x.shape) * 0.01,
bl_noise(x.shape) * 0.01,
bl_noise(x.shape) * 0.01,
dx,
params,
source_functions=source_functions,
)
def get_data():
G, X, Y = model_g.numpy()
x_scale = 0.1
y_scale = 0.1
return (
G[64, 64],
X[64, 64] * x_scale,
Y[64, 64] * y_scale,
)
G, X, Y = get_data()
plots = []
plots.extend(pylab.plot(z[0, 0], G))
plots.extend(pylab.plot(z[0, 0], X))
plots.extend(pylab.plot(z[0, 0], Y))
pylab.ylim(-0.5, 0.5)
def update(frame):
model_g.step()
G, X, Y = get_data()
plots[0].set_ydata(G)
plots[1].set_ydata(X)
plots[2].set_ydata(Y)
return plots
FuncAnimation(pylab.gcf(),
update,
frames=range(100),
init_func=lambda: plots,
blit=True,
repeat=True,
interval=20)
pylab.show()
G, X, Y = model_g.numpy()
plots = [pylab.imshow(X[64])]
def update(frame):
model_g.step()
G, X, Y = model_g.numpy()
plots[0].set_data(X[64])
return plots
FuncAnimation(pylab.gcf(),
update,
frames=range(100),
init_func=lambda: plots,
blit=True,
repeat=True,
interval=20)
pylab.show()
fig = pylab.figure()
ax = fig.add_subplot(111, projection='3d')
G, X, Y = model_g.numpy()
m = X.max() - (X.max() - X.min()) * 0.3
points = []
for _ in range(1000000):
px = np.random.randint(x.shape[0])
py = np.random.randint(y.shape[1])
pz = np.random.randint(z.shape[2])
c = X[px, py, pz]
if c > m:
points.append((px, py, pz, c))
if len(points) > 20000:
break
xs, ys, zs, cs = zip(*points)
ax.scatter3D(xs, ys, zs, c=cs)
pylab.show()
def random_2D():
r = np.random.randn
params = {
"A": 2 + r() * 0.1,
"B": 10 + r(),
"k2": 1.0 + 0.1 * r(),
"k-2": 0.1 + 0.01 * r(),
"k5": 0.9 + 0.1 * r(),
"D_G": 1.0,
"D_X": 1.0 + 0.1 * r(),
"D_Y": 2.0 + 0.1 * r(),
}
print(params)
x = np.linspace(-16, 16, 256)
dx = x[1] - x[0]
x, y = np.meshgrid(x, x)
def source_G(t):
center = np.exp(-0.5 * (t - 20)**2) * 10
gradient = (1 + np.tanh(t - 40)) * 0.0005
print("t = {}\tcenter potential = {}\tx-gradient = {}".format(
t, center, gradient))
return -np.exp(-0.5 * (x * x + y * y)) * center + x * gradient
source_functions = {
'G': source_G,
}
model_g = ModelG(
bl_noise(x.shape) * 0.01,
bl_noise(x.shape) * 0.01,
bl_noise(x.shape) * 0.01,
dx,
0.1 * dx,
params,
source_functions=source_functions,
)
def get_data():
G, X, Y = model_g.numpy()
x_scale = 0.1
y_scale = 0.1
return (
G[64],
X[64] * x_scale,
Y[64] * y_scale,
)
G, X, Y = get_data()
plots = []
plots.extend(pylab.plot(x[0], G))
plots.extend(pylab.plot(x[0], X))
plots.extend(pylab.plot(x[0], Y))
pylab.ylim(-0.5, 0.5)
def update(frame):
model_g.step()
G, X, Y = get_data()
plots[0].set_ydata(G)
plots[1].set_ydata(X)
plots[2].set_ydata(Y)
return plots
FuncAnimation(pylab.gcf(),
update,
frames=range(100),
init_func=lambda: plots,
blit=True,
repeat=True,
interval=20)
pylab.show()
G, X, Y = model_g.numpy()
plots = [pylab.imshow(X)]
def update(frame):
model_g.step()
G, X, Y = model_g.numpy()
plots[0].set_data(X)
return plots
FuncAnimation(pylab.gcf(),
update,
frames=range(100),
init_func=lambda: plots,
blit=True,
repeat=True,
interval=20)
pylab.show()