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nonlinearssfm.py
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from solvers import PeriodicSim, PeriodicSim1D
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm, animation
import argparse
plt.rcParams['animation.ffmpeg_path'] = '/usr/bin/ffmpeg'
parser = argparse.ArgumentParser()
parser.add_argument('filename')
args = parser.parse_args()
def gauss(x, y):
return np.exp(-x * x - y * y)
def sqr_mod(x):
return x.real * x.real + x.imag * x.imag
def exactsol(x, y, t, a, m):
return (a / (a + 1.0j * t / m)) \
* np.exp(-(x * x + y * y) / (2 * (a + 1.0j * t / m)))
startX = -10
endX = 10
startY = -10
endY = 10
samples = 256
dx = (endX - startX) / samples
x = np.arange(startX, endX, dx)
xv, yv = np.meshgrid(x, x)
# *(1-(xv/5)**6*(yv/5)**6)
dt = 0.01
nframes = 200
fps = 12
t = dt * np.arange(1,nframes+1)
psi0 = 10*gauss(xv, yv)
alpha = 1
def Vlinear(x, y, wavefunction):
return (x*x + y*y)
def V(x, y, wavefunction):
return (x*x + y*y) + alpha*sqr_mod(wavefunction)
fftsim = PeriodicSim(psi0, xv, yv, 0.5, V)
fig, ax = plt.subplots()
im = ax.imshow(sqr_mod(fftsim.psi),
cmap=cm.viridis,
origin='lower',
extent=[startX, endX, startY, endY])
# fig, ax = plt.subplots(subplot_kw={'projection': '3d'})
# surf = ax.plot_surface(xv, yv, sqr_mod(diff), cmap=cm.viridis, antialiased=False)
fig.colorbar(im, ax=ax)
#plt.show()
def init():
return [im]
def animate_heatmap(frame):
fftsim.step(dt)
vmin = np.min(sqr_mod(fftsim.psi))
vmax = np.max(sqr_mod(fftsim.psi))
ax.set_title(f"t = {fftsim.t:.3f}")
im.set_data(sqr_mod(fftsim.psi))
im.set_clim(vmin, vmax)
return [im]
# print("animate function has been processed")
# def animate_surface_diff(frame):
# fftsim.step(dt)
# exactpsi = exactsol(xv, yv, t[frame], 0.5, 0.5)
# diff = exactpsi - fftsim.psi
# ax.clear()
# surf = ax.plot_surface(xv,
# yv,
# sqr_mod(diff),
# cmap=cm.viridis,
# antialiased=False)
# surf._facecolors2d = surf._facecolor3d
# surf._edgecolors2d = surf._facecolor3d
# return [surf]
# def animate_surface_fft(frame):
# fftsim.step(dt)
# ax.clear()
# surf = ax.plot_surface(xv,
# yv,
# sqr_mod(fftsim.psi),
# cmap=cm.viridis,
# antialiased=False)
# surf._facecolors2d = surf._facecolor3d
# surf._edgecolors2d = surf._edgecolor3d
# return [surf]
# def animate_surface_exact(frame):
# exactpsi = exactsol(xv, yv, t[frame], 0.5, 0.5)
# ax.clear()
# surf = ax.plot_surface(xv,
# yv,
# sqr_mod(exactpsi),
# cmap=cm.viridis,
# antialiased=False)
# surf._facecolors2d = surf._facecolor3d
# surf._edgecolors2d = surf._edgecolor3d
# return [surf]
anim = animation.FuncAnimation(fig,
animate_heatmap,
init_func=init,
frames=nframes,
blit=False)
FFwriter = animation.FFMpegWriter(fps=fps,
metadata={'copyright': 'Public Domain'})
anim.save(args.filename, writer=FFwriter)