File:QHO-Fockstate0123-animation-color.gif

#!/usr/bin/python
# -*- coding: utf8 -*-

from math import *
import matplotlib.pyplot as plt
from matplotlib import animation, colors, colorbar
import numpy as np
from numpy.polynomial.hermite import Hermite
import colorsys
from scipy.interpolate import interp1d
import os, sys

plt.rc('path', snap=False)
plt.rc('mathtext', default='regular')

# image settings
fname = 'QHO-Fockstate0123-animation-color'
width, height = 300, 300
ml, mr, mt, mb, mh, mc = 35, 19, 22, 45, 12, 6
x0, x1 = -4, 4
y0, y1 = 0.0, 0.7
nframes = 3 * 5 * 7
fps = 20

# physics settings
omega = 2 * pi

def color(phase):
    hue = (phase / (2*pi) + 2./3.) % 1
    light = interp1d([0, 1, 2, 3, 4, 5, 6], # adjust lightness
                     [0.64, 0.5, 0.55, 0.48, 0.70, 0.57, 0.64])(6 * hue)
    hls = (hue, light, 1.0) # maximum saturation
    rgb = colorsys.hls_to_rgb(*hls)
    return rgb

def animate(nframe):
    print str(nframe) + ' ',; sys.stdout.flush()
    t = 2.0 * float(nframe) / nframes
    
    for nfock in range(4):
        ax = axi[3-nfock]
        fig.sca(ax)
        ax.cla()
        ax.grid(True)
        ax.axis((x0, x1, y0, y1))
        if nfock != 0:
            ax.set_xticklabels([])
        plt.yticks([0.0, 0.2, 0.4, 0.6], ['0.0', '0.2', '0.4', ''])
        
        # dummy plot for legend
        ax.plot(0, 0, color=(1,1,1,0), label=r'$\vert{}\rangle$'.format(nfock))
        
        # Definition of Fock-states in terms of Hermite functions:
        # https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator
        psi_fock = np.eye(1, nfock+1, nfock).flatten()
        a_hermite = [psi_fock[n] * pi**-0.25 / sqrt(2.**n*factorial(n))
                        * e**(-1j * omega * (n+0.5) * t) for n in range(1+nfock)]
        # doc: http://docs.scipy.org/doc/numpy/reference/generated/numpy.polynomial.hermite.Hermite.html
        H = Hermite(a_hermite)
        
        x = np.linspace(x0, x1, int(ceil(1+w_px)))
        x2 = x - px_w/2.
        psi_x = np.exp(-x**2 / 2.0) * H(x)
        phi_x = np.angle(np.exp(-(x2)**2 / 2.0) * H(x2))
        y = np.abs(psi_x)**2
        
        # plot color filling
        for x_, phi_, y_ in zip(x, phi_x, y):
            ax.plot([x_, x_], [0, y_], color=color(phi_), lw=2*0.72)
        
        ax.plot(x, y, lw=2, color='black')
        leg = ax.legend(handlelength=0, handletextpad=0, borderpad=0.1,
                  borderaxespad=0.35, loc='upper left', fontsize=17)
        leg.get_frame().set_linewidth(0.0)

# create figure and axes
plt.close('all')
fig, axi = plt.subplots(4, sharey=True,
                        figsize=(width/100., height/100.))
bounds = [float(ml)/width, float(mb)/height,
          1.0 - float(mr+mc+mh)/width, 1.0 - float(mt)/height]
fig.subplots_adjust(left=bounds[0], bottom=bounds[1],
                    right=bounds[2], top=bounds[3], hspace=0)
w_px = width - (ml+mr+mc+mh) # plot width in pixels
px_w = float(x1 - x0) / w_px # width of one pixel in plot units

# axes labels
fig.text(0.5 + 0.5 * float(ml-mh-mc-mr)/width, 4./height,
         r'$x\ \ [(\hbar/(m\omega))^{1/2}]$', ha='center')
fig.text(5./width, 1.0, '$|\psi|^2$', va='top')

# colorbar for phase
cax = fig.add_axes([1.0 - float(mr+mc)/width, float(mb)/height,
                    float(mc)/width, 1.0 - float(mb+mt)/height])
cax.yaxis.set_tick_params(length=2)
cmap = colors.ListedColormap([color(phase) for phase in
                              np.linspace(0, 2*pi, 384, endpoint=False)])
norm = colors.Normalize(0, 2*pi)
cbar = colorbar.ColorbarBase(cax, cmap=cmap, norm=norm,
                    orientation='vertical', ticks=np.linspace(0, 2*pi, 3))
cax.set_yticklabels(['$0$', r'$\pi$', r'$2\pi$'], rotation=90)
fig.text(1.0 - 10./width, 1.0, '$arg(\psi)$', ha='right', va='top')

# start animation
if 0 != os.system('convert -version > ' +  os.devnull):
    print 'imagemagick not installed!'
    # warning: imagemagick produces somewhat jagged and therefore large gifs
    anim = animation.FuncAnimation(fig, animate, frames=nframes)
    anim.save(fname + '.gif', writer='imagemagick', fps=fps)
else:
    # unfortunately the matplotlib imagemagick backend does not support
    # options which are necessary to generate high quality output without
    # framewise color palettes. Therefore save all frames and convert then.
    if not os.path.isdir(fname):
        os.mkdir(fname)
    fnames = []
    
    for frame in range(nframes):
        animate(frame)
        imgname = os.path.join(fname, fname + '{:03d}'.format(frame) + '.png')
        fig.savefig(imgname)
        fnames.append(imgname)
    
    # compile optimized animation with ImageMagick
    cmd = 'convert -loop 0 -delay ' + str(100 / fps) + ' '
    cmd += ' '.join(fnames) # now create optimized palette from all frames
    cmd += r' \( -clone 0--1 \( -clone 0--1 -fill black -colorize 100% \) '
    cmd += '-append +dither -colors 255 -unique-colors '
    cmd += '-write mpr:colormap +delete \) +dither -map mpr:colormap '
    cmd += '-alpha activate -layers OptimizeTransparency '
    cmd += fname + '.gif'
    os.system(cmd)
    
    for fnamei in fnames:
        os.remove(fnamei)
    os.rmdir(fname)