Python 中由于未知原因缺少 Matplotlib 图的标题
Matplotlib plot's title is missing for unknown reason in Python
谁能告诉我这段代码有什么问题？它来自 https://jakevdp.github.io/blog/2012/09/05/quantum-python/ 。
里面的一切都成功了除了情节的标题。我想不通。
它应该是这样的
但是当代码是运行时，它会这样
这是给出的代码：-
"""
General Numerical Solver for the 1D Time-Dependent Schrodinger's equation.
author: Jake Vanderplas
email: vanderplas@astro.washington.edu
website: http://jakevdp.github.com
license: BSD
Please feel free to use and modify this, but keep the above information. Thanks!
"""
import numpy as np
from matplotlib import pyplot as pl
from matplotlib import animation
from scipy.fftpack import fft,ifft
class Schrodinger(object):
"""
Class which implements a numerical solution of the time-dependent
Schrodinger equation for an arbitrary potential
"""
def __init__(self, x, psi_x0, V_x,
k0 = None, hbar=1, m=1, t0=0.0):
"""
Parameters
----------
x : array_like, float
length-N array of evenly spaced spatial coordinates
psi_x0 : array_like, complex
length-N array of the initial wave function at time t0
V_x : array_like, float
length-N array giving the potential at each x
k0 : float
the minimum value of k. Note that, because of the workings of the
fast fourier transform, the momentum wave-number will be defined
in the range
k0 < k < 2*pi / dx
where dx = x[1]-x[0]. If you expect nonzero momentum outside this
range, you must modify the inputs accordingly. If not specified,
k0 will be calculated such that the range is [-k0,k0]
hbar : float
value of planck's constant (default = 1)
m : float
particle mass (default = 1)
t0 : float
initial tile (default = 0)
"""
# Validation of array inputs
self.x, psi_x0, self.V_x = map(np.asarray, (x, psi_x0, V_x))
N = self.x.size
assert self.x.shape == (N,)
assert psi_x0.shape == (N,)
assert self.V_x.shape == (N,)
# Set internal parameters
self.hbar = hbar
self.m = m
self.t = t0
self.dt_ = None
self.N = len(x)
self.dx = self.x[1] - self.x[0]
self.dk = 2 * np.pi / (self.N * self.dx)
# set momentum scale
if k0 == None:
self.k0 = -0.5 * self.N * self.dk
else:
self.k0 = k0
self.k = self.k0 + self.dk * np.arange(self.N)
self.psi_x = psi_x0
self.compute_k_from_x()
# variables which hold steps in evolution of the
self.x_evolve_half = None
self.x_evolve = None
self.k_evolve = None
# attributes used for dynamic plotting
self.psi_x_line = None
self.psi_k_line = None
self.V_x_line = None
def _set_psi_x(self, psi_x):
self.psi_mod_x = (psi_x * np.exp(-1j * self.k[0] * self.x)
* self.dx / np.sqrt(2 * np.pi))
def _get_psi_x(self):
return (self.psi_mod_x * np.exp(1j * self.k[0] * self.x)
* np.sqrt(2 * np.pi) / self.dx)
def _set_psi_k(self, psi_k):
self.psi_mod_k = psi_k * np.exp(1j * self.x[0]
* self.dk * np.arange(self.N))
def _get_psi_k(self):
return self.psi_mod_k * np.exp(-1j * self.x[0] *
self.dk * np.arange(self.N))
def _get_dt(self):
return self.dt_
def _set_dt(self, dt):
if dt != self.dt_:
self.dt_ = dt
self.x_evolve_half = np.exp(-0.5 * 1j * self.V_x
/ self.hbar * dt )
self.x_evolve = self.x_evolve_half * self.x_evolve_half
self.k_evolve = np.exp(-0.5 * 1j * self.hbar /
self.m * (self.k * self.k) * dt)
psi_x = property(_get_psi_x, _set_psi_x)
psi_k = property(_get_psi_k, _set_psi_k)
dt = property(_get_dt, _set_dt)
def compute_k_from_x(self):
self.psi_mod_k = fft(self.psi_mod_x)
def compute_x_from_k(self):
self.psi_mod_x = ifft(self.psi_mod_k)
def time_step(self, dt, Nsteps = 1):
"""
Perform a series of time-steps via the time-dependent
Schrodinger Equation.
Parameters
----------
dt : float
the small time interval over which to integrate
Nsteps : float, optional
the number of intervals to compute. The total change
in time at the end of this method will be dt * Nsteps.
default is N = 1
"""
self.dt = dt
if Nsteps > 0:
self.psi_mod_x *= self.x_evolve_half
for i in xrange(Nsteps - 1):
self.compute_k_from_x()
self.psi_mod_k *= self.k_evolve
self.compute_x_from_k()
self.psi_mod_x *= self.x_evolve
self.compute_k_from_x()
self.psi_mod_k *= self.k_evolve
self.compute_x_from_k()
self.psi_mod_x *= self.x_evolve_half
self.compute_k_from_x()
self.t += dt * Nsteps
######################################################################
# Helper functions for gaussian wave-packets
def gauss_x(x, a, x0, k0):
"""
a gaussian wave packet of width a, centered at x0, with momentum k0
"""
return ((a * np.sqrt(np.pi)) ** (-0.5)
* np.exp(-0.5 * ((x - x0) * 1. / a) ** 2 + 1j * x * k0))
def gauss_k(k,a,x0,k0):
"""
analytical fourier transform of gauss_x(x), above
"""
return ((a / np.sqrt(np.pi))**0.5
* np.exp(-0.5 * (a * (k - k0)) ** 2 - 1j * (k - k0) * x0))
######################################################################
# Utility functions for running the animation
def theta(x):
"""
theta function :
returns 0 if x<=0, and 1 if x>0
"""
x = np.asarray(x)
y = np.zeros(x.shape)
y[x > 0] = 1.0
return y
def square_barrier(x, width, height):
return height * (theta(x) - theta(x - width))
######################################################################
# Create the animation
# specify time steps and duration
dt = 0.01
N_steps = 50
t_max = 120
frames = int(t_max / float(N_steps * dt))
# specify constants
hbar = 1.0 # planck's constant
m = 1.9 # particle mass
# specify range in x coordinate
N = 2 ** 11
dx = 0.1
x = dx * (np.arange(N) - 0.5 * N)
# specify potential
V0 = 1.5
L = hbar / np.sqrt(2 * m * V0)
a = 3 * L
x0 = -60 * L
V_x = square_barrier(x, a, V0)
V_x[x < -98] = 1E6
V_x[x > 98] = 1E6
# specify initial momentum and quantities derived from it
p0 = np.sqrt(2 * m * 0.2 * V0)
dp2 = p0 * p0 * 1./80
d = hbar / np.sqrt(2 * dp2)
k0 = p0 / hbar
v0 = p0 / m
psi_x0 = gauss_x(x, d, x0, k0)
# define the Schrodinger object which performs the calculations
S = Schrodinger(x=x,
psi_x0=psi_x0,
V_x=V_x,
hbar=hbar,
m=m,
k0=-28)
######################################################################
# Set up plot
fig = pl.figure()
# plotting limits
xlim = (-100, 100)
klim = (-5, 5)
# top axes show the x-space data
ymin = 0
ymax = V0
ax1 = fig.add_subplot(211, xlim=xlim,
ylim=(ymin - 0.2 * (ymax - ymin),
ymax + 0.2 * (ymax - ymin)))
psi_x_line, = ax1.plot([], [], c='r', label=r'$|\psi(x)|$')
V_x_line, = ax1.plot([], [], c='k', label=r'$V(x)$')
center_line = ax1.axvline(0, c='k', ls=':',
label = r"$x_0 + v_0t$")
title = ax1.set_title("")
ax1.legend(prop=dict(size=12))
ax1.set_xlabel('$x$')
ax1.set_ylabel(r'$|\psi(x)|$')
# bottom axes show the k-space data
ymin = abs(S.psi_k).min()
ymax = abs(S.psi_k).max()
ax2 = fig.add_subplot(212, xlim=klim,
ylim=(ymin - 0.2 * (ymax - ymin),
ymax + 0.2 * (ymax - ymin)))
psi_k_line, = ax2.plot([], [], c='r', label=r'$|\psi(k)|$')
p0_line1 = ax2.axvline(-p0 / hbar, c='k', ls=':', label=r'$\pm p_0$')
p0_line2 = ax2.axvline(p0 / hbar, c='k', ls=':')
mV_line = ax2.axvline(np.sqrt(2 * V0) / hbar, c='k', ls='--',
label=r'$\sqrt{2mV_0}$')
ax2.legend(prop=dict(size=12))
ax2.set_xlabel('$k$')
ax2.set_ylabel(r'$|\psi(k)|$')
V_x_line.set_data(S.x, S.V_x)
######################################################################
# Animate plot
def init():
psi_x_line.set_data([], [])
V_x_line.set_data([], [])
center_line.set_data([], [])
psi_k_line.set_data([], [])
title.set_text("")
return (psi_x_line, V_x_line, center_line, psi_k_line, title)
def animate(i):
S.time_step(dt, N_steps)
psi_x_line.set_data(S.x, 4 * abs(S.psi_x))
V_x_line.set_data(S.x, S.V_x)
center_line.set_data(2 * [x0 + S.t * p0 / m], [0, 1])
psi_k_line.set_data(S.k, abs(S.psi_k))
title.set_text("t = %.2f" % S.t)
return (psi_x_line, V_x_line, center_line, psi_k_line, title)
# call the animator. blit=True means only re-draw the parts that have changed.
anim = animation.FuncAnimation(fig, animate, init_func=init,
frames=frames, interval=30, blit=True)
# uncomment the following line to save the video in mp4 format. This
# requires either mencoder or ffmpeg to be installed on your system
#anim.save('schrodinger_barrier.mp4', fps=15, extra_args=['-vcodec', 'libx264'])
pl.show()
为了您的方便，我提到了我怀疑错误的代码行是行号 238,247,255,286,287,296,297
提前致谢
当 blit=False 时问题已解决，但它可能会减慢您的动画速度。
只是引用以前的回答：
“可能的解决方案是：
将标题放在坐标区内。
不要使用 blitting
参见：How to update plot title with matplotlib using animation?
您还需要安装 ffmpeg。 Whosebug 上还有其他答案可以帮助您完成该安装。但是对于这个脚本，这里是我推荐的你需要添加的新行，假设你使用的是 Windows:
pl.rcParams['animation.ffmpeg_path'] = r"PUT_YOUR_FULL_PATH_TO_FFMPEG_HERE\ffmpeg.exe"
Writer = animation.writers['ffmpeg']
然后将anim.save()行调整为：
anim.save('schrodinger_barrier.mp4', writer=Writer(fps=15, codec='libx264'))
谁能告诉我这段代码有什么问题？它来自 https://jakevdp.github.io/blog/2012/09/05/quantum-python/ 。 里面的一切都成功了除了情节的标题。我想不通。
它应该是这样的
但是当代码是运行时，它会这样
这是给出的代码：-
"""
General Numerical Solver for the 1D Time-Dependent Schrodinger's equation.
author: Jake Vanderplas
email: vanderplas@astro.washington.edu
website: http://jakevdp.github.com
license: BSD
Please feel free to use and modify this, but keep the above information. Thanks!
"""
import numpy as np
from matplotlib import pyplot as pl
from matplotlib import animation
from scipy.fftpack import fft,ifft
class Schrodinger(object):
"""
Class which implements a numerical solution of the time-dependent
Schrodinger equation for an arbitrary potential
"""
def __init__(self, x, psi_x0, V_x,
k0 = None, hbar=1, m=1, t0=0.0):
"""
Parameters
----------
x : array_like, float
length-N array of evenly spaced spatial coordinates
psi_x0 : array_like, complex
length-N array of the initial wave function at time t0
V_x : array_like, float
length-N array giving the potential at each x
k0 : float
the minimum value of k. Note that, because of the workings of the
fast fourier transform, the momentum wave-number will be defined
in the range
k0 < k < 2*pi / dx
where dx = x[1]-x[0]. If you expect nonzero momentum outside this
range, you must modify the inputs accordingly. If not specified,
k0 will be calculated such that the range is [-k0,k0]
hbar : float
value of planck's constant (default = 1)
m : float
particle mass (default = 1)
t0 : float
initial tile (default = 0)
"""
# Validation of array inputs
self.x, psi_x0, self.V_x = map(np.asarray, (x, psi_x0, V_x))
N = self.x.size
assert self.x.shape == (N,)
assert psi_x0.shape == (N,)
assert self.V_x.shape == (N,)
# Set internal parameters
self.hbar = hbar
self.m = m
self.t = t0
self.dt_ = None
self.N = len(x)
self.dx = self.x[1] - self.x[0]
self.dk = 2 * np.pi / (self.N * self.dx)
# set momentum scale
if k0 == None:
self.k0 = -0.5 * self.N * self.dk
else:
self.k0 = k0
self.k = self.k0 + self.dk * np.arange(self.N)
self.psi_x = psi_x0
self.compute_k_from_x()
# variables which hold steps in evolution of the
self.x_evolve_half = None
self.x_evolve = None
self.k_evolve = None
# attributes used for dynamic plotting
self.psi_x_line = None
self.psi_k_line = None
self.V_x_line = None
def _set_psi_x(self, psi_x):
self.psi_mod_x = (psi_x * np.exp(-1j * self.k[0] * self.x)
* self.dx / np.sqrt(2 * np.pi))
def _get_psi_x(self):
return (self.psi_mod_x * np.exp(1j * self.k[0] * self.x)
* np.sqrt(2 * np.pi) / self.dx)
def _set_psi_k(self, psi_k):
self.psi_mod_k = psi_k * np.exp(1j * self.x[0]
* self.dk * np.arange(self.N))
def _get_psi_k(self):
return self.psi_mod_k * np.exp(-1j * self.x[0] *
self.dk * np.arange(self.N))
def _get_dt(self):
return self.dt_
def _set_dt(self, dt):
if dt != self.dt_:
self.dt_ = dt
self.x_evolve_half = np.exp(-0.5 * 1j * self.V_x
/ self.hbar * dt )
self.x_evolve = self.x_evolve_half * self.x_evolve_half
self.k_evolve = np.exp(-0.5 * 1j * self.hbar /
self.m * (self.k * self.k) * dt)
psi_x = property(_get_psi_x, _set_psi_x)
psi_k = property(_get_psi_k, _set_psi_k)
dt = property(_get_dt, _set_dt)
def compute_k_from_x(self):
self.psi_mod_k = fft(self.psi_mod_x)
def compute_x_from_k(self):
self.psi_mod_x = ifft(self.psi_mod_k)
def time_step(self, dt, Nsteps = 1):
"""
Perform a series of time-steps via the time-dependent
Schrodinger Equation.
Parameters
----------
dt : float
the small time interval over which to integrate
Nsteps : float, optional
the number of intervals to compute. The total change
in time at the end of this method will be dt * Nsteps.
default is N = 1
"""
self.dt = dt
if Nsteps > 0:
self.psi_mod_x *= self.x_evolve_half
for i in xrange(Nsteps - 1):
self.compute_k_from_x()
self.psi_mod_k *= self.k_evolve
self.compute_x_from_k()
self.psi_mod_x *= self.x_evolve
self.compute_k_from_x()
self.psi_mod_k *= self.k_evolve
self.compute_x_from_k()
self.psi_mod_x *= self.x_evolve_half
self.compute_k_from_x()
self.t += dt * Nsteps
######################################################################
# Helper functions for gaussian wave-packets
def gauss_x(x, a, x0, k0):
"""
a gaussian wave packet of width a, centered at x0, with momentum k0
"""
return ((a * np.sqrt(np.pi)) ** (-0.5)
* np.exp(-0.5 * ((x - x0) * 1. / a) ** 2 + 1j * x * k0))
def gauss_k(k,a,x0,k0):
"""
analytical fourier transform of gauss_x(x), above
"""
return ((a / np.sqrt(np.pi))**0.5
* np.exp(-0.5 * (a * (k - k0)) ** 2 - 1j * (k - k0) * x0))
######################################################################
# Utility functions for running the animation
def theta(x):
"""
theta function :
returns 0 if x<=0, and 1 if x>0
"""
x = np.asarray(x)
y = np.zeros(x.shape)
y[x > 0] = 1.0
return y
def square_barrier(x, width, height):
return height * (theta(x) - theta(x - width))
######################################################################
# Create the animation
# specify time steps and duration
dt = 0.01
N_steps = 50
t_max = 120
frames = int(t_max / float(N_steps * dt))
# specify constants
hbar = 1.0 # planck's constant
m = 1.9 # particle mass
# specify range in x coordinate
N = 2 ** 11
dx = 0.1
x = dx * (np.arange(N) - 0.5 * N)
# specify potential
V0 = 1.5
L = hbar / np.sqrt(2 * m * V0)
a = 3 * L
x0 = -60 * L
V_x = square_barrier(x, a, V0)
V_x[x < -98] = 1E6
V_x[x > 98] = 1E6
# specify initial momentum and quantities derived from it
p0 = np.sqrt(2 * m * 0.2 * V0)
dp2 = p0 * p0 * 1./80
d = hbar / np.sqrt(2 * dp2)
k0 = p0 / hbar
v0 = p0 / m
psi_x0 = gauss_x(x, d, x0, k0)
# define the Schrodinger object which performs the calculations
S = Schrodinger(x=x,
psi_x0=psi_x0,
V_x=V_x,
hbar=hbar,
m=m,
k0=-28)
######################################################################
# Set up plot
fig = pl.figure()
# plotting limits
xlim = (-100, 100)
klim = (-5, 5)
# top axes show the x-space data
ymin = 0
ymax = V0
ax1 = fig.add_subplot(211, xlim=xlim,
ylim=(ymin - 0.2 * (ymax - ymin),
ymax + 0.2 * (ymax - ymin)))
psi_x_line, = ax1.plot([], [], c='r', label=r'$|\psi(x)|$')
V_x_line, = ax1.plot([], [], c='k', label=r'$V(x)$')
center_line = ax1.axvline(0, c='k', ls=':',
label = r"$x_0 + v_0t$")
title = ax1.set_title("")
ax1.legend(prop=dict(size=12))
ax1.set_xlabel('$x$')
ax1.set_ylabel(r'$|\psi(x)|$')
# bottom axes show the k-space data
ymin = abs(S.psi_k).min()
ymax = abs(S.psi_k).max()
ax2 = fig.add_subplot(212, xlim=klim,
ylim=(ymin - 0.2 * (ymax - ymin),
ymax + 0.2 * (ymax - ymin)))
psi_k_line, = ax2.plot([], [], c='r', label=r'$|\psi(k)|$')
p0_line1 = ax2.axvline(-p0 / hbar, c='k', ls=':', label=r'$\pm p_0$')
p0_line2 = ax2.axvline(p0 / hbar, c='k', ls=':')
mV_line = ax2.axvline(np.sqrt(2 * V0) / hbar, c='k', ls='--',
label=r'$\sqrt{2mV_0}$')
ax2.legend(prop=dict(size=12))
ax2.set_xlabel('$k$')
ax2.set_ylabel(r'$|\psi(k)|$')
V_x_line.set_data(S.x, S.V_x)
######################################################################
# Animate plot
def init():
psi_x_line.set_data([], [])
V_x_line.set_data([], [])
center_line.set_data([], [])
psi_k_line.set_data([], [])
title.set_text("")
return (psi_x_line, V_x_line, center_line, psi_k_line, title)
def animate(i):
S.time_step(dt, N_steps)
psi_x_line.set_data(S.x, 4 * abs(S.psi_x))
V_x_line.set_data(S.x, S.V_x)
center_line.set_data(2 * [x0 + S.t * p0 / m], [0, 1])
psi_k_line.set_data(S.k, abs(S.psi_k))
title.set_text("t = %.2f" % S.t)
return (psi_x_line, V_x_line, center_line, psi_k_line, title)
# call the animator. blit=True means only re-draw the parts that have changed.
anim = animation.FuncAnimation(fig, animate, init_func=init,
frames=frames, interval=30, blit=True)
# uncomment the following line to save the video in mp4 format. This
# requires either mencoder or ffmpeg to be installed on your system
#anim.save('schrodinger_barrier.mp4', fps=15, extra_args=['-vcodec', 'libx264'])
pl.show()
为了您的方便，我提到了我怀疑错误的代码行是行号 238,247,255,286,287,296,297
提前致谢
当 blit=False 时问题已解决，但它可能会减慢您的动画速度。
只是引用以前的回答：
“可能的解决方案是：
将标题放在坐标区内。
不要使用 blitting
参见：How to update plot title with matplotlib using animation?
您还需要安装 ffmpeg。 Whosebug 上还有其他答案可以帮助您完成该安装。但是对于这个脚本，这里是我推荐的你需要添加的新行，假设你使用的是 Windows:
pl.rcParams['animation.ffmpeg_path'] = r"PUT_YOUR_FULL_PATH_TO_FFMPEG_HERE\ffmpeg.exe"
Writer = animation.writers['ffmpeg']
然后将anim.save()行调整为：
anim.save('schrodinger_barrier.mp4', writer=Writer(fps=15, codec='libx264'))