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The iteration update very slow, n+=3 for each time only but my data has 10000 elements.Like, It tries to update every single frame n=1,n=2,n=3.. but the hist function is really power consuming. I don't know if there are any way I could skip frames like from n=1 go straight to n=500 and to n=1000.

import matplotlib.animation as animation
import numpy as np
import matplotlib.pyplot as plt
n=10000
def update(curr):
 if curr==n:
 a.event_source.stop()
 first_histogram.cla()
 sec_histogram.cla()
 thi_histogram.cla()
 for_histogram.cla() 
 first_histogram.hist(x1[:curr], bins=np.arange(-6,2,0.5))
 sec_histogram.hist(x2[:curr], bins=np.arange(-1,15,1))
 thi_histogram.hist(x3[:curr], bins=np.arange(2,22,1))
 for_histogram.hist(x4[:curr], bins=np.arange(13,21,1))
 first_histogram.set_title('n='.format(curr))
fig=plt.figure()
gspec=gridspec.GridSpec(2,2)
first_histogram=plt.subplot(gspec[0,0])
sec_histogram=plt.subplot(gspec[0,1])
thi_histogram=plt.subplot(gspec[1,0])
for_histogram=plt.subplot(gspec[1,1])
a = animation.FuncAnimation(fig,update,blit=True,interval=1,repeat=False)

How can I make it faster ? Thank you!

There are several things to note here.

blit=True is not useful when clearing the axes in between. It would either not take effect, or you would get wrong tick labels on the axes.
It would only be useful if the axes limits do not change from frame to frame. However in a normal histogram, where more and more data is animated, this would necessarily need to be the case, else your bars either grow out of the axes, or you do not see the low numbers at the start. As an alternative, you could plot a normalized histogram (i.e. a density plot).

Also, interval=1 is not useful. You will not be able to animate 4 subplots with a 1 millisecond frame rate on any normal system. Matplotlib is too slow for that. However, consider that the human brain can usually not resolve framerates above some 25 fps, i.e. 40 ms, anyways. That's probably the frame rate to aim at (although matplotlib may not achieve that)

So a way to set this up is simply via

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation

x1 = np.random.normal(-2.5, 1, 10000)

def update(curr):
 ax.clear()
 ax.hist(x1[:curr], bins=np.arange(-6,2,0.5))
 ax.set_title('n='.format(curr))

fig, ax = plt.subplots()
a = animation.FuncAnimation(fig, update, frames=len(x1), interval=40, repeat=False, blit=False)

plt.show()

If you feel like you want to arrive more quickly at the final number of items in the list, use less frames. E.g. for a 25 times faster animation, show only every 25th state,

a = animation.FuncAnimation(fig, update, frames=np.arange(0, len(x1)+1, 25),
 interval=40, repeat=False, blit=False)

This code runs with a framerate of 11 fps (interval of ~85 ms), so it's slower than specified, which in turn means, we could directly set interval=85.

In order to increase the frame rate one may use blitting.
For that, you will need to not update the axes limits at all. To optimize further you may precompute all the histograms to show. Note however that the axes limits should then not change, so we set them at the beginning, which leads to a different plot.

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation

x1 = np.random.normal(-2.5, 1, 10000)
bins = np.arange(-6,2,0.5)
hist = np.empty((len(x1), len(bins)-1))
for i in range(len(x1)):
 hist[i, :], _ = np.histogram(x1[:i], bins=bins) 

def update(i):
 for bar, y in zip(bars, hist[i,:]):
 bar.set_height(y)
 text.set_text('n='.format(i))
 return list(bars) + [text]

fig, ax = plt.subplots()
ax.set_ylim(0,hist.max()*1.05)
bars = ax.bar(bins[:-1], hist[0,:], width=np.diff(bins), align="edge")
text = ax.text(.99,.99, "", ha="right", va="top", transform=ax.transAxes)

ani = animation.FuncAnimation(fig, update, frames=len(x1), interval=1, repeat=False, blit=True)

plt.show()

Running this code give me a framerate of 215 fps, (4.6 ms per frame), so we could set the interval to 4.6 ms.