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from pandas import *
from matplotlib import animation
import numpy as np
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import sys
sys.path.append('C:\Python27\Lib\site-packages\JSAnimation')
from JSAnimation.IPython_display import display_animation
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"""
This example shows how to use a path patch to draw a bunch of
rectangles for an animated histogram
"""
from JSAnimation import IPython_display
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as patches
import matplotlib.path as path
import matplotlib.animation as animation
fig = plt.figure()
ax = fig.add_subplot(111)
# histogram our data with numpy
data = np.random.randn(1000)
n, bins = np.histogram(data, 100)
# get the corners of the rectangles for the histogram
left = np.array(bins[:-1])
right = np.array(bins[1:])
bottom = np.zeros(len(left))
top = bottom + n
nrects = len(left)
# here comes the tricky part -- we have to set up the vertex and path
# codes arrays using moveto, lineto and closepoly
# for each rect: 1 for the MOVETO, 3 for the LINETO, 1 for the
# CLOSEPOLY; the vert for the closepoly is ignored but we still need
# it to keep the codes aligned with the vertices
nverts = nrects*(1+3+1)
verts = np.zeros((nverts, 2))
codes = np.ones(nverts, int) * path.Path.LINETO
codes[0::5] = path.Path.MOVETO
codes[4::5] = path.Path.CLOSEPOLY
verts[0::5,0] = left
verts[0::5,1] = bottom
verts[1::5,0] = left
verts[1::5,1] = top
verts[2::5,0] = right
verts[2::5,1] = top
verts[3::5,0] = right
verts[3::5,1] = bottom
barpath = path.Path(verts, codes)
patch = patches.PathPatch(barpath, facecolor='green', edgecolor='yellow', alpha=0.5)
ax.add_patch(patch)
ax.set_xlim(left[0], right[-1])
ax.set_ylim(bottom.min(), top.max())
def animate(i):
# simulate new data coming in
data = np.random.randn(1000)
n, bins = np.histogram(data, 100)
top = bottom + n
verts[1::5,1] = top
verts[2::5,1] = top
ani = animation.FuncAnimation(fig, animate, 100, repeat=False)
display_animation(ani, default_mode='once')
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"""
Matplotlib Animation Example
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!
"""
# First set up the figure, the axis, and the plot element we want to animate
fig = plt.figure()
ax = plt.axes(xlim=(0, 2), ylim=(-2, 2))
line, = ax.plot([], [], lw=2)
# initialization function: plot the background of each frame
def init():
line.set_data([], [])
return line,
# animation function. This is called sequentially
def animate(i):
x = np.linspace(0, 2, 1000)
y = np.sin(2 * np.pi * (x - 0.01 * i))
line.set_data(x, y)
return line,
# call the animator. blit=True means only re-draw the parts that have changed.
anim = animation.FuncAnimation(fig, animate, init_func=init,
frames=200, interval=20, blit=True)
# save the animation as an mp4. This requires ffmpeg or mencoder to be
# installed. The extra_args ensure that the x264 codec is used, so that
# the video can be embedded in html5. You may need to adjust this for
# your system: for more information, see
# http://matplotlib.sourceforge.net/api/animation_api.html
#anim.save('basic_animation.mp4', fps=30, extra_args=['-vcodec', 'libx264'])
display_animation(anim)
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"""
Animation of Elastic collisions with Gravity
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 scipy.spatial.distance import pdist, squareform
import matplotlib.pyplot as plt
import scipy.integrate as integrate
import matplotlib.animation as animation
class ParticleBox:
"""Orbits class
init_state is an [N x 4] array, where N is the number of particles:
[[x1, y1, vx1, vy1],
[x2, y2, vx2, vy2],
... ]
bounds is the size of the box: [xmin, xmax, ymin, ymax]
"""
def __init__(self,
init_state = [[1, 0, 0, -1],
[-0.5, 0.5, 0.5, 0.5],
[-0.5, -0.5, -0.5, 0.5]],
bounds = [-2, 2, -2, 2],
size = 0.04,
M = 0.05,
G = 9.8):
self.init_state = np.asarray(init_state, dtype=float)
self.M = M * np.ones(self.init_state.shape[0])
self.size = size
self.state = self.init_state.copy()
self.time_elapsed = 0
self.bounds = bounds
self.G = G
def step(self, dt):
"""step once by dt seconds"""
self.time_elapsed += dt
# update positions
self.state[:, :2] += dt * self.state[:, 2:]
# find pairs of particles undergoing a collision
D = squareform(pdist(self.state[:, :2]))
ind1, ind2 = np.where(D < 2 * self.size)
unique = (ind1 < ind2)
ind1 = ind1[unique]
ind2 = ind2[unique]
# update velocities of colliding pairs
for i1, i2 in zip(ind1, ind2):
# mass
m1 = self.M[i1]
m2 = self.M[i2]
# location vector
r1 = self.state[i1, :2]
r2 = self.state[i2, :2]
# velocity vector
v1 = self.state[i1, 2:]
v2 = self.state[i2, 2:]
# relative location & velocity vectors
r_rel = r1 - r2
v_rel = v1 - v2
# momentum vector of the center of mass
v_cm = (m1 * v1 + m2 * v2) / (m1 + m2)
# collisions of spheres reflect v_rel over r_rel
rr_rel = np.dot(r_rel, r_rel)
vr_rel = np.dot(v_rel, r_rel)
v_rel = 2 * r_rel * vr_rel / rr_rel - v_rel
# assign new velocities
self.state[i1, 2:] = v_cm + v_rel * m2 / (m1 + m2)
self.state[i2, 2:] = v_cm - v_rel * m1 / (m1 + m2)
# check for crossing boundary
crossed_x1 = (self.state[:, 0] < self.bounds[0] + self.size)
crossed_x2 = (self.state[:, 0] > self.bounds[1] - self.size)
crossed_y1 = (self.state[:, 1] < self.bounds[2] + self.size)
crossed_y2 = (self.state[:, 1] > self.bounds[3] - self.size)
self.state[crossed_x1, 0] = self.bounds[0] + self.size
self.state[crossed_x2, 0] = self.bounds[1] - self.size
self.state[crossed_y1, 1] = self.bounds[2] + self.size
self.state[crossed_y2, 1] = self.bounds[3] - self.size
self.state[crossed_x1 | crossed_x2, 2] *= -1
self.state[crossed_y1 | crossed_y2, 3] *= -1
# add gravity
self.state[:, 3] -= self.M * self.G * dt
#------------------------------------------------------------
# set up initial state
np.random.seed(0)
init_state = -0.5 + np.random.random((50, 4))
init_state[:, :2] *= 3.9
box = ParticleBox(init_state, size=0.04)
dt = 1. / 30 # 30fps
#------------------------------------------------------------
# set up figure and animation
fig = plt.figure()
fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
ax = fig.add_subplot(111, aspect='equal', autoscale_on=False,
xlim=(-3.2, 3.2), ylim=(-2.4, 2.4))
# particles holds the locations of the particles
particles, = ax.plot([], [], 'bo', ms=6)
# rect is the box edge
rect = plt.Rectangle(box.bounds[::2],
box.bounds[1] - box.bounds[0],
box.bounds[3] - box.bounds[2],
ec='none', lw=2, fc='none')
ax.add_patch(rect)
def init():
"""initialize animation"""
global box, rect
particles.set_data([], [])
rect.set_edgecolor('none')
return particles, rect
def animate(i):
"""perform animation step"""
global box, rect, dt, ax, fig
box.step(dt)
ms = int(fig.dpi * 2 * box.size * fig.get_figwidth()
/ np.diff(ax.get_xbound())[0])
# update pieces of the animation
rect.set_edgecolor('k')
particles.set_data(box.state[:, 0], box.state[:, 1])
particles.set_markersize(ms)
return particles, rect
ani = animation.FuncAnimation(fig, animate, frames=600,
interval=10, blit=True, init_func=init)
# save the animation as an mp4. This requires ffmpeg or mencoder to be
# installed. The extra_args ensure that the x264 codec is used, so that
# the video can be embedded in html5. You may need to adjust this for
# your system: for more information, see
# http://matplotlib.sourceforge.net/api/animation_api.html
#ani.save('particle_box.mp4', fps=30, extra_args=['-vcodec', 'libx264'])
display_animation(ani)
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!git add "Central Limit Theroem.ipynb"
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!git commit
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