one, 3D picture

Create a 3D picture in Matploylib. The first thing to do is to create AXES3D class

from mpl_toolkits.mplot3d.axes3d import Axes3D

1. Draw the surface

import matplotlib.pyplot as plt
from matplotlib import *
from numpy import *
from math import pi
from mpl_toolkits.mplot3d.axes3d import Axes3D
alpha = 0.7
phi_ext = 2 * pi * 0.5

def flux_qubit_potential(phi_m, phi_p):
    return 2 + alpha - 2 * cos(phi_p)*cos(phi_m) - alpha * cos(phi_ext - 2*phi_p)

phi_m = linspace(0, 2*pi, 100)
phi_p = linspace(0, 2*pi, 100)
X,Y = meshgrid(phi_p, phi_m)
Z = flux_qubit_potential(X, Y).T
fig = plt.figure(figsize=(14,6))

# `ax` is a 3D-aware axis instance because of the projection='3d' keyword argument to add_subplot
ax = fig.add_subplot(1, 2, 1, projection='3d')

p = ax.plot_surface(X, Y, Z, rstride=4, cstride=4, linewidth=0)

# surface_plot with color grading and color bar
ax = fig.add_subplot(1, 2, 2, projection='3d')
p = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm, linewidth=0, antialiased=False)
cb = fig.colorbar(p, shrink=0.5)
fig

2. Draw a wire frame

fig = plt.figure(figsize=(8,6))

ax = fig.add_subplot(1, 1, 1, projection='3d')

p = ax.plot_wireframe(X, Y, Z, rstride=4, cstride=4)
fig

3. Draw the projection contour

fig = plt.figure(figsize=(8,6))

ax = fig.add_subplot(1,1,1, projection='3d')

ax.plot_surface(X, Y, Z, rstride=4, cstride=4, alpha=0.25)
cset = ax.contour(X, Y, Z, zdir='z', offset=-pi, cmap=cm.coolwarm)
cset = ax.contour(X, Y, Z, zdir='x', offset=-pi, cmap=cm.coolwarm)
cset = ax.contour(X, Y, Z, zdir='y', offset=3*pi, cmap=cm.coolwarm)

ax.set_xlim3d(-pi, 2*pi);
ax.set_ylim3d(0, 3*pi);
ax.set_zlim3d(-pi, 2*pi);
fig

4. Change view angle

view_initcan change the view angle and read two parameters:elevation and azimuthangle

fig = plt.figure(figsize=(12,6))

ax = fig.add_subplot(1,2,1, projection='3d')
ax.plot_surface(X, Y, Z, rstride=4, cstride=4, alpha=0.25)
ax.view_init(30, 45)

ax = fig.add_subplot(1,2,2, projection='3d')
ax.plot_surface(X, Y, Z, rstride=4, cstride=4, alpha=0.25)
ax.view_init(70, 30)

fig.tight_layout()

2, animation

The

FuncAnimationfunction can generate animation according to a series of diagrams. It has the following parameters:

fig: The canvas of the picture

func: The function of the update graph

init_func: The function of the initialization diagram

frame: The quantity of the figure

blit: Tell the animation function to update the change part:

def init():
    # setup figure

def update(frame_counter):
    # update figure for new frame

anim = animation.FuncAnimation(fig, update, init_func=init, frames=200, blit=True)

anim.save('animation.mp4', fps=30) # fps = frames per second

In order to use the animation characteristics, the module first loadsmatplotlib.animation：

from matplotlib import animation


# solve the ode problem of the double compound pendulum again

from scipy.integrate import odeint

g = 9.82; L = 0.5; m = 0.1

def dx(x, t):
    x1, x2, x3, x4 = x[0], x[1], x[2], x[3]

    dx1 = 6.0/(m*L**2) * (2 * x3 - 3 * cos(x1-x2) * x4)/(16 - 9 * cos(x1-x2)**2)
    dx2 = 6.0/(m*L**2) * (8 * x4 - 3 * cos(x1-x2) * x3)/(16 - 9 * cos(x1-x2)**2)
    dx3 = -0.5 * m * L**2 * ( dx1 * dx2 * sin(x1-x2) + 3 * (g/L) * sin(x1))
    dx4 = -0.5 * m * L**2 * (-dx1 * dx2 * sin(x1-x2) + (g/L) * sin(x2))
    return [dx1, dx2, dx3, dx4]

x0 = [pi/2, pi/2, 0, 0]  # initial state
t = linspace(0, 10, 250) # time coordinates
x = odeint(dx, x0, t)    # solve the ODE problem

Movement of double -oriented sports animation:

fig, ax = plt.subplots(figsize=(5,5))

ax.set_ylim([-1.5, 0.5])
ax.set_xlim([1, -1])

pendulum1, = ax.plot([], [], color="red", lw=2)
pendulum2, = ax.plot([], [], color="blue", lw=2)

def init():
    pendulum1.set_data([], [])
    pendulum2.set_data([], [])

def update(n): 
    # n = frame counter
    # calculate the positions of the pendulums
    x1 = + L * sin(x[n, 0])
    y1 = - L * cos(x[n, 0])
    x2 = x1 + L * sin(x[n, 1])
    y2 = y1 - L * cos(x[n, 1])

    # update the line data
    pendulum1.set_data([0 ,x1], [0 ,y1])
    pendulum2.set_data([x1,x2], [y1,y2])

anim = animation.FuncAnimation(fig, update, init_func=init, frames=len(t), blit=True)

# anim.save can be called in a few different ways, some which might or might not work
# on different platforms and with different versions of matplotlib and video encoders
#anim.save('animation.mp4', fps=20, extra_args=['-vcodec', 'libx264'], writer=animation.FFMpegWriter())
#anim.save('animation.mp4', fps=20, extra_args=['-vcodec', 'libx264'])
#anim.save('animation.mp4', fps=20, writer="ffmpeg", codec="libx264")
anim.save('animation.mp4', fps=20, writer="avconv", codec="libx264")

plt.close(fig)

In order to generate animation, you need to install libav-time

sudo apt-get install libav-tools

Run: AVPlay Animation.mp4

3, backend

MATPLOTLIB has a lot of back end for rendering pictures:

print(matplotlib.rcsetup.all_backends)

['GTK', 'GTKAgg', 'GTKCairo', 'MacOSX', 'Qt4Agg', 'TkAgg', 'WX', 'WXAgg', 'CocoaAgg', 'GTK3Cairo', 'GTK3Agg', 'WebAgg', 'agg', 'cairo', 'emf', 'gdk', 'pdf', 'pgf', 'ps', 'svg', 'template']

The default back end is AGG, which is suitable for generating grating maps, such as PNG.

In general, you do n’t need to switch the back end, but if you want to generate a high -definition vector, you can switch to PDF or GTKCAIIRO.

1. Use SVG back end to generate SVG pictures

# RESTART THE NOTEBOOK: the matplotlib backend can only be selected before pylab is imported!
# (e.g. Kernel > Restart)

import matplotlib
matplotlib.use('svg')
import matplotlib.pylab as plt
import numpy
from IPython.display import Image, SVG

# Now we are using the svg backend to produce SVG vector graphics
fig, ax = plt.subplots()
t = numpy.linspace(0, 10, 100)
ax.plot(t, numpy.cos(t)*numpy.sin(t))
plt.savefig("test.svg")

# Show the produced SVG file. 
SVG(filename="test.svg")

2. Interactive back end

When using the interactive back end, you need to callplt.show()can the picture be displayed.

# RESTART THE NOTEBOOK: the matplotlib backend can only be selected before pylab is imported!
# (e.g. Kernel > Restart)

import matplotlib
matplotlib.use('Qt4Agg') # or for example MacOSX
import matplotlib.pylab as plt
import numpy

# Now, open an interactive plot window with the Qt4Agg backend
fig, ax = plt.subplots()
t = numpy.linspace(0, 10, 100)
ax.plot(t, numpy.cos(t)*numpy.sin(t))
plt.show()