[PYTHON] Create interactive 3D graphs on JupyterLab using matplotlib

1.First of all

• Interactive graphs are useful when you want to see the behavior of numbers.
• Also, when displaying a 3D graph, it is convenient to be able to change the viewing direction interactively.
• When I was using Jupyter notebook, I was able to create interactive graphs using a mechanism called ipywidget. However, I don't think Jupyter Lab supports it at this time.
• I didn't think there were many articles on JupyterLab that introduced such a mechanism, so I decided to post it.

2. Overview

• By using the widget mechanism of matplotlib, it is possible to create an interactive widget that is placed in Axes without depending on the GUI backend.

• The following is an excerpt from widget documentation.

Widgets that are designed to work for any of the GUI backends. All of these widgets require you to predefine a matplotlib.axes.Axes instance and pass that as the first arg.

• You can easily create a graph like this on JupyterLab. (This graph runs on the browser Jupyer Lab.)

3. Specific method

So, I will explain how to create a graph like the one above. In addition, I made the following on Jupyter Lab, but as I explained earlier, matplotlib.widget does not depend on GUI Backend, so the same result can be obtained not only on Jupyter notebook but also on Linux, Windows, Mac GUI. I think it will be. (I haven't tried it at hand)

(1) Import the required library

First, import the required libraries. You also need to set the backend to widget.

%matplotlib widget
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.widgets import Slider
import numpy as np

(2) Create data to be displayed as a sample

Here, as an example, let's draw a graph of $ z = x ^ 2 + 2y ^ 2 $.

x = y = np.arange(-20, 20, 0.5)
X, Y = np.meshgrid(x, y)
Z = X*X + 2 * Y*Y

(3) Create a figure

As you know, a figure is like a campus where you draw graphs with matplotlib. It is an image of putting Axes on the figure and plotting on it.

#Figure settings
fig = plt.figure(figsize=(5,5))

(4) Creating Axes

Next, create Axes on the figure.

• This time, we will create one Axes for plotting the 3D graph and two Axes for displaying the Slider.
• Any method is fine, but this time I tried using gridspec,
• By executing the code below, you can divide the figure into 20x20 as shown in the figure, and place the axes for 3D graph drawing on the 1st to 17th lines and the axes for Slider on the 18th and 19th lines, respectively. I will.

#Added 3D graph and Axes for Slider in the figure
axcolor = 'gold'
gs = fig.add_gridspec(20, 20)
ax1 = fig.add_subplot(gs[:17,:], projection='3d')
ax_slider_z = fig.add_subplot(gs[18,:], facecolor=axcolor)
ax_slider_xy = fig.add_subplot(gs[19,:], facecolor=axcolor)

(5) Slider settings

Next, create a Slider object. In the code below

• Create Sider objects called slider_z and slider_xy, and draw them on ax_slider_z and ax_slider_xy created above, respectively.
• Slider has a range of movement -180 to 180
• Set z0 (= 0) as the initial value of Slider
• Set delta (= 10) as the width of movement of the Slider

I am doing.

#Slider settings
z0 = 0
xy0 = 0
delta = 10
slider_z = Slider(ax_slider_z, 'z-axis', -180, 180, valinit=z0, valstep=delta)
slider_xy = Slider(ax_slider_xy, 'xy-axis', -180, 180, valinit=xy0, valstep=delta)

(6) After setting the initial value of the viewing angle of the 3D graph, display the 3D graph.

Next, set the initial values of the visible angles around the z-axis and around the xy plane of the 3D graph. By changing this value, you can move the viewing angle of the 3D graph.

#Set the initial value of the viewing direction of the 3D graph
ax1.view_init(elev=z0, azim=xy0)

#Display 3D graph
ax1.plot_surface(X, Y, Z)

(7) Create a callback function that is called when the Slider is moved

Next, create a callback function that will be called when you run Slider. Here, you can create a moving graph by specifying the viewing angle of the 3D graph and redrawing the graph.

#Callback function called when the Slider is moved
def view_change(val):

    sz = slider_z.val
    sxy = slider_xy.val
    ax1.view_init(elev=sxy, azim=sz)
    fig.canvas.draw_idle()    

(8) Callback function settings

Finally, set the Slider object to the callback function you just created.

slider_z.on_changed(view_change)
slider_xy.on_changed(view_change)
plt.show()

Now you can easily create a graph that works on JupyterLab! I also put gist in here, so please use it if you like. (Same as the one explained above ...)