Data Visualization: Matplotlib and Mayavi

Bikash Santra

Research Scholar, Indian Statistical Institute, Kolkata

Plotting with Matplotlib

import matplotlib.pyplot as plt
# OR, from matplotlib import pyplot as plt
import numpy as np

# The inline is important for the notebook, so that plots are displayed in the notebook and not in a new window.
%matplotlib inline

1D Plotting

x = np.arange(-100,100,0.5) # Return evenly spaced values within a given interval
y = x**2
# print(x)

plt.plot(x,y)
plt.xlabel('X-axis')
plt.ylabel('Y-label')
plt.title('Test Plot')
plt.show()

x = np.linspace(0, 3, 20)
y = np.linspace(0, 9, 20)
plt.plot(x, y)

plt.plot(x, y, 'o')  # dot plot 

# Using default setting
X = np.linspace(-np.pi, np.pi, 256, endpoint=True)
C, S = np.cos(X), np.sin(X)

plt.plot(X, C)

plt.plot(X, S)

plt.show()

# Customized

X = np.linspace(-np.pi, np.pi, 256, endpoint=True)
C, S = np.cos(X), np.sin(X)


#------ Setting figure size -------------
# Create a figure of size 8x6 inches, 80 dots per inch
plt.figure(figsize=(8, 6), dpi=80)


#----- Changing colors and line widths -------
# Plot cosine with a blue continuous line of width 1 (pixels)
plt.plot(X, C, color="blue", linewidth=1.0, linestyle="-")
# Plot sine with a green continuous line of width 1 (pixels)
plt.plot(X, S, color="green", linewidth=1.0, linestyle="-")


#------- Setting limits -------
# Set x limits
plt.xlim(-4.0, 4.0)
# Set y limits
plt.ylim(-1.0, 1.0)


#-------- Setting ticks --------
# Set x ticks
plt.xticks(np.linspace(-4, 4, 9, endpoint=True))
# Set y ticks
plt.yticks(np.linspace(-1, 1, 5, endpoint=True))


#------- Saving figure in drive -------
# Save figure using 72 dots per inch
plt.savefig("exercise_2.png", dpi=72)


# Show result on screen
plt.show()

# More Customized

X = np.linspace(-np.pi, np.pi, 256, endpoint=True)
C, S = np.cos(X), np.sin(X)


#------ Setting figure size -------------
# Create a figure of size 8x6 inches, 80 dots per inch
plt.figure(figsize=(8, 6), dpi=80)


#----- Changing colors and line widths -------     Adding a legend  ---------
# Plot cosine with a blue continuous line of width 1 (pixels)
plt.plot(X, C, color="blue", linewidth=1.0, linestyle="-", label = "Cosine")
# Plot sine with a green continuous line of width 1 (pixels)
plt.plot(X, S, color="green", linewidth=1.0, linestyle="-", label = "Sine")

plt.legend(loc='upper left')

#------- Setting limits -------
# Set x limits
plt.xlim(-4.0, 4.0)
# Set y limits
plt.ylim(-1.0, 1.0)


#-------- Setting ticks --------
# Set x ticks
plt.xticks(np.linspace(-4, 4, 9, endpoint=True))
# Set y ticks
plt.yticks(np.linspace(-1, 1, 5, endpoint=True))


#-------- Moving spines ----------------
ax = plt.gca()  # gca stands for 'get current axis'
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.spines['bottom'].set_position(('data',0))
ax.yaxis.set_ticks_position('left')
ax.spines['left'].set_position(('data',0))


#-------- Annotate some points -------------
t = 2 * np.pi / 3
plt.plot([t, t], [0, np.cos(t)], color='blue', linewidth=2.5, linestyle="--")
plt.scatter([t, ], [np.cos(t), ], 50, color='blue')

plt.annotate(r'$cos(\frac{2\pi}{3})=-\frac{1}{2}$',
             xy=(t, np.cos(t)), xycoords='data',
             xytext=(-90, -50), textcoords='offset points', fontsize=16,
             arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))

plt.plot([t, t],[0, np.sin(t)], color='red', linewidth=2.5, linestyle="--")
plt.scatter([t, ],[np.sin(t), ], 50, color='red')

plt.annotate(r'$sin(\frac{2\pi}{3})=\frac{\sqrt{3}}{2}$',
             xy=(t, np.sin(t)), xycoords='data',
             xytext=(+10, +30), textcoords='offset points', fontsize=16,
             arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))


#--------- Devil is in the details ------------
for label in ax.get_xticklabels() + ax.get_yticklabels():
    label.set_fontsize(16)
    label.set_bbox(dict(facecolor='white', edgecolor='None', alpha=0.65))
    
    
# Show result on screen
plt.show()

# Add label, title, legends

# Compute the x and y coordinates for points on sine and cosine curves
x = np.arange(0, 3 * np.pi, 0.1)
y_sin = np.sin(x)
y_cos = np.cos(x)

# Plot the points using matplotlib
plt.plot(x, y_sin)
plt.plot(x, y_cos)
plt.xlabel('x axis label')
plt.ylabel('y axis label')
plt.title('Sine and Cosine')
plt.legend(['Sine', 'Cosine'])
plt.show()

x = np.arange(1,101)
marks = np.random.randint(1,100,100)
marks1 = np.random.randint(1,100,100)

width = 0.5
plt.bar(x,marks)
plt.show()

plt.plot(x,marks,'*') # displaying points
plt.plot(x,marks1,'+')
plt.show()

Subplot

fig = plt.figure()
fig.subplots_adjust(bottom=0.025, left=0.025, top = 0.975, right=0.975)

plt.subplot(2, 1, 1)
plt.xticks(()), plt.yticks(())

plt.subplot(2, 3, 4)
plt.xticks(())
plt.yticks(())

plt.subplot(2, 3, 5)
plt.xticks(())
plt.yticks(())

plt.subplot(2, 3, 6)
plt.xticks(())
plt.yticks(())

plt.show()

# Compute the x and y coordinates for points on sine and cosine curves
x = np.arange(0, 3 * np.pi, 0.1)
y_sin = np.sin(x)
y_cos = np.cos(x)

# Set up a subplot grid that has height 2 and width 1,
# and set the first such subplot as active.
plt.subplot(2, 1, 1)

# Make the first plot
plt.plot(x, y_sin)
plt.title('Sine')

# Set the second subplot as active, and make the second plot.
plt.subplot(2, 1, 2)
plt.plot(x, y_cos)
plt.title('Cosine')

# Show the figure.
plt.show()

2D Plotting

image = np.random.rand(30, 30)
plt.imshow(image, cmap=plt.cm.hot)
plt.show()

plt.imshow(image, cmap=plt.cm.hot)
plt.colorbar()
plt.show()

Yet Another Plots

# Regular Plots
n = 256
X = np.linspace(-np.pi, np.pi, n, endpoint=True)
Y = np.sin(2 * X)

plt.axes([0.025, 0.025, 0.95, 0.95])

plt.plot(X, Y + 1, color='blue', alpha=1.00)
plt.fill_between(X, 1, Y + 1, color='blue', alpha=.25)

plt.plot(X, Y - 1, color='blue', alpha=1.00)
plt.fill_between(X, -1, Y - 1, (Y - 1) > -1, color='blue', alpha=.25)
plt.fill_between(X, -1, Y - 1, (Y - 1) < -1, color='red',  alpha=.25)

plt.xlim(-np.pi, np.pi)
plt.xticks(())
plt.ylim(-2.5, 2.5)
plt.yticks(())

plt.show()

# Scaller Plot
n = 1024
X = np.random.normal(0, 1, n)
Y = np.random.normal(0, 1, n)
T = np.arctan2(Y, X)

plt.axes([0.025, 0.025, 0.95, 0.95])
plt.scatter(X, Y, s=75, c=T, alpha=.5)

plt.xlim(-1.5, 1.5)
plt.xticks(())
plt.ylim(-1.5, 1.5)
plt.yticks(())

plt.show()

# Bar plots
n = 12
X = np.arange(n)
Y1 = (1 - X / float(n)) * np.random.uniform(0.5, 1.0, n)
Y2 = (1 - X / float(n)) * np.random.uniform(0.5, 1.0, n)

plt.axes([0.025, 0.025, 0.95, 0.95])
plt.bar(X, +Y1, facecolor='#9999ff', edgecolor='white')
plt.bar(X, -Y2, facecolor='#ff9999', edgecolor='white')

for x, y in zip(X, Y1):
    plt.text(x + 0.4, y + 0.05, '%.2f' % y, ha='center', va= 'bottom')

for x, y in zip(X, Y2):
    plt.text(x + 0.4, -y - 0.05, '%.2f' % y, ha='center', va= 'top')

plt.xlim(-.5, n)
plt.xticks(())
plt.ylim(-1.25, 1.25)
plt.yticks(())

plt.show()

# Contour plots
def f(x,y):
    return (1 - x / 2 + x**5 + y**3) * np.exp(-x**2 -y**2)

n = 256
x = np.linspace(-3, 3, n)
y = np.linspace(-3, 3, n)
X,Y = np.meshgrid(x, y)

plt.axes([0.025, 0.025, 0.95, 0.95])

plt.contourf(X, Y, f(X, Y), 8, alpha=.75, cmap=plt.cm.hot)
C = plt.contour(X, Y, f(X, Y), 8, colors='black', linewidth=.5)
plt.clabel(C, inline=1, fontsize=10)

plt.xticks(())
plt.yticks(())
plt.show()

# Imshow
def f(x, y):
    return (1 - x / 2 + x ** 5 + y ** 3 ) * np.exp(-x ** 2 - y ** 2)

n = 10
x = np.linspace(-3, 3, 3.5 * n)
y = np.linspace(-3, 3, 3.0 * n)
X, Y = np.meshgrid(x, y)
Z = f(X, Y)

plt.axes([0.025, 0.025, 0.95, 0.95])
plt.imshow(Z, interpolation='nearest', cmap='bone', origin='lower')
plt.colorbar(shrink=.92)

plt.xticks(())
plt.yticks(())
plt.show()

# Pie charts
n = 20
Z = np.ones(n)
Z[-1] *= 2

plt.axes([0.025, 0.025, 0.95, 0.95])

plt.pie(Z, explode=Z*.05, colors = ['%f' % (i/float(n)) for i in range(n)])
plt.axis('equal')
plt.xticks(())
plt.yticks()

plt.show()

# Quiver Plots
n = 8
X, Y = np.mgrid[0:n, 0:n]
T = np.arctan2(Y - n / 2., X - n/2.)
R = 10 + np.sqrt((Y - n / 2.0) ** 2 + (X - n / 2.0) ** 2)
U, V = R * np.cos(T), R * np.sin(T)

plt.axes([0.025, 0.025, 0.95, 0.95])
plt.quiver(X, Y, U, V, R, alpha=.5)
plt.quiver(X, Y, U, V, edgecolor='k', facecolor='None', linewidth=.5)

plt.xlim(-1, n)
plt.xticks(())
plt.ylim(-1, n)
plt.yticks(())

plt.show()

# Grids
ax = plt.axes([0.025, 0.025, 0.95, 0.95])

ax.set_xlim(0,4)
ax.set_ylim(0,3)
ax.xaxis.set_major_locator(plt.MultipleLocator(1.0))
ax.xaxis.set_minor_locator(plt.MultipleLocator(0.1))
ax.yaxis.set_major_locator(plt.MultipleLocator(1.0))
ax.yaxis.set_minor_locator(plt.MultipleLocator(0.1))
ax.grid(which='major', axis='x', linewidth=0.75, linestyle='-', color='0.75')
ax.grid(which='minor', axis='x', linewidth=0.25, linestyle='-', color='0.75')
ax.grid(which='major', axis='y', linewidth=0.75, linestyle='-', color='0.75')
ax.grid(which='minor', axis='y', linewidth=0.25, linestyle='-', color='0.75')
ax.set_xticklabels([])
ax.set_yticklabels([])

plt.show()

# Polar Axis
ax = plt.axes([0.025, 0.025, 0.95, 0.95], polar=True)

N = 20
theta = np.arange(0.0, 2 * np.pi, 2 * np.pi / N)
radii = 10 * np.random.rand(N)
width = np.pi / 4 * np.random.rand(N)
bars = plt.bar(theta, radii, width=width, bottom=0.0)

for r,bar in zip(radii, bars):
    bar.set_facecolor(plt.cm.jet(r/10.))
    bar.set_alpha(0.5)

ax.set_xticklabels([])
ax.set_yticklabels([])
plt.show()

# 3D Plots
from mpl_toolkits.mplot3d import Axes3D


fig = plt.figure()
ax = Axes3D(fig)
X = np.arange(-4, 4, 0.25)
Y = np.arange(-4, 4, 0.25)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X ** 2 + Y ** 2)
Z = np.sin(R)

ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=plt.cm.hot)
ax.contourf(X, Y, Z, zdir='z', offset=-2, cmap=plt.cm.hot)
ax.set_zlim(-2, 2)

plt.show()

# Text printing
eqs = []
eqs.append((r"$W^{3\beta}_{\delta_1 \rho_1 \sigma_2} = U^{3\beta}_{\delta_1 \rho_1} + \frac{1}{8 \pi 2} \int^{\alpha_2}_{\alpha_2} d \alpha^\prime_2 \left[\frac{ U^{2\beta}_{\delta_1 \rho_1} - \alpha^\prime_2U^{1\beta}_{\rho_1 \sigma_2} }{U^{0\beta}_{\rho_1 \sigma_2}}\right]$"))
eqs.append((r"$\frac{d\rho}{d t} + \rho \vec{v}\cdot\nabla\vec{v} = -\nabla p + \mu\nabla^2 \vec{v} + \rho \vec{g}$"))
eqs.append((r"$\int_{-\infty}^\infty e^{-x^2}dx=\sqrt{\pi}$"))
eqs.append((r"$E = mc^2 = \sqrt{{m_0}^2c^4 + p^2c^2}$"))
eqs.append((r"$F_G = G\frac{m_1m_2}{r^2}$"))

plt.axes([0.025, 0.025, 0.95, 0.95])

for i in range(24):
    index = np.random.randint(0, len(eqs))
    eq = eqs[index]
    size = np.random.uniform(12, 32)
    x,y = np.random.uniform(0, 1, 2)
    alpha = np.random.uniform(0.25, .75)
    plt.text(x, y, eq, ha='center', va='center', color="#11557c", alpha=alpha,
         transform=plt.gca().transAxes, fontsize=size, clip_on=True)
plt.xticks(())
plt.yticks(())

plt.show()

matplotlib: imporatnt plotting tutorials

Pyplot - http://matplotlib.org/users/pyplot_tutorial.html
Image - http://matplotlib.org/users/image_tutorial.html
Text - http://matplotlib.org/users/index_text.html
Artist - http://matplotlib.org/users/artists.html
Path - http://matplotlib.org/users/path_tutorial.html
Transforms - http://matplotlib.org/users/transforms_tutorial.html

3D Plotting with Mayavi

Important tutorial - http://docs.enthought.com/mayavi/mayavi/mlab.html
Installation guide
-----------------------
i) pip install mayavi
ii) pip install PyQt5
iii) jupyter nbextension install --py mayavi --user
iv) jupyter nbextension enable --py mayavi --user

from mayavi import mlab
# mlab.init_notebook() # for inline

# Points
x, y, z, value = np.random.random((4, 40))
mlab.points3d(x, y, z, value) 
mlab.show() #use this if inline is disabled

# Lines
mlab.clf()  # Clear the figure
t = np.linspace(0, 20, 200)
mlab.plot3d(np.sin(t), np.cos(t), 0.1*t, t)
mlab.show() #use this if inline is disabled

# Elevation surface
mlab.clf()
x, y = np.mgrid[-10:10:100j, -10:10:100j]
r = np.sqrt(x**2 + y**2)
z = np.sin(r)/r
mlab.surf(z, warp_scale='auto')
mlab.show() #use this if inline is disabled

# Arbitrary regular mesh
mlab.clf()
phi, theta = np.mgrid[0:np.pi:11j, 0:2*np.pi:11j]
x = np.sin(phi) * np.cos(theta)
y = np.sin(phi) * np.sin(theta)
z = np.cos(phi)
mlab.mesh(x, y, z)
mlab.mesh(x, y, z, representation='wireframe', color=(0, 0, 0))
mlab.show() #use this if inline is disabled

References

a) https://www.scipy-lectures.org/intro/matplotlib/index.html
b) https://www.scipy-lectures.org/packages/3d_plotting/index.html
c) https://github.com/kuleshov/cs228-material/blob/master/tutorials/python/cs228-python-tutorial.ipynb

Click here to download the source code of this tutorial.