Plotting with matplotlib

Simple line/scatter plots

One of the most widely used Python plotting libraries is matplotlib. Matplotlib is open source and produces static images.

%matplotlib inline
import matplotlib.pyplot as plt
plt.figure(figsize=(10,8))
from numpy import linspace, sin
x = linspace(0.01,1,300)
y = sin(1/x)
plt.plot(x, y, 'bo-')
plt.xlabel('x', fontsize=18)
plt.ylabel('f(x)', fontsize=18)
# plt.show()       # not needed inside the Jupyter notebook
# plt.savefig('tmp.png')

Let’s add the second line, the labels, and the legend. Note that matplotlib automatically adjusts the axis ranges to fit both plots:

%matplotlib inline
import matplotlib.pyplot as plt
plt.figure(figsize=(10,8))
from numpy import linspace, sin
x = linspace(0.01,1,300)
y = sin(1/x)
plt.plot(x, y, 'bo-', label='one')
plt.plot(x+0.3, 2*sin(10*x), 'r-', label='two')
plt.legend(loc='lower right')
plt.xlabel('x', fontsize=18)
plt.ylabel('f(x)', fontsize=18)

Let’s plot these two functions side-by-side:

%matplotlib inline
import matplotlib.pyplot as plt
fig = plt.figure(figsize=(12,4))
from numpy import linspace, sin
x = linspace(0.01,1,300)
y = sin(1/x)

ax = fig.add_subplot(121)   # on 1x2 layout create plot #1 (`axes` object with some data space)
a1 = plt.plot(x, y, 'bo-', label='one')
ax.set_ylim(-1.5, 1.5)
/Users/razoumov/Library/Group Containers/3L68KQB4HG.group.com.readdle.smartemail/databases/messagesData/2/92721/nbody.jl/Users/razoumov/Library/Group Containers/3L68KQB4HG.group.com.readdle.smartemail/databases/messagesData/2/92721/nbody.jlplt.xlabel('x')
plt.ylabel('f1')

ax = fig.add_subplot(122)   # on 1x2 layout create plot #2
a2 = plt.plot(x+0.2, 2*sin(10*x), 'r-', label='two')
plt.xlabel('x')
plt.ylabel('f2')

Instead of indices, we could specify the absolute coordinates of each plot with fig.add_axes():

  1. adjust the size fig = plt.figure(figsize=(12,4))
  2. replace the first fig.add_subplot with ax = fig.add_axes([0.1, 0.7, 0.8, 0.3]) # left, bottom, width, height
  3. replace the second fig.add_subplot with ax = fig.add_axes([0.1, 0.2, 0.8, 0.4]) # left, bottom, width, height

The 3rd option is plt.axes() – it creates an axes object (a region of the figure with some data space). These two lines are equivalent - both create a new figure with one subplot:

fig = plt.figure(figsize=(8,8)); ax = fig.add_subplot(111)
fig = plt.figure(figsize=(8,8)); ax = plt.axes()

Exercise: break the plot into two subplots, the fist taking 1/3 of the space on the left, the second one 2/3 of the space on the right.

Let’s plot a simple line in the x-y plane:

import matplotlib.pyplot as plt
import numpy as np
fig = plt.figure(figsize=(12,12))
ax = fig.add_subplot(111)
x = np.linspace(0,1,100)
plt.plot(2*np.pi*x, x, 'b-')
plt.xlabel('x')
plt.ylabel('f1')

Replace ax = fig.add_subplot(111) with ax = fig.add_subplot(111, projection='polar'). Now we have a plot in the phi-r plane, i.e. in polar coordinates. Phi goes [0,2\pi], whereas r goes [0,1].

?fig.add_subplot    # look into `projection` parameter

import matplotlib.pyplot as plt
import numpy as np
fig = plt.figure(figsize=(12,12))
ax = fig.add_subplot(111, projection='mollweide')
x = np.radians([30,40, 50])
y = np.radians([15, 16, 17])
plt.plot(x, y, 'bo-')

Later, we’ll learn how to use this projection parameter with cartopy to map your 2D data from one projection to another.

Let’s try a scatter plot:

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
plt.figure(figsize=(10,8))
x = np.random.random(size=1000)   # 1D array of 1000 random numbers in [0.,1.]
y = np.random.random(size=1000)
size = 1 + 50*np.random.random(size=1000)
plt.scatter(x, y, s=size, color='lightblue')

For other plot types click on any example in the Matplotlib gallery.

For colours, see Choosing Colormaps in Matplotlib.

Heatmaps

Let’s plot a heatmap of monthly temperatures at the South Pole:

%matplotlib inline
import matplotlib.pyplot as plt
from matplotlib import cm
import numpy as np
plt.figure(figsize=(15,10))

months = ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec', 'Year']
recordHigh = [-14.4,-20.6,-26.7,-27.8,-25.1,-28.8,-33.9,-32.8,-29.3,-25.1,-18.9,-12.3,-12.3]
averageHigh = [-26.0,-37.9,-49.6,-53.0,-53.6,-54.5,-55.2,-54.9,-54.4,-48.4,-36.2,-26.3,-45.8]
dailyMean = [-28.4,-40.9,-53.7,-57.8,-58.0,-58.9,-59.8,-59.7,-59.1,-51.6,-38.2,-28.0,-49.5]
averageLow = [-29.6,-43.1,-56.8,-60.9,-61.5,-62.8,-63.4,-63.2,-61.7,-54.3,-40.1,-29.1,-52.2]
recordLow = [-41.1,-58.9,-71.1,-75.0,-78.3,-82.8,-80.6,-79.3,-79.4,-72.0,-55.0,-41.1,-82.8]

vlabels = ['record high', 'average high', 'daily mean', 'average low', 'record low']

Z = np.stack((recordHigh,averageHigh,dailyMean,averageLow,recordLow))
plt.imshow(Z, cmap=cm.winter)
plt.colorbar(orientation='vertical', shrink=0.45, aspect=20)
plt.xticks(range(13), months, fontsize=15)
plt.yticks(range(5), vlabels, fontsize=12)
plt.ylim(-0.5, 4.5)

for i in range(len(months)):
    for j in range(len(vlabels)):
        text = plt.text(i, j, Z[j,i],
                       ha="center", va="center", color="w", fontsize=14, weight='bold')

Exercise: Change the text colour to black in the brightest (green) rows and columns. You can do this either by specifying rows/columns explicitly, or (better) by setting a threshold background colour.

Exercise: Modify the code to display only 4 seasons instead of the individual months.

3D topographic elevation

For this we need a data file – let’s download it. Open a terminal inside your Jupyter dashboard. Inside the terminal, type:

wget http://bit.ly/pythfiles -O pfiles.zip
unzip pfiles.zip && rm pfiles.zip        # this should unpack into the directory data-python/

You can now close the terminal panel. Let’s switch back to our Python notebook and check our location:

%pwd       # simply run a bash command with a prefix
%ls        # make sure you see data-python/

Let's plot tabulated topographic elevation data:

```py
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.colors import LightSource
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

table = pd.read_csv('data-python/mt_bruno_elevation.csv')
z = np.array(table)
nrows, ncols = z.shape
x = np.linspace(0,1,ncols)
y = np.linspace(0,1,nrows)
x, y = np.meshgrid(x, y)
ls = LightSource(270, 45)
rgb = ls.shade(z, cmap=cm.gist_earth, vert_exag=0.1, blend_mode='soft')

fig, ax = plt.subplots(subplot_kw=dict(projection='3d'), figsize=(10,10))    # figure with one subplot
ax.view_init(20, 30)      # (theta, phi) viewpoint
surf = ax.plot_surface(x, y, z, facecolors=rgb, linewidth=0, antialiased=False, shade=False)

Exercise: replace fig, ax = plt.subplots() with fig = plt.figure() followed by ax = fig.add_subplot(). Don’t forget about the 3d projection.

Let’s replace the last two lines with (running this takes ~10s on my laptop):

ax.view_init(20, 30)
surf = ax.plot_surface(x, y, z, facecolors=rgb, linewidth=0, antialiased=False, shade=False)
for angle in range(90):
    print(angle)
    ax.view_init(20, 30+angle)
    plt.savefig('frame%04d'%(angle)+'.png')

And then we can create a movie in bash:

ffmpeg -r 30 -i frame%04d.png -c:v libx264 -pix_fmt yuv420p -vf "scale=trunc(iw/2)*2:trunc(ih/2)*2" spin.mp4

3D parametric plot

Here is something visually very different, still using ax.plot_surface():

from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.colors import LightSource
import matplotlib.pyplot as plt
from numpy import pi, sin, cos, mgrid

dphi, dtheta = pi/250, pi/250    # 0.72 degrees
[phi, theta] = mgrid[0:pi+dphi*1.5:dphi, 0:2*pi+dtheta*1.5:dtheta]
        # define two 2D grids: both phi and theta are (252,502) numpy arrays
r = sin(4*phi)**3 + cos(2*phi)**3 + sin(6*theta)**2 + cos(6*theta)**4
x = r*sin(phi)*cos(theta)   # x is also (252,502)
y = r*cos(phi)              # y is also (252,502)
z = r*sin(phi)*sin(theta)   # z is also (252,502)

ls = LightSource(270, 45)
rgb = ls.shade(z, cmap=cm.gist_earth, vert_exag=0.1, blend_mode='soft')

fig, ax = plt.subplots(subplot_kw=dict(projection='3d'), figsize=(10,10))
ax.view_init(20, 30)
surf = ax.plot_surface(x, y, z, facecolors=rgb, linewidth=0, antialiased=False, shade=False)