matplotlib

Matplotlib is the core plotting package in scientific python. There are others to explore as well (which we’ll chat about on slack).

Note

There are different interfaces for interacting with matplotlib, an interactive, function-driven (state machine) command-set and an object-oriented version. We’ll focus on the OO interface.

import numpy as np
import matplotlib.pyplot as plt

Matplotlib concepts

Matplotlib was designed with the following goals (from mpl docs):

• Plots should look great—publication quality (e.g. antialiased)

• Postscript/PDF output for inclusion with TeX documents

• Embeddable in a graphical user interface for application development

• Code should be easy to understand it and extend

• Making plots should be easy

Matplotlib is mostly for 2-d data, but there are some basic 3-d (surface) interfaces.

Volumetric data requires a different approach

Gallery

Matplotlib has a great gallery on their webpage – find something there close to what you are trying to do and use it as a starting point:

https://matplotlib.org/stable/gallery/index.html

Importing

There are several different interfaces for matplotlib (see https://matplotlib.org/3.1.1/faq/index.html)

Basic ideas:

• matplotlib is the entire package

• matplotlib.pyplot is a module within matplotlib that provides easy access to the core plotting routines

• pylab combines pyplot and numpy into a single namespace to give a MatLab like interface. You should avoid this—it might be removed in the future.

There are a number of modules that extend its behavior, e.g. basemap for plotting on a sphere, mplot3d for 3-d surfaces

Anatomy of a figure

Figures are the highest level object and can include multiple axes

(figure from: http://matplotlib.org/faq/usage_faq.html#parts-of-a-figure )

Backends

Interactive backends: pygtk, wxpython, tkinter, …

Hardcopy backends: PNG, PDF, PS, SVG, …

Basic plotting

plot() is the most basic command. Here we also see that we can use LaTeX notation for the axes

x = np.linspace(0, 2*np.pi, 100)
y = np.cos(x)

fig, ax = plt.subplots()

ax.plot(x, y)
ax.set_xlabel(r"$x$")
ax.set_ylabel(r"$\cos(x)$")
ax.set_xlim(0, 2*np.pi)

(0.0, 6.283185307179586)

Quick Exercise

We can plot 2 lines on a plot simply by calling plot twice. Make a plot with both sin(x) and cos(x) drawn

we can use symbols instead of lines pretty easily too—and label them

fig, ax = plt.subplots()

ax.plot(x, np.sin(x), "o", label="sine")
ax.plot(x, np.cos(x), "x", label="cosine")
ax.set_xlim(0.0, 2.0*np.pi)
ax.legend()

<matplotlib.legend.Legend at 0x7fa638901d50>

Here we specified the format using a “format string” (see https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.plot.html)

This has the form '[marker][line][color]'

most functions take a number of optional named arguments too

ax.clear()
ax.plot(x, np.sin(x), linestyle="--", linewidth=3.0)
ax.plot(x, np.cos(x), linestyle="-")
fig

there is a command setp() that can also set the properties. We can get the list of settable properties as

There are predefined styles that can be used too. Generally you need to start from the figure creation for these to take effect

plt.style.available

['Solarize_Light2',
 '_classic_test_patch',
 '_mpl-gallery',
 '_mpl-gallery-nogrid',
 'bmh',
 'classic',
 'dark_background',
 'fast',
 'fivethirtyeight',
 'ggplot',
 'grayscale',
 'seaborn-v0_8',
 'seaborn-v0_8-bright',
 'seaborn-v0_8-colorblind',
 'seaborn-v0_8-dark',
 'seaborn-v0_8-dark-palette',
 'seaborn-v0_8-darkgrid',
 'seaborn-v0_8-deep',
 'seaborn-v0_8-muted',
 'seaborn-v0_8-notebook',
 'seaborn-v0_8-paper',
 'seaborn-v0_8-pastel',
 'seaborn-v0_8-poster',
 'seaborn-v0_8-talk',
 'seaborn-v0_8-ticks',
 'seaborn-v0_8-white',
 'seaborn-v0_8-whitegrid',
 'tableau-colorblind10']

plt.style.use("fivethirtyeight")

fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(x, np.sin(x), linestyle="--", linewidth=3.0)
ax.plot(x, np.cos(x), linestyle="-")
ax.set_xlim(0.0, 2.0*np.pi)

(0.0, 6.283185307179586)

plt.style.use("default")

Multiple axes

There are a wide range of methods for putting multiple axes on a grid. We’ll look at the simplest method.

The add_subplot() method we’ve been using can take 3 numbers: the number of rows, number of columns, and current index

fig = plt.figure()

ax1 = fig.add_subplot(211)

x = np.linspace(0,5,100)
ax1.plot(x, x**3 - 4*x)
ax1.set_xlabel("x")
ax1.set_ylabel(r"$x^3 - 4x$", fontsize="large")

ax2 = fig.add_subplot(212)

ax2.plot(x, np.exp(-x**2))
ax2.set_xlabel("x")
ax2.set_ylabel("Gaussian")

# log scale
ax2.set_yscale("log")

# set the figure size
fig.set_size_inches(6, 8)

# tight_layout() makes sure things don't overlap
fig.tight_layout()

Visualizing 2-d array data

2-d datasets consist of (x, y) pairs and a value associated with that point. Here we create a 2-d Gaussian, using the meshgrid() function to define a rectangular set of points.

def g(x, y):
    return np.exp(-((x-0.5)**2)/0.1**2 - ((y-0.5)**2)/0.2**2)

N = 100

x = np.linspace(0.0, 1.0, N)
y = x.copy()

xv, yv = np.meshgrid(x, y)

A “heatmap” style plot assigns colors to the data values. A lot of work has gone into the latest matplotlib to define a colormap that works good for colorblindness and black-white printing.

fig, ax = plt.subplots()

im = ax.imshow(g(xv, yv), origin="lower")
fig.colorbar(im, ax=ax)

<matplotlib.colorbar.Colorbar at 0x7fa6388f2090>

Sometimes we want to show just contour lines—like on a topographic map. The contour() function does this for us.

fig, ax = plt.subplots()

contours = ax.contour(g(xv, yv))
ax.axis("equal")   # this adjusts the size of image to make x and y lengths equal

(0.0, 99.0, 0.0, 99.0)

Quick Exercise

Contour plots can label the contours, using the ax.clabel() function. Try adding labels to this contour plot.

Error bars

For experiments, we often have errors associated with the \(y\) values. Here we create some data and add some noise to it, then plot it with errors.

def y_experiment(a1, a2, sigma, x):
    """ return the experimental data in a linear + random fashion a1
        is the intercept, a2 is the slope, and sigma is the error """

    N = len(x)

    # randn gives samples from the "standard normal" distribution
    r = np.random.randn(N)
    y = a1 + a2*x + sigma*r
    return y

N = 40
x = np.linspace(0.0, 100.0, N)
sigma = 25.0*np.ones(N)
y = y_experiment(10.0, 3.0, sigma, x)

fig, ax = plt.subplots()
ax.errorbar(x, y, yerr=sigma, fmt="o")

<ErrorbarContainer object of 3 artists>

Annotations

adding text and annotations is easy

xx = np.linspace(0, 2.0*np.pi, 1000)

fig, ax = plt.subplots()
ax.plot(xx, np.sin(xx))
ax.text(np.pi/2, np.sin(np.pi/2), r"maximum")

Text(1.5707963267948966, 1.0, 'maximum')

we can also turn off the top and right “splines”

ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
ax.xaxis.set_ticks_position('bottom')                                           
ax.yaxis.set_ticks_position('left') 
fig

Annotations with an arrow are also possible

#example from http://matplotlib.org/examples/pylab_examples/annotation_demo.html
fig = plt.figure()
ax = fig.add_subplot(111, projection='polar')
r = np.arange(0, 1, 0.001)
theta = 2*2*np.pi*r
line, = ax.plot(theta, r, color='#ee8d18', lw=3)

ind = 800
thisr, thistheta = r[ind], theta[ind]
ax.plot([thistheta], [thisr], 'o')
ax.annotate('a polar annotation',
            xy=(thistheta, thisr),  # theta, radius
            xytext=(0.05, 0.05),    # fraction, fraction
            textcoords='figure fraction',
            arrowprops=dict(facecolor='black', shrink=0.05),
            horizontalalignment='left',
            verticalalignment='bottom',
            )

Text(0.05, 0.05, 'a polar annotation')

Surface plots

matplotlib can’t deal with true 3-d data (i.e., x,y,z + a value), but it can plot 2-d surfaces and lines in 3-d.

from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = plt.axes(projection="3d")

# parametric curves
N = 100
theta = np.linspace(-4*np.pi, 4*np.pi, N)
z = np.linspace(-2, 2, N)
r = z**2 + 1

x = r*np.sin(theta)
y = r*np.cos(theta)

ax.plot(x,y,z)

[<mpl_toolkits.mplot3d.art3d.Line3D at 0x7fa638618290>]

fig = plt.figure()
ax = plt.axes(projection="3d")

X = np.arange(-5,5, 0.25)
Y = np.arange(-5,5, 0.25)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X**2 + Y**2)
Z = np.sin(R)

surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap="coolwarm")

# and the view (note: most interactive backends will allow you to rotate this freely)
ax.azim = 90
ax.elev = 40

Plotting on a sphere

the map funcationality expects stuff in longitude and latitude, so if you want to plot x,y,z on the surface of a sphere using the idea of spherical coordinates, remember that the spherical angle from z (theta) is co-latitude

note: you need the python-basemap package installed for this to work

This also illustrates getting access to a matplotlib toolkit

def to_lonlat(x, y, z):
    SMALL = 1.e-100
    rho = np.sqrt((x + SMALL)**2 + (y + SMALL)**2)
    R = np.sqrt(rho**2 + (z + SMALL)**2)
    
    theta = np.degrees(np.arctan2(rho, z + SMALL))
    phi = np.degrees(np.arctan2(y + SMALL, x + SMALL))
    
    # latitude is 90 - the spherical theta
    return (phi, 90-theta)

from mpl_toolkits.basemap import Basemap

# other projections are allowed, e.g. "ortho", moll"
map = Basemap(projection='moll', lat_0 = 45, lon_0 = 45,
              resolution = 'l', area_thresh = 1000.)

map.drawmapboundary()

map.drawmeridians(np.arange(0, 360, 15), color="0.5", latmax=90)
map.drawparallels(np.arange(-90, 90, 15), color="0.5", latmax=90) #, labels=[1,0,0,1])

# unit vectors (+x, +y, +z)
points = [(1,0,0), (0,1,0), (0,0,1)]
labels = ["+x", "+y", "+z"]

for i in range(len(points)):
    p = points[i]
    print(p)
    lon, lat = to_lonlat(p[0], p[1], p[2])
    xp, yp = map(lon, lat)
    s = plt.text(xp, yp, labels[i], color="b", zorder=10)

# draw a great circle arc between two points
lats = [0, 0]
lons = [0, 90]

map.drawgreatcircle(lons[0], lats[0], lons[1], lats[1], linewidth=2, color="r")

(1, 0, 0)
(0, 1, 0)
(0, 0, 1)

[<matplotlib.lines.Line2D at 0x7fa6206cbc90>]

also, if you really are interested in earth…

map = Basemap(projection='ortho', lat_0 = 45, lon_0 = 45,
              resolution = 'l', area_thresh = 1000.)

map.drawcoastlines()
map.drawmapboundary()

<matplotlib.patches.Ellipse at 0x7fa620a10d90>

Histograms

here we generate a bunch of gaussian-normalized random numbers and make a histogram. The probability distribution should match $\(y(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-x^2/(2\sigma^2)}\)$

N = 10000
r = np.random.randn(N)

fig, ax = plt.subplots()
ax.hist(r, density=True, bins=20)

x = np.linspace(-5,5,200)
sigma = 1.0
ax.plot(x, np.exp(-x**2/(2*sigma**2)) / (sigma*np.sqrt(2.0*np.pi)),
        c="r", lw=2)
ax.set_xlabel("x")

Text(0.5, 0, 'x')

Plotting data from a file

numpy.loadtxt() provides an easy way to read columns of data from an ASCII file

data = np.loadtxt("test1.exact.128.out")
print(data.shape)

(128, 8)

fig, ax = plt.subplots()
ax.plot(data[:,1], data[:,2]/np.max(data[:,2]), label=r"$\rho$")
ax.plot(data[:,1], data[:,3]/np.max(data[:,3]), label=r"$u$")
ax.plot(data[:,1], data[:,4]/np.max(data[:,4]), label=r"$p$")
ax.plot(data[:,1], data[:,5]/np.max(data[:,5]), label=r"$T$")
ax.set_ylim(0,1.1)
ax.legend(frameon=False, fontsize=12)

<matplotlib.legend.Legend at 0x7fa620601d50>

Final fun

if you want to make things look hand-drawn in the style of xkcd, rerun these examples after doing plt.xkcd()

plt.xkcd()

<contextlib.ExitStack at 0x7fa638979610>