Appendix L — Matplotlib: Plotting and Visualization

L.1 Importing matplotlib

import numpy as np
import sympy

import matplotlib as mpl
import matplotlib.pyplot as plt
mpl.rcParams['font.size'] = 12.0
print('matplotlib:', mpl.__version__)
print('numpy:     ', np.__version__)
print('sympy:     ', sympy.__version__)
matplotlib: 3.10.0
numpy:      2.3.1
sympy:      1.14.0

L.2 Getting started

x = np.linspace(-5, 2, 100)

y1 = x**3 +5*x**2 +10
y2 = 3*x**2 +10*x
y3 = 6*x +10

#---------------------------------------

fig, ax = plt.subplots(figsize=(6, 4))

ax.plot(x, y1, color="blue", label="$y(x)$")
ax.plot(x, y2, color="red", label="$y'(x)$")
ax.plot(x, y3, color="green", label="$y''(x)$")

ax.set_xlabel("$x$")
ax.set_ylabel("$y$")
ax.legend()

plt.show()

fig, ax = plt.subplots(figsize=(6, 4))

ax.plot(x, y1, lw=1.5, color="blue", label=r"$y(x)$")
ax.plot(x, y2, lw=1.5, color="red", label=r"$y'(x)$")
ax.plot(x, y3, lw=1.5, color="green", label=r"$y''(x)$")

ax.plot(x, np.zeros_like(x), lw=0.5, color="black")
ax.plot([-3.33], [(-3.33)**3 + 5*(-3.33)**2 + 10], 
        lw=0.5, marker='o', color="blue")
ax.plot([0], [10], lw=0.5, marker='o', color="blue")
ax.plot([-3.33, -3.33], [0, (-3.33)**3 + 5*(-3.33)**2 + 10], 
        ls='--', lw=0.5, color="black")
ax.plot([0, 0], [0, 10], ls='--', lw=0.5, color="black")

ax.set_xlim([-5, 2.5])
ax.set_xticks([-5, -2.5, 0, 2.5])
ax.set_ylim(-20, 40)
ax.set_yticks([-20, -10, 0, 10, 20, 30, 40])

ax.set_xlabel("$x$", fontsize=14)
ax.set_ylabel("$y$", fontsize=14)

ax.legend(loc=2, ncol=3, fontsize=14, frameon=False)

plt.show()

L.3 Figure

x = np.linspace(-2, 2, 1000)

y1 = np.cos(40*x)
y2 = np.exp(-x**2)

#---------------------------------------

# the width and height of the figure canvas in inches
fig = plt.figure(figsize=(6, 3), facecolor="#f1f1f1") 

# axes coordinates as fractions of 
# the canvas width and height
left, bottom, width, height = 0.1, 0.1, 0.8, 0.8
ax = fig.add_axes((left, bottom, width, height), 
                    facecolor="#e1e1e1")

ax.plot(x, y1 *y2)
ax.plot(x, y2, 'g')
ax.plot(x,-y2, 'g')

ax.set_xlabel("x")
ax.set_ylabel("y")

plt.show()

fig.savefig("./figures/matplotlib_savefig.png", dpi=100, facecolor="#f1f1f1")
fig.savefig("./figures/matplotlib_savefig.pdf", dpi=300, facecolor="#f1f1f1")

L.4 Axes

  • Matplotlib provides several different Axes layout managers, which create and place Axes instances within a figure canvas following different strategies

  • To facilitate the forthcoming examples, \(\,\)we here briefly look at one of these layout managers:

       plt.subplots

    Earlier in this appendix, \(\,\)we already used this function to conveniently generate new Figure and Axes objects in one function call

  • However, \(\,\)the plt.subplots function is also capable of filling a figure with a grid of Axes instances, which is specified using the first and the second arguments, or alternatively with the nrows and ncols arguments, which, as the names implies, creates a grid of Axes objects, \(\,\)with the given number of rows and columns

       fig, axes = plt.subplots(nrows=3, ncols=2)

  • Here, the function plt.subplots returns a tuple (fig, axes), where fig is a figure and axes is a numpy array of size (ncols, nrows), \(\,\)in which each element is an Axes instance that has been appropriately placed in the corresponding figure canvas. \(\,\)At this point we can also specify that columns and/or rows should share x and y axes, using the sharex and sharey arguments, which can be set to True or False

  • The plt.subplots function also takes two special keyword arguments fig_kw and subplot_kw, which are dictionaries with keyword arguments that are used when creating the Figure and Axes instances, respectively. This allows us to set and retain full control of the properties of the Figure and Axes objects with plt.subplots, \(\,\)a similar way is possible when directly using plt.figure and the add_axes method

L.5 Plot types

  • Matplotlib implements many types of plotting techniques as methods of the Axes object

    For details, see Matplotlib’s plot types

def hide_labels(fig, ax, fignum):
       
  ax.set_xticks([])
  ax.set_yticks([])

  ax.xaxis.set_ticks_position('none')
  ax.yaxis.set_ticks_position('none')

  ax.axis('tight')

  fignum += 1
  #fig.savefig(f"./figures/plot_types_{fignum}.pdf")
x = np.linspace(-3, 3, 25)
y1 = x**3 +3*x**2 +10
y2 = -1.5*x**3 +10*x**2 -15
fig, ax = plt.subplots(figsize=(6, 4))

ax.plot(x, y1)
ax.plot(x, y2)

hide_labels(fig, ax, 1)

fig, ax = plt.subplots(figsize=(6, 4))

ax.step(x, y1)
ax.step(x, y2)

hide_labels(fig, ax, 2)

fig, ax = plt.subplots(figsize=(6, 4))

width = 6/50

ax.bar(x - width/2, y1, width=width, color="blue")
ax.bar(x + width/2, y2, width=width, color="green")

hide_labels(fig, ax, 3)

fig, ax = plt.subplots(figsize=(6, 4))

ax.hist(y2, bins=15, edgecolor="black")
ax.hist(y1, bins=15, edgecolor="black")

hide_labels(fig, ax, 4)

fig, ax = plt.subplots(figsize=(6, 4))

ax.errorbar(x, y2, yerr=y1, lw=0.6, fmt='--o', capsize=5)

hide_labels(fig, ax, 5)

fig, ax = plt.subplots(figsize=(6, 4))

ax.fill_between(x, y1, y2, edgecolor="black")

hide_labels(fig, ax, 6)

fig, ax = plt.subplots(figsize=(6, 4))

ax.stem(x, y1, linefmt='b', markerfmt='bs')
ax.stem(x, y2, linefmt='r', markerfmt='ro')

hide_labels(fig, ax, 7)

fig, ax = plt.subplots(figsize=(6, 4))

x = np.linspace(0, 5, 50)

ax.scatter(x, -1 +x +0.25*x**2 +2*np.random.rand(len(x)))
ax.scatter(x, np.sqrt(x) +2*np.random.rand(len(x)), color="green")

hide_labels(fig, ax, 8)

x = y = np.linspace(-np.pi, np.pi, 16)
X, Y = np.meshgrid(x, y)
U = np.sin(X)
V = np.cos(Y)

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

ax.quiver(X, Y, U, V)
hide_labels(fig, ax, 9)

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

ax.streamplot(X, Y, U, V)
hide_labels(fig, ax, 9)

plt.style.use('_mpl-gallery')

# make data:
np.random.seed(10)
D = np.random.normal((3, 5, 4), (1.25, 1.00, 1.25), (100, 3))

# plot
fig, ax = plt.subplots(figsize=(5, 5))
VP = ax.boxplot(D, 
                positions=[2, 4, 6], 
                widths=1.5, 
                patch_artist=True,
                showmeans=False, 
                showfliers=False,
                medianprops={"color": "white", "linewidth": 0.5},
                boxprops={"facecolor": "C0", "edgecolor": "white",
                          "linewidth": 0.5},
                whiskerprops={"color": "C0", "linewidth": 1.5},
                capprops={"color": "C0", "linewidth": 1.5})

ax.set(xlim=(0, 8), xticks=[],
       ylim=(0, 8), yticks=[])

plt.show()

plt.style.use('_mpl-gallery-nogrid')

# make data
x = [1, 2, 3, 4]
colors = plt.get_cmap('Blues')(np.linspace(0.2, 0.7, len(x)))

# plot
fig, ax = plt.subplots(figsize=(5, 5))
ax.pie(x, colors=colors, radius=3, center=(4, 4),
       wedgeprops={"linewidth": 1, "edgecolor": "white"}, frame=True)

ax.set(xlim=(0, 8), xticks=[],
       ylim=(0, 8), yticks=[])

plt.show()

L.6 Line properties

  • In matplotlib, \(\,\)we set the line properties with keyword arguments to the plot methods, such as for example plot, step, bar
def axes_settings(fig, ax, title, ymax):
     
  ax.set_title(title)
  ax.set_ylim(0, ymax +1)
  ax.set_xticks([])
  ax.set_yticks([])
    
x = np.linspace(-5, 5, 5)
y = np.ones_like(x)
fig, ax = plt.subplots(figsize=(6, 4))

# Line width
linewidths = [0.5, 1.0, 2.0, 4.0]
for n, linewidth in enumerate(linewidths):
  ax.plot(x, y + n, color="blue", linewidth=linewidth)
    
axes_settings(fig, ax, "linewidth", len(linewidths))

fig, ax = plt.subplots(figsize=(6, 4))  

# Line style
linestyles = ['-', '--', '-.', ':']
for n, linestyle in enumerate(linestyles):
  ax.plot(x, y + n, color="blue", linestyle=linestyle)

# Custom dash style
line, = ax.plot(x, y + len(linestyles), color="red", lw=2)
length1, gap1, length2, gap2 = 5, 2, 10, 2
line.set_dashes([length1, gap1, length2, gap2])
    
axes_settings(fig, ax, "linestyle", len(linestyles) + 1)

fig, ax = plt.subplots(figsize=(6, 4))
 
# Marker types
markers = ['+', 'o', '*', 's', '.', '1', '2', '3', '4']
for n, marker in enumerate(markers):
  
  ax.plot(x, y + n, color="blue", lw=0, marker=marker)
    
axes_settings(fig, ax, "markers", len(markers))

fig, ax = plt.subplots(figsize=(6, 4))

# Marker size and color
markersizeandcolors = [(4, "white"), (8, "red"), (12, "yellow"), (16, "lightgreen")]
for n, (markersize, markercolor) in enumerate(markersizeandcolors):
  ax.plot(x, y + n, color="blue", lw=1, ls='-', 
          marker='o',
          markersize=markersize,
          markerfacecolor=markercolor, 
          markeredgewidth=2)
    
axes_settings(fig, ax, "marker size/color", len(markersizeandcolors))

# a symboloc variable for x, and a numerical array with specific values of x
sym_x = sympy.Symbol("x")
x = np.linspace(-2*np.pi, 2*np.pi, 100)

def sin_expansion(x, n):
  """
  Evaluate the n-th order Taylor series expansion of sin(x)
  for numerical values in the numpy array x
  """
    
  return sympy.lambdify(sym_x, sympy.sin(sym_x).series(n=n).removeO(), 'numpy')(x)
fig, ax = plt.subplots(figsize=(6, 4))

ax.plot(x, np.sin(x), lw=4, color="red", label='exact')

colors = ["blue", "black"]
linestyles =[':', '-.', '--']

for idx, n in enumerate(range(2, 13, 2)):
    
  ax.plot(x, sin_expansion(x, n), 
          color=colors[idx //3], 
          ls=linestyles[idx %3], 
          lw=3, 
          label=f'O({n})')
    
ax.set_xlim(-1.5*np.pi, 1.5*np.pi)
ax.set_ylim(-1.25, 1.25) 

# place a legend outside of the Axes
ax.legend(bbox_to_anchor=(1.02, 1), loc=2, borderaxespad=0.0)

data1 = np.random.randn(200, 2) *np.array([3, 1])
data2 = np.random.randn(200, 2) *np.array([1, 3])

fig, axes = plt.subplots(2, 1, figsize=(6, 8), sharey=True)

axes[0].scatter(data1[:, 0], data1[:, 1], color="g", marker="s", s=30, alpha=0.5)
axes[0].scatter(data2[:, 0], data2[:, 1], color="b", marker="o", s=30, alpha=0.5)

axes[1].hist([data1[:, 1], data2[:, 1]], 
    bins=15, 
    color=["g", "b"], 
    alpha=0.5, 
    orientation='horizontal')

plt.show()

L.7 Legends

  • See help(plt.legend) for details. \(\,\)The loc argument allows us to specify where in the Axes area the legend is to be added: loc=1 for upper right corner, loc=2 for upper left corner, loc=3 for the lower-left corner, and loc=4 for lower right corner

  • In the example of the previous section, \(\,\)we used the bbox_to_anchor, \(\,\)which helps the legend be placed at an arbitrary location within the figure canvas. The bbox_to_anchor argument takes the value of a tuple on the form (x, y), \(~\)where x and y are the canvas coordinates within the Axes object. That is, \(\,\)the point (0, 0) corresponds to the lower-left corner, and (1, 1) corresponds to the upper right corner. \(\,\)Note that x and y can be smaller than 0 and larger than 1, in this case, which indicates that the legend is to be placed outside the Axes area, \(\,\)as was used in the previous section

  • By default, all lines in the legend are shown in a vertical arrangement. Using the ncols argument, it is possible to split the legend labels into multiple columns

x = np.linspace(0, 1, 100)

fig, axes = plt.subplots(4, 1, figsize=(6, 12), sharex=True)

for n in range(4):
  axes[n].plot(x, x, label="$y(x) = x$")
  axes[n].plot(x, x +x**2, label="$y(x) = x + x^2$")
  axes[n].legend(loc=n + 1)
  axes[n].set_title(f'legend: loc={n + 1}')

x = np.linspace(-1, 1, 100)

def linear_eqn(x, slope):
  return slope *x

fig, ax = plt.subplots(figsize=(6, 3))

colors = ['blue', 'green', 'red', 'cyan',
          'magenta', 'yellow', 'black', 'orange']

for slope in range(1, 9):
  ax.plot(x, 
          linear_eqn(x, slope), 
          color=colors[slope -1],
          label=f"$y(x)={slope:d}x$")
    
ax.set_xlim(-1, 1)
ax.set_ylim(-8, 8)

ax.tick_params(axis='x', pad=10)
    
ax.legend(bbox_to_anchor=(-0.01, 1.05), ncol=4, loc=3, borderaxespad=0.0)

L.8 Text formatting and annotations

  • Matplotlib provides several ways of configuring fonts properties. \(\,\)The default values can be set in the matplotlib resource file. \(\,\)To display where the currently active matplotlib file is loaded from, \(\,\)one can do the following:

    mpl.matplotlib_fname()

  • And session-wide configuration can be set in the mpl.rcParams dictionary: \(~\)for example,

    mpl.rcParams['font.size'] = 12.0

  • Try print(mpl.rcParams) to get a list of possible configuration parameters and their current values

  • Matplotlib provides excellent support for LaTeX markup within its text labels: Any text label in matplotlib can include LaTeX math by enclosing it within $ signs: \(\,\) for example 'Regular text: $f(x)=1-x^2$'

  • By default, \(\,\) matplotlib uses an internal LaTeX rendering, \(\,\)which supports a subset of LaTeX language. However, by setting the configuration parameter mpl.rcParams['text.usetex']=True, \(~\)it is also possible to use an external full-featured LaTeX engine

  • When embedding LaTeX code in strings there is a common stumbling block: Python uses \ as escape character, \(\,\)while in LaTeX it is used to denote the start of commands. \(\,\)To prevent the Python interpreter from escaping characters in strings containing LaTeX expressions, \(\,\)it is convenient to use raw strings, \(\,\)which are literal string expressions that are prepended with an r, \(\,\)for example: r"$\int f(x) dx$" and r'$x_{\rm A}$'

x = np.linspace(-20, 20, 100)
y = np.sin(x) /x

fig, ax = plt.subplots(figsize=(6, 4))

ax.plot(x, y)

ax.set_xlabel("x label")
ax.set_ylabel("y label")

for label in ax.get_xticklabels() +ax.get_yticklabels():
  label.set_rotation(45)

fig, ax = plt.subplots(figsize=(6, 3))

ax.set_xticks([])
ax.set_yticks([])
ax.set_xlim(-0.50, 3.50)
ax.set_ylim(-0.05, 0.25)
ax.axhline(0)

# text label
ax.text(0, 0.1, "Text label", fontsize=14, family="serif")

# annotation
ax.plot(1, 0, "o")
ax.annotate("Annotation", fontsize=14, family="serif",
            xy=(1, 0), 
            xycoords="data",
            xytext=(20, 50), 
            textcoords="offset points",
            arrowprops=dict(arrowstyle="->", connectionstyle="arc3, rad=.5"))

# equation
ax.text(2, 0.1, 
        r"Equation: $i\hbar\partial_t \Psi = \hat{H}\Psi$", 
        fontsize=14, family="serif")

plt.show()

mpl.rc('font', family='NanumGothic')
mpl.rcParams['axes.unicode_minus'] = False
data = 1000 +np.random.randint(-100, 100, 50).cumsum()

fig, ax = plt.subplots(figsize=(6, 4))

ax.plot(range(50), data, 'r')

ax.set_title('시간대별 가격 추이')
ax.set_ylabel('주식 가격, [원]')
ax.set_xlabel('시간, [분]')
plt.show()

mpl.rc('font', family='serif')
mpl.rcParams['axes.unicode_minus'] = True

L.9 Axis properties

L.9.1 Axis labels and titles

x = np.linspace(0, 50, 500)
y = np.sin(x) *np.exp(-x /10)

fig, ax = plt.subplots(figsize=(6, 2), subplot_kw={'facecolor': "#ebf5ff"})

ax.plot(x, y, lw=2)

ax.set_xlim([0, 50])
ax.set_ylim([-1.0, 1.0])

ax.set_xlabel("x", labelpad=5, fontsize=14, fontname='serif', color='blue')
ax.set_ylabel("f(x)", labelpad=5, fontsize=14, fontname='serif', color='blue')

ax.set_title("Axis labels and Title example", 
             fontsize=14, fontname='serif', color='blue', loc='center')

plt.show()

L.9.2 Axis range

x = np.linspace(0, 30, 500)
y = np.sin(x) *np.exp(-x /10)

fig, axes = plt.subplots(4, 1, figsize=(6, 12), 
                         subplot_kw={'facecolor': '#ebf5ff'})

axes[0].plot(x, y, lw=2)
axes[0].set_xlim(-5, 35)
axes[0].set_ylim(-1, 1)
axes[0].set_title("set_[x/y]lim")

axes[1].plot(x, y, lw=2)
axes[1].axis('tight')
axes[1].set_title("axis('tight')")

axes[2].plot(x, y, lw=2)
axes[2].axis('equal')
axes[2].set_title("axis('equal')")

axes[3].plot(x, y, lw=2)
axes[3].autoscale(True)
axes[3].set_title("autoscale(True)")

plt.show()

L.9.3 Axis ticks, tick labels, and grids

\(~\)

x = np.linspace(-2*np.pi, 2*np.pi, 500)
y = np.sin(x) *np.exp(-x**2/20)

fig, axes = plt.subplots(2, 1, figsize=(6, 8))

axes[0].plot(x, y, lw=2)
axes[0].set_title("default ticks")
axes[0].tick_params(which='both', direction='in')

axes[1].plot(x, y, lw=2)
axes[1].set_title("set_[x/y]ticks")
axes[1].set_xticks([-5, 0, 5])
axes[1].set_yticks([-1, 0, 1])
axes[1].tick_params(which='both', direction='in')

fig, axes = plt.subplots(2, 1, figsize=(6, 8))

axes[0].plot(x, y, lw=2)
axes[0].set_title("set_major/minor_locator")
axes[0].xaxis.set_major_locator(mpl.ticker.MaxNLocator(4))
axes[0].xaxis.set_minor_locator(mpl.ticker.MaxNLocator(8))
axes[0].yaxis.set_major_locator(mpl.ticker.MaxNLocator(4))
axes[0].yaxis.set_minor_locator(mpl.ticker.MaxNLocator(8))
axes[0].tick_params(which='both', direction='in')

axes[1].plot(x, y, lw=2)
axes[1].set_title("set_[x/y]ticklabels")
axes[1].set_xticks([-2*np.pi, -np.pi, 0, np.pi, 2*np.pi])
axes[1].set_xticklabels(['$-2\pi$', '$-\pi$', '$0$', '$\pi$', '$2\pi$'])
axes[1].xaxis.set_minor_locator(
  mpl.ticker.FixedLocator([-3*np.pi/2, -np.pi/2, 0, np.pi/2, 3*np.pi/2]))
axes[1].set_yticks([-1, 0, 1])
axes[1].yaxis.set_minor_locator(mpl.ticker.MaxNLocator(8))
axes[1].tick_params(which='both', direction='in')
<>:14: SyntaxWarning: invalid escape sequence '\p'
<>:14: SyntaxWarning: invalid escape sequence '\p'
<>:14: SyntaxWarning: invalid escape sequence '\p'
<>:14: SyntaxWarning: invalid escape sequence '\p'
<>:14: SyntaxWarning: invalid escape sequence '\p'
<>:14: SyntaxWarning: invalid escape sequence '\p'
<>:14: SyntaxWarning: invalid escape sequence '\p'
<>:14: SyntaxWarning: invalid escape sequence '\p'
/var/folders/4x/8kn2nym12cn7x7qmg_6s4b8h0000gn/T/ipykernel_76769/2527598018.py:14: SyntaxWarning: invalid escape sequence '\p'
  axes[1].set_xticklabels(['$-2\pi$', '$-\pi$', '$0$', '$\pi$', '$2\pi$'])
/var/folders/4x/8kn2nym12cn7x7qmg_6s4b8h0000gn/T/ipykernel_76769/2527598018.py:14: SyntaxWarning: invalid escape sequence '\p'
  axes[1].set_xticklabels(['$-2\pi$', '$-\pi$', '$0$', '$\pi$', '$2\pi$'])
/var/folders/4x/8kn2nym12cn7x7qmg_6s4b8h0000gn/T/ipykernel_76769/2527598018.py:14: SyntaxWarning: invalid escape sequence '\p'
  axes[1].set_xticklabels(['$-2\pi$', '$-\pi$', '$0$', '$\pi$', '$2\pi$'])
/var/folders/4x/8kn2nym12cn7x7qmg_6s4b8h0000gn/T/ipykernel_76769/2527598018.py:14: SyntaxWarning: invalid escape sequence '\p'
  axes[1].set_xticklabels(['$-2\pi$', '$-\pi$', '$0$', '$\pi$', '$2\pi$'])

fig, axes = plt.subplots(3, 1, figsize=(6, 12))

for ax in axes:
  ax.plot(x, y, lw=2)
  ax.xaxis.set_major_locator(mpl.ticker.MultipleLocator(4))
  ax.xaxis.set_minor_locator(mpl.ticker.MultipleLocator(0.5))
  ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(1))
  ax.yaxis.set_minor_locator(mpl.ticker.MultipleLocator(0.25))
    
axes[0].set_title("default grid")
axes[0].grid()

axes[1].set_title("major/minor grid")
axes[1].grid(color="blue", which="both", ls=':', lw=0.5)

axes[2].set_title("individual x/y major/minor grid")
axes[2].grid(color="gray", which="major", axis='x', ls='-', lw=0.5)
axes[2].grid(color="gray", which="minor", axis='x', ls=':', lw=0.25)
axes[2].grid(color="gray", which="major", axis='y', ls='-', lw=0.5)

x = np.linspace(0, 1e5, 100)
y = x**2

fig, axes = plt.subplots(2, 1, figsize=(6, 8))

axes[0].plot(x, y, 'b.')
axes[0].set_title("default labels", loc='right')

axes[1].plot(x, y, 'b')
axes[1].set_title("scientific notation labels", loc='right')

formatter = mpl.ticker.ScalarFormatter(useMathText=True)
formatter.set_powerlimits((-1, 2))

axes[1].xaxis.set_major_formatter(formatter)
axes[1].yaxis.set_major_formatter(formatter)

L.9.4 Log lots

x = np.linspace(0, 1e3, 100)
y1, y2 = x**3, x**4

fig, axes = plt.subplots(3, 1, figsize=(6, 12))

axes[0].set_title('loglog')
axes[0].loglog(x, y1, 'b', x, y2, 'r')

axes[1].set_title('semilogy')
axes[1].semilogy(x, y1, 'b', x, y2, 'r')

axes[2].set_title('plot set_[x/y]scale')
axes[2].plot(x, y1, 'b', x, y2, 'r')
axes[2].set_xscale('log')
axes[2].set_yscale('log')

L.9.5 Twin axes

radius = np.linspace(0, 5, 100)
area = 4 *np.pi *radius**2         # area
volume = (4 *np.pi /3) *radius**3  # volume
ig, ax1 = plt.subplots(figsize=(6, 4))

ax1.set_title("Surface area and Volume of a sphere", fontsize=16)
ax1.set_xlabel("radius, [m]", fontsize=16)

ax1.plot(radius, area, lw=2, color="blue")
ax1.set_ylabel(r"Surface area, [$m^2$]", fontsize=16, color="blue")
ax1.set_xlim(0, 5)
ax1.set_ylim(0, 350)

for label in ax1.get_yticklabels():
  label.set_color("blue")
    
ax2 = ax1.twinx()
ax2.plot(radius, volume, lw=2, color="red")
ax2.set_ylabel(r"Volume, [$m^3$]", fontsize=16, color="red")
ax2.set_ylim(0, 600)
for label in ax2.get_yticklabels():
  label.set_color("red")

L.9.6 Spines

x = np.linspace(-10, 10, 500)
y = np.sin(x) /x

fig, ax = plt.subplots(figsize=(6, 4))

ax.plot(x, y, lw=2)

ax.set_xticks([-10, -5, 5, 10])
ax.set_yticks([0.5, 1])

# remove top and right spines
ax.spines['top'].set_color('none')
ax.spines['right'].set_color('none')

# set only bottom and left spine ticks
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')

# move bottom and left spines to x = 0 and y = 0
ax.spines['bottom'].set_position(('data', 0))
ax.spines['left'].set_position(('data', 0))

L.10 Advanced axes layouts

L.10.1 Insets

def f(x):
  return 1 /(1 +x**2) +0.1 /(1 +((3 -x) /0.1)**2)

def plot_and_format_axes(ax, x, f, fontsize):
  ax.plot(x, f(x), lw=2)
  ax.xaxis.set_major_locator(mpl.ticker.MaxNLocator(5))
  ax.yaxis.set_major_locator(mpl.ticker.MaxNLocator(4))

  ax.set_xlabel("$x$", fontsize=fontsize)
  ax.set_ylabel("$f(x)$", fontsize=fontsize)

  for label in ax.get_xticklabels() +ax.get_yticklabels():
    label.set_fontsize(fontsize)

  ax.tick_params(which='both', direction='in')
x = np.linspace(-4, 14, 1000)    
    
fig = plt.figure(figsize=(6.5, 4))    

# main graph
ax = fig.add_axes([0.1, 0.15, 0.8, 0.8], facecolor="#f5f5f5")
plot_and_format_axes(ax, x, f, 12)

x0, x1 = 2.5, 3.5
x = np.linspace(x0, x1, 1000)

ax.axvline(x0, ymax=0.3, color="gray", ls=':')
ax.axvline(x1, ymax=0.3, color="gray", ls=':')

# inset
ax1 = fig.add_axes([0.5, 0.5, 0.38, 0.42], facecolor='none') 
plot_and_format_axes(ax1, x, f, 10)

L.10.2 Subplots

x1 = np.random.randn(100)
x2 = np.random.randn(100)

# squeeze=False, the axes is always a two-dimensional array
fig, axes = plt.subplots(2, 2, figsize=(7, 7), 
                        sharex=True, 
                        sharey=True, 
                        squeeze=False) 

axes[0, 0].set_title("Uncorrelated", fontsize=12)             
axes[0, 0].scatter(x1, x2)

axes[0, 1].set_title("Weakly positively correlated", fontsize=12)
axes[0, 1].scatter(x1, x1 +x2)

axes[1, 0].set_title("Weakly negatively correlated", fontsize=12)
axes[1, 0].scatter(x1,-x1 +x2)

axes[1, 1].set_title("Strongly correlated", fontsize=12)
axes[1, 1].scatter(x1, x1 +0.15*x2)

axes[1, 1].set_xlabel("x")
axes[1, 0].set_xlabel("x")
axes[0, 0].set_ylabel("y")
axes[1, 0].set_ylabel("y")

plt.subplots_adjust(left=0.1, 
                    right=0.95, 
                    bottom=0.1, 
                    top=0.95, 
                    wspace=0.1, 
                    hspace=0.2)

L.10.3 Subplot2grid

def plot_and_format_axes(ax, ax_number):
  ax.set_xlim(0, 6)
  ax.set_ylim(0, 6)    
  
  ax.xaxis.set_major_locator(mpl.ticker.MaxNLocator(6))
  ax.yaxis.set_major_locator(mpl.ticker.MaxNLocator(6))
  
  ax.tick_params(which='both', direction='in', top=True, right=True)
  ax.set_xticklabels([])
  ax.set_yticklabels([])
  ax.text(3, 3, f'ax{ax_number}', 
    horizontalalignment='center', 
    verticalalignment='center')
plt.figure(figsize=(6, 6))

ax0 = plt.subplot2grid((3, 3), (0, 0))
ax1 = plt.subplot2grid((3, 3), (0, 1))
ax2 = plt.subplot2grid((3, 3), (1, 0), colspan=2)
ax3 = plt.subplot2grid((3, 3), (2, 0), colspan=3)
ax4 = plt.subplot2grid((3, 3), (0, 2), rowspan=2)

axes = [ax0, ax1, ax2, ax3, ax4]

for i in range(5):
  plot_and_format_axes(axes[i], i)

L.10.4 GridSpec

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

gs = mpl.gridspec.GridSpec(4, 4)

ax0, ax1 = fig.add_subplot(gs[0, 0]),  fig.add_subplot(gs[1, 1])
ax2, ax3 = fig.add_subplot(gs[2, 2]),  fig.add_subplot(gs[3, 3])
ax4, ax5 = fig.add_subplot(gs[0, 1:]), fig.add_subplot(gs[1:, 0])
ax6, ax7 = fig.add_subplot(gs[1, 2:]), fig.add_subplot(gs[2:, 1])
ax8, ax9 = fig.add_subplot(gs[2, 3]),  fig.add_subplot(gs[3, 2])

axes = [ax0, ax1, ax2, ax3, ax4, ax5, ax6, ax7, ax8, ax9]

for i in range(10):
  plot_and_format_axes(axes[i], i)

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

gs = mpl.gridspec.GridSpec(2, 2, 
                    width_ratios=[4, 1], 
                    height_ratios=[1, 4],
                    wspace=0.05, 
                    hspace=0.05)

ax0 = fig.add_subplot(gs[1, 0])
ax1 = fig.add_subplot(gs[0, 0])
ax2 = fig.add_subplot(gs[1, 1])

axes = [ax0, ax1, ax2]

for i in range(3):
  plot_and_format_axes(axes[i], i)

L.11 Colormap plots

x = y = np.linspace(-2, 2, 150)
X, Y = np.meshgrid(x, y)

R1 = np.sqrt((X +0.5)**2 +(Y +0.5)**2)
R2 = np.sqrt((X +0.5)**2 +(Y -0.5)**2)
R3 = np.sqrt((X -0.5)**2 +(Y +0.5)**2)
R4 = np.sqrt((X -0.5)**2 +(Y -0.5)**2)
fig, ax = plt.subplots(figsize=(7, 6))

Z = np.sin(10 *R1) /(10 *R1) +np.sin(20 *R4) /(20 *R4)
Z = Z[:-1, :-1]

p = ax.pcolor(X, Y, Z, cmap='seismic', vmin=-abs(Z).max(), vmax=abs(Z).max())

ax.axis('tight')

ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_title('pcolor')

ax.xaxis.set_major_locator(mpl.ticker.MaxNLocator(4))
ax.yaxis.set_major_locator(mpl.ticker.MaxNLocator(4))

cb = fig.colorbar(p, ax=ax)
cb.set_label('z')
cb.set_ticks([-1, -.5, 0, .5, 1])

fig, ax = plt.subplots(figsize=(7, 6))

Z = 1/R1 -1/R2 -1/R3 +1/R4

im = ax.imshow(Z, vmin=-1, vmax=1, cmap=mpl.cm.bwr,
               extent=[x.min(), x.max(), y.min(), y.max()])
im.set_interpolation('bilinear')

ax.axis('tight')

ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_title('imshow')

ax.xaxis.set_major_locator(mpl.ticker.MaxNLocator(4))
ax.yaxis.set_major_locator(mpl.ticker.MaxNLocator(4))

cb = fig.colorbar(im, ax=ax)
cb.set_label('z')
cb.set_ticks([-1, -.5, 0, .5, 1])

x = y = np.linspace(0, 1, 75)
X, Y = np.meshgrid(x, y)
Z = (-2 *np.cos(2 *np.pi *X) *np.cos(2 *np.pi *Y) 
     -0.7 *np.cos(np.pi -4 *np.pi *X))
fig, ax = plt.subplots(figsize=(6, 6))

c = ax.contour(X, Y, Z, 15, cmap=mpl.cm.RdBu, vmin=-1, vmax=1)

ax.axis('tight')

ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_title("contour")

ax.xaxis.set_major_locator(mpl.ticker.MaxNLocator(4))
ax.yaxis.set_major_locator(mpl.ticker.MaxNLocator(4))

fig, ax = plt.subplots(figsize=(6, 6))

c = ax.contourf(X, Y, Z, 15, cmap=mpl.cm.RdBu, vmin=-1, vmax=1)

ax.axis('tight')

ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_title("contourf")

ax.xaxis.set_major_locator(mpl.ticker.MaxNLocator(4))
ax.yaxis.set_major_locator(mpl.ticker.MaxNLocator(4))

fig.tight_layout()

x = y = np.linspace(-10, 10, 150)

X, Y = np.meshgrid(x, y)
Z = np.cos(X) *np.cos(Y) *np.exp(-(X/5)**2 -(Y/5)**2)
P = Z[:-1, :-1]

norm = mpl.colors.Normalize(-abs(Z).max(), abs(Z).max())

def plot_and_format_axes(fig, ax, p):
  ax.axis('tight')
  ax.set_xlabel(r"$x$", fontsize=12)
  ax.set_ylabel(r"$y$", fontsize=12)

  ax.xaxis.set_major_locator(mpl.ticker.MaxNLocator(4))
  ax.yaxis.set_major_locator(mpl.ticker.MaxNLocator(4))
    
  ax.tick_params(which='both', direction='in', top=True, right=True)

  cb0 = fig.colorbar(p, ax=ax)
  cb0.set_label(r"$z$", fontsize=14)
  cb0.set_ticks([-1, -0.5, 0, 0.5, 1])
fig, axes = plt.subplots(2, 1, figsize=(7, 12))

p = axes[0].pcolor(X, Y, P, norm=norm, cmap=mpl.cm.bwr)
plot_and_format_axes(fig, axes[0], p)

axes[1].contour(X, Y, Z, np.linspace(-1.0, 1.0, 20), norm=norm, cmap=mpl.cm.bwr)
plot_and_format_axes(fig, axes[1], p)

plt.subplots_adjust(hspace=0.15)

X, Y = np.meshgrid(np.linspace(-2, 2, 100), np.linspace(-2, 2, 100))

# A low hump with a spike coming out
# needs to have z/colour axis on a log scale so we see both hump and spike

Z1 = np.exp(-X**2 -Y**2)
Z2 = np.exp(-(10 *X)**2 -(10 *Y)**2)
Z = Z1 +50 *Z2

fig, axes = plt.subplots(2, 1, figsize=(7, 12))

c = axes[0].pcolor(X, Y, Z, 
      norm=mpl.colors.LogNorm(vmin=Z.min(), vmax=Z.max()), cmap='PuBu_r')
fig.colorbar(c, ax=axes[0])

# linear scale only shows the spike
c = axes[1].pcolor(X, Y, Z, cmap='PuBu_r') 
fig.colorbar(c, ax=axes[1])

plt.subplots_adjust(hspace=0.1)

  • Matplotlib has a number of built-in colormaps accessible via matplotlib.colormaps. To get a list of all registered colormaps, you can do:

       from matplotlib import colormaps
   list(colormaps)

L.12 3D plots

  • In matplotlib, \(\,\)drawing 3D graphs requires using a different axes object, namely the Axes3D object that is available from the mpl_toolkits.mplot3d.axes3d module. \(\,\)We can create a 3D-ware axes instance explicitly using the constructor of the Axes3D class, \(\,\)by passing a Figure instance as argument:

       ax = Axes3D(fig)

  • Alternatively, \(\,\)we can use the add_subplot function with the projection='3d' argument:

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

  • or use plt.subplots with the subplot_kw={'projection':'3d'} argument:

       fig, ax = plt.subplots(1, 1, 
                 figsize=(6, 6), subplot_kw={'projection':'3d'})
from mpl_toolkits.mplot3d.axes3d import Axes3D

x = y = np.linspace(-3, 3, 74)
X, Y = np.meshgrid(x, y)
R = np.sqrt(X**2 +Y**2)
Z = np.sin(4 *R) /R

norm = mpl.colors.Normalize(-abs(Z).max(), abs(Z).max())

def title_and_labels(ax, title):
  ax.set_title(title)
  
  ax.set_xlabel("$x$", labelpad=0.05, fontsize=12)
  ax.set_ylabel("$y$", labelpad=0.05, fontsize=12)
  ax.set_zlabel("$z$", labelpad=0.05, fontsize=12)
  ax.set_box_aspect(None, zoom=0.85)
  ax.tick_params(axis='both', pad=0.01)  
fig, axes = plt.subplots(3, 1, figsize=(6, 16), subplot_kw={'projection': '3d'})

p = axes[0].plot_surface(X, Y, Z, rstride=1, cstride=1, lw=0, 
                  antialiased=False, norm=norm, cmap=mpl.cm.Blues)
title_and_labels(axes[0], "plot_surface") 

axes[1].plot_wireframe(X, Y, Z, rstride=3, cstride=3, color="darkgrey")
title_and_labels(axes[1], "plot_wireframe")

axes[2].contour(X, Y, Z, zdir='z', offset=0, norm=norm, cmap=mpl.cm.Blues)
axes[2].contour(X, Y, Z, zdir='y', offset=3, norm=norm, cmap=mpl.cm.Blues)
title_and_labels(axes[2], "contour") 

plt.subplots_adjust(left=0.05, right=0.95, bottom=0.1, top=0.95, hspace=0.1) 

fig, axes = plt.subplots(3, 1, figsize=(6, 16), subplot_kw={'projection': '3d'})

r = np.linspace(0, 10, 100)

p = axes[0].plot(np.cos(r), np.sin(r), 6 -r)
title_and_labels(axes[0], "plot")

p = axes[1].scatter(np.cos(r), np.sin(r), 6 -r)
title_and_labels(axes[1], "scatter")

r = np.linspace(0, 6, 30)

p = axes[2].bar3d(np.cos(r), np.sin(r), np.zeros_like(r), 
                  0.05*np.ones_like(r), 0.05*np.ones_like(r), 6 -r)
title_and_labels(axes[2], "bar3d")

plt.subplots_adjust(left=0.05, right=0.95, bottom=0.1, top=0.95, hspace=0.1)

L.13 CheatSheets and Handouts