matplotlib

Lecture 10

Dr. Colin Rundel

matplotlib & pyplot

matplotlib is a comprehensive library for creating static, animated, and interactive visualizations in Python.

import matplotlib as mpl
import matplotlib.pyplot as plt


Why do we usually import only pyplot then?

Matplotlib is the whole package; matplotlib.pyplot is a module in matplotlib; and pylab is a module that gets installed alongside matplotlib.

Pyplot provides the state-machine interface to the underlying object-oriented plotting library. The state-machine implicitly and automatically creates figures and axes to achieve the desired plot.

Plot anatomy

  • Figure - The entire plot (including subplots)

  • Axes - Subplot attached to a figure, contains the region for plotting data and x & y axis

  • Axis - Set the scale and limits, generate ticks and ticklabels

  • Artist - Everything visible on a figure: text, lines, axis, axes, etc.

Basic plot - OO style

x = np.linspace(0, 2*np.pi, 100)
y1 = np.sin(x)
y2 = np.cos(x)

fig, ax = plt.subplots(figsize=(6, 3))
ax.plot(x, y1, label="sin(x)")
ax.plot(x, y2, label="cos(x)")
ax.set_title("Simple Plot")
ax.legend()

Basic plot - pyplot style

x = np.linspace(0, 2*np.pi, 100)
y1 = np.sin(x)
y2 = np.cos(x)

plt.figure(figsize=(6, 3))
plt.plot(x, y1, label="sin(x)")
plt.plot(x, y2, label="cos(x)")
plt.title("Simple Plot")
plt.legend()

Subplots (OO)

x = np.linspace(0, 2*np.pi, 30)
y1 = np.sin(x)
y2 = np.cos(x)

fig, (ax1, ax2) = plt.subplots(
  2, 1, figsize=(6, 6)
)

fig.suptitle("Main title")

ax1.plot(x, y1, "--b", label="sin(x)")
ax1.set_title("subplot 1")
ax1.legend()

ax2.plot(x, y2, ".-r", label="cos(x)")
ax2.set_title("subplot 2")
ax2.legend()

Subplots (pyplot)

x = np.linspace(0, 2*np.pi, 30)
y1 = np.sin(x)
y2 = np.cos(x)

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

plt.suptitle("Main title")

plt.subplot(211)
plt.plot(x, y1, "--b", label="sin(x)")
plt.title("subplot 1")
plt.legend()

plt.subplot(2,1,2)
plt.plot(x, y2, ".-r", label="cos(x)")
plt.title("subplot 2")
plt.legend()

plt.show()

More subplots

x = np.linspace(-2, 2, 101)

fig, axs = plt.subplots(2, 2, figsize=(5, 5))

fig.suptitle("More subplots")

axs[0,0].plot(x, x, "b", label="linear")
axs[0,1].plot(x, x**2, "r", label="quadratic")
axs[1,0].plot(x, x**3, "g", label="cubic")
axs[1,1].plot(x, x**4, "c", label="quartic")

[ax.legend() for row in axs for ax in row]

Fancy subplots (mosaic)

x = np.linspace(-2, 2, 101)

fig, axd = plt.subplot_mosaic(
  [['upleft', 'right'],
   ['lowleft', 'right']],
  figsize=(5, 5)
)

axd['upleft' ].plot(x, x,    "b", label="linear")
axd['lowleft'].plot(x, x**2, "r", label="quadratic")
axd['right'  ].plot(x, x**3, "g", label="cubic")

axd['upleft'].set_title("Linear")
axd['lowleft'].set_title("Quadratic")
axd['right'].set_title("Cubic")

Format strings

For quick formating of plots (scatter and line) format strings are a useful shorthand, generally they use the format '[marker][line][color]',


character shape
. point
, pixel
o circle
v triangle down
^ triangle up
< triangle left
> triangle right
… + more
character line style
- solid
-- dashed
-. dash-dot
: dotted
character color
b blue
g green
r red
c cyan
m magenta
y yellow
k black
w white

Plotting data

Beyond creating plots for arrays (and lists), addressable objects like dicts and DataFrames can be used via data,

np.random.seed(19680801)
d = {'x': np.arange(50),
     'color': np.random.randint(0, 50, 50),
     'size': np.abs(np.random.randn(50)) * 100}
d['y'] = d['x'] + 10 * np.random.randn(50)


plt.figure(figsize=(6, 3))
plt.scatter(
  'x', 'y', c='color', s='size', 
  data=d
)
plt.xlabel("x-axis")
plt.ylabel("y-axis")

plt.show()

Constrained layout

To fix the legend clipping we can use the “contrained” layout to adjust automatically,

np.random.seed(19680801)
d = {'x': np.arange(50),
     'color': np.random.randint(0, 50, 50),
     'size': np.abs(np.random.randn(50)) * 100}
d['y'] = d['x'] + 10 * np.random.randn(50)


plt.figure(
  figsize=(6, 3), 
  layout="constrained"
)
plt.scatter(
  'x', 'y', c='color', s='size', 
  data=d
)
plt.xlabel("x-axis")
plt.ylabel("y-axis")

plt.show()

pyplot w/ pandas data

Data can also come from DataFrame objects or series,

df = pd.DataFrame({
  "x": np.random.normal(size=10000)
}).assign(
  y = lambda d: np.random.normal(0.75*d.x, np.sqrt(1-0.75**2), size=10000)
)

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

ax.scatter('x', 'y', c='k', data=df, alpha=0.1, s=0.5)

ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_title("Bivariate normal ($\\rho=0.75$)")

pyplot w/ pandas data

pyplot w/ pandas series

Series objects can also be plotted directly, the index is used as the x axis labels,

s = pd.Series(
  np.cumsum( np.random.normal(size=100) ),
  index = pd.date_range("2022-01-01", 
                        periods=100, freq="D")
)
plt.figure(figsize=(3, 3), layout="constrained")
plt.plot(s)
plt.show()

plt.figure(figsize=(3, 3), layout="constrained")
plt.plot(s.index, s.values)
plt.xticks(rotation=45)
plt.show()

Scales

Axis scales can be changed via plt.xscale(), plt.yscale(), ax.set_xscale(), or ax.set_yscale(), supported values are “linear”, “log”, “symlog”, and “logit”.

y = np.sort( np.random.sample(size=1000) )
x = np.arange(len(y))

plt.figure(layout="constrained")

scales = ['linear', 'log', 'symlog', 'logit']
for i, scale in zip(range(4), scales):
  plt.subplot(221+i)
  plt.plot(x, y)
  plt.grid(True)
  if scale == 'symlog':
    plt.yscale(scale, linthresh=0.01)
  else:
    plt.yscale(scale)
  plt.title(scale)


plt.show()

Categorical data

df = pd.DataFrame({
  "cat": ["A", "B", "C", "D", "E"],
  "value": np.exp(range(5))
})

plt.figure(figsize=(4, 6), layout="constrained")

plt.subplot(321)
plt.scatter("cat", "value", data=df)
plt.subplot(322)
plt.scatter("value", "cat", data=df)

plt.subplot(323)
plt.plot("cat", "value", data=df)
plt.subplot(324)
plt.plot("value", "cat", data=df)

plt.subplot(325)
b = plt.bar("cat", "value", data=df)
plt.subplot(326)
b = plt.bar("value", "cat", data=df)

plt.show()

Histograms

df = pd.DataFrame({
  "x1": np.random.normal(size=100),
  "x2": np.random.normal(1,2, size=100)
})

plt.figure(figsize=(4, 6), layout="constrained")

plt.subplot(311)
h = plt.hist("x1", bins=10, data=df, alpha=0.5)
h = plt.hist("x2", bins=10, data=df, alpha=0.5)

plt.subplot(312)
h = plt.hist(df, alpha=0.5)

plt.subplot(313)
h = plt.hist(df, stacked=True, alpha=0.5)

plt.show()

Boxplots

df = pd.DataFrame({
  "x1": np.random.normal(size=100),
  "x2": np.random.normal(1,2, size=100),
  "x3": np.random.normal(-1,3, size=100)
}).melt()

df
    variable     value
0         x1  0.085670
1         x1  1.660256
2         x1  1.596326
3         x1 -1.167331
4         x1  0.221311
..       ...       ...
295       x3 -0.822684
296       x3  2.081603
297       x3  2.082767
298       x3 -0.046562
299       x3  0.373482

[300 rows x 2 columns]
plt.figure(figsize=(4, 4), layout="constrained")

plt.boxplot("value", positions="variable", data=df)
Error: ValueError: List of boxplot statistics and `positions` values must have same the length
plt.boxplot(df.value, positions=df.variable)
Error: ValueError: List of boxplot statistics and `positions` values must have same the length

Boxplots (cont.)

df = pd.DataFrame({
  "x1": np.random.normal(size=100),
  "x2": np.random.normal(1,2, size=100),
  "x3": np.random.normal(-1,3, size=100)
})

plt.figure(figsize=(4, 6), layout="constrained")

plt.subplot(211)
b = plt.boxplot(df)

plt.subplot(212)
v = plt.violinplot(df)

plt.show()

Other Plot Types

Exercise 1

To the best of your ability recreate the following plot,

Plotting with pandas

plot methods

Both Series and DataFrame objects have a plot method which can be used to create visualizations - dtypes determine the type of plot produced.

s = pd.Series(
  np.cumsum( np.random.normal(size=100) ),
  index = pd.date_range("2022-01-01", 
                        periods=100, freq="D")
)

plt.figure(figsize=(3,3), layout="constrained")
s.plot()
plt.show()

DataFrame plot

df = pd.DataFrame(
  np.cumsum( np.random.normal(size=(100,4)), axis=0),
  index = pd.date_range("2022-01-01", periods=100, freq="D"),
  columns = list("ABCD")
)

plt.figure(layout="constrained")
df.plot(figsize=(5,3))
plt.show()

DataFrame line styles

df.plot(
  figsize=(5,3),
  style = {
    "A": "-b",
    "B": "--y",
    "C": "-.g",
    "D": ":r"
  }
)

DataFrame plot - categorical

df = pd.DataFrame({
 "x": list("ABCD"),
 "y": np.random.poisson(lam=2, size=4)
})

df.plot(figsize=(5,3), legend=False)

df.set_index("x").plot(figsize=(5,3),legend=False)

df.set_index("x").plot(
  figsize=(5,3), kind="bar", legend=False
)

Other plot types

Plot types can be changed via the kind argument or using one of the DataFrame.plot.<kind> method,

df.set_index("x").plot.bar(
  legend=False, figsize=(5,5)
)

df.set_index("x").plot.barh(
  legend=False, figsize=(5,5)
)

Wide vs long - histograms

df = pd.DataFrame({
  "x1": np.random.normal(size=100),
  "x2": np.random.normal(1,1.5, size=100),
  "x3": np.random.normal(-1,2, size=100)
})

df.plot.hist(figsize=(5,3), alpha=0.5, bins=15)

df_wide = df.melt()
df_wide.plot.hist(figsize=(5,3), alpha=0.5, bins=15)

df_wide.set_index("variable").plot.hist(
  figsize=(5,3), alpha=0.5, bins=15
)

plot and groupby

df_wide
    variable     value
0         x1  1.471225
1         x1 -0.178315
2         x1  0.156732
3         x1  0.291983
4         x1  1.593502
..       ...       ...
295       x3 -3.202525
296       x3 -4.066616
297       x3  0.095091
298       x3 -2.446253
299       x3 -1.810505

[300 rows x 2 columns]
plt.figure(figsize=(5,5))

h = ( df_wide
  .groupby("variable")["value"]
  .plot.hist(
    alpha=0.5, legend=True, bins=15
  )
)

plt.show()

pandas and subplots

plt.figure(figsize=(5,3))
plt.subplot(211)
df[["x1"]].plot.hist(bins=15, figsize=(5,3))
plt.subplot(212)
df[["x2"]].plot.hist(bins=15, figsize=(5,3))

plt.show()

fig, (ax1, ax2) = plt.subplots(2,1, figsize=(5,5))

df[["x1"]].plot.hist(ax = ax1, bins=15)
df[["x2"]].plot.hist(ax = ax2, bins=15)

plt.show()

Using by

ax = df_wide.plot.hist(bins=15, by="variable", legend=False, figsize=(5,5))
plt.show()

Higher level plots - pair plot

The pandas library also provides the plotting submodule with several useful higher level plots,

cov = np.identity(5)
cov[1,2] = cov[2,1] = 0.5
cov[3,0] = cov[0,3] = -0.8

df = pd.DataFrame(
  np.random.multivariate_normal(
    mean=[0]*5, cov=cov, size=1000
  ).round(3),
  columns = ["x1","x2","x3","x4","x5"]
)

df
        x1     x2     x3     x4     x5
0   -0.676 -0.073  0.536 -0.481  0.829
1    0.868 -0.100  0.015 -1.404  0.466
2    0.028 -1.573 -2.680 -1.031 -0.655
3    0.435 -0.571  0.447 -0.424 -1.337
4    0.321  0.295  0.835 -0.262 -0.648
..     ...    ...    ...    ...    ...
995 -0.643  1.501  0.245  0.473  0.445
996  1.482  0.903  1.271 -1.003 -0.817
997  0.001  1.001 -0.196 -0.430 -0.767
998 -2.009  0.979 -0.347  1.501  0.670
999  1.703  0.235  1.582 -0.722  0.334

[1000 rows x 5 columns]
pd.plotting.scatter_matrix(
  df, alpha=0.2, diagonal="kde"
)
plt.show()

Autocorrelation plots

rw = pd.Series(
  np.cumsum( np.random.normal(size=100) ),
)

pd.plotting.autocorrelation_plot(rw)
plt.show()

wn = pd.Series(
  np.random.normal(size=100),
)

pd.plotting.autocorrelation_plot(wn)
plt.show()

Sta 663 - Spring 2023