Share @ LinkedIn Facebook  datascience, datavisulisation, matplotlib
matplotlib - Sample Plots

Matplotlib - Sample Plots

Simple Plot

Create a simple plot.

In [8]:
import matplotlib
import matplotlib.pyplot as plt
import numpy as np

# Data for plotting
t = np.arange(0.0, 3.0, 0.01)
s = 1 + np.sin(2 * np.pi * t)

fig, ax = plt.subplots()
ax.plot(t, s)

ax.set(xlabel='time (s)', ylabel='voltage (mV)',
       title='About as simple as it gets, folks')
ax.grid()

fig.savefig("test.png")
plt.show()

Multiple Subplots In One Figure

Multiple axes (i.e. subplots) are created with the subplot() function:

In [10]:
import numpy as np
import matplotlib.pyplot as plt


x1 = np.linspace(0.0, 5.0)
x2 = np.linspace(0.0, 2.0)

y1 = np.cos(2 * np.pi * x1) * np.exp(-x1)
y2 = np.cos(2 * np.pi * x2)

plt.subplot(2, 1, 1)
plt.plot(x1, y1, 'o-')
plt.title('A tale of 2 subplots')
plt.ylabel('Damped oscillation')

plt.subplot(2, 1, 2)
plt.plot(x2, y2, '.-')
plt.xlabel('time (s)')
plt.ylabel('Undamped')

plt.show()

Contouring And Pseudocolor

The pcolormesh() function can make a colored representation of a two-dimensional array, even if the horizontal dimensions are unevenly spaced. The contour() function is another way to represent the same data:

pcolormesh

Shows how to combine Normalization and Colormap instances to draw "levels" in pcolor(), pcolormesh() and imshow() type plots in a similar way to the levels keyword argument to contour/contourf.

In [14]:
import matplotlib
import matplotlib.pyplot as plt
from matplotlib.colors import BoundaryNorm
from matplotlib.ticker import MaxNLocator
import numpy as np


# make these smaller to increase the resolution
dx, dy = 0.05, 0.05

# generate 2 2d grids for the x & y bounds
y, x = np.mgrid[slice(1, 5 + dy, dy),
                slice(1, 5 + dx, dx)]

z = np.sin(x)**10 + np.cos(10 + y*x) * np.cos(x)

# x and y are bounds, so z should be the value *inside* those bounds.
# Therefore, remove the last value from the z array.
z = z[:-1, :-1]
levels = MaxNLocator(nbins=10).tick_values(z.min(), z.max())


# pick the desired colormap, sensible levels, and define a normalization
# instance which takes data values and translates those into levels.
cmap = plt.get_cmap('PiYG')
norm = BoundaryNorm(levels, ncolors=cmap.N, clip=True)

fig, (ax0, ax1) = plt.subplots(nrows=2)

im = ax0.pcolormesh(x, y, z, cmap=cmap, norm=norm)
fig.colorbar(im, ax=ax0)
ax0.set_title('pcolormesh with levels')


# contours are *point* based plots, so convert our bound into point
# centers
cf = ax1.contourf(x[:-1, :-1] + dx/3.,
                  y[:-1, :-1] + dy/3., z, levels=levels,
                  cmap=cmap)
fig.colorbar(cf, ax=ax1)
ax1.set_title('contourf with levels')

# adjust spacing between subplots so `ax1` title and `ax0` tick labels
# don't overlap
fig.tight_layout()

plt.show()

Histograms

The hist() function automatically generates histograms and returns the bin counts or probabilities:

Histogram (hist) function with a few features

In addition to the basic histogram, this demo shows a few optional features:

  • Setting the number of data bins.
  • The normed flag, which normalizes bin heights so that the integral of the histogram is 1. The resulting histogram is an approximation of the probability density function.
  • Setting the face color of the bars.
  • Setting the opacity (alpha value).
  • Selecting different bin counts and sizes can significantly affect the shape of a histogram. The Astropy docs have a great section on how to select these parameters.
In [25]:
#!/usr/bin/env python
import numpy as np
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt

mu, sigma = 100, 15
x = mu + sigma*np.random.randn(10000)

# the histogram of the data
n, bins, patches = plt.hist(x, 50, normed=1, facecolor='pink', alpha=0.75)

# add a 'best fit' line
y = mlab.normpdf( bins, mu, sigma)
l = plt.plot(bins, y, 'r--', linewidth=1)

plt.xlabel('Smarts')
plt.ylabel('Probability')
plt.title(r'$\mathrm{Histogram\ of\ IQ:}\ \mu=100,\ \sigma=15$')
plt.axis([40, 160, 0, 0.03])
plt.grid(True)

plt.show()

Paths

You can add arbitrary paths in Matplotlib using the matplotlib.path module:

In [26]:
import matplotlib.path as mpath
import matplotlib.patches as mpatches
import matplotlib.pyplot as plt


fig, ax = plt.subplots()

Path = mpath.Path
path_data = [
    (Path.MOVETO, (1.58, -2.57)),
    (Path.CURVE4, (0.35, -1.1)),
    (Path.CURVE4, (-1.75, 2.0)),
    (Path.CURVE4, (0.375, 2.0)),
    (Path.LINETO, (0.85, 1.15)),
    (Path.CURVE4, (2.2, 3.2)),
    (Path.CURVE4, (3, 0.05)),
    (Path.CURVE4, (2.0, -0.5)),
    (Path.CLOSEPOLY, (1.58, -2.57)),
    ]
codes, verts = zip(*path_data)
path = mpath.Path(verts, codes)
patch = mpatches.PathPatch(path, facecolor='r', alpha=0.5)
ax.add_patch(patch)

# plot control points and connecting lines
x, y = zip(*path.vertices)
line, = ax.plot(x, y, 'go-')

ax.grid()
ax.axis('equal')
plt.show()

Three-dimensional plotting

The mplot3d toolkit has support for simple 3d graphs including surface, wireframe, scatter, and bar charts.

3D surface (color map)

Demonstrates plotting a 3D surface colored with the coolwarm color map. The surface is made opaque by using antialiased=False.

It also demonstrates using the LinearLocator and custom formatting for the z axis tick labels.

In [28]:
# This import registers the 3D projection, but is otherwise unused.
from mpl_toolkits.mplot3d import Axes3D  # noqa: F401 unused import

import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import numpy as np


fig = plt.figure()
ax = fig.gca(projection='3d')

# Make data.
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)

# Plot the surface.
surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm,
                       linewidth=0, antialiased=False)

# Customize the z axis.
ax.set_zlim(-1.01, 1.01)
ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))

# Add a color bar which maps values to colors.
fig.colorbar(surf, shrink=0.5, aspect=9)

plt.show()

Streamplot

A stream plot, or streamline plot, is used to display 2D vector fields. This example shows a few features of the streamplot() function:

  • Varying the color along a streamline.
  • Varying the density of streamlines.
  • Varying the line width along a streamline.
  • Controlling the starting points of streamlines.
  • Streamlines skipping masked regions and NaN values.
In [37]:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec

w = 3
Y, X = np.mgrid[-w:w:100j, -w:w:100j]
U = -1 - X**2 + Y
V = 1 + X - Y**2
speed = np.sqrt(U*U + V*V)

fig = plt.figure(figsize=(7, 9))
gs = gridspec.GridSpec(nrows=3, ncols=2, height_ratios=[1, 1, 2])

#  Varying density along a streamline
ax0 = fig.add_subplot(gs[0, 0])
ax0.streamplot(X, Y, U, V, density=[0.5, 1])
ax0.set_title('Varying Density')

# Varying color along a streamline
ax1 = fig.add_subplot(gs[0, 1])
strm = ax1.streamplot(X, Y, U, V, color=U, linewidth=2, cmap='autumn')
fig.colorbar(strm.lines)
ax1.set_title('Varying Color')

plt.tight_layout()
plt.show()
In [39]:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec

w = 3
Y, X = np.mgrid[-w:w:100j, -w:w:100j]
U = -1 - X**2 + Y
V = 1 + X - Y**2
speed = np.sqrt(U*U + V*V)

fig = plt.figure(figsize=(7, 9))
gs = gridspec.GridSpec(nrows=3, ncols=2, height_ratios=[1, 1, 2])

#  Varying density along a streamline
ax0 = fig.add_subplot(gs[0, 0])
ax0.streamplot(X, Y, U, V, density=[0.5, 1])
ax0.set_title('Varying Density')

# Varying color along a streamline
ax1 = fig.add_subplot(gs[0, 1])
strm = ax1.streamplot(X, Y, U, V, color=U, linewidth=2, cmap='autumn')
fig.colorbar(strm.lines)
ax1.set_title('Varying Color')

#  Varying line width along a streamline
ax2 = fig.add_subplot(gs[1, 0])
lw = 5*speed / speed.max()
ax2.streamplot(X, Y, U, V, density=0.6, color='k', linewidth=lw)
ax2.set_title('Varying Line Width')

plt.tight_layout()
plt.show()

This feature complements the quiver() function for plotting vector fields. Thanks to Tom Flannaghan and Tony Yu for adding the streamplot function.

Ellipses

In support of the Phoenix mission to Mars (which used Matplotlib to display ground tracking of spacecraft), Michael Droettboom built on work by Charlie Moad to provide an extremely accurate 8-spline approximation to elliptical arcs (see Arc), which are insensitive to zoom level.

In [44]:
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.patches import Ellipse

NUM = 250

ells = [Ellipse(xy=np.random.rand(2) * 10,
                width=np.random.rand(), height=np.random.rand(),
                angle=np.random.rand() * 360)
        for i in range(NUM)]

fig, ax = plt.subplots(subplot_kw={'aspect': 'equal'})
for e in ells:
    ax.add_artist(e)
    e.set_clip_box(ax.bbox)
    e.set_alpha(np.random.rand())
    e.set_facecolor(np.random.rand(3))

ax.set_xlim(0, 10)
ax.set_ylim(0, 10)

plt.show()
In [45]:
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.patches import Ellipse

delta = 45.0  # degrees

angles = np.arange(0, 360 + delta, delta)
ells = [Ellipse((1, 1), 4, 2, a) for a in angles]

a = plt.subplot(111, aspect='equal')

for e in ells:
    e.set_clip_box(a.bbox)
    e.set_alpha(0.1)
    a.add_artist(e)

plt.xlim(-2, 4)
plt.ylim(-1, 3)

plt.show()
In [46]:
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.collections import EllipseCollection

x = np.arange(10)
y = np.arange(15)
X, Y = np.meshgrid(x, y)

XY = np.column_stack((X.ravel(), Y.ravel()))

ww = X / 10.0
hh = Y / 15.0
aa = X * 9


fig, ax = plt.subplots()

ec = EllipseCollection(ww, hh, aa, units='x', offsets=XY,
                       transOffset=ax.transData)
ec.set_array((X + Y).ravel())
ax.add_collection(ec)
ax.autoscale_view()
ax.set_xlabel('X')
ax.set_ylabel('y')
cbar = plt.colorbar(ec)
cbar.set_label('X+Y')
plt.show()

Bar Charts

Use the bar() function to make bar charts, which includes customizations such as error bars:

Bar charts of many shapes and sizes with Matplotlib.

Bar charts are useful for visualizing counts, or summary statistics with error bars. These examples show a few ways to do this with Matplotlib.

In [47]:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.ticker import MaxNLocator
from collections import namedtuple


n_groups = 5

means_men = (20, 35, 30, 35, 27)
std_men = (2, 3, 4, 1, 2)

means_women = (25, 32, 34, 20, 25)
std_women = (3, 5, 2, 3, 3)

fig, ax = plt.subplots()

index = np.arange(n_groups)
bar_width = 0.35

opacity = 0.4
error_config = {'ecolor': '0.3'}

rects1 = ax.bar(index, means_men, bar_width,
                alpha=opacity, color='b',
                yerr=std_men, error_kw=error_config,
                label='Men')

rects2 = ax.bar(index + bar_width, means_women, bar_width,
                alpha=opacity, color='r',
                yerr=std_women, error_kw=error_config,
                label='Women')

ax.set_xlabel('Group')
ax.set_ylabel('Scores')
ax.set_title('Scores by group and gender')
ax.set_xticks(index + bar_width / 2)
ax.set_xticklabels(('A', 'B', 'C', 'D', 'E'))
ax.legend()

fig.tight_layout()
plt.show()
In [48]:
Student = namedtuple('Student', ['name', 'grade', 'gender'])
Score = namedtuple('Score', ['score', 'percentile'])

# GLOBAL CONSTANTS
testNames = ['Pacer Test', 'Flexed Arm\n Hang', 'Mile Run', 'Agility',
             'Push Ups']
testMeta = dict(zip(testNames, ['laps', 'sec', 'min:sec', 'sec', '']))


def attach_ordinal(num):
    """helper function to add ordinal string to integers

    1 -> 1st
    56 -> 56th
    """
    suffixes = {str(i): v
                for i, v in enumerate(['th', 'st', 'nd', 'rd', 'th',
                                       'th', 'th', 'th', 'th', 'th'])}

    v = str(num)
    # special case early teens
    if v in {'11', '12', '13'}:
        return v + 'th'
    return v + suffixes[v[-1]]


def format_score(scr, test):
    """
    Build up the score labels for the right Y-axis by first
    appending a carriage return to each string and then tacking on
    the appropriate meta information (i.e., 'laps' vs 'seconds'). We
    want the labels centered on the ticks, so if there is no meta
    info (like for pushups) then don't add the carriage return to
    the string
    """
    md = testMeta[test]
    if md:
        return '{0}\n{1}'.format(scr, md)
    else:
        return scr


def format_ycursor(y):
    y = int(y)
    if y < 0 or y >= len(testNames):
        return ''
    else:
        return testNames[y]


def plot_student_results(student, scores, cohort_size):
    #  create the figure
    fig, ax1 = plt.subplots(figsize=(9, 7))
    fig.subplots_adjust(left=0.115, right=0.88)
    fig.canvas.set_window_title('Eldorado K-8 Fitness Chart')

    pos = np.arange(len(testNames))

    rects = ax1.barh(pos, [scores[k].percentile for k in testNames],
                     align='center',
                     height=0.5, color='m',
                     tick_label=testNames)

    ax1.set_title(student.name)

    ax1.set_xlim([0, 100])
    ax1.xaxis.set_major_locator(MaxNLocator(11))
    ax1.xaxis.grid(True, linestyle='--', which='major',
                   color='grey', alpha=.25)

    # Plot a solid vertical gridline to highlight the median position
    ax1.axvline(50, color='grey', alpha=0.25)
    # set X-axis tick marks at the deciles
    cohort_label = ax1.text(.5, -.07, 'Cohort Size: {0}'.format(cohort_size),
                            horizontalalignment='center', size='small',
                            transform=ax1.transAxes)

    # Set the right-hand Y-axis ticks and labels
    ax2 = ax1.twinx()

    scoreLabels = [format_score(scores[k].score, k) for k in testNames]

    # set the tick locations
    ax2.set_yticks(pos)
    # make sure that the limits are set equally on both yaxis so the
    # ticks line up
    ax2.set_ylim(ax1.get_ylim())

    # set the tick labels
    ax2.set_yticklabels(scoreLabels)

    ax2.set_ylabel('Test Scores')

    ax2.set_xlabel(('Percentile Ranking Across '
                    '{grade} Grade {gender}s').format(
                        grade=attach_ordinal(student.grade),
                        gender=student.gender.title()))

    rect_labels = []
    # Lastly, write in the ranking inside each bar to aid in interpretation
    for rect in rects:
        # Rectangle widths are already integer-valued but are floating
        # type, so it helps to remove the trailing decimal point and 0 by
        # converting width to int type
        width = int(rect.get_width())

        rankStr = attach_ordinal(width)
        # The bars aren't wide enough to print the ranking inside
        if width < 5:
            # Shift the text to the right side of the right edge
            xloc = width + 1
            # Black against white background
            clr = 'black'
            align = 'left'
        else:
            # Shift the text to the left side of the right edge
            xloc = 0.98*width
            # White on magenta
            clr = 'white'
            align = 'right'

        # Center the text vertically in the bar
        yloc = rect.get_y() + rect.get_height()/2.0
        label = ax1.text(xloc, yloc, rankStr, horizontalalignment=align,
                         verticalalignment='center', color=clr, weight='bold',
                         clip_on=True)
        rect_labels.append(label)

    # make the interactive mouse over give the bar title
    ax2.fmt_ydata = format_ycursor
    # return all of the artists created
    return {'fig': fig,
            'ax': ax1,
            'ax_right': ax2,
            'bars': rects,
            'perc_labels': rect_labels,
            'cohort_label': cohort_label}

student = Student('Johnny Doe', 2, 'boy')
scores = dict(zip(testNames,
                  (Score(v, p) for v, p in
                   zip(['7', '48', '12:52', '17', '14'],
                       np.round(np.random.uniform(0, 1,
                                                  len(testNames))*100, 0)))))
cohort_size = 62  # The number of other 2nd grade boys

arts = plot_student_results(student, scores, cohort_size)
plt.show()

Pie Charts

The pie() function allows you to create pie charts. Optional features include auto-labeling the percentage of area, exploding one or more wedges from the center of the pie, and a shadow effect. Take a close look at the attached code, which generates this figure in just a few lines of code.

Demo of a basic pie chart plus a few additional features.

In addition to the basic pie chart, this demo shows a few optional features:

  • slice labels
  • auto-labeling the percentage
  • offsetting a slice with "explode"
  • drop-shadow
  • custom start angle

Note about the custom start angle:

The default startangle is 0, which would start the "Frogs" slice on the positive x-axis. This example sets startangle = 90 such that everything is rotated counter-clockwise by 90 degrees, and the frog slice starts on the positive y-axis.

In [50]:
import matplotlib.pyplot as plt

# Pie chart, where the slices will be ordered and plotted counter-clockwise:
labels = 'Ice-Cream', 'Pizza', 'HotDogs', 'Burger'
sizes = [15, 30, 45, 10]
explode = (0, 0.1, 0, 0)  # only "explode" the 2nd slice (i.e. 'Hogs')

fig1, ax1 = plt.subplots()
ax1.pie(sizes, explode=explode, labels=labels, autopct='%1.1f%%',
        shadow=True, startangle=90)
ax1.axis('equal')  # Equal aspect ratio ensures that pie is drawn as a circle.

plt.show()

Table

In [51]:
import numpy as np
import matplotlib.pyplot as plt


data = [[ 66386, 174296,  75131, 577908,  32015],
        [ 58230, 381139,  78045,  99308, 160454],
        [ 89135,  80552, 152558, 497981, 603535],
        [ 78415,  81858, 150656, 193263,  69638],
        [139361, 331509, 343164, 781380,  52269]]

columns = ('Freeze', 'Wind', 'Flood', 'Quake', 'Hail')
rows = ['%d year' % x for x in (100, 50, 20, 10, 5)]

values = np.arange(0, 2500, 500)
value_increment = 1000

# Get some pastel shades for the colors
colors = plt.cm.BuPu(np.linspace(0, 0.5, len(rows)))
n_rows = len(data)

index = np.arange(len(columns)) + 0.3
bar_width = 0.4

# Initialize the vertical-offset for the stacked bar chart.
y_offset = np.zeros(len(columns))

# Plot bars and create text labels for the table
cell_text = []
for row in range(n_rows):
    plt.bar(index, data[row], bar_width, bottom=y_offset, color=colors[row])
    y_offset = y_offset + data[row]
    cell_text.append(['%1.1f' % (x / 1000.0) for x in y_offset])
# Reverse colors and text labels to display the last value at the top.
colors = colors[::-1]
cell_text.reverse()

# Add a table at the bottom of the axes
the_table = plt.table(cellText=cell_text,
                      rowLabels=rows,
                      rowColours=colors,
                      colLabels=columns,
                      loc='bottom')

# Adjust layout to make room for the table:
plt.subplots_adjust(left=0.2, bottom=0.2)

plt.ylabel("Loss in ${0}'s".format(value_increment))
plt.yticks(values * value_increment, ['%d' % val for val in values])
plt.xticks([])
plt.title('Loss by Disaster')

plt.show()

Scatter Plot

In [53]:
import numpy as np
import matplotlib.pyplot as plt

# Fixing random state for reproducibility
np.random.seed(19680801)


N = 50
x = np.random.rand(N)
y = np.random.rand(N)
colors = np.random.rand(N)
area = (30 * np.random.rand(N))**2  # 0 to 15 point radii

plt.scatter(x, y, s=area, c=colors, alpha=0.5)
plt.show()

Subplot Example

Many plot types can be combined in one figure to create powerful and flexible representations of data.

In [54]:
import matplotlib.pyplot as plt
import numpy as np

np.random.seed(19680801)
data = np.random.randn(2, 100)

fig, axs = plt.subplots(2, 2, figsize=(5, 5))
axs[0, 0].hist(data[0])
axs[1, 0].scatter(data[0], data[1])
axs[0, 1].plot(data[0], data[1])
axs[1, 1].hist2d(data[0], data[1])

plt.show()

Working With Fill Plot

  • Multiple curves with a single command.
  • Setting the fill color.
  • Setting the opacity (alpha value).
In [57]:
import numpy as np
import matplotlib.pyplot as plt

x = [0, 1, 2, 1]
y = [1, 2, 1, 0]

fig, ax = plt.subplots()
ax.fill(x, y)
plt.show()
In [58]:
import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0, 1.5 * np.pi, 500)
y1 = np.sin(x)
y2 = np.sin(3 * x)

fig, ax = plt.subplots()

ax.fill(x, y1, 'b', x, y2, 'r', alpha=0.3)

# Outline of the region we've filled in
ax.plot(x, y1, c='b', alpha=0.8)
ax.plot(x, y2, c='r', alpha=0.8)
ax.plot([x[0], x[-1]], [y1[0], y1[-1]], c='b', alpha=0.8)
ax.plot([x[0], x[-1]], [y2[0], y2[-1]], c='r', alpha=0.8)

plt.show()

Logarithmic Graph Plotting

In [65]:
import numpy as np
import matplotlib.pyplot as plt

# Data for plotting
t = np.arange(0.01, 20.0, 0.01)

# Create figure
fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2)

# log y axis
ax1.semilogy(t, np.exp(-t / 5.0))
ax1.set(title='semilogy')
ax1.grid()

# log x axis
ax2.semilogx(t, np.sin(2 * np.pi * t))
ax2.set(title='semilogx')
ax2.grid()

# log x and y axis
ax3.loglog(t, 20 * np.exp(-t / 10.0), basex=2)
ax3.set(title='loglog base 2 on x')
ax3.grid()

# With errorbars: clip non-positive values
# Use new data for plotting
x = 10.0**np.linspace(0.0, 2.0, 20)
y = x**2.0

ax4.set_xscale("log", nonposx='clip')
ax4.set_yscale("log", nonposy='clip')
ax4.set(title='Errorbars go negative')
ax4.errorbar(x, y, xerr=0.1 * x, yerr=5.0 + 0.75 * y)
# ylim must be set after errorbar to allow errorbar to autoscale limits
ax4.set_ylim(bottom=0.1)

fig.tight_layout()
plt.show()

Working With Polar Axis

In [66]:
import numpy as np
import matplotlib.pyplot as plt


r = np.arange(0, 2, 0.01)
theta = 2 * np.pi * r

ax = plt.subplot(111, projection='polar')
ax.plot(theta, r)
ax.set_rmax(2)
ax.set_rticks([0.5, 1, 1.5, 2])  # Less radial ticks
ax.set_rlabel_position(-22.5)  # Move radial labels away from plotted line
ax.grid(True)

ax.set_title("A line plot on a polar axis", va='bottom')
plt.show()

Legend Using Pre-Defined Labels

In [67]:
import numpy as np
import matplotlib.pyplot as plt

# Make some fake data.
a = b = np.arange(0, 3, .02)
c = np.exp(a)
d = c[::-1]

# Create plots with pre-defined labels.
fig, ax = plt.subplots()
ax.plot(a, c, 'k--', label='Model length')
ax.plot(a, d, 'k:', label='Data length')
ax.plot(a, c + d, 'k', label='Total message length')

legend = ax.legend(loc='upper center', shadow=True, fontsize='x-large')

# Put a nicer background color on the legend.
legend.get_frame().set_facecolor('C0')

plt.show()

Sunny Solanki  Sunny Solanki