Scatter plots- SOLVED
Contents
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
Scatter plots- SOLVED#
Another y-vs-x plot, which can take some additional arguments is the scatter plot. It is often most appropriate when plotting unordered data. We give a set of data below.
Exercise 2.1#
Edit the example below to add plot labels, title and adjust axes limits etc. to make the plot more presentable.
# EXERCISE DATA: run this cell to load the data
#An array of miles driven
miles_driven = np.array([434.04176413, 58.37912319, 274.49347372, 187.58345291,
110.44926801, 297.90761681, 427.3174571 , 40.08715083,
247.86116708, 38.89521804, 300.07810287, 401.12704009,
106.67851003, 181.12323573, 166.38794894, 44.99799719,
34.51051553, 237.9278912 , 334.86250092, 401.45589443])
#A second array giving the number of litres of fuel used
litres_of_fuel_used = np.array([29.75678795, 8.03556788, 18.4741211 , 17.77530259, 8.16607936,
20.3677596 , 58.68917566, 2.69293311, 27.78266044, 3.00068322,
20.71372582, 50.88017624, 8.41255259, 25.94509149, 22.77377999,
3.29926235, 3.00036682, 35.79350616, 25.93291949, 30.63069581])
# Use plt.scatter? (and online help pages) to see the options that this plot can take. Use this to tweak the plot
# after creating it if you want to make it nicer!
plt.scatter(miles_driven, litres_of_fuel_used, marker='x')
plt.title("An example scatter plot")
plt.xlabel("Miles Driven")
plt.ylabel("Litres of fuel used")
plt.xlim((0,460))
plt.ylim((0,65))
plt.show()
# ADD CODE HERE
Exercise 2.2#
Plot the functions \(f(x) = x^2\), \(f(x) = x^3\) and \(f(x) = x^4\) datasets used above with the plt.scatter plot command over the range \(0 \leq x \leq 1\).
x = np.linspace(0,1,50)
f1 = x**2
f2 = x**3
f3 = x**4
plt.clf()
plt.scatter(x,f1,label = "$y=x^{2}$",marker="*")
plt.xlabel("x")
plt.ylabel("f(x)")
plt.legend()
plt.show()
plt.clf()
plt.scatter(x,f2,label = "$y=x^{3}$",marker="*")
plt.xlabel("x")
plt.ylabel("f(x)")
plt.legend()
plt.show()
plt.clf()
plt.scatter(x,f3,label = "$y=x^{4}$",marker="*")
plt.xlabel("x")
plt.ylabel("f(x)")
plt.legend()
plt.show()
Exercise 2.3#
We have provided two datasets below, but they are not well structured. These are a list of length-2 tuples. Each tuple contains an x and y value (x is the first element of the tuple, y the second element). Use the plotting skills and indexing skills learnt so far, plot y as a function of x. That is, x-values should be on the horizontal (x) axis, and y-values should be on the vertical (y) axies. Make sure to include a line connecting the points.
HINT: These datasets are not sorted, you will probably need to sort them before plotting to ensure that the line makes sense!
Can you identify what function each dataset represents?
data_set_one = [(11, 403.31159963300337), (6, 90.18163074019441), (7, 131.64181424216494), (13, 611.3381655534142),
(14, 735.3648478076925), (16, 1026.0), (17, 1193.577525803504), (12, 500.8306325798367),
(4, 34.0), (9, 245.0), (8, 183.01933598375618), (15, 873.4212528966688), (1, 3.0),
(3, 17.588457268119896), (18, 1376.6155826266483), (0, 2.0), (2, 7.656854249492381),
(10, 318.22776601683796), (19, 1575.562518618183), (5, 57.90169943749474)]
data_set_two = [(4.25, -1.2460874899137928), (5.5, -0.09133022570874005), (2.0, -1.2161468365471424),
(1.5, -0.7292627983322971), (2.5, -1.6011436155469339), (2.25, -1.428173622722739),
(0.75, -0.06831113112617915), (4.75, -0.7623978471120235), (0.5, 0.07758256189037271),
(4.5, -1.0107957994307797), (3.0, -1.7899924966004455), (5.25, -0.28791452275815943),
(1.25, -0.48467763760473137), (3.25, -1.7941296760805463), (1.75, -0.9782460556494921),
(3.5, -1.7364566872907963), (1.0, -0.2596976941318603), (4.0, -1.453643620863612),
(0.0, 0.19999999999999996), (0.25, 0.1689124217106447), (5.75, 0.061192417161520796),
(5.0, -0.5163378145367737), (3.75, -1.6205593573395607), (2.75, -1.7243023786324636)]
#sort the datasets
#sort the datasets
#data_set_one.sort()
#d2 = np.array(data_set_two)
#data_set_two.sort()
#d1 = np.array(data_set_one)
print(data_set_two)
print(type(data_set_two))
print(type(data_set_two[1]))
[(4.25, -1.2460874899137928), (5.5, -0.09133022570874005), (2.0, -1.2161468365471424), (1.5, -0.7292627983322971), (2.5, -1.6011436155469339), (2.25, -1.428173622722739), (0.75, -0.06831113112617915), (4.75, -0.7623978471120235), (0.5, 0.07758256189037271), (4.5, -1.0107957994307797), (3.0, -1.7899924966004455), (5.25, -0.28791452275815943), (1.25, -0.48467763760473137), (3.25, -1.7941296760805463), (1.75, -0.9782460556494921), (3.5, -1.7364566872907963), (1.0, -0.2596976941318603), (4.0, -1.453643620863612), (0.0, 0.19999999999999996), (0.25, 0.1689124217106447), (5.75, 0.061192417161520796), (5.0, -0.5163378145367737), (3.75, -1.6205593573395607), (2.75, -1.7243023786324636)]
<class 'list'>
<class 'tuple'>
#plot data set one
data_set_one.sort()
data_set_two.sort()
d2 = np.array(data_set_two)
d1 = np.array(data_set_one)
print(d2)
plt.clf()
plt.plot(d1[:,0],d1[:,1],label="Data set 1")
plt.ylabel("y")
plt.xlabel("x")
plt.legend()
plt.title("Data set 1")
# OR (slower, but perhaps clearer)
x_vals = []
y_vals = []
for entry in data_set_one:
x_vals.append(entry[0])
y_vals.append(entry[1])
plt.figure()
plt.plot(x_vals,y_vals,label="Data set 1")
plt.ylabel("y")
plt.xlabel("x")
plt.legend()
plt.title("Data set 1")
[[ 0. 0.2 ]
[ 0.25 0.16891242]
[ 0.5 0.07758256]
[ 0.75 -0.06831113]
[ 1. -0.25969769]
[ 1.25 -0.48467764]
[ 1.5 -0.7292628 ]
[ 1.75 -0.97824606]
[ 2. -1.21614684]
[ 2.25 -1.42817362]
[ 2.5 -1.60114362]
[ 2.75 -1.72430238]
[ 3. -1.7899925 ]
[ 3.25 -1.79412968]
[ 3.5 -1.73645669]
[ 3.75 -1.62055936]
[ 4. -1.45364362]
[ 4.25 -1.24608749]
[ 4.5 -1.0107958 ]
[ 4.75 -0.76239785]
[ 5. -0.51633781]
[ 5.25 -0.28791452]
[ 5.5 -0.09133023]
[ 5.75 0.06119242]]
Text(0.5, 1.0, 'Data set 1')
#plot data set two
plt.clf()
plt.plot(d2[:,0],d2[:,1],label="Data set 2")
plt.xlabel("x")
plt.ylabel("y")
plt.legend()
plt.title("Data set 2")
Text(0.5, 1.0, 'Data set 2')
