CPDS in Python Lab - Matplotlib

Matplotlib is a Python package used for data visualization. Graphs help us see trends, relationships, comparisons, distributions, and differences between observations and predictions.

The plotting module is imported as:

import matplotlib.pyplot as plt

1. Importing Matplotlib

The pyplot module contains the plotting functions we will use.

Question 1

Import matplotlib.pyplot using the alias plt.

import matplotlib.pyplot as plt

2. Line Plot

A line plot displays numerical values as points connected by line segments.

Question 2

Plot \(y=[1,4,9,16,25]\). Before running the code, predict the x-values.

y = [1,4,9,16,25]
plt.plot(y,'o-')

If only y is supplied to plt.plot(y), Python automatically uses the indices \(0,1,2,\ldots\) as the horizontal coordinates.

3. Plotting y Against x

Question 3

Plot \(y=[1,4,9,16,25]\) against \(x=[1,2,3,4,5]\).

x = [1,2,3,4,5]
y = [1,4,9,16,25]

plt.plot(x,y)
plt.show()

4. Labels and Titles

Question 4

Add x-axis and y-axis labels and the title "Simple Plot" to the previous graph.

plt.plot(x,y)

plt.plot(x,y)
plt.title("Simple plot")

Text(0.5, 1.0, 'Simple plot')

plt.plot(x,y)
plt.title("Simple plot")
plt.xlabel("time")
plt.ylabel("displacement")
plt.show()

Use plt.xlabel(), plt.ylabel() and plt.title() to explain what a graph represents.

Assignment 61 — Matplotlib Basics

Import matplotlib.pyplot as plt.
Plot y = [1, 4, 9, 16, 25].
Plot y against x = [1, 2, 3, 4, 5].
Add x-axis and y-axis labels.
Add the title "Simple Plot".

import matplotlib.pyplot as plt
y = [1,4,9,16,25]
x = [1,2,3,4,5]
plt.plot(x,y)
plt.title("Simple plot")
plt.xlabel("time")
plt.ylabel("displacement")
plt.show()

5. Plotting Mathematical Functions

Question 5

Generate 100 equally spaced points between 0 and 10 and plot \(y=x^2\).

import numpy as np
x = np.linspace(0,10,100)
y = x**2
plt.plot(x,y)

plt.plot(x,x**2)

Question 6

Plot \(y=\sin(x)\) for 100 points between 0 and 10.

x = np.linspace(0,10,100)
plt.plot(x,np.sin(x))

Question 7

Plot \(y=\cos(x)\) for the same interval.

x = np.linspace(0,10,100)
plt.plot(x,np.cos(x))

7. Multiple Curves

Question 8

Plot \(\sin(x)\) and \(\cos(x)\) on the same graph.

plt.plot(x,np.sin(x))
plt.plot(x,np.cos(x))

plt.plot(x,np.sin(x))
plt.show()
plt.plot(x,np.cos(x))
plt.show()

8. Legend and Grid

A legend identifies different curves.

Question 9

Add a legend and grid to the sine-cosine graph.

plt.plot(x,np.sin(x), label = "Sine")
plt.plot(x,np.cos(x), label = "Cosine")
plt.legend()
plt.show()

plt.plot(x,np.sin(x), label = "Sine")
plt.plot(x,np.cos(x), label = "Cosine")
plt.legend(ncols = 2)
plt.grid()
plt.show()

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
/tmp/ipykernel_1796/3983006052.py in <cell line: 0>()
----> 1 plt.plot(x,np.sin(x), label = "Sine")
      2 plt.plot(x,np.cos(x), label = "Cosine")
      3 plt.legend(ncols = 2)
      4 plt.grid()
      5 plt.show()

NameError: name 'x' is not defined

Grid lines are added using plt.grid(True).

9. Markers and Line Styles

Question 10

Plot the experimental data below with circular markers and a dashed line.

\(x=[0,1,2,3,4,5]\), \(y=[0,2,5,9,14,20]\).

plt.plot(x,np.sin(x),'--')
plt.plot(x,np.sin(x),'*')

plt.plot([1,2,3,4,5,6,7,8,9],'o')

10. Scatter Plots

A scatter plot displays each observation as an individual point without joining the points. It is useful for studying relationships, correlations, clusters and outliers.

Question 11

Study hours are [1,2,3,4,5,6] and marks are [42,50,58,67,76,85]. Draw a scatter plot.

plt.scatter([1,2,3,4,5,6],[42,50,60,43,55,55])

Use plt.scatter(x,y).

11. Bar Plots

A bar plot compares numerical quantities associated with different categories.

Question 13

Plot marks [92,88,90,95] for ["Math","Physics","Chemistry","Python"].

plt.bar(["Math","Physics","Chem","Py"],[92,88,90,95])

Use plt.bar(categories, values).

Assignment 64 - Bar Plot

Store four subject names.
Store corresponding marks.
Create a bar plot.
Add axis labels.
Add a title.

sub_names = ["math", "Phy"]
sub_marks = [92,90]

plt.bar(sub_names,sub_marks)
plt.title("Marks")
plt.xlabel("Subjects")
plt.ylabel("Marks")
plt.show()

12. Horizontal Bar Plots

Question 14

Compare execution times: Euler = 2.1 s, Runge-Kutta = 4.8 s, Finite Difference = 3.5 s.

plt.barh(["Euler","RK", "FD"], [2.1,4.8,3.5])

plt.barh(categories,values) produces horizontal bars and is useful when category names are long.

13. Histograms

A histogram shows the distribution of numerical data. It divides values into intervals called bins and counts how many observations fall in each interval.

Question 15

Draw a histogram of the following marks using 5 bins.

plt.hist([92,43,98])

(array([1., 0., 0., 0., 0., 0., 0., 0., 1., 1.]),
 array([43. , 48.5, 54. , 59.5, 65. , 70.5, 76. , 81.5, 87. , 92.5, 98. ]),
 <BarContainer object of 10 artists>)

plt.hist([92,43,98], bins = 1)

plt.hist([92,43,98], bins = 5)

(array([1., 0., 0., 0., 2.]),
 array([43., 54., 65., 76., 87., 98.]),
 <BarContainer object of 5 artists>)

Use plt.hist(data,bins=...).

14. Why Does the Number of Bins Matter?

Few bins give a coarse view; more bins reveal finer detail. The chosen number of bins affects how we interpret a distribution.

Question 16

Display the same marks first with 4 bins and then with 10 bins.

Assignment 65 - Histogram

Create a list of student marks.
Draw a histogram.
Use 5 bins.
Label the axes.

marks = [20,19,18,15]
plt.hist(marks, bins = 5)
plt.xlabel("marks")

Text(0.5, 0, 'marks')

15. Multiple Mathematical Curves

Multiple curves are useful for direct comparison.

Question 17

Generate x-values from 0 to 3 and plot \(y=x\), \(y=x^2\), and \(y=x^3\) on the same graph. Add a legend and grid.

x = np.linspace(0,3,100)
plt.plot(x,x, label = "x")
plt.plot(x,x**2, label = "x^2")
plt.plot(x,x**3, label = "x^3")
plt.legend()
plt.grid()

16. Subplots

A subplot places separate graphs inside one figure.

Question 18

Display \(\sin(x)\) and \(\cos(x)\) side by side.

plt.subplot(1,2,1)
plt.plot(x,np.sin(x))
plt.subplot(1,2,2)
plt.plot(x,np.cos(x))

plt.subplot(2,1,1)
plt.plot(x,np.sin(x))
plt.subplot(2,1,2)
plt.plot(x,np.cos(x))

import numpy as np
x = np.linspace(0,1,100)
plt.subplot(2,2,1)
plt.plot(x,np.sin(x))
plt.subplot(2,2,3)
plt.plot(x,np.cos(x))
plt.subplot(2,2,4)
plt.plot(x,np.exp(x))

import numpy as np

x = np.linspace(0,1,5)

plt.subplot(6,2,1)
plt.plot(x,np.sin(x))
plt.subplot(6,2,2)
plt.scatter(x,np.cos(x))
plt.subplot(6,1,2)
plt.scatter(x,np.exp(x))
plt.subplot(6,4,12)
plt.bar(x,np.exp(-x))

plt.subplot(1,2,1) means 1 row, 2 columns, first position.
plt.subplot(1,2,2) selects the second position.

17. Visualization for Machine Learning

ML visualizations compares actual observations with model predictions.

A useful representation is:

actual observations → scatter points,
predicted values → line.

Question 19

Take some actual and predicted values, display both on the same graph.

exact_tempurature = [40,42,43,44,45,46,44]
pred_temputure = [39, 44, 50, 50, 40,50,44]

plt.plot(exact_tempurature, label = "Exact")
plt.plot(pred_temputure, label = "Pred")
plt.legend()

Assignment 68 - Visualization for ML

Given:

x = [1, 2, 3, 4, 5]
y = [3, 5, 7, 9, 11]
y_pred = [2.8, 5.1, 7.2, 8.9, 11.1]

Plot actual observations using scatter.
Plot predicted values as a line.
Display both on the same graph.
Add a legend.
Explain what a good prediction should look like.

# Try it

Experiment and Model

time = [0, 1, 2, 3, 4, 5]
measurement = [0.2, 1.1, 4.2, 8.8, 16.3, 24.7]
prediction = [0, 1, 4, 9, 16, 25]

Question 22

Create a graph that:

shows measurements as scatter points,
shows predictions as a line,
labels both axes,
adds the title "Experiment and Model",
adds a legend,
adds grid lines.

Then decide whether the model appears to represent the data reasonably well.

# Try it

import matplotlib.pyplot as plt

plt.plot(x, y)                 
plt.scatter(x, y)              
plt.bar(categories, values)    
plt.barh(categories, values)   
plt.hist(data, bins=5)         

plt.xlabel("...")
plt.ylabel("...")
plt.title("...")
plt.legend()
plt.grid(True)

plt.subplot(rows, columns, position)
plt.show()