Plotting in Python¶

"Matplotlib is a comprehensive library for creating static, animated, and interactive visualizations in Python." There are several tutorials, where you can learn the usage. "matplotlib.pyplot is a collection of functions that make matplotlib work like MATLAB. Each pyplot function makes some change to a figure: e.g., creates a figure, creates a plotting area in a figure, plots some lines in a plotting area, decorates the plot with labels, etc."

In [1]:

import matplotlib.pyplot as plt
import random

In [2]:

list1 = range(5)

In [3]:

plt.plot(list1)

Out[3]:

[<matplotlib.lines.Line2D at 0x12330de20>]

No description has been provided for this image

In [4]:

list2 = [random.random() for _ in range(5)]
print(list2)

[0.6023701644412124, 0.9214737578152091, 0.3815190793139095, 0.07394087879905908, 0.03513324571452825]

In [5]:

plt.plot(list1, list2)

Out[5]:

[<matplotlib.lines.Line2D at 0x122e7eb40>]

In [6]:

plt.plot(list1, list2, 'gs') # try: 'r^' 'gs' 'k--' 'b:' 'ro-'

Out[6]:

[<matplotlib.lines.Line2D at 0x123354dd0>]

In [7]:

plt.scatter(list1, list2)

Out[7]:

<matplotlib.collections.PathCollection at 0x123257c80>

In [8]:

plt.bar(list1, list2, .7)

Out[8]:

<BarContainer object of 5 artists>

In [9]:

t = [i*0.01 for i in range(251)]
t2 = [(i*0.01)**2 for i in range(251)]
t3 = [(i*0.01)**3 for i in range(251)]

In [10]:

plt.plot(t, t2)

Out[10]:

[<matplotlib.lines.Line2D at 0x1235b52e0>]

In [11]:

plt.plot(t, t2, 'r', t, t3, 'g')

Out[11]:

[<matplotlib.lines.Line2D at 0x1235dcd10>,
 <matplotlib.lines.Line2D at 0x12371a330>]

In [12]:

plt.figure(figsize=(12, 3))

plt.subplot(131)
plt.bar(list1,list2)

plt.subplot(132)
plt.scatter(list1,list2)

plt.subplot(133)
plt.plot(list1,list2)

plt.suptitle('Functions')
plt.show()

In [13]:

plt.figure(figsize=(8, 12))

plt.subplot(311)
plt.bar(list1,list2)
plt.title("Bar")

plt.subplot(312)
plt.scatter(list1,list2)
plt.title("Scattered")

plt.subplot(313)
plt.plot(list1,list2)
plt.title("Plot")

plt.suptitle('Functions')

plt.tight_layout()         
plt.show()

Exercise: Copy the next code into a file named 4test.py and run it from a terminal with the command python3 4test.py 4

import matplotlib.pyplot as plt
import random
import sys

def my_plot():
    """
    Plotting n random values.
    n is read in from the terminal.
    """
    
    n = int(sys.argv[1])
    
    list1 = range(n)
    list2 = [random.random() for _ in range(n)]
    list3 = [i**2 for i in list2]
    
    plt.subplot(311)
    plt.bar(list1,list1)
    plt.subplot(312)
    plt.bar(list1,list2)
    plt.subplot(313)
    plt.bar(list1,list3)
    plt.show()

def main():
    my_plot()

if __name__ == "__main__":
    main()

For calculating factorial, binomial coefficient, exponential function you may use the math module:

Using the `math` module¶

To compute the factorial or the exponential function you can use the math module.

In [14]:

import math

math.factorial(5)

Out[14]:

Write a comb function to calculate the binomial coefficient (from Python 3.8 there also exists a function math.comb() for this):

In [15]:

def comb(n, m):
    return math.factorial(n)//math.factorial(m)//math.factorial(n-m)

In [16]:

comb(25, 10)

Out[16]:

In [17]:

math.exp(1), math.exp(2) # the e^x function

Out[17]:

(2.718281828459045, 7.38905609893065)

Exercise: Throw a die 10 times. What is the probability that you get 6 exactly 2 times. Calculate with the formula for the binomial distribution (the parameters will be $n=10$, $p=1/6$), and approximate it with Poisson-distribution, with the parameter $\lambda$, where $\lambda=n\cdot p$ is the expected value of the binomial distribution.

In [18]:

n = 10
p = 1/6
m = 2
l = n*p  # lambda

binomial_dist = comb(n, m) * p**m * (1-p)**(n-m)
poison_dist = l**m * math.exp(-l) / math.factorial(m)

In [19]:

binomial_dist, poison_dist

Out[19]:

(0.2907100492017224, 0.2623272261632803)

In [ ]:

Plotting in Python¶

Using the math module¶

Using the `math` module¶