5 Creative Ways to Plot a Function Defined with def in Python Matplotlib

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💡 Problem Formulation: In Python programming, particularly data visualization, it’s common to define functions that represent mathematical expressions or data transformations. The challenge arises when one wants to visualize these functions as graphs. This article will explore how a Python function – defined using the def statement – can be plotted using the Matplotlib library, taking the reader from input (the function definition) to the desired output (a visual graph of the function).

Method 1: Using the plot Function

The plot function in Matplotlib is the most straightforward method for plotting a Python function. This method involves generating a range of x-values, applying the function to these values to get the corresponding y-values, and then plotting x versus y.

Here’s an example:

import matplotlib.pyplot as plt
import numpy as np

def my_func(x):
    return np.sin(x)

x = np.linspace(0, 2*np.pi, 100)
y = my_func(x)

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

The output will be a plot of the sine function over the interval from 0 to \(2\pi\).

This snippet creates a range of x-values using NumPy’s linspace function, then calculates the corresponding y-values by applying my_func to each x-value. The plot method of Matplotlib is then used to generate the curve, and show displays it.

Method 2: Using a List Comprehension

Another efficient way to plot a function in Matplotlib is to use a list comprehension to compute the y-values. This can be a concise and Pythonic alternative to using loops.

Here’s an example:

import matplotlib.pyplot as plt

def my_func(x):
    return x ** 2

x = range(-10, 11)
y = [my_func(i) for i in x]

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

The output is a parabola representing the function \(f(x) = x^2\).

In this code, x is defined as a range of integer values. A list comprehension is then used to apply my_func to each value of x, generating y. These values are plotted using Matplotlib’s plot method.

Method 3: Using the scatter Function for Discrete Points

The scatter function is optimal for visualizing the function as a sequence of discrete points, which can be particularly useful for highlighting individual data points or when dealing with a non-continuous function.

Here’s an example:

import matplotlib.pyplot as plt

def my_func(x):
    return x * x - x

x = range(1, 10)
y = [my_func(i) for i in x]

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

The output shows the discrete points of the function \(f(x) = x^2 – x\) for integer values of x from 1 to 9.

This code snippet employs a similar approach to the previous methods but uses scatter instead of plot to display individual points rather than connecting them with lines.

Method 4: Using the plot Function with a Custom Domain

If your function has a specific domain, you can use the plot function and NumPy’s capabilities to generate the appropriate range of x-values and compute y-values only within this domain.

Here’s an example:

import matplotlib.pyplot as plt
import numpy as np

def my_func(x):
    return np.log(x)

x = np.linspace(0.1, 10, 100) # Avoiding log(0) which is undefined
y = my_func(x)

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

The output is the plot of the logarithmic function over the interval from 0.1 to 10, avoiding the singularity at 0.

This code defines a function for the natural logarithm, which is undefined at 0. To handle this, the domain is specified to start slightly above 0. The plot function then displays the graph over the specified domain.

Bonus One-Liner Method 5: Lambda Functions

For simple functions, you can use a lambda function directly within the plot command to generate a quick visual of the function without explicitly defining it beforehand.

Here’s an example:

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-5, 5, 100)
plt.plot(x, (lambda z: z**3 + z**2)(x))
plt.show()

The output is the plot of the cubic function \(f(z) = z^3 + z^2\) over the interval from -5 to 5.

This one-liner uses a lambda function to define the function to be plotted directly within the call to plot, alongside the generation of the x-values. This arrangement offers simplicity for quick plotting tasks.

Summary/Discussion

  • Method 1: Using the plot Function. Strengths: Simple and effective for continuous functions. Weaknesses: Requires two separate arrays for x and y values.
  • Method 2: Using a List Comprehension. Strengths: Efficient and Pythonic. Weaknesses: Less suitable for large datasets due to memory overhead from list comprehension.
  • Method 3: Using the scatter Function for Discrete Points. Strengths: Good for emphasizing discrete data points. Weaknesses: Does not show continuity of the function.
  • Method 4: Using the plot Function with a Custom Domain. Strengths: Allows for flexibility in defining the range of the function’s domain. Weaknesses: Requires domain knowledge to avoid undefined function values.
  • Bonus Method 5: Lambda Functions. Strengths: Ideal for quick plotting and inline function definitions. Weaknesses: Not as readable or reusable for complex functions.