NumPy Linspace – Mastering Python

Understanding NumPy’s linspace

The linspace function, short for “linearly spaced,” creates a sequence of numbers evenly distributed between a specified start and end point. It takes three primary arguments:

start: The starting value of the sequence.
stop: The end value of the sequence. Note that the stop value is included in the generated array.
num: The number of samples to generate. This determines the total number of elements in the resulting array.

The function returns a NumPy array containing the evenly spaced numbers.

Basic Usage

The simplest application of linspace involves creating a basic sequence:

import numpy as np

evenly_spaced_numbers = np.linspace(0, 1, 5)
print(evenly_spaced_numbers)

This generates an array with five elements, spaced equally between 0 and 1.

Controlling the Endpoint

By default, linspace includes the stop value. If you need to exclude it, you can use np.linspace(start, stop, num, endpoint=False):

evenly_spaced_numbers_exclusive = np.linspace(0, 1, 5, endpoint=False)
print(evenly_spaced_numbers_exclusive)

Applications in Plotting

linspace is frequently used to generate x-coordinates for plotting functions:

import matplotlib.pyplot as plt

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

plt.plot(x, y)
plt.xlabel("x")
plt.ylabel("sin(x)")
plt.title("Sine Wave")
plt.show()

This code generates 100 evenly spaced points between 0 and 2π, providing a smooth representation of the sine wave.

Creating Sequences with Non-Integer Steps

While linspace focuses on the number of samples, you can indirectly control the step size by adjusting the num parameter. For example, to approximate a step size of 0.1 between 0 and 1, you might use:

approximate_step = np.linspace(0, 1, 11)  # 11 points to include 0 and 1
print(approximate_step)

This demonstrates how to achieve nearly equally spaced numbers, even without explicitly defining the step size.

Beyond the Basics: Reshaping and Further Manipulation

The array generated by linspace can be further manipulated using other NumPy functions. For instance, you can reshape it into different dimensions using reshape():

reshaped_array = np.linspace(0, 1, 10).reshape(2, 5)
print(reshaped_array)

This showcases the flexibility of integrating linspace within a broader NumPy workflow. This allows for powerful array manipulations and computations based on evenly-spaced numerical sequences.