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Generating Numerical Sequences (arange, linspace, logspace)0%
Generating Numerical Sequences (arange, linspace, logspace)
Beginner12 min read•Updated: Jul 11, 2026
Generating Numerical Sequences (arange, linspace, logspace)
Mathematical modeling, data plotting, and algorithm testing often require continuous sequences of evenly distributed numbers. NumPy provides three core sequence generation engines: np.arange(), np.linspace(), and np.logspace().
1. Step-Based Sequences with np.arange()
np.arange() is the NumPy counterpart to Python's built-in range(), but returns a contiguous ndarray and supports floating-point steps:
import numpy as np
# Syntax: np.arange([start,] stop[, step,], dtype=None)
# 0 to 9 (start=0 default, step=1 default)
a = np.arange(10)
print(a) # [0 1 2 3 4 5 6 7 8 9] (Stop value 10 is EXCLUDED!)
# 10 to 50 with step of 5
b = np.arange(10, 50, 5)
print(b) # [10 15 20 25 30 35 40 45]
# Floating point step
c = np.arange(0.0, 1.0, 0.2)
print(c) # [0. 0.2 0.4 0.6 0.8]
The Floating-Point Step Hazard in arange:
Because computer hardware stores floating-point numbers in binary fractions, steps like
0.1 have minor precision rounding errors. Sometimes np.arange(0, 0.3, 0.1) returns 3 elements, and sometimes 4 depending on floating-point round-off!
For floating-point sequences, ALWAYS use np.linspace() instead!
Click to Zoom2. Sample-Count Sequences with np.linspace()
When generating sample points for charting (such as generating 100 points between $0$ and $2pi$ to plot a smooth Sine wave), you do not know the step size; you know how many points you want. np.linspace() solves this perfectly:
# Syntax: np.linspace(start, stop, num=50, endpoint=True)
# Generate exactly 5 evenly spaced points between 0 and 1
pts = np.linspace(0, 1, 5)
print(pts) # [0. 0.25 0.5 0.75 1. ]
Key Properties of linspace:
- Endpoint is Included: Unlike
arange(), thestopvalue is included by default! - Calculating the Step: NumPy calculates the exact step internally:
step = (stop - start) / (num - 1). - Retaining the Step Size: Pass
retstep=Trueto get both the array and the calculated step delta:
arr, step = np.linspace(0, 100, 5, retstep=True)
print(step) # 25.0
3. Logarithmic Scales with np.logspace()
For frequencies, decibels, seismic Richter scales, or machine learning hyperparameter tuning (e.g., testing learning rates across orders of magnitude from $10^{-4}$ to $10^{1}$):
# Syntax: np.logspace(start, stop, num=50, base=10.0)
# Generates 5 points spaced evenly on a log scale from 10^1 (10) to 10^4 (10000)
log_pts = np.logspace(1, 4, num=4)
print(log_pts) # [ 10. 100. 1000. 10000.]
# Powers of 2: from 2^0 (1) to 2^8 (256)
powers_of_two = np.logspace(0, 8, num=9, base=2)
print(powers_of_two) # [ 1. 2. 4. 8. 16. 32. 64. 128. 256.]
Interactive Quiz
Multiple Choice Questions
Question 1
What will 'np.arange(2, 10, 2)' return?
Question 2
Why is 'np.linspace()' strongly preferred over 'np.arange()' when generating floating-point ranges for data visualization?
Question 3
By default, is the 'stop' value included or excluded in 'np.linspace(0, 10, 5)'?
Question 4
What will 'np.linspace(0, 100, 5)' produce?
Question 5
What does the first argument 'start=2' represent in 'np.logspace(2, 5, num=4, base=10)'?
Next Lesson
NumPy Data Types (dtype) & Type Casting (astype)
Continue learning with hands-on practice, examples, and exercises in the upcoming topic.
Related Lessons
| Previous Lesson | Next Lesson |
|---|---|
| Built-in Creation Routines (zeros, ones, full, empty) | NumPy Data Types (dtype) & Type Casting (astype) |
Practice Quiz
Test your understanding of this lesson with 5 questions. Each question has one correct answer.