Pre-Read Notes: Optimising Numerical Code
Prerequisites: Basic Python
programming, familiarity with NumPy arrays, basic loops and functions in
Python.
What You'll Gain from This Pre-Read
After reading, you'll be able to:
- Recognize how vectorised patterns can replace
loops for faster computation.
- Understand why Cython and Numba are used to
speed up numerical code.
- Identify when and where to apply these
techniques in real-world applications.
- Ask informed questions as you explore
performance optimization in Python.
Think of this as: Learning
shortcuts for efficient work—you’ll still understand the steps, but your code
will run faster and scale better.
What This Pre-Read Covers
This pre-read will:
- Introduce core concepts of vectorised patterns
and JIT compilation.
- Explain why these topics matter for
performance in data-heavy applications.
- Show simple, foundational examples of
vectorisation and accelerated loops.
- Build curiosity and confidence in writing
efficient numerical Python code.
Part 1: The Big Picture - Why Does This
Matter?
Opening hook: Have you ever
waited minutes for a Python loop to process a large dataset, only to realize it
could have been done in seconds?
Expand on the hook: In data
science, finance, simulations, or machine learning, computations often involve
millions of numbers. Writing simple Python loops can be intuitive but slow.
Optimising numerical code ensures that your programs scale efficiently, saving
both time and computational resources.
Where You'll Use This:
Job roles:
- Data Scientist: Speed up preprocessing and
feature engineering on large datasets.
- Machine Learning Engineer: Train models faster
using vectorised operations and JIT compilation.
- Quantitative Analyst: Run complex simulations
efficiently without waiting hours.
Real products:
- Netflix and Spotify: Real-time recommendations
rely on fast numerical operations.
- Google Maps: Quick calculations for routing
millions of users simultaneously.
- Scientific simulations: Physics engines and
climate models compute millions of iterations efficiently.
What you can build:
- High-speed data pipelines for analytics.
- Machine learning models handling large-scale
datasets.
- Simulation engines for research and engineering
tasks.
Think of it like this: Optimising code
is like preparing ingredients for a recipe. Instead of chopping vegetables one
by one (loops), you use a food processor (vectorisation), making the process
faster without changing the outcome.
Limitation: The analogy
breaks down for specialized operations that require step-by-step
logic—vectorisation may not always replace every loop.
Part 2: Your Roadmap Through This Topic
Here's what we'll
explore together:
1. Vectorised Patterns
You'll discover how
applying operations to entire NumPy arrays at once can replace slow loops and
simplify your code.
2. NumPy Arrays and Broadcasting
We'll explore how
NumPy arrays work with vectorised patterns and broadcasting rules to perform
calculations across different shapes effortlessly.
3. Cython Primer
Learn how Cython
converts Python code to compiled C code to achieve near-native performance on
loops and numerical operations.
4. Numba Primer
See how Numba's
just-in-time (JIT) compilation accelerates Python functions dynamically, making
heavy computations faster.
The journey: We'll start
with understanding vectorised operations, learn to accelerate loops with Cython
and Numba, and then see how these tools improve real-world numerical tasks.
Part 3: Key Terms to Listen For
Vectorisation
Performing operations
on entire arrays rather than looping through elements.
Example: Adding two
NumPy arrays directly without iterating.
Broadcasting
Automatically
aligning arrays of different shapes to perform operations.
Think of it as: Stretching a
smaller dataset to match a bigger one for math operations, like applying a
single sauce recipe to multiple batches.
Cython
A superset of Python
that compiles to C for faster execution.
In practice: Converts Python
loops into compiled code that runs much faster.
Numba
A just-in-time (JIT)
compiler that accelerates Python functions.
Example: Adding@jitto a Python function
allows loops over large arrays to run hundreds of times faster.
Efficiency
Writing code that
reduces computation time and resource usage without sacrificing correctness.
💡 Key Insight: Vectorisation, Cython, and Numba all
aim to make Python numerical code faster, but in slightly different
ways—vectorisation leverages array operations, Cython compiles code
ahead-of-time, and Numba compiles code just-in-time.
Part 4: Concepts in Action
Seeing Vectorised
Patterns in Action
The scenario: You have daily
sales data for 10,000 stores. You want to calculate the percentage increase in
sales from one day to the next. Looping through each store is slow.
Our approach: Use NumPy array
operations to compute all percentage increases simultaneously.
python
import numpy as np
# Step 1: Create random sales data for
10,000 stores over 7 days
sales = np.random.randint(100, 1000,
size=(10000, 7))
# Step 2: Calculate daily percentage
change using vectorised operations
pct_change = (sales[:, 1:] - sales[:,
:-1]) / sales[:, :-1] * 100
# Result: Each row now shows the
percentage change day-to-day
print(pct_change.shape)
What's happening
here: We subtract each day’s sales from the next day for all stores at once,
then divide by the previous day’s sales. NumPy handles all rows in parallel
without a Python loop.
The output/result:(10000,
6)array of percentage changes.
Key takeaway:
Vectorised patterns allow fast, clean calculations over large datasets without
explicit loops.
⚠️ Common Misconception: Beginners often think loops are unavoidable; in
fact, most array-based calculations can be vectorised.
Seeing Cython in
Action
The scenario: You need to sum
squares of numbers in a list of 10 million elements. Python loops are slow.
Our approach: Convert the
function to Cython for faster execution.
# my_cython_code.pyx
def sum_squares(double[:] arr):
cdef int i
cdef double result = 0
for i in range(arr.shape[0]):
result += arr[i] * arr[i]
return result
What's happening
here: Cython compiles the loop into C code. Thecdefkeyword declares C
types for speed, and the loop executes in compiled C rather than Python.
Key takeaway: Cython
drastically reduces runtime for heavy numerical loops while keeping Python-like
syntax.
⚠️ Common Misconception: Cython requires rewriting all code—only
performance-critical parts need to be converted.
Seeing Numba in
Action
The scenario: Calculating
pairwise distances between points in a 2D space for 1 million points.
Our approach: Use Numba’s@jitdecorator to
accelerate the computation.
python
from numba import jit
import numpy as np
points = np.random.rand(1000000, 2)
@jit(nopython=True)
def pairwise_distances(points):
n = points.shape[0]
dists = np.zeros((n, n))
for i in range(n):
for j in range(n):
dists[i, j] =
np.sqrt((points[i,0]-points[j,0])**2 + (points[i,1]-points[j,1])**2)
return dists
# Calculate distances
# dist_matrix =
pairwise_distances(points)
What's happening
here: The double loop is compiled just-in-time to machine code. The computation
becomes hundreds of times faster compared to pure Python.
Key takeaway: Numba
can accelerate Python loops dynamically with minimal code changes.
⚠️ Common Misconception: JIT compilation can be slow the first time the
function runs, but subsequent calls are very fast.
Seeing Combined
Approach in Action
The scenario: Normalize a
large dataset and compute a transformed value for every row.
Our approach: Combine
vectorised operations with Numba for optimal speed.
python
import numpy as np
from numba import jit
data = np.random.rand(1000000, 5)
@jit(nopython=True)
def transform_data(arr):
# Vectorised normalization
mean = np.mean(arr, axis=1)
std = np.std(arr, axis=1)
normalized = (arr - mean[:, None]) / std[:, None]
return normalized ** 2 #
element-wise square
transformed = transform_data(data)
What's happening
here: Vectorisation handles row-wise normalization, and Numba speeds up any
remaining loops or calculations.
Key takeaway:
Combining vectorisation and JIT compilation offers the best of both worlds:
readability and speed.
⚠️ Common Misconception: Vectorisation alone is always fastest—sometimes
combining with JIT yields better performance on extremely large datasets.
Part 5: Bringing It All Together
Vectorised Patterns in Practice
- Vectorised operations let you perform
calculations on entire arrays instead of individual elements.
- Useful for tasks like data normalization,
image transformations, and mathematical simulations.
Cython/Numba for Speed
- Cython compiles Python code to C for heavy
computations.
- Numba dynamically accelerates Python functions
with JIT compilation.
- Combining these with vectorisation results in
highly efficient numerical code.
In short: You can write
clear Python code that handles millions of data points efficiently,
using these tools together.
Part 6: Key Takeaways
|
Concept |
What
It Means |
Why
It Matters |
|
Vectorised Patterns |
Apply operations on
arrays at once |
Avoids slow Python
loops |
|
NumPy Arrays |
Efficient storage
for numbers |
Foundation for
vectorisation |
|
Cython |
Compile Python to C |
Speeds up loops and
heavy computation |
|
Numba |
Just-in-time
compiler |
Accelerates Python
functions dynamically |
|
Efficiency |
Optimised code for
performance |
Essential for
handling large-scale data |
💬 Summary Thought:
Optimising numerical
code is crucial in data-heavy tasks. Vectorisation simplifies code, and
Cython/Numba dramatically improve execution speed. Mastering these gives you
a competitive edge in real-world data processing.
✅ By the end of this pre-read, you should be able to:
- Replace Python loops with vectorised
operations.
- Apply Cython and Numba to speed up numerical
functions.
- Understand performance trade-offs and choose
the right optimization.
- Recognize situations where these techniques
save time in practice.
Next Steps
- Practice vectorisation: Convert loops to array
operations in NumPy.
- Experiment
with Numba: Apply@jitto Python functions and
benchmark speed-ups.
- Explore Cython: Compile slow Python
code and compare performance.
- Try real-world data: Use large datasets and
observe differences in execution time.
