NumExpr: The “Faster than Numpy” Library Most Data Scientists Have Never Used

the opposite day, I got here throughout a library I’d by no means heard of earlier than. It was referred to as NumExpr.

I used to be instantly due to some claims made concerning the library. Particularly, it acknowledged that for some complicated numerical calculations, it was as much as 15 occasions quicker than NumPy. 

I used to be intrigued as a result of, up till now, NumPy has remained unchallenged in its dominance within the numerical computation area in Python. Particularly with Data Science, NumPy is a cornerstone for machine studying, exploratory information evaluation and mannequin coaching. Something we are able to use to squeeze out each final little bit of efficiency in our methods will probably be welcomed. So, I made a decision to place the claims to the check myself.

You’ll find a hyperlink to the NumExpr repository on the finish of this text.

What’s NumExpr?

In response to its GitHub web page, NumExpr is a quick numerical expression evaluator for Numpy. Utilizing it, expressions that function on arrays are accelerated and use much less reminiscence than performing the identical calculations in Python with different numerical libraries, corresponding to NumPy.

As well as, as it’s multithreaded, NumExpr can use all of your CPU cores, which typically ends in substantial efficiency scaling in comparison with NumPy.

Organising a improvement surroundings

Earlier than we begin coding, let’s arrange our improvement surroundings. The very best follow is to create a separate Python surroundings the place you may set up any crucial software program and experiment with coding, realizing that something you do on this surroundings gained’t have an effect on the remainder of your system. I take advantage of conda for this, however you should utilize no matter methodology finest that fits you.

If you wish to go down the Miniconda route and don’t have already got it, you should set up Miniconda first. Get it utilizing this hyperlink:

https://www.anaconda.com/docs/main

1/ Create our new dev surroundings and set up the required libraries

(base) $ conda create -n numexpr_test python=3.12-y
(base) $ conda activate numexpr
(numexpr_test) $ pip set up numexpr
(numexpr_test) $ pip set up jupyter

2/ Begin Jupyter
Now kind in jupyter pocket book into your command immediate. It is best to see a jupyter pocket book open in your browser. If that doesn’t occur mechanically, you’ll seemingly see a screenful of knowledge after the jupyter pocket book command. Close to the underside, you can see a URL that it is best to copy and paste into your browser to launch the Jupyter Pocket book.

Your URL will probably be totally different to mine, nevertheless it ought to look one thing like this:-

http://127.0.0.1:8888/tree?token=3b9f7bd07b6966b41b68e2350721b2d0b6f388d248cc69

Evaluating NumExpr and NumPy efficiency

To match the efficiency, we’ll run a collection of numerical computations utilizing NumPy and NumExpr, and time each methods.

Instance 1 — A easy array addition calculation
On this instance, we run a vectorised addition of two massive arrays 5000 occasions.

import numpy as np
import numexpr as ne
import timeit

a = np.random.rand(1000000)
b = np.random.rand(1000000)

# Utilizing timeit with lambda capabilities
time_np_expr = timeit.timeit(lambda: 2*a + 3*b, quantity=5000)
time_ne_expr = timeit.timeit(lambda: ne.consider("2*a + 3*b"), quantity=5000)

print(f"Execution time (NumPy): {time_np_expr} seconds")
print(f"Execution time (NumExpr): {time_ne_expr} seconds")

>>>>>>>>>>>


Execution time (NumPy): 12.03680682599952 seconds
Execution time (NumExpr): 1.8075962659931974 seconds

I’ve to say, that’s a fairly spectacular begin from the NumExpr library already. I make {that a} 6 occasions enchancment over the NumPy runtime.

Let’s double-check that each operations return the identical consequence set.

# Arrays to retailer the outcomes
result_np = 2*a + 3*b
result_ne = ne.consider("2*a + 3*b")

# Guarantee the 2 new arrays are equal
arrays_equal = np.array_equal(result_np, result_ne)
print(f"Arrays equal: {arrays_equal}")

>>>>>>>>>>>>

Arrays equal: True

Instance 2 — Calculate Pi utilizing a Monte Carlo simulation

Our second instance will study a extra difficult use case with extra real-world functions.

Monte Carlo simulations contain working many iterations of a random course of to estimate a system’s properties, which may be computationally intensive.

On this case, we’ll use Monte Carlo to calculate the worth of Pi. It is a well-known instance the place we take a sq. with a facet size of 1 unit and inscribe 1 / 4 circle inside it with a radius of 1 unit. The ratio of the quarter circle’s space to the sq.’s space is (π/4)/1, and we are able to multiply this expression by 4 to get π by itself.

So, if we contemplate quite a few random (x,y) factors that each one lie inside or on the bounds of the sq., as the full variety of these factors tends to infinity, the ratio of factors that lie on or contained in the quarter circle to the full variety of factors tends in direction of Pi.

First, the NumPy implementation.

import numpy as np
import timeit

def monte_carlo_pi_numpy(num_samples):
    x = np.random.rand(num_samples)
    y = np.random.rand(num_samples)
    inside_circle = (x**2 + y**2) <= 1.0
    pi_estimate = (np.sum(inside_circle) / num_samples) * 4
    return pi_estimate

# Benchmark the NumPy model
num_samples = 1000000
time_np_expr = timeit.timeit(lambda: monte_carlo_pi_numpy(num_samples), quantity=1000)
pi_estimate = monte_carlo_pi_numpy(num_samples)

print(f"Estimated Pi (NumPy): {pi_estimate}")
print(f"Execution Time (NumPy): {time_np_expr} seconds")

>>>>>>>>

Estimated Pi (NumPy): 3.144832
Execution Time (NumPy): 10.642843848007033 seconds

Now, utilizing NumExpr.

import numpy as np
import numexpr as ne
import timeit

def monte_carlo_pi_numexpr(num_samples):
    x = np.random.rand(num_samples)
    y = np.random.rand(num_samples)
    inside_circle = ne.consider("(x**2 + y**2) <= 1.0")
    pi_estimate = (np.sum(inside_circle) / num_samples) * 4  # Use NumPy for summation
    return pi_estimate

# Benchmark the NumExpr model
num_samples = 1000000
time_ne_expr = timeit.timeit(lambda: monte_carlo_pi_numexpr(num_samples), quantity=1000)
pi_estimate = monte_carlo_pi_numexpr(num_samples)

print(f"Estimated Pi (NumExpr): {pi_estimate}")
print(f"Execution Time (NumExpr): {time_ne_expr} seconds")

>>>>>>>>>>>>>>>

Estimated Pi (NumExpr): 3.141684
Execution Time (NumExpr): 8.077501275009126 seconds

OK, so the speed-up was not as spectacular that point, however a 20% enchancment isn’t horrible both. A part of the reason being that NumExpr doesn’t have an optimised SUM() perform, so we needed to default again to NumPy for that operation.

Instance 3 — Implementing a Sobel picture filter

On this instance, we’ll implement a Sobel filter for photos. The Sobel filter is often utilized in picture processing for edge detection. It calculates the picture depth gradient at every pixel, highlighting edges and depth transitions. Our enter picture is of the Taj Mahal in India.

Let’s see the NumPy code working first and time it.

import numpy as np
from scipy.ndimage import convolve
from PIL import Picture
import timeit

# Sobel kernels
sobel_x = np.array([[-1, 0, 1],
                    [-2, 0, 2],
                    [-1, 0, 1]])

sobel_y = np.array([[-1, -2, -1],
                    [ 0,  0,  0],
                    [ 1,  2,  1]])

def sobel_filter_numpy(picture):
    """Apply Sobel filter utilizing NumPy."""
    img_array = np.array(picture.convert('L'))  # Convert to grayscale
    gradient_x = convolve(img_array, sobel_x)
    gradient_y = convolve(img_array, sobel_y)
    gradient_magnitude = np.sqrt(gradient_x**2 + gradient_y**2)
    gradient_magnitude *= 255.0 / gradient_magnitude.max()  # Normalize to 0-255
    
    return Picture.fromarray(gradient_magnitude.astype(np.uint8))

# Load an instance picture
picture = Picture.open("/mnt/d/check/taj_mahal.png")

# Benchmark the NumPy model
time_np_sobel = timeit.timeit(lambda: sobel_filter_numpy(picture), quantity=100)
sobel_image_np = sobel_filter_numpy(picture)
sobel_image_np.save("/mnt/d/check/sobel_taj_mahal_numpy.png")

print(f"Execution Time (NumPy): {time_np_sobel} seconds")

>>>>>>>>>

Execution Time (NumPy): 8.093792188999942 seconds

And now the NumExpr code.

import numpy as np
import numexpr as ne
from scipy.ndimage import convolve
from PIL import Picture
import timeit

# Sobel kernels
sobel_x = np.array([[-1, 0, 1],
                    [-2, 0, 2],
                    [-1, 0, 1]])

sobel_y = np.array([[-1, -2, -1],
                    [ 0,  0,  0],
                    [ 1,  2,  1]])

def sobel_filter_numexpr(picture):
    """Apply Sobel filter utilizing NumExpr for gradient magnitude computation."""
    img_array = np.array(picture.convert('L'))  # Convert to grayscale
    gradient_x = convolve(img_array, sobel_x)
    gradient_y = convolve(img_array, sobel_y)
    gradient_magnitude = ne.consider("sqrt(gradient_x**2 + gradient_y**2)")
    gradient_magnitude *= 255.0 / gradient_magnitude.max()  # Normalize to 0-255
    
    return Picture.fromarray(gradient_magnitude.astype(np.uint8))

# Load an instance picture
picture = Picture.open("/mnt/d/check/taj_mahal.png")

# Benchmark the NumExpr model
time_ne_sobel = timeit.timeit(lambda: sobel_filter_numexpr(picture), quantity=100)
sobel_image_ne = sobel_filter_numexpr(picture)
sobel_image_ne.save("/mnt/d/check/sobel_taj_mahal_numexpr.png")

print(f"Execution Time (NumExpr): {time_ne_sobel} seconds")

>>>>>>>>>>>>>

Execution Time (NumExpr): 4.938702256011311 seconds

On this event, utilizing NumExpr led to an awesome consequence, with a efficiency that was near double that of NumPy.

Here’s what the edge-detected picture seems like.

Instance 4 —  Fourier collection approximation

It’s well-known that complicated periodic capabilities may be simulated by making use of a collection of sine waves superimposed on one another. On the excessive, even a sq. wave may be simply modelled on this method. The tactic known as the Fourier collection approximation. Though an approximation, we are able to get as near the goal wave form as reminiscence and computational capability permit. 

The maths behind all this isn’t the first focus. Simply remember that after we enhance the variety of iterations, the run-time of the answer rises markedly.

import numpy as np
import numexpr as ne
import time
import matplotlib.pyplot as plt

# Outline the fixed pi explicitly
pi = np.pi

# Generate a time vector and a sq. wave sign
t = np.linspace(0, 1, 1000000) # Lowered measurement for higher visualization
sign = np.signal(np.sin(2 * np.pi * 5 * t))

# Variety of phrases within the Fourier collection
n_terms = 10000

# Fourier collection approximation utilizing NumPy
start_time = time.time()
approx_np = np.zeros_like(t)
for n in vary(1, n_terms + 1, 2):
    approx_np += (4 / (np.pi * n)) * np.sin(2 * np.pi * n * 5 * t)
numpy_time = time.time() - start_time

# Fourier collection approximation utilizing NumExpr
start_time = time.time()
approx_ne = np.zeros_like(t)
for n in vary(1, n_terms + 1, 2):
    approx_ne = ne.consider("approx_ne + (4 / (pi * n)) * sin(2 * pi * n * 5 * t)", local_dict={"pi": pi, "n": n, "approx_ne": approx_ne, "t": t})
numexpr_time = time.time() - start_time

print(f"NumPy Fourier collection time: {numpy_time:.6f} seconds")
print(f"NumExpr Fourier collection time: {numexpr_time:.6f} seconds")

# Plotting the outcomes
plt.determine(figsize=(10, 6))

plt.plot(t, sign, label='Unique Sign (Sq. Wave)', shade='black', linestyle='--')
plt.plot(t, approx_np, label='Fourier Approximation (NumPy)', shade='blue')
plt.plot(t, approx_ne, label='Fourier Approximation (NumExpr)', shade='purple', linestyle='dotted')

plt.title('Fourier Collection Approximation of a Sq. Wave')
plt.xlabel('Time')
plt.ylabel('Amplitude')
plt.legend()
plt.grid(True)
plt.present()

And the output?

That’s one other fairly good consequence. NumExpr exhibits a 5 occasions enchancment over Numpy on this event.

Abstract

NumPy and NumExpr are each highly effective libraries used for Python numerical computations. They every have distinctive strengths and use instances, making them appropriate for various kinds of duties. Right here, we in contrast their efficiency and suitability for particular computational duties, specializing in examples corresponding to easy array addition to extra complicated functions, like utilizing a Sobel filter for picture edge detection. 

Whereas I didn’t fairly see the claimed 15x pace enhance over NumPy in my assessments, there’s little question that NumExpr may be considerably quicker than NumPy in lots of instances.

Should you’re a heavy person of NumPy and have to extract each little bit of efficiency out of your code, I like to recommend making an attempt the NumExpr library. Moreover the truth that not all NumPy code may be replicated utilizing NumExpr, there’s virtually no draw back, and the upside may shock you.

For extra particulars on the NumExpr library, take a look at the GitHub web page here.