Optimizing Numpy Operations in Python Lambda Calculations

Introduction

As data scientists and engineers, we often encounter complex calculations that can significantly impact the performance of our applications. In this article, we will focus on optimizing a specific calculation involving numpy operations in Python using lambda functions.

The calculation in question involves finding percentile values from an image array and then calculating the variance of the differences between these percentile values. We’ll explore how to optimize this calculation using Numba, a library that provides high-performance support for the Python programming language.

Background

Before we dive into the optimization techniques, let’s first understand the basics of numpy and lambda functions in Python:

Numpy: The NumPy (Numerical Python) library is a fundamental package for scientific computing with Python. It provides support for large, multi-dimensional arrays and matrices, along with a wide range of high-performance mathematical functions to operate on these arrays.
Lambda Functions: Lambda functions are anonymous functions in Python that can be defined inline within a larger expression. They’re often used when you need a small, one-time-use function.

The Original Calculation

The original calculation involves the following steps:

Loop through an image array (winw2_grp) and find percentile values at every 7th step.
Calculate the difference between these percentile values.
Find the variance of these differences.

Here’s a code snippet illustrating this calculation using a lambda function:

Inner_diff_grp = np.var(list(map(lambda x : np.percentile(winw2_grp,x[0]) - np.percentile(winw2_grp,x[1])  ,[(i+7,i) for i in range(0,98,7)])))

Optimizing the Calculation using Numba

The original calculation involves multiple loops and lambda functions, which can lead to performance issues. To optimize this calculation, we can use Numba’s jit function to compile a Python function into a high-performance C code.

Here’s an updated version of the calculation using Numba:

import numba as nb

@nb.jit(nopython=True, fastmath=True)
def numba_perc_calc(win):
    arr = [0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98]
    perc = np.percentile(win, arr)
    dif = np.diff(perc)
    var_of_percs = np.var(dif)
    return var_of_percs

In this updated version:

We’ve imported Numba and decorated the numba_perc_calc function with the @nb.jit decorator.
We’ve set nopython=True to enable compile-time evaluation of Python objects, which can lead to significant performance improvements.
We’ve set fastmath=True to use fast math operations, which can also improve performance.

Further Optimizations

Besides using Numba’s jit function, there are a few more techniques we can use to further optimize this calculation:

Parallel Execution: Since we’re dealing with a large number of images (100,000), parallel execution can help speed up the calculation. We can use Python’s built-in threading or multiprocessing modules to achieve this.
Pooling: As mentioned in the original question, pooling involves dividing the workload across multiple CPUs. This can be achieved using Numba’s parallel_for function.

Here’s an updated version of the calculation that uses parallel execution:

import numba as nb
from numba import parallel

@nb.jit(nopython=True, fastmath=True)
def numba_perc_calc(win):
    arr = [0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98]
    perc = np.percentile(win, arr)
    dif = np.diff(perc)
    var_of_percs = np.var(dif)
    return var_of_percs

def parallel_numba_perc_calc(image_array):
    with parallel.for(range(len(image_array)), 'i'):
        result[i] = numba_perc_calc(image_array[i])

image_array = ...  # load your image array here
result = np.zeros_like(image_array)  # create a result array
parallel_numba_perc_calc(image_array)

In this updated version:

We’ve imported Numba’s parallel module.
We’ve decorated the numba_perc_calc function with the @nb.jit decorator, just like before.
We’ve created a new function called parallel_numba_perc_calc, which takes an image array as input and uses parallel execution to calculate the result.

Example Use Case

Let’s say we have an image array winw2_grp with shape (5, 5). We want to calculate the inner difference group (IDG) for each pixel in this array. Here’s how we can do it using our optimized function:

import numpy as np
import numba as nb

# Load the image array
image_array = ...  # load your image array here

# Calculate the IDG for each pixel
result = np.zeros_like(image_array)
with parallel.for(range(len(image_array)), 'i'):
    result[i] = numba_perc_calc(image_array[i])

print(result)

In this example:

We’ve loaded an image array using Numpy.
We’ve created a result array with the same shape as the input array.
We’ve used parallel execution to calculate the IDG for each pixel in the input array.

Conclusion

Optimizing numpy operations in Python can significantly improve application performance. By using techniques such as Numba’s jit function, parallel execution, and pooling, we can achieve significant speedups. In this article, we’ve explored how to optimize a specific calculation involving lambda functions and showed an example use case for our optimized function.

Additional Resources

Numba Documentation: For more information on using Numba, check out their official documentation: https://numba.pydata.org/
NumPy Documentation: For more information on NumPy, check out their official documentation: https://numpy.org/doc/

Last modified on 2024-02-28