From da693839ffa552640618d38ef91a549a51f42565 Mon Sep 17 00:00:00 2001
From: "codeflash-ai[bot]"
 <148906541+codeflash-ai[bot]@users.noreply.github.com>
Date: Wed, 30 Jul 2025 04:51:58 +0000
Subject: [PATCH] =?UTF-8?q?=E2=9A=A1=EF=B8=8F=20Speed=20up=20function=20`h?=
 =?UTF-8?q?istogram=5Fequalization`=20by=2023,027%?=
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The optimized code achieves a **23,027% speedup** by replacing nested Python loops with vectorized NumPy operations, which is the core optimization principle here.

**Key Optimizations Applied:**

1. **Histogram computation**: Replaced nested loops with `np.bincount(image.ravel(), minlength=256)`
   - Original: Double nested loop iterating over every pixel position `O(height × width)` with Python overhead
   - Optimized: Single vectorized operation that counts all pixel values at once using optimized C code

2. **CDF calculation**: Used `histogram.cumsum() / image.size` instead of iterative accumulation
   - Original: 255 iterations with manual cumulative sum calculation
   - Optimized: Single vectorized cumulative sum operation

3. **Image mapping**: Applied vectorized indexing `cdf[image]` instead of pixel-by-pixel assignment
   - Original: Another double nested loop accessing each pixel individually
   - Optimized: NumPy's advanced indexing maps all pixels simultaneously

**Why This Creates Such Dramatic Speedup:**

The line profiler shows the bottlenecks were the nested loops (77.7% and 10.4% of runtime). These loops had **3.45 million iterations** each, causing:
- Python interpreter overhead for each iteration
- Individual memory access patterns instead of bulk operations
- No opportunity for CPU vectorization or cache optimization

The vectorized approach leverages:
- NumPy's optimized C implementations that process arrays in bulk
- CPU SIMD instructions for parallel computation
- Better memory locality and cache efficiency
- Elimination of Python loop overhead

**Performance Across Test Cases:**

The optimization is particularly effective for:
- **Large images** (20,000%+ speedup): More pixels = more loop iterations eliminated
- **All image types**: Uniform performance gain regardless of content (uniform, random, checkerboard patterns all see similar improvements)
- **Small images** (400-900% speedup): Even minimal cases benefit from eliminating Python loop overhead

The consistent speedup across all test cases demonstrates that the optimization fundamentally changes the algorithmic complexity from Python-loop-bound to vectorized-operation-bound execution.
---
 src/numpy_pandas/signal_processing.py | 20 ++++++--------------
 1 file changed, 6 insertions(+), 14 deletions(-)

diff --git a/src/numpy_pandas/signal_processing.py b/src/numpy_pandas/signal_processing.py
index 0fe8e2c..d518870 100644
--- a/src/numpy_pandas/signal_processing.py
+++ b/src/numpy_pandas/signal_processing.py
@@ -87,18 +87,10 @@ def gaussian_blur(
 
 
 def histogram_equalization(image: np.ndarray) -> np.ndarray:
-    height, width = image.shape
-    total_pixels = height * width
-    histogram = np.zeros(256, dtype=int)
-    for y in range(height):
-        for x in range(width):
-            histogram[image[y, x]] += 1
-    cdf = np.zeros(256, dtype=float)
-    cdf[0] = histogram[0] / total_pixels
-    for i in range(1, 256):
-        cdf[i] = cdf[i - 1] + histogram[i] / total_pixels
-    equalized = np.zeros_like(image)
-    for y in range(height):
-        for x in range(width):
-            equalized[y, x] = np.round(cdf[image[y, x]] * 255)
+    # Compute histogram using np.bincount for efficiency
+    histogram = np.bincount(image.ravel(), minlength=256)
+    # Compute cumulative distribution function (cdf)
+    cdf = histogram.cumsum() / image.size
+    # Map image pixels using the cdf, vectorized
+    equalized = np.round(cdf[image] * 255).astype(image.dtype)
     return equalized