⚡️ Speed up function numpy_matmul by 5,996%#239
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codeflash-ai[bot] wants to merge 1 commit intomainfrom
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⚡️ Speed up function numpy_matmul by 5,996%#239codeflash-ai[bot] wants to merge 1 commit intomainfrom
numpy_matmul by 5,996%#239codeflash-ai[bot] wants to merge 1 commit intomainfrom
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The optimized code achieves a **~60x speedup** by replacing the innermost loop with NumPy's `np.dot()` function. This is a critical optimization because: **What Changed:** - **Original**: Triple nested loop with element-wise operations: `result[i, j] += A[i, k] * B[k, j]` - **Optimized**: Two nested loops with vectorized dot product: `result[i, j] = np.dot(A[i, :], B[:, j])` **Why It's Faster:** 1. **Eliminates ~50 million Python loop iterations**: The innermost loop (accounting for 30% of runtime in profiling) is removed entirely, replaced by a single vectorized operation 2. **Leverages optimized BLAS libraries**: `np.dot()` calls highly optimized low-level linear algebra routines (BLAS) written in C/Fortran, which use SIMD instructions and cache-efficient algorithms 3. **Reduces array indexing overhead**: Instead of ~50 million individual array accesses (`A[i, k] * B[k, j]`), the code performs ~700K dot products on array slices, dramatically reducing Python interpreter overhead 4. **Better memory access patterns**: Vectorized operations have better cache locality compared to scattered element-wise access **Performance Characteristics from Tests:** - **Small matrices (2x2, 3x3)**: Mixed results (some 10-30% slower) due to function call overhead dominating for tiny workloads - **Medium matrices (100x100)**: **4411% faster** - sweet spot where vectorization overhead is amortized - **Large matrices (500x200 * 200x300)**: **8683% faster** - massive gains as BLAS optimizations fully activate - **Sparse matrices**: **12497% faster** - vectorized operations handle zeros efficiently without branching - **Vector operations (1x500 * 500x1)**: **5904% faster** - dot products are optimal for this pattern **Trade-offs:** - Slightly slower for very small matrices (1x1, small 2x2) where function call overhead exceeds loop savings - Minor slowdown for outer product patterns (column × row vectors) where the original loop structure was more natural The optimization is highly effective for real-world matrix operations (typically involving matrices >10x10), making it suitable for numerical computing, machine learning, and scientific applications where matrix multiplication is in performance-critical paths.
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📄 5,996% (59.96x) speedup for
numpy_matmulinsrc/numerical/linear_algebra.py⏱️ Runtime :
38.9 seconds→638 milliseconds(best of12runs)📝 Explanation and details
The optimized code achieves a ~60x speedup by replacing the innermost loop with NumPy's
np.dot()function. This is a critical optimization because:What Changed:
result[i, j] += A[i, k] * B[k, j]result[i, j] = np.dot(A[i, :], B[:, j])Why It's Faster:
np.dot()calls highly optimized low-level linear algebra routines (BLAS) written in C/Fortran, which use SIMD instructions and cache-efficient algorithmsA[i, k] * B[k, j]), the code performs ~700K dot products on array slices, dramatically reducing Python interpreter overheadPerformance Characteristics from Tests:
Trade-offs:
The optimization is highly effective for real-world matrix operations (typically involving matrices >10x10), making it suitable for numerical computing, machine learning, and scientific applications where matrix multiplication is in performance-critical paths.
✅ Correctness verification report:
🌀 Click to see Generated Regression Tests
To edit these changes
git checkout codeflash/optimize-numpy_matmul-mjsd18s0and push.