Issue A2: Performance Optimization — Accelerate `accorr` Metric

[Ramdam17]

Description:

Optimize the accorr (adjusted circular correlation) metric computation, which is currently a performance bottleneck.

Context:
The accorr metric in analyses.py is slow for large datasets. Users have reported long computation times that limit practical use. We need to explore optimization strategies.

Current implementation location: hypyp/analyses.py

Optimization strategies to explore:

1. Pre-computing

   • Identify repeated computations that can be cached
   • Pre-compute frequency band signals once, reuse across metrics

2. Parallelization

   • Use joblib for parallel computation across epochs/channels
   • Consider numba JIT compilation for inner loops
   • Explore numpy vectorization improvements

3. Algorithm optimization

   • Profile current code to find bottlenecks
   • Review circular statistics libraries (e.g., pycircstat, astropy.stats)
   • Consider approximations for large datasets

Tasks:

• Profile current accorr implementation (use cProfile or line_profiler)
• Identify top 3 bottlenecks
• Implement at least one optimization strategy
• Benchmark: before vs. after (varying data sizes)
• Ensure numerical accuracy is preserved (compare outputs)
• Add tests for optimized code

Acceptance Criteria:

• Profiling report identifying bottlenecks
• At least 2x speedup on benchmark dataset
• Benchmark script included in PR
• Unit tests pass (numerical accuracy preserved)
• Documentation of optimization approach

Benchmark template:

import time
import numpy as np
from hypyp import analyses

# Generate test data of varying sizes
sizes = [(10, 32, 1000), (50, 64, 2000), (100, 64, 5000)]

for n_epochs, n_channels, n_samples in sizes:
    data = generate_test_data(n_epochs, n_channels, n_samples)
    
    start = time.time()
    result = analyses.compute_sync(data, metric='accorr')
    elapsed = time.time() - start
    
    print(f"Size {n_epochs}x{n_channels}x{n_samples}: {elapsed:.2f}s")

---