Cython vs Python Performance for Array Operations

When performing element wise operations on large arrays, different implementation strategies (pure Python loops, Cython compiled loops, NumPy vectorized calls) exhibit dramatically different performance characteristics. Understanding these tradeoffs is essential for optimizing ML pipelines. Implement a function analyze array performance that models and compares the execution time of array operations across three implementation approaches, given their performance parameters. The function receives: n: the array size (number of elements) operations: a list of dictionaries, each describing one array operation with keys: name (string), python per elem ns (per element cost in nanoseconds for pure Python), cython per elem ns (per element cost for Cython), numpy per elem ns (per element cost for NumPy), python overhead ns (fixed overhead for Python), cython overhead ns (fixed overhead for Cython), numpy overhead ns (fixed overhead for NumPy). For each operation and each method, the total execution time in nanoseconds follows the model: overhead ns + n per elem ns. Convert all times to microseconds for the output. For each operation, compute: Execution time in microseconds for each method, rounded to 2 decimal places Speedup of Cython over Python and NumPy over Python, each rounded to 2 decimal places The best method (the one with lowest time; prefer the method that appears first alphabetically among ties: cython < numpy < python) Also compute the crossover size for each operation: the minimum integer array size at which NumPy becomes faster than Cython. If Cython's per element cost is less than or equal to NumPy's, return 1 (no crossover). If NumPy is always faster (crossover value is zero or negative), return 0. Finally, compute pipeline totals (sum of times across all operations for each method, rounded to 2 decimal places) and identify the overall recommended method (lowest total pipeline time, same tie breaking rule). Return a dictionary with keys: operations: list of dicts with name, python us, cython us, numpy us, cython speedup, numpy speedup, best pipeline python us, pipeline cython us, pipeline numpy us: total pipeline times recommended: overall best method name crossover sizes: dict mapping operation name to crossover integer