⚡️ Speed up function _gridmake2 by 884%

[codeflash-ai]

📄 884% (8.84x) speedup for _gridmake2 in code_to_optimize/discrete_riccati.py

⏱️ Runtime : 1.07 milliseconds → 109 microseconds (best of 85 runs)

📝 Explanation and details

Performance Optimization Summary

The optimized code achieves an 884% speedup (from 1.07ms to 109μs) by replacing NumPy's high-level array operations with Numba JIT-compiled explicit loops.

Key Optimizations

1. Numba JIT Compilation (@njit(cache=True))

• Compiles the function to machine code at runtime, eliminating Python interpreter overhead
• The cache=True flag stores the compiled version, avoiding recompilation costs on subsequent runs
• Particularly effective here because the function contains simple arithmetic and array indexing operations that Numba optimizes well

2. Explicit Loop-Based Construction vs. NumPy Broadcasting

• Original approach: Used np.tile(), np.repeat(), and np.column_stack() which create multiple intermediate arrays and perform memory allocations
• Optimized approach: Pre-allocates the output array once with np.empty() and fills it directly using nested loops
• This eliminates intermediate array creation and reduces memory allocation overhead

3. Why This Works

From the line profiler, the original code spent:

• 76.4% of time in np.column_stack([np.tile(...)])
• 8.5% in np.repeat()
• 9.3% in np.tile() for the 2D case

These NumPy operations, while convenient, involve:

• Multiple temporary array allocations
• Memory copies during stacking operations
• Python-level function call overhead

Numba's compiled loops avoid all of this by directly computing each output element in place.

Impact on Workloads

Based on function_references, _gridmake2 is called from gridmake() which:

• Calls it once for 2 input arrays
• Calls it iteratively for 3+ arrays (once initially, then in a loop for remaining arrays)

For multi-array scenarios (3+ inputs), the speedup compounds significantly since _gridmake2 is called multiple times per gridmake() invocation. The nearly 9x speedup per call translates to substantial gains in computational economics applications where Cartesian products are frequently computed for state space expansions.

Trade-offs

• First call incurs JIT compilation overhead (~tens of milliseconds), but cache=True mitigates this for subsequent calls
• Code is more verbose but dramatically faster for repeated execution patterns
• Best suited for scenarios where the function is called multiple times (amortizing compilation cost)

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	✅ 31 Passed
🌀 Generated Regression Tests	🔘 None Found
⏪ Replay Tests	🔘 None Found
🔎 Concolic Coverage Tests	🔘 None Found
📊 Tests Coverage	100.0%

⚙️ Click to see Existing Unit Tests

Test File::Test Function	Original ⏱️	Optimized ⏱️	Speedup
test_gridmake2.py::TestGridmake2EdgeCases.test_both_empty_arrays	65.1μs	2.38μs	2640%✅
test_gridmake2.py::TestGridmake2EdgeCases.test_empty_arrays_raise_or_return_empty	65.5μs	3.83μs	1609%✅
test_gridmake2.py::TestGridmake2EdgeCases.test_float_dtype_preserved	65.5μs	2.21μs	2865%✅
test_gridmake2.py::TestGridmake2EdgeCases.test_integer_dtype_preserved	66.0μs	2.33μs	2731%✅
test_gridmake2.py::TestGridmake2NotImplemented.test_1d_first_2d_second_raises	49.2μs	27.8μs	76.7%✅
test_gridmake2.py::TestGridmake2NotImplemented.test_both_2d_raises	49.0μs	30.2μs	61.8%✅
test_gridmake2.py::TestGridmake2With1DArrays.test_basic_two_element_arrays	69.3μs	7.88μs	780%✅
test_gridmake2.py::TestGridmake2With1DArrays.test_different_length_arrays	66.5μs	2.54μs	2514%✅
test_gridmake2.py::TestGridmake2With1DArrays.test_float_arrays	66.2μs	3.25μs	1936%✅
test_gridmake2.py::TestGridmake2With1DArrays.test_larger_arrays	65.9μs	2.42μs	2627%✅
test_gridmake2.py::TestGridmake2With1DArrays.test_negative_values	65.8μs	2.17μs	2937%✅
test_gridmake2.py::TestGridmake2With1DArrays.test_result_shape	65.8μs	2.50μs	2530%✅
test_gridmake2.py::TestGridmake2With1DArrays.test_single_element_arrays	39.3μs	2.46μs	1500%✅
test_gridmake2.py::TestGridmake2With1DArrays.test_single_element_with_multi_element	66.2μs	2.25μs	2841%✅
test_gridmake2.py::TestGridmake2With2DFirst.test_2d_first_1d_second	41.9μs	3.25μs	1188%✅
test_gridmake2.py::TestGridmake2With2DFirst.test_2d_multiple_columns	12.7μs	2.17μs	486%✅
test_gridmake2.py::TestGridmake2With2DFirst.test_2d_single_column	41.3μs	2.17μs	1805%✅
test_gridmake2_torch.py::TestGridmake2TorchCPU.test_2d_and_1d_matches_numpy	43.9μs	3.88μs	1033%✅
test_gridmake2_torch.py::TestGridmake2TorchCPU.test_both_1d_matches_numpy	68.5μs	3.33μs	1955%✅

To edit these changes git checkout codeflash/optimize-_gridmake2-mjq2prhv and push.