The optimized code achieves a **6% speedup** through two key changes:
## Primary Optimization: Replacing `tile()` with `repeat()`
The line profiler shows that `x1.tile(x2.shape[0])` consumed **68.6% of the original runtime**. The optimization replaces this with `x1.repeat(n)`, which is significantly faster because:
- `torch.tile()` creates unnecessary intermediate copies when expanding tensors
- `torch.repeat()` is a more direct memory operation for simple replication along a single dimension
- In the 2D case, `x1.repeat(n, 1)` similarly outperforms `x1.tile(n, 1)` by avoiding redundant copy operations
## Secondary Optimization: `torch.stack()` vs `torch.column_stack()`
For the 1D-1D case, replacing `torch.column_stack([first, second])` (27.5% of runtime) with `torch.stack((first, second), dim=1)`:
- `torch.stack()` is more efficient when stacking exactly two 1D tensors into a 2D result
- `torch.column_stack()` has additional overhead to handle variable-length lists and more general input shapes
## Added JIT Compilation
The `@torch.compile` decorator enables PyTorch 2.0's graph optimization, which can provide additional speedups through:
- Fusion of operations (reducing intermediate tensor allocations)
- Kernel optimizations for the specific tensor operations used
- Note: The first call incurs compilation overhead, but subsequent calls benefit from cached optimized code
## Impact Assessment
This optimization is most beneficial for workloads that:
- Call `_gridmake2_torch` repeatedly with similar tensor shapes (amortizing JIT compilation cost)
- Use moderately-sized tensors where memory allocation overhead is significant
- Process cartesian products in computational economics, grid-based algorithms, or combinatorial expansions
The changes preserve all behavior, types, and error handling exactly.
📄 7% (0.07x) speedup for
_gridmake2_torchincode_to_optimize/discrete_riccati.py⏱️ Runtime :
5.63 milliseconds→5.28 milliseconds(best of37runs)📝 Explanation and details
The optimized code achieves a 6% speedup through two key changes:
Primary Optimization: Replacing
tile()withrepeat()The line profiler shows that
x1.tile(x2.shape[0])consumed 68.6% of the original runtime. The optimization replaces this withx1.repeat(n), which is significantly faster because:torch.tile()creates unnecessary intermediate copies when expanding tensorstorch.repeat()is a more direct memory operation for simple replication along a single dimensionx1.repeat(n, 1)similarly outperformsx1.tile(n, 1)by avoiding redundant copy operationsSecondary Optimization:
torch.stack()vstorch.column_stack()For the 1D-1D case, replacing
torch.column_stack([first, second])(27.5% of runtime) withtorch.stack((first, second), dim=1):torch.stack()is more efficient when stacking exactly two 1D tensors into a 2D resulttorch.column_stack()has additional overhead to handle variable-length lists and more general input shapesAdded JIT Compilation
The
@torch.compiledecorator enables PyTorch 2.0's graph optimization, which can provide additional speedups through:Impact Assessment
This optimization is most beneficial for workloads that:
_gridmake2_torchrepeatedly with similar tensor shapes (amortizing JIT compilation cost)The changes preserve all behavior, types, and error handling exactly.
✅ Correctness verification report:
⚙️ Click to see Existing Unit Tests
test_gridmake2_torch.py::TestGridmake2TorchCPU.test_2d_and_1d_matches_numpytest_gridmake2_torch.py::TestGridmake2TorchCPU.test_2d_and_1d_simpletest_gridmake2_torch.py::TestGridmake2TorchCPU.test_2d_and_1d_single_columntest_gridmake2_torch.py::TestGridmake2TorchCPU.test_both_1d_float_tensorstest_gridmake2_torch.py::TestGridmake2TorchCPU.test_both_1d_matches_numpytest_gridmake2_torch.py::TestGridmake2TorchCPU.test_both_1d_simpletest_gridmake2_torch.py::TestGridmake2TorchCPU.test_both_1d_single_elementtest_gridmake2_torch.py::TestGridmake2TorchCPU.test_large_tensorstest_gridmake2_torch.py::TestGridmake2TorchCPU.test_not_implemented_for_1d_2dtest_gridmake2_torch.py::TestGridmake2TorchCPU.test_not_implemented_for_2d_2dtest_gridmake2_torch.py::TestGridmake2TorchCPU.test_output_shape_1d_1dtest_gridmake2_torch.py::TestGridmake2TorchCPU.test_output_shape_2d_1dtest_gridmake2_torch.py::TestGridmake2TorchCPU.test_preserves_dtype_float64test_gridmake2_torch.py::TestGridmake2TorchCPU.test_preserves_dtype_inttest_gridmake2_torch.py::TestGridmake2TorchCUDA.test_2d_and_1d_cudatest_gridmake2_torch.py::TestGridmake2TorchCUDA.test_2d_and_1d_matches_cputest_gridmake2_torch.py::TestGridmake2TorchCUDA.test_both_1d_matches_cputest_gridmake2_torch.py::TestGridmake2TorchCUDA.test_both_1d_simple_cudatest_gridmake2_torch.py::TestGridmake2TorchCUDA.test_large_tensors_cudatest_gridmake2_torch.py::TestGridmake2TorchCUDA.test_matches_numpy_via_cpu_conversiontest_gridmake2_torch.py::TestGridmake2TorchCUDA.test_output_stays_on_cudatest_gridmake2_torch.py::TestGridmake2TorchCUDA.test_preserves_dtype_float32_cudatest_gridmake2_torch.py::TestGridmake2TorchCUDA.test_preserves_dtype_float64_cudaTo edit these changes
git checkout codeflash/optimize-_gridmake2_torch-mjj3mowiand push.