Add a README.md for the folder benchmarks

benchmarks/README.md

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+## Benchmarks
+
+This directory contains all the scripts and configuration files needed to reproduce the numerical results presented in the paper **Recovering Sparse DFT from Missing Signals via Interior Point Method on GPU**.
+
+## Overview
+
+Each script in this folder benchmarks different aspects of our GPU-accelerated interior-point solver and FFT implementations, comparing them against CPU-based references.
+
+## Requirements
+
+Ensure you have the appropriate hardware drivers installed (CUDA for NVIDIA GPUs, ROCm for AMD GPUs).
+
+## Installation
+
+1. Launch Julia with the project environment:
+```shell
+julia --project=.
+```
+2. Instantiate the environment:
+```julia
+using Pkg
+Pkg.instantiate()
+```
+
+## Usage
+
+To run a benchmark script, use one of the following commands:
+```shell
+julia --project=. -e 'include("benchmarks_cufft.jl")'
+julia --project=. -e 'include("benchmarks_rocfft.jl")'
+julia --project=. -e 'include("cpu_vs_gpu.jl")'
+julia --project=. -e 'include("crystal.jl")'
+```
+
+## Scripts
+
+- **benchmarks_cufft.jl**  
+
+Compares **cuFFT** (via CUDA.jl) against **FFTW** (via FFTW.jl) on problems of various sizes.
+Measures execution time for `fft` and `ifft` operations on random data.
+
+- **benchmarks_rocfft.jl**  
+
+Compares **rocFFT** (via AMDGPU.jl) against **FFTW** (via FFTW.jl).
+Similar to the cuFFT benchmarks; results were not included in the final paper.
+
+- **cpu_vs_gpu.jl**  
+
+ Benchmarks our compressed sensing solver on CPU vs GPU across a range of problem sizes (artificial test cases).
+
+- **crystal.jl**  
+
+Applies the same solver to a real-world problem of **104 million variables**, comparing CPU and GPU performance on a crystallographic dataset.
+
+## Preferences
+
+To enable unified memory by default on the GH200, create a file named `LocalPreferences.toml` in this directory with the following content:
+
+```toml
+[CUDA]
+default_memory = "unified"
+```
+
+## Acknowledgments
+
+We thank [JLSE](https://www.jlse.anl.gov/) for providing access to the [NVIDIA GH200](https://www.jlse.anl.gov/nvidia-gh200) used in our experiments.