---
title: "Performance & Scalability Benchmarks"
output: rmarkdown::html_vignette
vignette: >
%\VignetteIndexEntry{Performance & Scalability Benchmarks}
%\VignetteEngine{knitr::rmarkdown}
%\VignetteEncoding{UTF-8}
---
```{r setup, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.width = 7,
fig.height = 5
)
```
## Executive Summary
Small Area Estimation often involves large administrative registries or extensive spatial networks with hundreds or thousands of domains. Traditional implementations in R often rely on interpreted loops, pure R Fisher-scoring routines, or large memory allocations for $D \times D$ dense covariance matrices.
**fastsae** re-architects core estimation algorithms in compiled C++ using `RcppArmadillo` and native `OpenMP` multi-threading, delivering:
- **Up to 364x faster** than `sae` and **12,300x faster** than `emdi` for Fay-Herriot models at $n = 1,000$.
- **Up to 80x faster** than `sae` for Spatial Fay-Herriot models at $n = 1,000$.
- **Up to 31x faster** than `sae` for Spatio-Temporal models at $n = 1,000$.
- **Massive RAM reduction**: Peak memory footprint stays under **25 MB** where existing packages require hundreds of megabytes or several gigabytes.
---
## Benchmark Results Table
The following benchmarks were conducted on simulated datasets across domain sizes ranging from $n = 30$ to $n = 1,000$ (with 5 auxiliary covariates):
| Metric | `fastsae` | `sae` (Molina & Rao) | `emdi` (Kreutzmann et al.) |
|:---|:---:|:---:|:---:|
| **Mean Time (EBLUP FH)** | **0.0015 s** | 0.291 s | 9.64 s |
| **Mean Time (Spatial FH)** | **0.165 s** | 12.60 s | 8.69 s |
| **Mean Time (Spatio-Temporal FH)** | **12.5 s** | 353.0 s | \- |
| **Peak Memory (EBLUP FH)** | **0.055 MB** | 16.3 MB | 824 MB |
| **Peak Memory (Spatial FH)** | **5.15 MB** | 408 MB | 824 MB |
| **Peak Memory (Spatio-Temporal FH)** | **0.289 MB** | 7,822 MB | \- |
| **Speedup at n = 1,000 (FH)** | **Baseline** | **~364x slower** | **~12,300x slower** |
---
## Interactive Benchmark Explorer
Use the interactive controls below to compare execution time, RAM consumption, and iterations per second across sample sizes:
```{=html}
Execution time (median, seconds) — FH · log scale
Speedup Factor (fastsae vs competitors) — FH
```
---
## Architectural Insights: Why is fastsae so Fast?
1. **Compiled C++ Linear Solvers**:
Instead of interpreting nested loops in R, `fastsae` implements Fisher-scoring parameter search and Woodbury identity matrix inversions in Armadillo C++, directly leveraging optimized BLAS/LAPACK routines.
2. **Zero-Copy Matrix Operations**:
Memory allocations for large intermediate structures ($V$, $V^{-1}$, $P$) are avoided or reused across Fisher iterations rather than reallocated on the heap.
3. **OpenMP Multi-Threaded Bootstrap**:
Bootstrap resampling runs natively in parallel across CPU cores using `#pragma omp parallel for`, avoiding the serialization overhead of R worker processes (`parallel::makeCluster` / `foreach`).
4. **Woodbury Identity for Panel Data**:
In `eblup_stfh`, inversion of the block $(DT \times DT)$ covariance matrix $V$ is reduced to operations on individual $D \times D$ and $T \times T$ blocks via Kronecker and Woodbury decomposition, transforming an $O((DT)^3)$ bottleneck into scalable $O(D^3 + T^3)$ steps.