README.md

---
title: FlexChunk SpMV Demo
emoji: ⚡
colorFrom: blue
colorTo: green
sdk: gradio
sdk_version: 4.39.0
app_file: app.py
pinned: false
---

# FlexChunk: Enabling Massive Out-of-Core SpMV

This interactive demo showcases **FlexChunk**, an algorithm for performing Sparse Matrix-Vector Multiplication (SpMV) on matrices too large to fit in RAM.

**Key Benefit:** Process matrices up to 300M×300M using only ~1.7 GB RAM by dividing them into manageable horizontal chunks.

## Interactive Demo

The application above provides two modes:
- **Standard Mode**: For matrices up to 200K×200K with optional SciPy comparison
- **Advanced Mode**: For matrices up to 300M×300M using FlexChunk only

You can adjust parameters including:
- Matrix size
- Density
- Number of chunks
- Matrix type (standard or challenging with extreme values)

## Performance Highlights

FlexChunk demonstrates near-linear scaling in both time and memory usage:

| Matrix Size        | Non-zero Elements | Total Time      | Peak RAM Usage |
|--------------------|-------------------|-----------------|----------------|
| 1.0M × 1.0M        | 1.2M              | 1.07 s          | 17.00 MB       |
| 10.0M × 10.0M      | 12.0M             | 10.21 s         | 170.00 MB      |
| 50.0M × 50.0M      | 62.5M             | 55.27 s         | 850.00 MB      |
| 100.0M × 100.0M    | 120.0M            | 1 min 47.1 s    | 1.70 GB        |

Our algorithm scales linearly to even larger matrices (up to 300M×300M) with proportional increases in processing time and memory.

## How It Works

FlexChunk operates in three main stages:
1. **Matrix Division**: Splits the matrix into horizontal chunks and saves to disk
2. **Sequential Processing**: Loads one chunk at a time to minimize memory usage
3. **Result Accumulation**: Combines partial results into the final vector

This approach makes it possible to multiply vectors with matrices that would otherwise exceed available RAM.

## Links

- **Source Code**: [GitHub Repository](https://github.com/DanielSwift1992/FlexChunk)
- **Full Article**: [FlexChunk: Enabling 100M×100M Out-of-Core SpMV](https://www.lesswrong.com/posts/zpRhsdDkWygTDScxb/flexchunk-enabling-100m-100m-out-of-core-spmv-1-8-min-1-7-gb)