docs: Document sqlite-vec faiss comparison (#1821)

# What does this PR do?
This PR documents and benchmarks the performance tradeoffs between
sqlite-vec and FAISS inline VectorDB providers.

# Closes https://github.com/meta-llama/llama-stack/issues/1165

## Test Plan

The test was run using this script:

<details>
<summary>CLICK TO SHOW SCRIPT 👋  </summary>

```python

import cProfile
import os
import uuid
import time
import random
import string
import matplotlib.pyplot as plt
import pandas as pd
from termcolor import cprint
from llama_stack_client.types import Document
from llama_stack.distribution.library_client import LlamaStackAsLibraryClient
from memory_profiler import profile
from line_profiler import LineProfiler

os.environ["INFERENCE_MODEL"] = "llama3.2:3b-instruct-fp16"
os.environ["LLAMA_STACK_CONFIG"] = "ollama"

def generate_random_chars(count=400):
    return ''.join(random.choices(string.ascii_letters, k=count))

def generate_documents(num_docs: int, num_chars: int):
    documents = [
        Document(
            document_id=f"doc-{i}",
            content=f"Document content for document {i} - {generate_random_chars(count=num_chars)}",
            mime_type="text/plain",
            metadata={},
        )
        for i in range(num_docs)
    ]
    return documents


@profile
def benchmark_write(client, vector_db_id, documents, batch_size=100):
    write_times = []
    for i in range(0, len(documents), batch_size):
        batch = documents[i:i + batch_size]
        start_time = time.time()
        client.tool_runtime.rag_tool.insert(
            documents=batch,
            vector_db_id=vector_db_id,
            chunk_size_in_tokens=512,
        )
        end_time = time.time()
        write_times.append(end_time - start_time)

    return write_times

@profile
def benchmark_read(client, provider_id, vector_db_id, user_prompts):
    response_times = []
    for prompt in user_prompts:
        start_time = time.time()
        response = client.vector_io.query(
            vector_db_id=vector_db_id,
            query=prompt,
        )
        end_time = time.time()
        response_times.append(end_time - start_time)
    return response_times

def profile_functions():
    profiler = LineProfiler()
    profiler.add_function(benchmark_write)
    profiler.add_function(benchmark_read)
    return profiler


def plot_results(output, batch_size):
    # Create a DataFrame for easy manipulation
    df_sqlite = pd.DataFrame(output['sqlite-vec'])
    df_faiss = pd.DataFrame(output['faiss'])

    df_sqlite['write_times'] *= 1000
    df_faiss['write_times'] *= 1000

    avg_write_sqlite = df_sqlite['write_times'].mean()
    avg_write_faiss = df_faiss['write_times'].mean()
    avg_read_sqlite = df_sqlite['read_times'].mean()
    avg_read_faiss = df_faiss['read_times'].mean()

    plt.figure(figsize=(12, 6))
    plt.hist(df_sqlite['write_times'], bins=10, alpha=0.5, color='blue', label='sqlite-vec Write Times')
    plt.hist(df_faiss['write_times'], bins=10, alpha=0.5, color='red', label='faiss Write Times')
    plt.axvline(avg_write_sqlite, color='blue', linestyle='--',
                label=f'Average Write Time (sqlite-vec): {avg_write_sqlite:.3f} ms')
    plt.axvline(avg_write_faiss, color='red', linestyle='--',
                label=f'Average Write Time (faiss): {avg_write_faiss:.3f} ms')
    plt.title(f'Histogram of Write Times for sqlite-vec and faiss\nn = {df_faiss.shape[0]} with batch size = {batch_size}')
    plt.xlabel('Time (milliseconds)')
    plt.ylabel('Density')
    plt.legend()
    plt.savefig('write_time_comparison.png')
    plt.close()

    plt.figure(figsize=(12, 6))
    plt.hist(df_sqlite['read_times'], bins=10, alpha=0.5, color='blue', label='sqlite-vec Read Times')
    plt.hist(df_faiss['read_times'], bins=10, alpha=0.5, color='red', label='faiss Read Times')
    plt.axvline(avg_read_sqlite, color='blue', linestyle='--',
                label=f'Average Read Time (sqlite-vec): {avg_read_sqlite:.3f} ms')
    plt.axvline(avg_read_faiss, color='red', linestyle='--',
                label=f'Average Read Time (faiss): {avg_read_faiss:.3f} ms')
    plt.title(f'Histogram of Read Times for sqlite-vec and faiss\nn = {df_faiss.shape[0]}')
    plt.xlabel('Time (milliseconds)')
    plt.ylabel('Density')
    plt.legend()
    plt.savefig('read_time_comparison.png')
    plt.close()

    plt.figure(figsize=(12, 6))
    plt.hist(df_sqlite['read_times'], bins=10, alpha=0.5, color='blue', label='sqlite-vec Read Times')
    plt.hist(df_faiss['read_times'], bins=10, alpha=0.5, color='red', label='faiss Read Times')
    plt.axvline(avg_read_sqlite, color='blue', linestyle='--',
                label=f'Average Read Time (sqlite-vec): {avg_read_sqlite:.3f} ms')
    plt.axvline(avg_read_faiss, color='red', linestyle='--',
                label=f'Average Read Time (faiss): {avg_read_faiss:.3f} ms')
    plt.title(f'Histogram of Read Times for sqlite-vec and faiss\nn = {df_faiss.shape[0]}')
    plt.xlabel('Time (milliseconds)')
    plt.ylabel('Density')
    plt.legend()
    plt.savefig('read_time_comparison.png')
    plt.close()

    plt.figure(figsize=(12, 6))
    plt.plot(df_sqlite.index, df_sqlite['write_times'],
             marker='o', markersize=4, linestyle='-', color='blue',
             label='sqlite-vec Write Times')
    plt.plot(df_faiss.index, df_faiss['write_times'],
             marker='x', markersize=4, linestyle='-', color='red',
             label='faiss Write Times')

    plt.title(f'Write Times by Operation Sequence\n(batch size = {batch_size})')
    plt.xlabel('Write Operation Sequence')
    plt.ylabel('Time (milliseconds)')
    plt.legend()
    plt.grid(True, linestyle='--', alpha=0.7)
    plt.tight_layout()
    plt.savefig('write_time_sequence.png')
    plt.close()
    # Print out the summary table
    print("\nPerformance Summary for sqlite-vec:")
    print(df_sqlite)

    # Print out the summary table
    print("\nPerformance Summary for faiss:")
    print(df_faiss)


def main():
    # Initialize the client
    client = LlamaStackAsLibraryClient("ollama")
    vector_db_id = f"test-vector-db-{uuid.uuid4().hex}"
    _ = client.initialize()

    # Generate a large dataset
    num_chars = 50
    num_docs = 100
    num_writes = 100
    write_batch_size = 100
    num_reads = 100

    documents = generate_documents(num_docs * write_batch_size, num_chars)
    user_prompts = [
        f"Tell me about document {i}" for i in range(1, num_reads + 1)
    ]

    providers = ["sqlite-vec", "faiss"]
    output = {
        provider_id: {"write_times": None, "read_times": None} for provider_id in providers
    }

    # Benchmark writes and reads for SQLite and Faiss
    for provider_id in providers:
        cprint(f"Benchmarking provider: {provider_id}", "yellow")
        client.vector_dbs.register(
            provider_id=provider_id,
            vector_db_id=vector_db_id,
            embedding_model="all-MiniLM-L6-v2",
            embedding_dimension=384,
        )
        write_times = benchmark_write(client, vector_db_id, documents, write_batch_size)

        average_write_time_ms = sum(write_times) / len(write_times) * 1000.
        cprint(f"Average write time for {provider_id} is {average_write_time_ms:.2f} milliseconds for {num_writes} runs", "blue")

        cprint(f"Benchmarking reads for provider: {provider_id}", "yellow")
        read_times = benchmark_read(client, provider_id, vector_db_id, user_prompts)

        average_read_time_ms = sum(read_times) / len(read_times) * 1000.
        cprint(f"Average read time for {provider_id} is {average_read_time_ms:.2f} milliseconds for {num_reads} runs", "blue")

        client.vector_dbs.unregister(vector_db_id=vector_db_id)
        output[provider_id]['write_times'] = write_times
        output[provider_id]['read_times'] = read_times
    # Generate plots and summary
    plot_results(output, write_batch_size)


if __name__ == "__main__":
    cProfile.run('main()', 'profile_output.prof')
```
</details>

---------

Signed-off-by: Francisco Javier Arceo <farceo@redhat.com>

docs/source/providers/vector_io/sqlite-vec.md

@@ -10,11 +10,57 @@ That means you're not limited to storing vectors in memory or in a separate serv
 ## Features
 
 - Lightweight and easy to use
-- Fully integrated with Llama Stack
+- Fully integrated with Llama Stacks
+- Uses disk-based storage for persistence, allowing for larger vector storage
+
+### Comparison to Faiss
+
+The choice between Faiss and sqlite-vec should be made based on the needs of your application,
+as they have different strengths.
+
+#### Choosing the Right Provider
+
+Scenario | Recommended Tool | Reason
+-- |-----------------| --
+Online Analytical Processing (OLAP) | Faiss           | Fast, in-memory searches
+Online Transaction Processing (OLTP) | sqlite-vec      | Frequent writes and reads
+Frequent writes | sqlite-vec      | Efficient disk-based storage and incremental indexing
+Large datasets | sqlite-vec      | Disk-based storage for larger vector storage
+Datasets that can fit in memory, frequent reads | Faiss | Optimized for speed, indexing, and GPU acceleration
+
+#### Empirical Example
+
+Consider the histogram below in which 10,000 randomly generated strings were inserted
+in batches of 100 into both Faiss and sqlite-vec using `client.tool_runtime.rag_tool.insert()`.
+
+```{image} ../../../../_static/providers/vector_io/write_time_comparison_sqlite-vec-faiss.png
+:alt: Comparison of SQLite-Vec and Faiss write times
+:width: 400px
+```
+
+You will notice that the average write time for `sqlite-vec` was 788ms, compared to
+47,640ms for Faiss. While the number is jarring, if you look at the distribution, you can see that it is rather
+uniformly spread across the [1500, 100000] interval.
+
+Looking at each individual write in the order that the documents are inserted you'll see the increase in
+write speed as Faiss reindexes the vectors after each write.
+```{image} ../../../../_static/providers/vector_io/write_time_sequence_sqlite-vec-faiss.png
+:alt: Comparison of SQLite-Vec and Faiss write times
+:width: 400px
+```
+
+In comparison, the read times for Faiss was on average 10% faster than sqlite-vec.
+The modes of the two distributions highlight the differences much further where Faiss
+will likely yield faster read performance.
+
+```{image} ../../../../_static/providers/vector_io/read_time_comparison_sqlite-vec-faiss.png
+:alt: Comparison of SQLite-Vec and Faiss read times
+:width: 400px
+```
 
 ## Usage
 
-To use SQLite-Vec in your Llama Stack project, follow these steps:
+To use sqlite-vec in your Llama Stack project, follow these steps:
 
 1. Install the necessary dependencies.
 2. Configure your Llama Stack project to use SQLite-Vec.