Bisect

Overview

Bisect is a deterministic, minimal-dependency numerical optimization engine engineered for robust scalar function evaluation. Built entirely from first principles following the mathematical frameworks in Edwin K. P. Chong & Stanislaw H. Zak's "An Introduction to Optimization", the system features a completely decoupled computational core (bisection_method.py) paired with an interactive visual dashboard built on Streamlit.

This system was originally developed as a standalone optimization tool for the CCS 239 - Optimization Theory and Applications course.

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Key Features

• Deterministic Core Solver: A standalone, highly decoupled Python module optimized for execution speed and floating-point precision tolerances.
• Symbolic Expression Parsing: Dynamic parsing of mathematical and polynomial functions via SymPy integration.
• Interval Boundary Validation: Automated runtime validation enforcing Intermediate Value Theorem thresholds before algorithm execution.
• Iterative Convergence Tracking: Generates granular execution logs and evaluation matrices for step-by-step matrix rendering.
• Visual Telemetry Dashboard: Interactive plotting layers that pinpoint calculated roots and dynamically map specified interval constraints.

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Bisect Image

Below is an image of the dashboard

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Module Usage

The core algorithm is decoupled from the rendering layer and can be imported seamlessly into any data pipeline as a standalone API.

from bisection_method import find_root

# Define target continuous function
def f(x):
    return x**3 - 4*x - 9

# Execute optimization solver
root, logs = find_root(
    interval=(2, 3),       # Packing bounds as (a, b)
    tolerance=0.0001,      # Target precision threshold (epsilon)
    f=f,                   # Objective function
    print_output=True,     # Iteration stdout mirroring
    get_logs=True          # Execution log matrix retrieval
)

print(f"Calculated Root: {root}")

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Local Setup & Deployment

This project prioritizes environment reproducibility. We strongly recommend using the uv package manager for automated dependency synchronization.

1. Environment Initialization

Install the uv package manager locally:

# MacOS / Linux Platforms
curl -LsSf [https://astral.sh/uv/install.sh](https://astral.sh/uv/install.sh) | sh

# Windows Platforms (Run PowerShell as Administrator)
powershell -ExecutionPolicy ByPass -c "irm [https://astral.sh/uv/install.ps1](https://astral.sh/uv/install.ps1) | iex"

2. Repository Cloning & Navigation

Clone the codebase and step into the project directory:

git clone https://github.com/hydraadra112/Bisect.git
cd Bisect/

3. Dependency Sync

Synchronize your local environment dependencies.

# Recommended: Automated synchronization via uv
uv sync

# Alternative: Manual installation via pip
pip install numpy==2.3.5 pandas==2.3.3 streamlit==1.51.0 sympy==1.14.0

# Active your environment variables
source .venv/bin/activate # MacOS or Linux

.venv\Scripts\activate # For Windows

4. Launch

Boot the Bisect locally

uv run -- streamlit run streamlit_app.py
# or 
streamlit run streamlit_app.py