rsr45-dual-autodiff 0.0.post33

A Python package for forward-mode automatic differentiation using dual numbers.

dual_autodiff

dual_autodiff is a Python package that provides automatic differentiation using dual numbers. It is designed to handle derivatives and mathematical operations efficiently. The package also includes dual_autodiff_x, a Cython-optimized version for enhanced performance.

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Features

• Automatic differentiation using dual numbers.
• Support for a wide range of mathematical funtions:
• Cython-optimized version (dual_autodiff_x) for improved speed.

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Installation

Prerequisites

• Python 3.9 or higher.
• pip for package installation.
• conda (optional) for managing virtual environments.

Installing dual_autodiff

Using pip

Clone the repository and install the package:

git clone 'https://gitlab.developers.cam.ac.uk/phy/data-intensive-science-mphil/assessments/c1_coursework1/rsr45.git'
cd dual_autodiff
pip install e .

Using conda

1. Create a virtual environment using the provided environment.yaml file:

conda env create -n dual_env -f environment.yaml

2. Activate the environment:

conda activate dual_env

3. Install the package within this environment:

pip install -e .

Usage

Using dual_autodiff

from dual_autodiff import Dual, sin, cos

# Create a Dual object
x = Dual(1.0, 1.0)  

# Perform operations
y = sin(x)
print(f"Value: {y.real}, Derivative: {y.dual}")

Available Functions

Dual Class Methods

The following methods are available in the Dual class:

Arithmetic Operations

• __add__, __radd__ - Addition
• __sub__, __rsub__ - Subtraction
• __mul__, __rmul__ - Multiplication
• __truediv__, __rtruediv__ - Division
• __pow__ - Power

Trigonometric Functions

• sin() - Sine
• cos() - Cosine
• tan() - Tangent
• asin() - Arcsine
• acos() - Arccosine
• atan() - Arctangent

Exponential and Logarithmic Functions

• exp() - Exponential
• log() - Natural Logarithm
• sqrt() - Square Root

Hyperbolic Functions

• sinh() - Hyperbolic Sine
• cosh() - Hyperbolic Cosine
• tanh() - Hyperbolic Tangent

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Global Functions in functions.py

These functions are global aliases for the corresponding Dual class methods, allowing them to be called directly with either float or Dual inputs:

Trigonometric Functions

• sin
• cos
• tan
• asin
• acos
• atan

Exponential and Logarithmic Functions

• exp
• log
• sqrt

Hyperbolic Functions

• sinh
• cosh
• tanh

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How It Works

Dual Numbers

Dual numbers are numbers of the form:

[ a + b $\epsilon$ ]

Where:

• a is the real part, representing the function value.
• b is the dual part, representing the derivative.
• $\epsilon$^2 = 0, making (\epsilon) infinitesimally small.

This structure allows for efficient computation of derivatives during operations.

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Cython Optimization

The dual_autodiff_x package uses Cython to compile critical operations into C, providing a significant speed boost for computationally intensive tasks.

Installing dual_autodiff_x

For the Cython-optimized version:

cd dual_autodiff_x
pip install e .

See the README.md file in dual_autodiff_x.