Dual Number

This module adds support for Dual Numbers and Forward Mode Auto Differentiation.

class einsteinpy.utils.dual.DualNumber(val, deriv)[source]

Bases: object

Numbers of the form, \(a + b\epsilon\), where \(\epsilon^2 = 0\) and \(\epsilon \ne 0\). Their addition and multiplication properties make them suitable for Automatic Differentiation (AD). EinsteinPy uses AD for solving Geodesics in arbitrary spacetimes. This module is based on 1.

References

1

Christian, Pierre and Chan, Chi-Kwan; “FANTASY: User-Friendly Symplectic Geodesic Integrator for Arbitrary Metrics with Automatic Differentiation”; 2021 ApJ 909 67

Constructor

Parameters
  • val (float) – Value

  • deriv (float) – Directional Derivative