srfm::tensor::DualNumber Struct Reference

#include <tensor.hpp>

Public Member Functions
constexpr DualNumber	operator+ (const DualNumber &o) const noexcept
constexpr DualNumber	operator- (const DualNumber &o) const noexcept
constexpr DualNumber	operator* (const DualNumber &o) const noexcept
constexpr DualNumber	operator/ (const DualNumber &o) const noexcept
constexpr DualNumber	operator+ (double s) const noexcept
constexpr DualNumber	operator- (double s) const noexcept
constexpr DualNumber	operator* (double s) const noexcept
constexpr DualNumber	operator/ (double s) const noexcept
constexpr DualNumber	operator- () const noexcept

Public Attributes
double	value
	Real part.
double	deriv
	Infinitesimal (ε) part: the directional derivative.

Friends
constexpr DualNumber	operator+ (double s, const DualNumber &d) noexcept
constexpr DualNumber	operator* (double s, const DualNumber &d) noexcept

Detailed Description

Forward-mode automatic differentiation scalar: x = value + deriv·ε, ε² = 0.

A dual number carries a real value and its directional derivative simultaneously. Arithmetic operations propagate both components according to the standard rules of dual-number algebra: (a+bε) + (c+dε) = (a+c) + (b+d)ε (a+bε) × (c+dε) = ac + (ad+bc)ε [ε² = 0] (a+bε) / (c+dε) = a/c + (bc−ad)/c²ε [c≠0]

Usage for metric derivatives

To compute ∂g_μν/∂x^σ exactly (without finite-difference truncation error):

// Seed coordinate σ with derivative 1; all others with derivative 0.
DualSpacetimePoint xd;
for (int k = 0; k < 4; ++k)
    xd[k] = DualNumber{x(k), k == sigma ? 1.0 : 0.0};
// Evaluate the dual-number metric; extract the .deriv component.
auto gd_mu_nu = dual_metric_fn(xd);
// gd_mu_nu(mu, nu).deriv == ∂g_μν/∂x^σ  (exact, no rounding)

Definition at line 80 of file tensor.hpp.

Member Function Documentation

operator*() [1/2]

constexpr DualNumber srfm::tensor::DualNumber::operator* ( const DualNumber &  o ) const

inlineconstexprnoexcept

Definition at line 92 of file tensor.hpp.

operator*() [2/2]

constexpr DualNumber srfm::tensor::DualNumber::operator* ( double  s ) const

inlineconstexprnoexcept

Definition at line 111 of file tensor.hpp.

operator+() [1/2]

constexpr DualNumber srfm::tensor::DualNumber::operator+ ( const DualNumber &  o ) const

inlineconstexprnoexcept

Definition at line 86 of file tensor.hpp.

operator+() [2/2]

constexpr DualNumber srfm::tensor::DualNumber::operator+ ( double  s ) const

inlineconstexprnoexcept

Definition at line 105 of file tensor.hpp.

operator-() [1/3]

constexpr DualNumber srfm::tensor::DualNumber::operator- ( ) const

inlineconstexprnoexcept

Definition at line 117 of file tensor.hpp.

operator-() [2/3]

constexpr DualNumber srfm::tensor::DualNumber::operator- ( const DualNumber &  o ) const

inlineconstexprnoexcept

Definition at line 89 of file tensor.hpp.

operator-() [3/3]

constexpr DualNumber srfm::tensor::DualNumber::operator- ( double  s ) const

inlineconstexprnoexcept

Definition at line 108 of file tensor.hpp.

operator/() [1/2]

constexpr DualNumber srfm::tensor::DualNumber::operator/ ( const DualNumber &  o ) const

inlineconstexprnoexcept

Definition at line 96 of file tensor.hpp.

operator/() [2/2]

constexpr DualNumber srfm::tensor::DualNumber::operator/ ( double  s ) const

inlineconstexprnoexcept

Definition at line 114 of file tensor.hpp.

Friends And Related Symbol Documentation

operator*

constexpr DualNumber operator* ( double  s, const DualNumber &  d  )

friend

Definition at line 124 of file tensor.hpp.

operator+

constexpr DualNumber operator+ ( double  s, const DualNumber &  d  )

friend

Definition at line 121 of file tensor.hpp.

Member Data Documentation

deriv

double srfm::tensor::DualNumber::deriv

Infinitesimal (ε) part: the directional derivative.

Definition at line 82 of file tensor.hpp.

value

double srfm::tensor::DualNumber::value

Real part.

Definition at line 81 of file tensor.hpp.

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The documentation for this struct was generated from the following file:

• include/srfm/tensor.hpp