celeritas::ArraySoftUnit< T > Class Template Reference

Test for being approximately a unit vector. More...

#include <ArraySoftUnit.hh>

Public Types
Type aliases
using	value_type = T

Public Member Functions
	ArraySoftUnit (value_type tol)
	Construct with explicit tolereance.
constexpr	ArraySoftUnit ()
	Construct with default tolereance.
template<::celeritas::size_type N>
constexpr bool	operator() (Array< T, N > const &arr) const
	Calculate whether the array is nearly a unit vector.

Detailed Description

template<class T = ::celeritas::real_type>
class celeritas::ArraySoftUnit< T >

Test for being approximately a unit vector.

Consider a unit vector v with a small perturbation along a unit vector e :

\[ \vec v + \epsilon \vec e \]

The magnitude of this "nearly unit" is

\[ m^2 = (v + \epsilon e) \cdot (v + \epsilon e) = 1 + 2 (v \cdot e) \epsilon + \epsilon^2 \]

Since by the triangle inequality

\[ |v \cdot e| <= |v||e| = 1 \]

, then the magnitude squared of a perturbed unit vector is bounded

\[ m^2 = 1 \pm 2 \epsilon + \epsilon^2 \]

Instead of calculating the square of the tolerance we use \( \epsilon^2 < \epsilon \) to make the "soft unit vector" condition

\[ | \vec v \vd \vec v - 1 | < 3 \epsilon . \]

Member Function Documentation

operator()()

template<class T >

template<::celeritas::size_type N>

constexpr bool celeritas::ArraySoftUnit< T >::operator() ( Array< T, N > const &  arr ) const

inlineconstexpr

Calculate whether the array is nearly a unit vector.

The calculation below is equivalent to

return SoftEqual{tol, tol}(1, dot_product(arr, arr));

.

---

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

• ArraySoftUnit.hh