Optimized 4D Newton-Raphson solver for systems of 4 equations in 4 unknowns. More...

#include <MathSys_NewtonTypes.hxx>
#include <gp_Pnt.hxx>
#include <gp_Vec.hxx>
#include <algorithm>
#include <array>
#include <cmath>

Namespaces
namespace	MathSys
	Shared types for specialized small-dimension Newton solvers.

namespace	MathSys::detail

Functions
bool	MathSys::detail::IsBoundsValid4D (const NewtonBoundsN< 4 > &theBounds)
	Check that NewtonBoundsN<4> has valid (min <= max) ranges.

bool	MathSys::detail::IsOptionsValid4D (const NewtonOptions &theOptions)
	Check that NewtonOptions fields are positive and valid.

double	MathSys::detail::MaxDomainSize4D (const NewtonBoundsN< 4 > &theBounds)
	Return the largest domain extent across all 4 dimensions (min 1.0).

void	MathSys::detail::Clamp4D (std::array< double, 4 > &theX, const NewtonBoundsN< 4 > &theBounds, bool theUseSoftBounds, double theSoftExtRatio)
	Clamp solution array to bounds, optionally extending by soft-bounds ratio.

bool	MathSys::detail::Solve4x4 (const double theJ[4][4], const double theF[4], double theDelta[4])
	Solve 4x4 linear system using Gaussian elimination with partial pivoting.

template<typename Function >
NewtonResultN< 4 >	MathSys::Solve4D (const Function &theFunc, const std::array< double, 4 > &theX0, const NewtonBoundsN< 4 > &theBounds, const NewtonOptions &theOptions=NewtonOptions())
	Solve a 4x4 nonlinear system by Newton iteration with bounds.

template<typename SurfaceEvaluator1 , typename SurfaceEvaluator2 >
NewtonResultN< 4 >	MathSys::SolveSurfaceSurfaceExtrema4D (const SurfaceEvaluator1 &theSurf1, const SurfaceEvaluator2 &theSurf2, const std::array< double, 4 > &theX0, const NewtonBoundsN< 4 > &theBounds, const NewtonOptions &theOptions=NewtonOptions())
	Optimized 4D Newton solver for surface-surface extrema.

Detailed Description

Optimized 4D Newton-Raphson solver for systems of 4 equations in 4 unknowns.

This solver is specifically optimized for 4D problems like:

Optimizations compared to general Newton:

Namespaces