MathSys_Newton2D.hxx File Reference

Optimized 2D Newton-Raphson solvers with strict convergence criteria. More...

#include <MathSys_NewtonTypes.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::IsOptionsValid (const NewtonOptions &theOptions)
	Check that NewtonOptions fields are positive and valid.
bool	MathSys::detail::IsBoundsValid2D (const NewtonBoundsN< 2 > &theBounds)
	Check that NewtonBoundsN<2> has valid (min <= max) ranges.
double	MathSys::detail::MaxDomainSize2D (const NewtonBoundsN< 2 > &theBounds)
	Return the largest domain extent across both dimensions (min 1.0).
void	MathSys::detail::Clamp2D (std::array< double, 2 > &theX, const NewtonBoundsN< 2 > &theBounds, bool theUseSoftBounds, double theSoftExtRatio)
	Clamp solution array to bounds, optionally extending by soft-bounds ratio.
bool	MathSys::detail::SolveSymmetric2x2SVD (double theJ11, double theJ12, double theJ22, double theF1, double theF2, double &theDU, double &theDV, double theTol=1.0e-15)
	Solve 2x2 symmetric system using eigenvalue decomposition (SVD fallback). More robust than Cramer's rule for ill-conditioned matrices.
template<typename Function >
NewtonResultN< 2 >	MathSys::Solve2D (const Function &theFunc, const std::array< double, 2 > &theX0, const NewtonBoundsN< 2 > &theBounds, const NewtonOptions &theOptions=NewtonOptions())
	Solve a general 2x2 nonlinear system by Newton iteration. Function contract: bool operator()(double u, double v, double f[2], double j[2][2]) const;.
template<typename Function >
NewtonResultN< 2 >	MathSys::Solve2DSymmetric (const Function &theFunc, const std::array< double, 2 > &theX0, const NewtonBoundsN< 2 > &theBounds, const NewtonOptions &theOptions=NewtonOptions())
	Solve a 2x2 system with symmetric Jacobian by robust Newton iteration. Function contract: bool ValueAndJacobian(double u, double v, double& f1, double& f2, double& j11, double& j12, double& j22) const; bool Value(double u, double v, double& f1, double& f2) const; // required if line search is enabled.

Variables
constexpr double	MathSys::detail::THE_SINGULAR_DET_TOL = 1.0e-25
constexpr double	MathSys::detail::THE_CRITICAL_GRAD_SQ = 1.0e-60
constexpr int	MathSys::detail::THE_LINE_SEARCH_MAX = 8
constexpr double	MathSys::detail::THE_ARMIJO_C1 = 1.0e-4

Detailed Description

Optimized 2D Newton-Raphson solvers with strict convergence criteria.

Specifically optimized for 2D problems like:

• Point-surface extrema (find u,v where gradient is zero)
• Curve intersection (find t1,t2 where curves meet)
• Surface intersection curves