MathSys::detail Namespace Reference

Functions
bool	IsOptionsValid (const NewtonOptions &theOptions)
	Check that NewtonOptions fields are positive and valid.
bool	IsBoundsValid2D (const NewtonBoundsN< 2 > &theBounds)
	Check that NewtonBoundsN<2> has valid (min <= max) ranges.
double	MaxDomainSize2D (const NewtonBoundsN< 2 > &theBounds)
	Return the largest domain extent across both dimensions (min 1.0).
void	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	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.
bool	IsBoundsValid3D (const NewtonBoundsN< 3 > &theBounds)
	Check that NewtonBoundsN<3> has valid (min <= max) ranges.
bool	IsOptionsValid3D (const NewtonOptions &theOptions)
	Check that NewtonOptions fields are positive and valid.
double	MaxDomainSize3D (const NewtonBoundsN< 3 > &theBounds)
	Return the largest domain extent across all 3 dimensions (min 1.0).
void	Clamp3D (std::array< double, 3 > &theX, const NewtonBoundsN< 3 > &theBounds, bool theUseSoftBounds, double theSoftExtRatio)
	Clamp solution array to bounds, optionally extending by soft-bounds ratio.
bool	Solve3x3 (const double theJ[3][3], const double theF[3], double theDelta[3])
	Solve 3x3 linear system J*x = -F using Cramer's rule with cofactor expansion.
bool	IsBoundsValid4D (const NewtonBoundsN< 4 > &theBounds)
	Check that NewtonBoundsN<4> has valid (min <= max) ranges.
bool	IsOptionsValid4D (const NewtonOptions &theOptions)
	Check that NewtonOptions fields are positive and valid.
double	MaxDomainSize4D (const NewtonBoundsN< 4 > &theBounds)
	Return the largest domain extent across all 4 dimensions (min 1.0).
void	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	Solve4x4 (const double theJ[4][4], const double theF[4], double theDelta[4])
	Solve 4x4 linear system using Gaussian elimination with partial pivoting.

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

Function Documentation

Clamp2D()

void MathSys::detail::Clamp2D ( std::array< double, 2 > & theX, const NewtonBoundsN< 2 > & theBounds, bool theUseSoftBounds, double theSoftExtRatio )

inline

Clamp solution array to bounds, optionally extending by soft-bounds ratio.

Clamp3D()

void MathSys::detail::Clamp3D ( std::array< double, 3 > & theX, const NewtonBoundsN< 3 > & theBounds, bool theUseSoftBounds, double theSoftExtRatio )

inline

Clamp solution array to bounds, optionally extending by soft-bounds ratio.

Clamp4D()

void MathSys::detail::Clamp4D ( std::array< double, 4 > & theX, const NewtonBoundsN< 4 > & theBounds, bool theUseSoftBounds, double theSoftExtRatio )

inline

Clamp solution array to bounds, optionally extending by soft-bounds ratio.

IsBoundsValid2D()

bool MathSys::detail::IsBoundsValid2D ( const NewtonBoundsN< 2 > & theBounds )

inline

Check that NewtonBoundsN<2> has valid (min <= max) ranges.

IsBoundsValid3D()

bool MathSys::detail::IsBoundsValid3D ( const NewtonBoundsN< 3 > & theBounds )

inline

Check that NewtonBoundsN<3> has valid (min <= max) ranges.

IsBoundsValid4D()

bool MathSys::detail::IsBoundsValid4D ( const NewtonBoundsN< 4 > & theBounds )

inline

Check that NewtonBoundsN<4> has valid (min <= max) ranges.

IsOptionsValid()

bool MathSys::detail::IsOptionsValid ( const NewtonOptions & theOptions )

inline

Check that NewtonOptions fields are positive and valid.

IsOptionsValid3D()

bool MathSys::detail::IsOptionsValid3D ( const NewtonOptions & theOptions )

inline

Check that NewtonOptions fields are positive and valid.

IsOptionsValid4D()

bool MathSys::detail::IsOptionsValid4D ( const NewtonOptions & theOptions )

inline

Check that NewtonOptions fields are positive and valid.

MaxDomainSize2D()

double MathSys::detail::MaxDomainSize2D ( const NewtonBoundsN< 2 > & theBounds )

inline

Return the largest domain extent across both dimensions (min 1.0).

MaxDomainSize3D()

double MathSys::detail::MaxDomainSize3D ( const NewtonBoundsN< 3 > & theBounds )

inline

Return the largest domain extent across all 3 dimensions (min 1.0).

MaxDomainSize4D()

double MathSys::detail::MaxDomainSize4D ( const NewtonBoundsN< 4 > & theBounds )

inline

Return the largest domain extent across all 4 dimensions (min 1.0).

Solve3x3()

bool MathSys::detail::Solve3x3 ( const double theJ[3][3], const double theF[3], double theDelta[3] )

inline

Solve 3x3 linear system J*x = -F using Cramer's rule with cofactor expansion.

Parameters

[in]	theJ	3x3 Jacobian matrix
[in]	theF	3-element right-hand side
[out]	theDelta	3-element solution vector

Returns

true if system was solved successfully (non-singular)

Solve4x4()

bool MathSys::detail::Solve4x4 ( const double theJ[4][4], const double theF[4], double theDelta[4] )

inline

Solve 4x4 linear system using Gaussian elimination with partial pivoting.

Parameters

[in]	theJ	4x4 Jacobian matrix
[in]	theF	4-element right-hand side
[out]	theDelta	4-element solution vector

Returns

true if system was solved successfully

SolveSymmetric2x2SVD()

bool MathSys::detail::SolveSymmetric2x2SVD ( double theJ11, double theJ12, double theJ22, double theF1, double theF2, double & theDU, double & theDV, double theTol = 1.0e-15 )

inline

Solve 2x2 symmetric system using eigenvalue decomposition (SVD fallback). More robust than Cramer's rule for ill-conditioned matrices.

Parameters

[in]	theJ11,theJ12,theJ22	symmetric Jacobian elements
[in]	theF1,theF2	right-hand side
[out]	theDU,theDV	solution components
[in]	theTol	tolerance for eigenvalue regularization

Returns

true if solution found

Variable Documentation

THE_ARMIJO_C1

constexpr double MathSys::detail::THE_ARMIJO_C1 = 1.0e-4

constexpr

THE_CRITICAL_GRAD_SQ

constexpr double MathSys::detail::THE_CRITICAL_GRAD_SQ = 1.0e-60

constexpr

THE_LINE_SEARCH_MAX

constexpr int MathSys::detail::THE_LINE_SEARCH_MAX = 8

constexpr

THE_SINGULAR_DET_TOL

constexpr double MathSys::detail::THE_SINGULAR_DET_TOL = 1.0e-25

constexpr