Functions
double	CriterionARHS (double const &norm_J, double const &norm_J_inverse, AdaptiveMultiplePrecisionConfig const &AMP_config)
	The right hand side of Criterion A, from [1], [2].
template<typename NumT>
bool	CriterionA (double const &norm_J, double const &norm_J_inverse, AdaptiveMultiplePrecisionConfig const &AMP_config)
	Check AMP Criterion A.
double	D (double const &norm_J, double const &norm_J_inverse, AdaptiveMultiplePrecisionConfig const &AMP_config)
	Compute the expression from the AMP papers [1], [2], [3].
double	CriterionBRHS (double const &norm_J, double const &norm_J_inverse, unsigned num_newton_iterations_remaining, NumErrorT const &tracking_tolerance, double const &norm_of_latest_newton_residual, AdaptiveMultiplePrecisionConfig const &AMP_config)
	Evaluate the right hand side of the inequality of Criterion B.
template<typename NumT>
bool	CriterionB (double const &norm_J, double const &norm_J_inverse, unsigned num_newton_iterations_remaining, NumErrorT const &tracking_tolerance, double const &norm_of_latest_newton_residual, AdaptiveMultiplePrecisionConfig const &AMP_config)
	Check AMP Criterion B.
double	CriterionCRHS (double const &norm_J_inverse, double const &norm_z, NumErrorT const &tracking_tolerance, AdaptiveMultiplePrecisionConfig const &AMP_config)
	Evaluate the right hand side of Criterion C.
template<typename Derived>
double	CriterionCRHS (double const &norm_J_inverse, const Eigen::MatrixBase< Derived > &z, NumErrorT tracking_tolerance, AdaptiveMultiplePrecisionConfig const &AMP_config)
	Evaluate the right hand side of Criterion C.
template<typename NumT, typename Derived>
bool	CriterionC (double const &norm_J_inverse, const Eigen::MatrixBase< Derived > &z, NumErrorT tracking_tolerance, AdaptiveMultiplePrecisionConfig const &AMP_config)
	Check AMP Criterion C.

Function Documentation

◆ CriterionA()

template<typename NumT>

bool bertini::tracking::amp::CriterionA	(	double const &	norm_J,
		double const &	norm_J_inverse,
		AdaptiveMultiplePrecisionConfig const &	AMP_config )

Check AMP Criterion A.

From [1], [2].

True means the check passed, and the precision is all good. False means something's gotta change, stepsize or precision.

Parameters

norm_J	The matrix norm of the Jacobian matrix
norm_J_inverse	An estimate on the norm of the inverse of the Jacobian matrix.
AMP_config	The settings for adaptive multiple precision.

Template Parameters

NumT	The real number type

Returns: True if criteria satisfied, false if violated and precision or step length should be adjusted.

◆ CriterionARHS()

double bertini::tracking::amp::CriterionARHS	(	double const &	norm_J,
		double const &	norm_J_inverse,
		AdaptiveMultiplePrecisionConfig const &	AMP_config )

inline

The right hand side of Criterion A, from [1], [2].

see CriterionA

◆ CriterionB()

template<typename NumT>

bool bertini::tracking::amp::CriterionB	(	double const &	norm_J,
		double const &	norm_J_inverse,
		unsigned	num_newton_iterations_remaining,
		NumErrorT const &	tracking_tolerance,
		double const &	norm_of_latest_newton_residual,
		AdaptiveMultiplePrecisionConfig const &	AMP_config )

Check AMP Criterion B.

This is Criterion B from [1], [2]. True means the check passed, and the precision is all good. False means something's gotta change, stepsize or precision.

Parameters

norm_J	The matrix norm of the Jacobian matrix
norm_J_inverse	An estimate on the norm of the inverse of the Jacobian matrix.
num_newton_iterations_remaining	The number of iterations which have yet to perform.
tracking_tolerance	The tightness to which the path should be tracked. This is the raw tracking tolerance (for now)
norm_of_latest_newton_residual	The norm of the length of the most recent Newton step.
AMP_config	The settings for adaptive multiple precision.

Template Parameters

NumT	The numeric type.

Returns: True if criteria satisfied, false if violated and precision or step length should be adjusted.

◆ CriterionBRHS()

double bertini::tracking::amp::CriterionBRHS	(	double const &	norm_J,
		double const &	norm_J_inverse,
		unsigned	num_newton_iterations_remaining,
		NumErrorT const &	tracking_tolerance,
		double const &	norm_of_latest_newton_residual,
		AdaptiveMultiplePrecisionConfig const &	AMP_config )

inline

Evaluate the right hand side of the inequality of Criterion B.

From [1], [2].

Parameters

norm_J	The matrix norm of the Jacobian matrix
norm_J_inverse	An estimate on the norm of the inverse of the Jacobian matrix.
num_newton_iterations_remaining	The number of iterations which have yet to perform.
tracking_tolerance	The tightness to which the path should be tracked. This is the raw tracking tolerance (for now)
norm_of_latest_newton_residual	The norm of the length of the most recent Newton step.
AMP_config	The settings for adaptive multiple precision.

Returns: The value of the right hand side of Criterion B

◆ CriterionC()

template<typename NumT, typename Derived>

bool bertini::tracking::amp::CriterionC	(	double const &	norm_J_inverse,
		const Eigen::MatrixBase< Derived > &	z,
		NumErrorT	tracking_tolerance,
		AdaptiveMultiplePrecisionConfig const &	AMP_config )

Check AMP Criterion C.

This is Criterion C from [1].

True means the check passed, and the precision is all good. False means something's gotta change, stepsize or precision.

Parameters

norm_J_inverse	An estimate on the norm of the inverse of the Jacobian matrix.
z	The current space point.
tracking_tolerance	The tightness to which the path should be tracked. This is the raw tracking tolerance
AMP_config	The settings for adaptive multiple precision.

Returns: A boolean indicating whether the criterion is satisfied. True means path tracking can continue without modifying tracking settings. False means that corrective action should be taken.

◆ CriterionCRHS() [1/2]

template<typename Derived>

double bertini::tracking::amp::CriterionCRHS	(	double const &	norm_J_inverse,
		const Eigen::MatrixBase< Derived > &	z,
		NumErrorT	tracking_tolerance,
		AdaptiveMultiplePrecisionConfig const &	AMP_config )

Evaluate the right hand side of Criterion C.

This is Criterion C from [1], [2].

Parameters

norm_J_inverse	An estimate on the norm of the inverse of the Jacobian matrix.
tracking_tolerance	The tightness to which the path should be tracked. This is the raw tracking tolerance
z	The current space point.
AMP_config	The settings for adaptive multiple precision.

Returns: The value of the right hand side of the inequality from Criterion C.

◆ CriterionCRHS() [2/2]

double bertini::tracking::amp::CriterionCRHS	(	double const &	norm_J_inverse,
		double const &	norm_z,
		NumErrorT const &	tracking_tolerance,
		AdaptiveMultiplePrecisionConfig const &	AMP_config )

inline

Evaluate the right hand side of Criterion C.

This is Criterion C, from [1], [2].

Parameters

norm_J_inverse	An estimate on the norm of the inverse of the Jacobian matrix.
tracking_tolerance	The tightness to which the path should be tracked. This is the raw tracking tolerance
norm_z	The norm of the current space point.
AMP_config	The settings for adaptive multiple precision.

Returns: The value of the right hand side of the inequality from Criterion C.

◆ D()

double bertini::tracking::amp::D	(	double const &	norm_J,
		double const &	norm_J_inverse,
		AdaptiveMultiplePrecisionConfig const &	AMP_config )

inline

Compute the expression $D$ from the AMP papers [1], [2], [3].

Parameters

norm_J	The matrix norm of the Jacobian matrix
norm_J_inverse	An estimate on the norm of the inverse of the Jacobian matrix.
AMP_config	The settings for adaptive multiple precision.

Returns: a double scalar, the quantity from the AMP papers [1], [2], [3].

Functions

Function Documentation

◆ CriterionA()

◆ CriterionARHS()

◆ CriterionB()

◆ CriterionBRHS()

◆ CriterionC()

◆ CriterionCRHS() [1/2]

◆ CriterionCRHS() [2/2]

◆ D()