Provides the Adaptive Multiple Precision criteria functions. More...

#include "bertini2/trackers/config.hpp"

Include dependency graph for amp_criteria.hpp:

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Functions
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.

double	bertini::tracking::amp::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	bertini::tracking::amp::CriterionB (double const &norm_J, double const &norm_J_inverse, unsigned num_newton_iterations_remaining, double const &tracking_tolerance, double const &norm_of_latest_newton_residual, AdaptiveMultiplePrecisionConfig const &AMP_config)
	Check AMP Criterion B.

double	bertini::tracking::amp::CriterionBRHS (double const &norm_J, double const &norm_J_inverse, unsigned num_newton_iterations_remaining, double 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, typename Derived>
bool	bertini::tracking::amp::CriterionC (double const &norm_J_inverse, const Eigen::MatrixBase< Derived > &z, double tracking_tolerance, AdaptiveMultiplePrecisionConfig const &AMP_config)
	Check AMP Criterion C.

template<typename Derived>
double	bertini::tracking::amp::CriterionCRHS (double const &norm_J_inverse, const Eigen::MatrixBase< Derived > &z, double tracking_tolerance, AdaptiveMultiplePrecisionConfig const &AMP_config)
	Evaluate the right hand side of Criterion C.

double	bertini::tracking::amp::CriterionCRHS (double const &norm_J_inverse, double const &norm_z, double const &tracking_tolerance, AdaptiveMultiplePrecisionConfig const &AMP_config)
	Evaluate the right hand side of Criterion C.

double	bertini::tracking::amp::D (double const &norm_J, double const &norm_J_inverse, AdaptiveMultiplePrecisionConfig const &AMP_config)
	Compute the expression \(D\) from the AMP papers [1], [2].

Detailed Description

Provides the Adaptive Multiple Precision criteria functions.

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,
		double 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,
		double 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,
		double	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,
		double	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,
		double 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].

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 \(D\) from the AMP papers [1], [2].

Functions

Detailed Description

Function Documentation

◆ CriterionA()

◆ CriterionARHS()

◆ CriterionB()

◆ CriterionBRHS()

◆ CriterionC()

◆ CriterionCRHS() [1/2]

◆ CriterionCRHS() [2/2]

◆ D()