Contains the AMPTracker type, and necessary functions. More...

#include <assert.h>
#include "bertini2/trackers/base_tracker.hpp"

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Classes
class	bertini::tracking::AMPTracker
	Functor-like class for tracking paths on a system. More...

Functions
double	bertini::tracking::ArithmeticCost (unsigned precision)
	Compute the cost function for arithmetic versus precision.

template<typename T>
T	bertini::tracking::max (T const &a, T const &b, T const &c)
	Three-argument form of `max`.

unsigned	bertini::tracking::MinDigitsForLogOfStepsize (mpfr_float const &log_of_stepsize, mpfr_float const &time_to_go, unsigned safety_digits=3)
	The minimum number of digits based on a log10 of a stepsize.

unsigned	bertini::tracking::MinDigitsForStepsizeInterval (mpfr_float const &min_stepsize, mpfr_float const &max_stepsize, mpfr_float const &time_to_go)
	For a given range of stepsizes under consideration, gives the minimum number of digits.

template<typename RealT>
void	bertini::tracking::MinimizeTrackingCost (unsigned &new_precision, RealT &new_stepsize, unsigned min_precision, RealT const &min_stepsize, unsigned max_precision, RealT const &max_stepsize, unsigned digits_B, unsigned num_newton_iterations, unsigned predictor_order=0)
	Compute precision and stepsize minimizing the ArithmeticCost() of tracking.

mpfr_float	bertini::tracking::MinStepSizeForPrecision (unsigned precision, mpfr_float const &time_to_go, int safety_digits=3)
	Just another name for MinTimeForCurrentPrecision.

mpfr_float	bertini::tracking::MinTimeForCurrentPrecision (unsigned precision, mpfr_float const &time_to_go, int safety_digits=3)

mpfr_float	bertini::tracking::StepsizeSatisfyingCriterionB (unsigned precision, unsigned digits_B, unsigned num_newton_iterations, unsigned predictor_order=0)
	Compute a stepsize satisfying AMP Criterion B with a given precision.

Detailed Description

Contains the AMPTracker type, and necessary functions.

Function Documentation

◆ ArithmeticCost()

double bertini::tracking::ArithmeticCost ( unsigned precision )

inline

Compute the cost function for arithmetic versus precision.

From [2], \(C(P)\). As currently implemented, this is \( 10.35 + 0.13 P \), where P is the precision. These numbers are stale, and need to be recomputed. Badly. Please do this.

This function tells you the relative cost of arithmetic at a given precision.

Todo: Recompute this cost function for boost::multiprecision::mpfr_float

Parameters

precision An integral number of digits – then this gives the cost for arithmetic

Returns: A double indicating how expensive arithmetic at a given precision is. 1 is the base-line for double-precision.

◆ max()

template<typename T>

T bertini::max	(	T const &	a,
		T const &	b,
		T const &	c )

Three-argument form of max.

Parameters

a	Input one
b	Input two
c	Input three

◆ MinDigitsForLogOfStepsize()

unsigned bertini::tracking::MinDigitsForLogOfStepsize	(	mpfr_float const &	log_of_stepsize,
		mpfr_float const &	time_to_go,
		unsigned	safety_digits = 3 )

inline

The minimum number of digits based on a log10 of a stepsize.

Parameters

log_of_stepsize	log10 of a stepsize
time_to_go	How much time you have left to track.
safety_digits	A buffer of extra digits to use, over the computed min. Yes, this is added in, in this function.

Returns: An integral number of necessary digits to use

◆ MinDigitsForStepsizeInterval()

unsigned bertini::tracking::MinDigitsForStepsizeInterval	(	mpfr_float const &	min_stepsize,
		mpfr_float const &	max_stepsize,
		mpfr_float const &	time_to_go )

inline

For a given range of stepsizes under consideration, gives the minimum number of digits.

Parameters

min_stepsize	The smallest stepsize under consideration
max_stepsize	The largest stepsize under consideration
time_to_go	How much time is left to track.

Returns: The min number of digits.

This function assumes you are going to time=0, or that you have taken care of that difference. That is, time_to_go should be a duration, not the current time, unless you are tracking to t=0, in which case current time is the duration left to go. Dig it?

◆ MinimizeTrackingCost()

template<typename RealT>

void bertini::tracking::MinimizeTrackingCost	(	unsigned &	new_precision,
		RealT &	new_stepsize,
		unsigned	min_precision,
		RealT const &	min_stepsize,
		unsigned	max_precision,
		RealT const &	max_stepsize,
		unsigned	digits_B,
		unsigned	num_newton_iterations,
		unsigned	predictor_order = 0 )

Compute precision and stepsize minimizing the ArithmeticCost() of tracking.

For a given range of precisions, an old stepsize, and a maximum stepsize, the Cost of tracking is computed, and a minimizer found.

This function is used in the AMPTracker tracking loop, both in case of successful steps and in Criterion errors.

Parameters

[out]	new_precision	The minimizing precision.
[out]	new_stepsize	The minimizing stepsize.
[in]	min_precision	The minimum considered precision.
[in]	min_stepsize	The minimum permitted stepsize.
[in]	max_precision	The maximum considered precision.
[in]	max_stepsize	The maximum permitted stepsize.
[in]	digits_B	The number of digits required, according to CriterionB from [1], [2]
[in]	num_newton_iterations	The number of allowed Newton corrector iterations.
[in]	predictor_order	The order of the predictor being used. This is the order itself, not the order of the error estimate.

See also: ArithmeticCost

◆ MinStepSizeForPrecision()

mpfr_float bertini::tracking::MinStepSizeForPrecision	(	unsigned	precision,
		mpfr_float const &	time_to_go,
		int	safety_digits = 3 )

inline

Just another name for MinTimeForCurrentPrecision.

Parameters

precision	The number of digits you want to use
time_to_go	The duration of remaining time to track
safety_digits	A buffer of extra digits to use

Returns: The smallest permissible stepsize

◆ MinTimeForCurrentPrecision()

mpfr_float bertini::tracking::MinTimeForCurrentPrecision	(	unsigned	precision,
		mpfr_float const &	time_to_go,
		int	safety_digits = 3 )

inline

The minimum time that can be represented effectively using a given precision

Parameters

precision	The number of digits you want to use
time_to_go	The duration of remaining time to track
safety_digits	A buffer of extra digits to use

Returns: The smallest permissible stepsize

Todo: This function has a hardcoded value which should be replaced

◆ StepsizeSatisfyingCriterionB()

mpfr_float bertini::tracking::StepsizeSatisfyingCriterionB	(	unsigned	precision,
		unsigned	digits_B,
		unsigned	num_newton_iterations,
		unsigned	predictor_order = 0 )

inline

Compute a stepsize satisfying AMP Criterion B with a given precision.

Parameters

precision	The current working precision
digits_B	The number of digits from Criterion B
num_newton_iterations	The number of remaining newton iterations allowed in the correction
predictor_order	The order of the predictor

Returns: The stepsize

Todo: Remove the default value of the predictor order, as that seems weird to have

Classes

Functions

Detailed Description

Function Documentation

◆ ArithmeticCost()

◆ max()

◆ MinDigitsForLogOfStepsize()

◆ MinDigitsForStepsizeInterval()

◆ MinimizeTrackingCost()

◆ MinStepSizeForPrecision()

◆ MinTimeForCurrentPrecision()

◆ StepsizeSatisfyingCriterionB()