interpolation.hpp File Reference

#include "bertini2/common/config.hpp"

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Functions
template<typename CT>
Vec< CT >	bertini::endgame::HermiteInterpolateAndSolve (CT const &target_time, const unsigned int num_sample_points, const TimeCont< CT > &times, const SampCont< CT > &samples, const SampCont< CT > &derivatives, ContStart shift_from=ContStart::Back)
	Estimates the root to interpolating polynomial.

Detailed Description

Contains interpolation and extrapolation functions used in the endgames for estimating singular (and nonsingular) roots.

Function Documentation

HermiteInterpolateAndSolve()

template<typename CT>

Vec< CT > bertini::endgame::HermiteInterpolateAndSolve	(	CT const &	target_time,
		const unsigned int	num_sample_points,
		const TimeCont< CT > &	times,
		const SampCont< CT > &	samples,
		const SampCont< CT > &	derivatives,
		ContStart	shift_from = ContStart::Back )

Estimates the root to interpolating polynomial.

Input: target_time is the time value that we wish to interpolate at. samples are space values that correspond to the time values in times. derivatives are the dx_dt or dx_ds values at the (time,sample) values.

Output: Since we have a target_time the function returns the corrsponding space value at that time.

Details: We compare our approximations to the tracked value to come up with the cycle number. Also, we use the Hermite interpolation to interpolate at the origin. Once two interpolants are withing FinalTol we say we have converged.

Parameters

[out]	endgame_tracker_	The tracker used to compute the samples we need to start an endgame.
	endgame_time	The time value at which we start the endgame.
	x_endgame_start	The current space point at endgame_time.
	times	A deque that will hold all the time values of the samples we are going to use to start the endgame.
	samples	a deque that will hold all the samples corresponding to the time values in times.

Template Parameters

CT	The complex number type.