bertini::algorithm::SolutionMetaData< ComplexT > Struct Template Reference

Per-solution metadata gathered during and after a path track. More...

#include <zero_dim_solve.hpp>

Public Types
using	SolnIndT = typename SolnCont<ComplexT>::size_type
	Index type for solutions/paths.

Public Member Functions
bool	operator== (const SolutionMetaData< ComplexT > &other)
	Equality comparison over the identity fields (path_time_seconds is excluded).

Public Attributes
SolnIndT	path_index
	Path number of the solution.
SolnIndT	solution_index
	Solution number.
bool	precision_changed = false
	Whether the working precision changed during the path.
ComplexT	time_of_first_prec_increase
	Time value of the first increase in precision.
decltype(DefaultPrecision())	max_precision_used = 0
	Highest precision (digits) used anywhere on the path, for every kind of tracker; a fixed-precision tracker reports its one precision.
double	path_time_seconds = 0.0
	Wall-clock time for the whole path (pre-endgame + endgame), seconds. Not an identity field (excluded from operator==).
unsigned	num_successful_steps = 0
	Predictor-corrector steps that succeeded on this path, pre-endgame and endgame together.
unsigned	num_failed_steps = 0
	Predictor-corrector steps that failed and were retried smaller on this path, pre-endgame and endgame together.
double	wall_clock_limit_seconds = 0
	The per-path wall-clock budget in force when this path ran (ZeroDimConfig::max_path_wall_clock_duration), seconds; 0 = none.
Vec< ComplexT >	latest_path_point
	Where the tracker was when it gave up: the last point reached, in the tracker's internal coordinates, on a path that did NOT succeed – whether it failed, was stopped, or ran out of budget, in either stage.
SuccessCode	pre_endgame_success_code = SuccessCode::NeverStarted
	Success code of the pre-endgame track.
NumErrorT	condition_number
	Spectral-norm condition number of the target system's Jacobian at the endpoint (the quantity condition_number_threshold is specified against).
Vec< NumErrorT >	singular_values
	The singular values of the (homogenized, patched) target system's Jacobian at the endpoint, largest first, at the endpoint's own precision – condition_number is the ratio of the first to the last.
NumErrorT	newton_residual
	The latest Newton residual.
ComplexT	final_time_used
	The last time value the path reached: the endgame's latest time for a successful path, the tracker's time when it stopped for one that did not succeed in either stage.
NumErrorT	accuracy_estimate_internal_coords
	Distance between the endgame's last two approximations, in the solver's internal coordinates (homogenized, on the patch). The quantity the convergence test compares with final_tolerance; it does not grow with the scale of the solution.
NumErrorT	accuracy_estimate_user_coords
	Distance between the endgame's last two approximations after each is dehomogenized: the absolute error in the units of the user's variables.
unsigned	cycle_num
	Cycle number used in extrapolations.
unsigned	precision_digits = 0
	Working precision (digits) the endgame finished this solution in.
unsigned	accuracy_digits = 0
	Trustworthy digit count, from the convergence agreement.
SuccessCode	endgame_success_code = SuccessCode::NeverStarted
	Success code of the endgame.
NumErrorT	function_residual
	The latest function residual.
int	multiplicity = 1
	Multiplicity of the solution.
bool	multiplicity_representative = true
	Whether this is the chosen single representative of its multiplicity cluster (the m copies share one point; exactly one is the representative).
bool	is_real = false
	Whether the (dehomogenized) endpoint is real.
bool	is_finite = false
	Whether the endpoint is finite (not at infinity).
bool	is_singular = false
	Whether the endpoint is singular (multiple, or ill-conditioned).
bool	crossing_unresolved = false
	Whether this path was flagged as crossing another at the endgame boundary and the crossing was NOT resolved by re-tracking.
bool	is_nonsolution = false
	Whether this finite, successful endpoint is not a solution of the actual target system (an extraneous root from squaring up an over-determined system).

Detailed Description

template<typename ComplexT>
struct bertini::algorithm::SolutionMetaData< ComplexT >

Per-solution metadata gathered during and after a path track.

Member Typedef Documentation

SolnIndT

template<typename ComplexT>

using bertini::algorithm::SolutionMetaData< ComplexT >::SolnIndT = typename SolnCont<ComplexT>::size_type

Index type for solutions/paths.

Member Function Documentation

operator==()

template<typename ComplexT>

bool bertini::algorithm::SolutionMetaData< ComplexT >::operator== ( const SolutionMetaData< ComplexT > & other )

inline

Equality comparison over the identity fields (path_time_seconds is excluded).

Member Data Documentation

accuracy_digits

template<typename ComplexT>

unsigned bertini::algorithm::SolutionMetaData< ComplexT >::accuracy_digits = 0

Trustworthy digit count, from the convergence agreement.

accuracy_estimate_internal_coords

template<typename ComplexT>

NumErrorT bertini::algorithm::SolutionMetaData< ComplexT >::accuracy_estimate_internal_coords

Distance between the endgame's last two approximations, in the solver's internal coordinates (homogenized, on the patch). The quantity the convergence test compares with final_tolerance; it does not grow with the scale of the solution.

accuracy_estimate_user_coords

template<typename ComplexT>

NumErrorT bertini::algorithm::SolutionMetaData< ComplexT >::accuracy_estimate_user_coords

Distance between the endgame's last two approximations after each is dehomogenized: the absolute error in the units of the user's variables.

condition_number

template<typename ComplexT>

NumErrorT bertini::algorithm::SolutionMetaData< ComplexT >::condition_number

Spectral-norm condition number of the target system's Jacobian at the endpoint (the quantity condition_number_threshold is specified against).

crossing_unresolved

template<typename ComplexT>

bool bertini::algorithm::SolutionMetaData< ComplexT >::crossing_unresolved = false

Whether this path was flagged as crossing another at the endgame boundary and the crossing was NOT resolved by re-tracking.

Its success codes may still read Success, but the library has already warned that this endpoint may be wrong; consumers that build on the endpoint should check this flag, not just the codes (b2#365).

cycle_num

template<typename ComplexT>

unsigned bertini::algorithm::SolutionMetaData< ComplexT >::cycle_num

Cycle number used in extrapolations.

endgame_success_code

template<typename ComplexT>

SuccessCode bertini::algorithm::SolutionMetaData< ComplexT >::endgame_success_code = SuccessCode::NeverStarted

Success code of the endgame.

final_time_used

template<typename ComplexT>

ComplexT bertini::algorithm::SolutionMetaData< ComplexT >::final_time_used

The last time value the path reached: the endgame's latest time for a successful path, the tracker's time when it stopped for one that did not succeed in either stage.

function_residual

template<typename ComplexT>

NumErrorT bertini::algorithm::SolutionMetaData< ComplexT >::function_residual

The latest function residual.

is_finite

template<typename ComplexT>

bool bertini::algorithm::SolutionMetaData< ComplexT >::is_finite = false

Whether the endpoint is finite (not at infinity).

is_nonsolution

template<typename ComplexT>

bool bertini::algorithm::SolutionMetaData< ComplexT >::is_nonsolution = false

Whether this finite, successful endpoint is not a solution of the actual target system (an extraneous root from squaring up an over-determined system).

is_real

template<typename ComplexT>

bool bertini::algorithm::SolutionMetaData< ComplexT >::is_real = false

Whether the (dehomogenized) endpoint is real.

is_singular

template<typename ComplexT>

bool bertini::algorithm::SolutionMetaData< ComplexT >::is_singular = false

Whether the endpoint is singular (multiple, or ill-conditioned).

latest_path_point

template<typename ComplexT>

Vec<ComplexT> bertini::algorithm::SolutionMetaData< ComplexT >::latest_path_point

Where the tracker was when it gave up: the last point reached, in the tracker's internal coordinates, on a path that did NOT succeed – whether it failed, was stopped, or ran out of budget, in either stage.

Read with final_time_used, which holds the matching time. Empty for a successful path (its endpoint is the solution itself) and for a path never started. On a Cauchy endgame the point may lie on a sample circle rather than on the real segment to the target.

max_precision_used

template<typename ComplexT>

decltype(DefaultPrecision()) bertini::algorithm::SolutionMetaData< ComplexT >::max_precision_used = 0

Highest precision (digits) used anywhere on the path, for every kind of tracker; a fixed-precision tracker reports its one precision.

multiplicity

template<typename ComplexT>

int bertini::algorithm::SolutionMetaData< ComplexT >::multiplicity = 1

Multiplicity of the solution.

multiplicity_representative

template<typename ComplexT>

bool bertini::algorithm::SolutionMetaData< ComplexT >::multiplicity_representative = true

Whether this is the chosen single representative of its multiplicity cluster (the m copies share one point; exactly one is the representative).

newton_residual

template<typename ComplexT>

NumErrorT bertini::algorithm::SolutionMetaData< ComplexT >::newton_residual

The latest Newton residual.

num_failed_steps

template<typename ComplexT>

unsigned bertini::algorithm::SolutionMetaData< ComplexT >::num_failed_steps = 0

Predictor-corrector steps that failed and were retried smaller on this path, pre-endgame and endgame together.

num_successful_steps

template<typename ComplexT>

unsigned bertini::algorithm::SolutionMetaData< ComplexT >::num_successful_steps = 0

Predictor-corrector steps that succeeded on this path, pre-endgame and endgame together.

path_index

template<typename ComplexT>

SolnIndT bertini::algorithm::SolutionMetaData< ComplexT >::path_index

Path number of the solution.

path_time_seconds

template<typename ComplexT>

double bertini::algorithm::SolutionMetaData< ComplexT >::path_time_seconds = 0.0

Wall-clock time for the whole path (pre-endgame + endgame), seconds. Not an identity field (excluded from operator==).

pre_endgame_success_code

template<typename ComplexT>

SuccessCode bertini::algorithm::SolutionMetaData< ComplexT >::pre_endgame_success_code = SuccessCode::NeverStarted

Success code of the pre-endgame track.

precision_changed

template<typename ComplexT>

bool bertini::algorithm::SolutionMetaData< ComplexT >::precision_changed = false

Whether the working precision changed during the path.

precision_digits

template<typename ComplexT>

unsigned bertini::algorithm::SolutionMetaData< ComplexT >::precision_digits = 0

Working precision (digits) the endgame finished this solution in.

singular_values

template<typename ComplexT>

Vec<NumErrorT> bertini::algorithm::SolutionMetaData< ComplexT >::singular_values

The singular values of the (homogenized, patched) target system's Jacobian at the endpoint, largest first, at the endpoint's own precision – condition_number is the ratio of the first to the last.

Published raw so a caller can read a numerical rank at a tolerance of ITS choosing: no single tolerance is right for every endpoint, and a rank verdict baked in here would misjudge someone's regular root (b2#409). Empty when the endgame did not succeed.

solution_index

template<typename ComplexT>

SolnIndT bertini::algorithm::SolutionMetaData< ComplexT >::solution_index

Solution number.

time_of_first_prec_increase

template<typename ComplexT>

ComplexT bertini::algorithm::SolutionMetaData< ComplexT >::time_of_first_prec_increase

Time value of the first increase in precision.

wall_clock_limit_seconds

template<typename ComplexT>

double bertini::algorithm::SolutionMetaData< ComplexT >::wall_clock_limit_seconds = 0

The per-path wall-clock budget in force when this path ran (ZeroDimConfig::max_path_wall_clock_duration), seconds; 0 = none.

Recorded with the path so a later run can tell whether it is asking more patience of an abandoned path than the run that abandoned it.