ScalingRootFinder Class Reference#

DiFfRG: DiFfRG::ScalingRootFinder Class Reference

DiFfRG

Discretization Framework for functional Renormalization Group flows

Bracketed root find accelerated by the critical scaling of the observable. More...

#include <root_finding.hh>

Classes
struct	Counts

Public Types
enum class	Acceptance { AtTarget , BelowTarget }
	What counts as an answer. More...

Public Member Functions
	ScalingRootFinder (FUN f, const double target, const double rel_tol=1e-3, const uint max_iter=40)

	ScalingRootFinder (FUN_NO_RESIDUAL f, const double target, const double rel_tol=1e-3, const uint max_iter=40)

double	search ()

Bracket
The bounds are hypotheses by default: if they turn out not to straddle, the search widens them geometrically instead of throwing, which is what makes one set of bounds usable across models whose critical points differ by orders of magnitude.
void	set_bounds (const double x_lo, const double x_hi)

void	set_bounds_are_hypotheses (const bool v)

void	set_expansion_factor (const double rho)

void	set_expansion_max_iter (const uint n)

Stopping
void	set_rel_tol (const double v)

void	set_one_sided (const bool v)

void	set_acceptance (const Acceptance a)

void	set_aim_fraction (const double v)

void	set_x_rel_floor (const double v)
	Bracket width, relative to the magnitude of the bounds, below which the search gives up.

void	set_max_iter (const uint v)

Model trust windows
The power law is asymptotic. Fitting points from outside its window does not degrade gracefully – it returns a confident, badly wrong critical point that sits inside the bracket, where the containment safeguard cannot catch it. These windows are load-bearing.
void	set_obs_window (const double v)
	Fit only points with obs <= window * target. Ignored when target == 0.

void	set_residual_window (const double v)

void	set_exponent_bounds (const double lo, const double hi)

void	set_theta_bounds (const double lo, const double hi)

void	set_endpoint_standoff (const double v)
	Fraction of the bracket width kept clear of either endpoint when clamping a proposal.

void	set_approach_factor (const double v)
	Fraction of the remaining distance to the critical point kept per approach step.

void	seed_exponent (const double beta)

Results
double	get_obs () const

double	get_x_critical () const

double	get_exponent () const

double	get_theta () const

bool	have_model () const

double	get_x_extrapolated () const
	Model extrapolation of the target point. NaN when no model was ever trusted.

bool	converged () const

uint	get_iter () const

double	bracket_width () const
	Live bracket width; infinite until both sides are known.

const std::vector< std::pair< double, double > > &	successes () const

const std::vector< std::pair< double, double > > &	failures () const

Counts	get_counts () const

Protected Types
using	FUN = std::function<bool(const double, double &, double &)>

using	FUN_NO_RESIDUAL = std::function<bool(const double, double &)>
	Compatibility shape matching BisectionRootFinderTarget. Disables the divergent-branch model.

Protected Member Functions
double	effective_target () const

double	extrapolate (const double x_c) const
	x at which the model predicts obs == effective_target(), given a critical point.

void	refit ()

void	fit_convergent ()
	Refit from the three convergent points closest to criticality (smallest obs).

void	fit_divergent ()
	Refit from the three divergent points closest to criticality (largest residual).

double	propose ()
	Propose the next x.

void	record (double x, bool ok, double obs, double residual)
	Record a probe outcome and update the bracket.

Static Protected Member Functions
static std::array< std::size_t, 3 >	select_triple (const std::size_t)
	The three candidates closest to criticality, out of n sorted by distance to it.

Protected Attributes
FUN	f

double	target

double	rel_tol

uint	max_iter

double	x_lo_init = NAN

double	x_hi_init = NAN

bool	bounds_are_hypotheses = true

double	expansion_factor = 2.

uint	expansion_max_iter = 24

bool	one_sided = true

Acceptance	acceptance = Acceptance::AtTarget

double	aim_fraction = 0.5

bool	answer_found = false

double	x_rel_floor = 1e-13

double	obs_window = 20.

double	residual_window = 0.

double	beta_min = 0.02

double	beta_max = 5.

double	theta_min = 0.5

double	theta_max = 8.

double	endpoint_standoff = 0.02

double	approach_factor = 0.1

double	seeded_exponent = NAN

double	x_lo_soft = -std::numeric_limits<double>::infinity()

double	x_lo_hard = -std::numeric_limits<double>::infinity()

double	x_hi = std::numeric_limits<double>::infinity()

std::vector< std::pair< double, double > >	S
	(x, obs) for every finite evaluation

std::vector< std::pair< double, double > >	F
	(x, residual) for every informative failure

bool	model_valid = false

double	model_x_c = NAN

double	model_beta = NAN

double	model_log_C = NAN

double	model_theta = NAN

double	model_x_c_prev = NAN

bool	divergent_valid = false

double	divergent_x_c = NAN

double	divergent_shift = NAN

double	best_x = NAN

double	best_obs = NAN

bool	have_success = false

bool	m_converged = false

uint	iter = 0

Counts	counts

double	w_prev = std::numeric_limits<double>::infinity()

double	w_prevprev = std::numeric_limits<double>::infinity()

bool	probed_hi_init = false

bool	probed_lo_init = false

uint	expansions = 0

double	w_init = NAN

Detailed Description

Bracketed root find accelerated by the critical scaling of the observable.

Solves obs(x) == target where obs is smooth and monotone on the convergent side of a critical point x_c < x, obeying obs = C (x - x_c)^beta, and where probes below x_c fail but expose a residual that grows as x_c is approached, r(x) = a - ln(x_c - x)/theta. Neither exponent is assumed; both are fitted from three points, and the same solve serves both branches (the divergent one via x -> -x, y -> exp(-r), which is why only the residual differences ever enter and no exponentials are formed).

Every model-based proposal is bracket-safeguarded Brent-style, so a wrong model costs at most a factor two over plain bisection and can never move the answer.

The callback reports three outcomes, not two:

returns true and writes a finite obs: a usable evaluation. Whether it lies above or below the target is the finder's business, not the callback's.
returns false and writes a finite residual: the evaluation ran away; the residual says how far it got.
returns false and writes nothing: it failed some other way and carries no information beyond its own x. Both obs and residual are NaN-initialised before every call, so "wrote nothing" needs no separate signal.

ScalingRootFinder search(
    [&](const double x, double &obs, double &residual) -> bool {
      return run_at(x, obs, residual);
    },
    zc_target, 1e-3, 40);
search.set_bounds(lower, upper);          // hypotheses; expanded if they do not straddle
search.set_residual_window(0.4 * final_time);
const double x = search.search();

Member Typedef Documentation

◆ FUN

using DiFfRG::ScalingRootFinder::FUN = std::function<bool(const double, double &, double &)>

protected

◆ FUN_NO_RESIDUAL

using DiFfRG::ScalingRootFinder::FUN_NO_RESIDUAL = std::function<bool(const double, double &)>

protected

Compatibility shape matching BisectionRootFinderTarget. Disables the divergent-branch model.

Member Enumeration Documentation

◆ Acceptance

enum class DiFfRG::ScalingRootFinder::Acceptance

strong

What counts as an answer.

AtTarget converges obs onto the target to within rel_tol. BelowTarget accepts the first evaluation that lands anywhere strictly between the critical point and the target crossing, which is a far easier thing to hit: on a cold Yang-Mills tune that interval is ~600x wider in the search variable than the AtTarget window, i.e. about nine bisections cheaper, and it lets a merely decent fit succeed on its first attempt instead of being refined until it is accurate to rel_tol.

Enumerator
AtTarget
BelowTarget

Constructor & Destructor Documentation

◆ ScalingRootFinder() [1/2]

DiFfRG::ScalingRootFinder::ScalingRootFinder	(	FUN	f,
		const double	target,
		const double	rel_tol = 1e-3,
		const uint	max_iter = 40 )

inline

◆ ScalingRootFinder() [2/2]

DiFfRG::ScalingRootFinder::ScalingRootFinder	(	FUN_NO_RESIDUAL	f,
		const double	target,
		const double	rel_tol = 1e-3,
		const uint	max_iter = 40 )

inline

Member Function Documentation

◆ bracket_width()

double DiFfRG::ScalingRootFinder::bracket_width ( ) const

inline

Live bracket width; infinite until both sides are known.

◆ converged()

bool DiFfRG::ScalingRootFinder::converged ( ) const

inline

◆ effective_target()

double DiFfRG::ScalingRootFinder::effective_target ( ) const

inlineprotected

The value actually aimed at. With one-sided acceptance the admissible window is [target, target(1+rel_tol)]; aiming at its centre rather than its lower edge keeps rounding in the extrapolation from landing just below and costing an extra evaluation.

◆ extrapolate()

double DiFfRG::ScalingRootFinder::extrapolate ( const double x_c ) const

inlineprotected

x at which the model predicts obs == effective_target(), given a critical point.

◆ failures()

const std::vector< std::pair< double, double > > & DiFfRG::ScalingRootFinder::failures ( ) const

inline

◆ fit_convergent()

void DiFfRG::ScalingRootFinder::fit_convergent ( )

inlineprotected

Refit from the three convergent points closest to criticality (smallest obs).

◆ fit_divergent()

void DiFfRG::ScalingRootFinder::fit_divergent ( )

inlineprotected

Refit from the three divergent points closest to criticality (largest residual).

◆ get_counts()

Counts DiFfRG::ScalingRootFinder::get_counts ( ) const

inline

◆ get_exponent()

double DiFfRG::ScalingRootFinder::get_exponent ( ) const

inline

◆ get_iter()

uint DiFfRG::ScalingRootFinder::get_iter ( ) const

inline

◆ get_obs()

double DiFfRG::ScalingRootFinder::get_obs ( ) const

inline

◆ get_theta()

double DiFfRG::ScalingRootFinder::get_theta ( ) const

inline

◆ get_x_critical()

double DiFfRG::ScalingRootFinder::get_x_critical ( ) const

inline

Best available critical point: the convergent fit when it is trusted, otherwise the divergent one, which is usable much further from criticality.

◆ get_x_extrapolated()

double DiFfRG::ScalingRootFinder::get_x_extrapolated ( ) const

inline

Model extrapolation of the target point. NaN when no model was ever trusted.

◆ have_model()

bool DiFfRG::ScalingRootFinder::have_model ( ) const

inline

◆ propose()

double DiFfRG::ScalingRootFinder::propose ( )

inlineprotected

Propose the next x.

◆ record()

void DiFfRG::ScalingRootFinder::record	(	double	x,
		bool	ok,
		double	obs,
		double	residual )

inlineprotected

Record a probe outcome and update the bracket.

◆ refit()

void DiFfRG::ScalingRootFinder::refit ( )

inlineprotected

Refit both branches. Called exactly once per evaluation, so that the consecutive-fit agreement test sees successive iterations rather than successive calls.

◆ search()

double DiFfRG::ScalingRootFinder::search ( )

inline

◆ seed_exponent()

void DiFfRG::ScalingRootFinder::seed_exponent ( const double beta )

inline

Seed the exponent from a nearby earlier search (another simplex step, a coarser fidelity). Exponents are far more portable than amplitudes; do not seed the latter.

◆ select_triple()

static std::array< std::size_t, 3 > DiFfRG::ScalingRootFinder::select_triple ( const std::size_t )

inlinestaticprotected

The three candidates closest to criticality, out of n sorted by distance to it.

Spreading the triple across the whole admissible range is better conditioned in principle – a bisecting search leaves the closest points tightly clustered – but measures worse: the far points are not asymptotic enough, the fit is rejected outright more often, and a cold SP tune stopped converging inside its budget. Both laws are asymptotic, so the fit stays in the asymptote.

◆ set_acceptance()

void DiFfRG::ScalingRootFinder::set_acceptance ( const Acceptance a )

inline

◆ set_aim_fraction()

void DiFfRG::ScalingRootFinder::set_aim_fraction ( const double v )

inline

Where inside (0, target) to aim in BelowTarget mode, as a fraction of the target. Aiming at the midpoint rather than just under the crossing leaves room for the fit to be wrong in either direction without either overshooting into the divergent region or missing.

◆ set_approach_factor()

void DiFfRG::ScalingRootFinder::set_approach_factor ( const double v )

inline

Fraction of the remaining distance to the critical point kept per approach step.

◆ set_bounds()

void DiFfRG::ScalingRootFinder::set_bounds	(	const double	x_lo,
		const double	x_hi )

inline

◆ set_bounds_are_hypotheses()

void DiFfRG::ScalingRootFinder::set_bounds_are_hypotheses ( const bool v )

inline

◆ set_endpoint_standoff()

void DiFfRG::ScalingRootFinder::set_endpoint_standoff ( const double v )

inline

Fraction of the bracket width kept clear of either endpoint when clamping a proposal.

◆ set_expansion_factor()

void DiFfRG::ScalingRootFinder::set_expansion_factor ( const double rho )

inline

◆ set_expansion_max_iter()

void DiFfRG::ScalingRootFinder::set_expansion_max_iter ( const uint n )

inline

◆ set_exponent_bounds()

void DiFfRG::ScalingRootFinder::set_exponent_bounds	(	const double	lo,
		const double	hi )

inline

◆ set_max_iter()

void DiFfRG::ScalingRootFinder::set_max_iter ( const uint v )

inline

◆ set_obs_window()

void DiFfRG::ScalingRootFinder::set_obs_window ( const double v )

inline

Fit only points with obs <= window * target. Ignored when target == 0.

◆ set_one_sided()

void DiFfRG::ScalingRootFinder::set_one_sided ( const bool v )

inline

Accept only probes at or above the target. Keeps the answer on the safe side of the critical point at a cost of at most one extra evaluation. AtTarget mode only.

◆ set_rel_tol()

void DiFfRG::ScalingRootFinder::set_rel_tol ( const double v )

inline

◆ set_residual_window()

void DiFfRG::ScalingRootFinder::set_residual_window ( const double v )

inline

Fit only failures whose residual is at least this large. Defaults to 0 (fit any three), because only the caller knows the residual's scale.

◆ set_theta_bounds()

void DiFfRG::ScalingRootFinder::set_theta_bounds	(	const double	lo,
		const double	hi )

inline

Bounds on the divergent-branch exponent. theta is an inverse unstable RG eigenvalue and sits near the tuned parameter's mass dimension – 2 for a mass squared, measured 1.92 on a cold Yang-Mills tune – so it is far more tightly constrained a priori than beta.

◆ set_x_rel_floor()

void DiFfRG::ScalingRootFinder::set_x_rel_floor ( const double v )

inline

Bracket width, relative to the magnitude of the bounds, below which the search gives up.

◆ successes()

const std::vector< std::pair< double, double > > & DiFfRG::ScalingRootFinder::successes ( ) const

inline

Member Data Documentation

◆ acceptance

Acceptance DiFfRG::ScalingRootFinder::acceptance = Acceptance::AtTarget

protected

◆ aim_fraction

double DiFfRG::ScalingRootFinder::aim_fraction = 0.5

protected

◆ answer_found

bool DiFfRG::ScalingRootFinder::answer_found = false

protected

◆ approach_factor

double DiFfRG::ScalingRootFinder::approach_factor = 0.1

protected

◆ best_obs

double DiFfRG::ScalingRootFinder::best_obs = NAN

protected

◆ best_x

double DiFfRG::ScalingRootFinder::best_x = NAN

protected

◆ beta_max

double DiFfRG::ScalingRootFinder::beta_max = 5.

protected

◆ beta_min

double DiFfRG::ScalingRootFinder::beta_min = 0.02

protected

◆ bounds_are_hypotheses

bool DiFfRG::ScalingRootFinder::bounds_are_hypotheses = true

protected

◆ counts

Counts DiFfRG::ScalingRootFinder::counts

protected

◆ divergent_shift

double DiFfRG::ScalingRootFinder::divergent_shift = NAN

protected

◆ divergent_valid

bool DiFfRG::ScalingRootFinder::divergent_valid = false

protected

◆ divergent_x_c

double DiFfRG::ScalingRootFinder::divergent_x_c = NAN

protected

◆ endpoint_standoff

double DiFfRG::ScalingRootFinder::endpoint_standoff = 0.02

protected

◆ expansion_factor

double DiFfRG::ScalingRootFinder::expansion_factor = 2.

protected

◆ expansion_max_iter

uint DiFfRG::ScalingRootFinder::expansion_max_iter = 24

protected

◆ expansions

uint DiFfRG::ScalingRootFinder::expansions = 0

protected

◆ F

std::vector<std::pair<double, double> > DiFfRG::ScalingRootFinder::F

protected

(x, residual) for every informative failure

◆ f

FUN DiFfRG::ScalingRootFinder::f

protected

◆ have_success

bool DiFfRG::ScalingRootFinder::have_success = false

protected

◆ iter

uint DiFfRG::ScalingRootFinder::iter = 0

protected

◆ m_converged

bool DiFfRG::ScalingRootFinder::m_converged = false

protected

◆ max_iter

uint DiFfRG::ScalingRootFinder::max_iter

protected

◆ model_beta

double DiFfRG::ScalingRootFinder::model_beta = NAN

protected

◆ model_log_C

double DiFfRG::ScalingRootFinder::model_log_C = NAN

protected

◆ model_theta

double DiFfRG::ScalingRootFinder::model_theta = NAN

protected

◆ model_valid

bool DiFfRG::ScalingRootFinder::model_valid = false

protected

◆ model_x_c

double DiFfRG::ScalingRootFinder::model_x_c = NAN

protected

◆ model_x_c_prev

double DiFfRG::ScalingRootFinder::model_x_c_prev = NAN

protected

◆ obs_window

double DiFfRG::ScalingRootFinder::obs_window = 20.

protected

◆ one_sided

bool DiFfRG::ScalingRootFinder::one_sided = true

protected

◆ probed_hi_init

bool DiFfRG::ScalingRootFinder::probed_hi_init = false

protected

◆ probed_lo_init

bool DiFfRG::ScalingRootFinder::probed_lo_init = false

protected

◆ rel_tol

double DiFfRG::ScalingRootFinder::rel_tol

protected

◆ residual_window

double DiFfRG::ScalingRootFinder::residual_window = 0.

protected

◆ S

std::vector<std::pair<double, double> > DiFfRG::ScalingRootFinder::S

protected

(x, obs) for every finite evaluation

◆ seeded_exponent

double DiFfRG::ScalingRootFinder::seeded_exponent = NAN

protected

◆ target

double DiFfRG::ScalingRootFinder::target

protected

◆ theta_max

double DiFfRG::ScalingRootFinder::theta_max = 8.

protected

◆ theta_min

double DiFfRG::ScalingRootFinder::theta_min = 0.5

protected

◆ w_init

double DiFfRG::ScalingRootFinder::w_init = NAN

protected

◆ w_prev

double DiFfRG::ScalingRootFinder::w_prev = std::numeric_limits<double>::infinity()

protected

◆ w_prevprev

double DiFfRG::ScalingRootFinder::w_prevprev = std::numeric_limits<double>::infinity()

protected

◆ x_hi

double DiFfRG::ScalingRootFinder::x_hi = std::numeric_limits<double>::infinity()

protected

◆ x_hi_init

double DiFfRG::ScalingRootFinder::x_hi_init = NAN

protected

◆ x_lo_hard

double DiFfRG::ScalingRootFinder::x_lo_hard = -std::numeric_limits<double>::infinity()

protected

◆ x_lo_init

double DiFfRG::ScalingRootFinder::x_lo_init = NAN

protected

◆ x_lo_soft

double DiFfRG::ScalingRootFinder::x_lo_soft = -std::numeric_limits<double>::infinity()

protected

◆ x_rel_floor

double DiFfRG::ScalingRootFinder::x_rel_floor = 1e-13

protected

The documentation for this class was generated from the following file:

/home/runner/work/DiFfRG_current/DiFfRG_current/DiFfRG/include/DiFfRG/common/root_finding.hh

ScalingRootFinder Class Reference#

Classes

Public Types

Public Member Functions

Protected Types

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ FUN

◆ FUN_NO_RESIDUAL

Member Enumeration Documentation

◆ Acceptance

Constructor & Destructor Documentation

◆ ScalingRootFinder() [1/2]

◆ ScalingRootFinder() [2/2]

Member Function Documentation

◆ bracket_width()

◆ converged()

◆ effective_target()

◆ extrapolate()

◆ failures()

◆ fit_convergent()

◆ fit_divergent()

◆ get_counts()

◆ get_exponent()

◆ get_iter()

◆ get_obs()

◆ get_theta()

◆ get_x_critical()

◆ get_x_extrapolated()

◆ have_model()

◆ propose()

◆ record()

◆ refit()

◆ search()

◆ seed_exponent()

◆ select_triple()

◆ set_acceptance()

◆ set_aim_fraction()

◆ set_approach_factor()

◆ set_bounds()

◆ set_bounds_are_hypotheses()

◆ set_endpoint_standoff()

◆ set_expansion_factor()

◆ set_expansion_max_iter()

◆ set_exponent_bounds()

◆ set_max_iter()

◆ set_obs_window()

◆ set_one_sided()

◆ set_rel_tol()

◆ set_residual_window()

◆ set_theta_bounds()

◆ set_x_rel_floor()

◆ successes()

Member Data Documentation

◆ acceptance

◆ aim_fraction

◆ answer_found

◆ approach_factor

◆ best_obs

◆ best_x

◆ beta_max

◆ beta_min

◆ bounds_are_hypotheses

◆ counts

◆ divergent_shift

◆ divergent_valid

◆ divergent_x_c

◆ endpoint_standoff

◆ expansion_factor

◆ expansion_max_iter

◆ expansions

◆ F

◆ f

◆ have_success

◆ iter

◆ m_converged

◆ max_iter