Namespaces
	detail

	logging

Classes
struct	Action_options

class	Algebraic_potential
	Implements a multi dimensional scalar field potential, which may be expressed as almost any algerbraic fucntion. More...

struct	Bubble_profiler_inputs

class	BVP_solver_error
	Exception indicating failure to integrate BVP. More...

class	Controlled_step_size_integrator

class	Domain_error
	Exception indicating function evaluation out of allowed domain. More...

class	Dummy_observer
	A default observer that does not perform any actions when called. More...

class	Error

class	Field_profiles
	Discretized set of field profiles. More...

class	Fixed_step_size_integrator

struct	Fubini_options

class	Gaussian_potential
	Potential composed of two multivariate Gaussian functions. More...

class	Generalized_fubini_observer

class	Generalized_fubini_potential

class	GSL_interpolator
	Provides routines for carrying out 1D interpolation. More...

class	GSL_root_finder

class	Instream_profile_guesser
	Provides guess for field profiles read from an input stream. More...

class	IO_error
	Exception indicating generic input/output error. More...

class	Kink_profile_guesser
	Computes an initial guess for the bubble profile using a kink ansatz. More...

class	Logarithmic_observer

struct	Logarithmic_options

class	Logarithmic_potential

class	NLopt_optimizer

class	No_convergence_error
	Exception indicating failure of iterative procedure to converge. More...

class	Not_implemented_error

class	Numerical_error
	Exception indicating generic numerical error. More...

class	Optimizer_error
	Exception indicating that the optimizer failed to converge. More...

class	Out_of_bounds_error
	Exception indicating out of bounds access error. More...

class	Out_of_memory_error
	Exception indicating that memory allocation failed. More...

class	Perturbations_ODE_system
	Class implementing the system of ODEs obeyed by profile perturbations. More...

class	Perturbative_profiler
	Bounce solver using perturbative method. More...

class	Potential
	Abstract base class for a generic potential. More...

class	Profile_convergence_tester

class	Profile_guesser
	Abstract class to represent ansatz generators. More...

class	Profile_observer
	Observes the profile during iteration and writes out profile, perturbations and action for each step to file. More...

struct	Profiler_result

class	RAII_guard
	Carries out provided clean-up actions at destruction. More...

class	Relative_convergence_tester

class	Restricted_quartic_potential

class	Root_finder

struct	Scale_options

class	Setup_error
	Exception indicating general setup error. More...

class	Shooting
	Solve the one-dimensional problem using the shooting method. More...

class	Shooting_profile_guesser
	Constructs a solution ansatz using the overshoot/undershoot method. More...

struct	Shooting_settings

struct	State_algebra_dispatcher

struct	Tabulate_options

class	Thin_wall_error
	Exception indicating a thin-wall ansatz which we can't solve (yet!) More...

class	Thin_wall_observer

struct	Thin_wall_options

class	Thin_wall_potential
	Example thin wall potential as given by Coleman. More...

Typedefs
using	Constant_step_size_RK4 = Fixed_step_size_integrator< double, Eigen::VectorXd >

using	Constant_step_size_euler = Fixed_step_size_integrator< double, Eigen::VectorXd, boost::numeric::odeint::euler< Eigen::VectorXd, double, Eigen::VectorXd, double, State_algebra_dispatcher< Eigen::VectorXd >::algebra_type > >

using	Controlled_step_size_RK4 = Controlled_step_size_integrator< double, Eigen::VectorXd, boost::numeric::odeint::runge_kutta_cash_karp54< Eigen::VectorXd, double, Eigen::VectorXd, double, State_algebra_dispatcher< Eigen::VectorXd >::algebra_type > >

using	Controlled_step_size_RKD5 = Controlled_step_size_integrator< double, Eigen::VectorXd, boost::numeric::odeint::runge_kutta_dopri5< Eigen::VectorXd, double, Eigen::VectorXd, double, State_algebra_dispatcher< Eigen::VectorXd >::algebra_type > >

using	Euler_perturbative_profiler = Perturbative_profiler< Constant_step_size_euler >

using	RK4_perturbative_profiler = Perturbative_profiler< Constant_step_size_RK4 >

using	CRK4_perturbative_profiler = Perturbative_profiler< Controlled_step_size_RK4 >

using	CRKD5_perturbative_profiler = Perturbative_profiler< Controlled_step_size_RKD5 >

using	Profiler_data = std::map< std::string, std::vector< Profiler_result > >

Enumerations
enum	Integration_rule { Integration_rule::GK15, Integration_rule::GK21, Integration_rule::GK31, Integration_rule::GK41, Integration_rule::GK51, Integration_rule::GK61 }

enum	Root_finder_status { Root_finder_status::SUCCESS, Root_finder_status::FAIL }

enum	Integration_algorithm : int { Integration_algorithm::Runge_kutta_4 = 0, Integration_algorithm::Euler }

Functions
double	calculate_kinetic_action (const Potential &potential, const Field_profiles &profiles, std::size_t max_intervals=1000, double rel_tol=1.e-4, double abs_tol=1.e-4, Integration_rule rule=Integration_rule::GK31)
	Calculates the action using only the kinetic term contributions. More...

double	calculate_potential_action (const Potential &potential, const Field_profiles &profiles, std::size_t max_intervals=1000, double rel_tol=1.e-4, double abs_tol=1.e-4, Integration_rule rule=Integration_rule::GK31)
	Calculates the action using only the potential term contributions. More...

double	calculate_full_action (const Potential &potential, const Field_profiles &profiles, std::size_t max_intervals=1000, double rel_tol=1.e-4, double abs_tol=1.e-4, Integration_rule rule=Integration_rule::GK31)
	Calculates the action using all terms in the action integrand. More...

double	calculate_action (const Potential &potential, const Field_profiles &profiles, std::size_t max_intervals=1000, double rel_tol=1.e-4, double abs_tol=1.e-4, Integration_rule rule=Integration_rule::GK31, bool use_kinetic=true)
	Calculates the action using either the kinetic or potential terms. More...

Eigen::VectorXd	interpolate_f_at (const Eigen::VectorXd &x_old, const Eigen::VectorXd &y_old, const Eigen::VectorXd &x_new)
	Computes interpolated function values at a new set of grid points. More...

Eigen::VectorXd	interpolate_f_at (const Eigen::VectorXd &x_old, const Eigen::VectorXd &y_old, int n_old, const Eigen::VectorXd &x_new, int n_new)
	Computes interpolated function values at a new set of grid points. More...

int	get_integration_rule_key (Integration_rule)

template<typename F >
std::tuple< int, double, double >	integrate_gsl_qag (F f, double a, double b, double abs_tol, double rel_tol, std::size_t max_intervals, Integration_rule rule)

template<typename F >
std::tuple< int, double, double >	integrate_gsl_qags (F f, double a, double b, double abs_tol, double rel_tol, std::size_t max_intervals)

template<typename F >
std::tuple< int, double, double, int >	integrate_gsl_cquad (F f, double a, double b, double abs_tol, double rel_tol, std::size_t n_intervals)

template<typename T >
T	Abs (T x) noexcept

template<typename T >
T	Abs (const std::complex< T > &z) noexcept

template<typename Order , typename Argument >
auto	BesselI (Order v, Argument z) -> decltype(boost::math::cyl_bessel_i(v, z))

template<typename Order , typename Argument >
auto	BesselJ (Order v, Argument z) -> decltype(boost::math::cyl_bessel_j(v, z))

template<typename Order , typename Argument >
auto	BesselK (Order v, Argument z) -> decltype(boost::math::cyl_bessel_k(v, z))

template<typename Order , typename Argument >
auto	BesselY (Order v, Argument z) -> decltype(boost::math::cyl_neumann(v, z))

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	Exp (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	Exp (T n) noexcept

template<typename T >
std::complex< T >	Exp (const std::complex< T > &z) noexcept

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	Log (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	Log (T n) noexcept

template<typename T >
std::complex< T >	Log (const std::complex< T > &z) noexcept

template<typename T >
int	Sign (const T &x)

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	Cos (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	Cos (T n) noexcept

template<typename T >
std::complex< T >	Cos (const std::complex< T > &z) noexcept

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	Sin (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	Sin (T n) noexcept

template<typename T >
std::complex< T >	Sin (const std::complex< T > &z) noexcept

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	Tan (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	Tan (T n) noexcept

template<typename T >
std::complex< T >	Tan (const std::complex< T > &z) noexcept

template<typename T >
auto	Cot (T x) noexcept-> decltype(Tan(x))

template<typename T >
auto	Csc (T x) noexcept-> decltype(Sin(x))

template<typename T >
auto	Sec (T x) noexcept-> decltype(Cos(x))

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	ArcCos (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	ArcCos (T n) noexcept

template<typename T >
std::complex< T >	ArcCos (const std::complex< T > &z) noexcept

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	ArcSin (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	ArcSin (T n) noexcept

template<typename T >
std::complex< T >	ArcSin (const std::complex< T > &z) noexcept

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	ArcTan (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	ArcTan (T n) noexcept

template<typename T >
std::complex< T >	ArcTan (const std::complex< T > &z) noexcept

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	Cosh (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	Cosh (T n) noexcept

template<typename T >
std::complex< T >	Cosh (const std::complex< T > &z) noexcept

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	Sinh (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	Sinh (T n) noexcept

template<typename T >
std::complex< T >	Sinh (const std::complex< T > &z) noexcept

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	Tanh (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	Tanh (T n) noexcept

template<typename T >
std::complex< T >	Tanh (const std::complex< T > &z) noexcept

template<typename T >
auto	Coth (T x) noexcept-> decltype(Tanh(x))

template<typename T >
auto	Csch (T x) noexcept-> decltype(Sinh(x))

template<typename T >
auto	Sech (T x) noexcept-> decltype(Cosh(x))

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	ArcCosh (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	ArcCosh (T n) noexcept

template<typename T >
std::complex< T >	ArcCosh (const std::complex< T > &z) noexcept

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	ArcSinh (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	ArcSinh (T n) noexcept

template<typename T >
std::complex< T >	ArcSinh (const std::complex< T > &z) noexcept

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	ArcTanh (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	ArcTanh (T n) noexcept

template<typename T >
std::complex< T >	ArcTanh (const std::complex< T > &z) noexcept

template<typename T , typename = typename std::enable_if< std::is_arithmetic<T>::value,T>::type>
T	Im (T) noexcept

template<typename T >
T	Im (const std::complex< T > &z) noexcept

template<typename T , typename = typename std::enable_if< std::is_arithmetic<T>::value,T>::type>
T	Re (T x) noexcept

template<typename T >
T	Re (const std::complex< T > &z) noexcept

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>
T	Sqrt (T x) noexcept

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>
double	Sqrt (T n) noexcept

bool	optimization_succeeded (nlopt::result)

double	area_n_sphere (int n)

double	asinch (double a)

double	asinc (double a)

double	approx_root_pos_4 (double a)

double	approx_root_neg_4 (double a)

template<typename F >
constexpr RAII_guard< F >	make_raii_guard (F f)

Eigen::MatrixXd	calculate_rotation_to_target (const Eigen::VectorXd &target)
	Calculate the rotation matrix for a rotation to the target vector. More...

template<typename Scalar , typename Data >
Scalar	linear_lagrange_interpolation_at_point (Scalar x, const Data &xdata, const Data &ydata)

template<typename Scalar , typename Data >
Scalar	quadratic_lagrange_interpolation_at_point (Scalar x, const Data &xdata, const Data &ydata)

double	Wm1 (double a)

double	series (double a)

void	validate (boost::any &v, const std::vector< std::string > &values, Integration_algorithm *, int)

Bubble_profiler_inputs	parse_cmd_line_args (int argc, const char *argv[])

void	write_action (double action, std::ostream &ostr)
	Write the value of the action to requested output stream. More...

void	write_profiles (const std::vector< std::string > &fields, const Field_profiles &profiles, std::ostream &ostr)
	Write the given field profiles to requested output stream. More...

Eigen::VectorXd	find_global_min (const Potential &potential, double opt_timeout)
	Find the global minimum of the given potential. More...

Eigen::VectorXd	find_one_dimensional_barrier (const Potential &potential, const Eigen::VectorXd &true_vacuum_loc, const Eigen::VectorXd &false_vacuum_loc, double opt_timeout)
	Find barrier directly between two minima of a 1D potential. More...

void	initialize_extrema (const Potential &potential, const Bubble_profiler_inputs &input, Eigen::VectorXd &true_vacuum_loc, Eigen::VectorXd &false_vacuum_loc)
	Locate the requested critical points if not already provided. More...

void	initialize_extrema (const Potential &potential, const Bubble_profiler_inputs &input, Eigen::VectorXd &true_vacuum_loc, Eigen::VectorXd &false_vacuum_loc, Eigen::VectorXd &barrier_loc)
	Locate the necessary critical points if not already provided. More...

std::tuple< double, Field_profiles >	run_shooting_profiler (const Bubble_profiler_inputs &input)
	Calculates the action and bubble profile using the shooting method. More...

template<class Profiler >
std::tuple< double, Field_profiles >	run_perturbative_profiler (const Bubble_profiler_inputs &input, Profiler &profiler)
	Calculates the action and bubble profile using the perturbative method. More...

std::tuple< double, Field_profiles >	run_perturbative_profiler (const Bubble_profiler_inputs &input)
	Calculates the action and bubble profile using the perturbative method. More...

void	run_profiler (const Bubble_profiler_inputs &input)
	Calculates the action and bubble profile for the given potential. More...

void	configure_logging (const Bubble_profiler_inputs &input)

void	print_usage ()

bool	starts_with (const std::string &option, const std::string &prefix)

std::string	get_option_value (const std::string &option, const std::string &sep="=")

void	parse_positional_args (const std::vector< std::string > &args, Fubini_options &options)

double	parse_global_min (const std::string &value)

std::tuple< double, Field_profiles >	solve_shooting (const Generalized_fubini_potential &potential, double true_min, bool calculate_profile)

std::tuple< double, Field_profiles >	solve_perturbative (Generalized_fubini_potential &potential, double true_min, const std::string &observer_file)

void	write_profile (std::ostream &ostr, const Field_profiles &numerical_profile, const Field_profiles &exact_profile)

void	write_action (std::ostream &ostr, double numerical_action, double exact_action)

void	parse_positional_args (const std::vector< std::string > &args, Logarithmic_options &options)

std::tuple< double, Field_profiles >	solve_shooting (const Logarithmic_potential &potential, double true_min, bool calculate_profile)

std::tuple< double, Field_profiles >	solve_perturbative (Logarithmic_potential &potential, double true_min, const std::string &observer_file)

void	parse_positional_args (const std::vector< std::string > &args, Action_options &options)

void	parse_positional_args (const std::vector< std::string > &args, Tabulate_options &options)

Profiler_result	run_shooting_profiler (const Restricted_quartic_potential &potential, int dim)

Profiler_result	run_perturbative_profiler (Restricted_quartic_potential potential, int dim)

Profiler_result	run_profiler (const std::string &profiler, const Restricted_quartic_potential &potential, int dim)

void	write_table_header (const std::vector< std::string > &profiler_labels)

void	write_table (int dim, double E, const std::vector< double > &alpha_data, const Profiler_data &profiler_data)

void	parse_positional_args (const std::vector< std::string > &args, Scale_options &options)

void	parse_positional_args (const std::vector< std::string > &args, Thin_wall_options &options)

std::tuple< double, Field_profiles >	solve_shooting (const Thin_wall_potential &potential, int dim, bool calculate_profile)

std::tuple< double, Field_profiles >	solve_perturbative (Thin_wall_potential &potential, int dim, const std::string &observer_file)

void	write_profile (std::ostream &ostr, const Field_profiles &numerical_profile)

Variables
const std::string	default_ansatz_file = ""

const double	default_domain_start = -1.

const double	default_domain_end = -1.

const double	default_initial_step_size = 1.e-2

const int	default_interp_fraction = 1.0

const Integration_algorithm	default_algorithm

const double	default_rtol_action = 1.e-3

const double	default_rtol_fields = 1.e-3

const std::string	default_output_file = "-"

const bool	default_write_perturbations = true

const bool	default_force_output = false

const double	default_opt_timeout = 10.

const int	default_max_iterations = -1

const bool	default_assume_origin_false_vacuum = false

const bool	default_use_perturbative = false

const bool	default_write_profiles = false

const bool	default_shooting_ansatz = false

const bool	default_verbose = false

const int	default_shoot_bisect_bits = 5

const double	default_action_arrived_rel = 1.e-3

const double	default_shoot_ode_abs = 1.e-4

const double	default_shoot_ode_rel = 1.e-4

const double	default_action_ode_abs = 1.e-6

const double	default_action_ode_rel = 1.e-6

const double	default_drho_frac = 1.e-3

const double	default_evolve_change_rel = 1.e-2

const double	default_bisect_lambda_max = 5.0

const int	default_iter_max = 100000

const double	default_periods_max = 1.e2

const double	default_f_y_max = 1.e6

const double	default_f_y_min = 1.e-3

const double	default_y_max = 1.e1

Typedef Documentation

using BubbleProfiler::Constant_step_size_euler = typedef Fixed_step_size_integrator< double, Eigen::VectorXd, boost::numeric::odeint::euler< Eigen::VectorXd, double, Eigen::VectorXd, double, State_algebra_dispatcher<Eigen::VectorXd>::algebra_type> >

Definition at line 35 of file default_integration_policy.hpp.

using BubbleProfiler::Constant_step_size_RK4 = typedef Fixed_step_size_integrator<double, Eigen::VectorXd>

Definition at line 27 of file default_integration_policy.hpp.

using BubbleProfiler::Controlled_step_size_RK4 = typedef Controlled_step_size_integrator< double, Eigen::VectorXd, boost::numeric::odeint::runge_kutta_cash_karp54< Eigen::VectorXd, double, Eigen::VectorXd, double, State_algebra_dispatcher<Eigen::VectorXd>::algebra_type> >

Definition at line 43 of file default_integration_policy.hpp.

using BubbleProfiler::Controlled_step_size_RKD5 = typedef Controlled_step_size_integrator< double, Eigen::VectorXd, boost::numeric::odeint::runge_kutta_dopri5< Eigen::VectorXd, double, Eigen::VectorXd, double, State_algebra_dispatcher<Eigen::VectorXd>::algebra_type> >

Definition at line 51 of file default_integration_policy.hpp.

using BubbleProfiler::CRK4_perturbative_profiler = typedef Perturbative_profiler<Controlled_step_size_RK4>

Definition at line 30 of file perturbative_profiler.hpp.

using BubbleProfiler::CRKD5_perturbative_profiler = typedef Perturbative_profiler<Controlled_step_size_RKD5>

Definition at line 32 of file perturbative_profiler.hpp.

using BubbleProfiler::Euler_perturbative_profiler = typedef Perturbative_profiler<Constant_step_size_euler>

Definition at line 26 of file perturbative_profiler.hpp.

using BubbleProfiler::Profiler_data = typedef std::map<std::string, std::vector<Profiler_result> >

Examples:: tabulate.cpp.

Definition at line 77 of file tabulate.cpp.

using BubbleProfiler::RK4_perturbative_profiler = typedef Perturbative_profiler<Constant_step_size_RK4>

Examples:: general_fubini.cpp, logarithmic.cpp, tabulate.cpp, and thin_wall.cpp.

Definition at line 28 of file perturbative_profiler.hpp.

Enumeration Type Documentation

enum BubbleProfiler::Integration_algorithm : int

strong

Enumerator
Runge_kutta_4
Euler

Definition at line 57 of file run_cmd_line_potential.cpp.

enum BubbleProfiler::Integration_rule

strong

Enumerator
GK15
GK21
GK31
GK41
GK51
GK61

Definition at line 31 of file integration_utils.hpp.

enum BubbleProfiler::Root_finder_status

strong

Enumerator
SUCCESS
FAIL

Definition at line 25 of file root_finder.hpp.

Function Documentation

template<typename T >

T BubbleProfiler::Abs ( T x )

noexcept

Definition at line 34 of file math_wrappers.hpp.

References Eigen::abs().

template<typename T >

T BubbleProfiler::Abs ( const std::complex< T > & z )

noexcept

Definition at line 40 of file math_wrappers.hpp.

References Eigen::abs().

double BubbleProfiler::approx_root_neg_4 ( double a )

Returns: Root of \( J_1(x) / x + a - 0.5 = 0 \)

See e.g., in Mathematica,

Numerical[a_] := x /. FindRoot[BesselJ[1, x]/x - 0.5 == -a, {x, 2}]
Taylor[a_] := 4. Sqrt[a]
Plot[{Numerical[a], Taylor[a]}, {a, 0, 1}]

Definition at line 108 of file numeric.cpp.

References Sqrt().

Referenced by BubbleProfiler::Shooting::calculate_roll_time().

double BubbleProfiler::approx_root_pos_4 ( double a )

Returns: Root of \(I_1(x) / x - a - 0.5 = 0\)

This is used in dimension \(d=4\) case. I use Taylor expansions and a large \(x\) approximation of \(I_1(x)\).

See e.g., in Mathematica,

Numerical[a_] := x /. FindRoot[BesselI[1, x] / x - 0.5 == a, {x, 10.}]
Taylor[a_] := 4. Sqrt[a]
Lambert[a_] := -(3/2) LambertW[-1, (2 (2/\[Pi])^(1/3))/(3 (-(1 + 2 a)^2)^(1/3))] // N // Re
Plot[{Numerical[a], Taylor[a], Lambert[a]}, {a, 0, 100}]

Definition at line 96 of file numeric.cpp.

References Sqrt(), and Wm1().

Referenced by BubbleProfiler::Shooting::calculate_roll_time().

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::ArcCos ( T x )

noexcept

Definition at line 210 of file math_wrappers.hpp.

References sm_plus_singlet::type.

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::ArcCos ( T n )

noexcept

Definition at line 218 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::ArcCos ( const std::complex< T > & z )

noexcept

Definition at line 224 of file math_wrappers.hpp.

References sm_plus_singlet::type.

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::ArcCosh ( T x )

noexcept

Definition at line 360 of file math_wrappers.hpp.

References sm_plus_singlet::type.

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::ArcCosh ( T n )

noexcept

Definition at line 368 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::ArcCosh ( const std::complex< T > & z )

noexcept

Definition at line 374 of file math_wrappers.hpp.

References sm_plus_singlet::type.

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::ArcSin ( T x )

noexcept

Definition at line 232 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Referenced by BubbleProfiler::Thin_wall_potential::get_global_minimum_location(), BubbleProfiler::Thin_wall_potential::get_local_maximum_location(), and BubbleProfiler::Thin_wall_potential::get_local_minimum_location().

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::ArcSin ( T n )

noexcept

Definition at line 240 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::ArcSin ( const std::complex< T > & z )

noexcept

Definition at line 246 of file math_wrappers.hpp.

References sm_plus_singlet::type.

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::ArcSinh ( T x )

noexcept

Definition at line 382 of file math_wrappers.hpp.

References sm_plus_singlet::type.

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::ArcSinh ( T n )

noexcept

Definition at line 390 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::ArcSinh ( const std::complex< T > & z )

noexcept

Definition at line 396 of file math_wrappers.hpp.

References sm_plus_singlet::type.

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::ArcTan ( T x )

noexcept

Definition at line 254 of file math_wrappers.hpp.

References sm_plus_singlet::type.

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::ArcTan ( T n )

noexcept

Definition at line 262 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::ArcTan ( const std::complex< T > & z )

noexcept

Definition at line 268 of file math_wrappers.hpp.

References sm_plus_singlet::type.

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::ArcTanh ( T x )

noexcept

Definition at line 404 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Referenced by BubbleProfiler::Kink_profile_guesser::guess_domain_end().

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::ArcTanh ( T n )

noexcept

Definition at line 412 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::ArcTanh ( const std::complex< T > & z )

noexcept

Definition at line 418 of file math_wrappers.hpp.

References sm_plus_singlet::type.

double BubbleProfiler::area_n_sphere ( int n )

Returns: Area of \(n\)-sphere from wiki

Parameters

n \(n\)

Definition at line 29 of file numeric.cpp.

Referenced by BubbleProfiler::Shooting::action(), calculate_full_action(), calculate_kinetic_action(), and calculate_potential_action().

double BubbleProfiler::asinc ( double a )

Returns: Approximate inverse of the sinc function, \(\sin x / x = a \)

See e.g., in Mathematica

Asinch[a_] := InverseFunction[Sinc][a] // N // Re
f[x_] := 2*x + 3*x^3/10 + 321*x^5/2800 + 3197*x^7/56000 +
445617*x^9/13798400 + 1766784699*x^11/89689600000 +
317184685563*x^13/25113088000000 +
14328608561991*x^15/1707689984000000 +
6670995251837391*x^17/1165411287040000000 +
910588298588385889*x^19/228420612259840000000
Approx[a_] := Sqrt[3./2.] * f[Sqrt[1. - a]]
Plot[{Asinch[a], Approx[a]}, {a, 0, 1}]
Plot[{Sinc[Approx[a]]}, {a, 0, 1}]

Definition at line 92 of file numeric.cpp.

References series(), and Sqrt().

Referenced by BubbleProfiler::Shooting::calculate_roll_time().

double BubbleProfiler::asinch ( double a )

Returns: Approximate inverse of the hyperbolic sinch function, \(\sinh x / x = a\)

I use Taylor expansions and \(\sinh x \approx e^x / 2\).

See e.g., in Mathematica,

Asinch[a_] := x /. FindRoot[Sinh[x] /x == a, {x, 5}]
Taylor[a_] := Sqrt[6. (a - 1)]
Lambert[a_] := -LambertW[-1, -0.5 / a]
Plot[{Asinch[a], Taylor[a], Lambert[a]}, {a, 1, 10}]

The Taylor expansion is more precise until about \(a \approx 1.5\).

Definition at line 63 of file numeric.cpp.

References Sqrt(), and Wm1().

Referenced by BubbleProfiler::Shooting::calculate_roll_time().

template<typename Order , typename Argument >

auto BubbleProfiler::BesselI	(	Order	v,
		Argument	z
	)		-> decltype(boost::math::cyl_bessel_i(v, z))

Definition at line 46 of file math_wrappers.hpp.

Referenced by BubbleProfiler::Shooting::calculate_roll_velocity(), BubbleProfiler::Shooting::interior(), and BubbleProfiler::Shooting::quadratic_potential_solution().

template<typename Order , typename Argument >

auto BubbleProfiler::BesselJ	(	Order	v,
		Argument	z
	)		-> decltype(boost::math::cyl_bessel_j(v, z))

Definition at line 53 of file math_wrappers.hpp.

Referenced by BubbleProfiler::Shooting::calculate_roll_velocity(), BubbleProfiler::Shooting::interior(), and BubbleProfiler::Shooting::quadratic_potential_solution().

template<typename Order , typename Argument >

auto BubbleProfiler::BesselK	(	Order	v,
		Argument	z
	)		-> decltype(boost::math::cyl_bessel_k(v, z))

Definition at line 60 of file math_wrappers.hpp.

Referenced by BubbleProfiler::Shooting_profile_guesser::get_large_distance_solution().

template<typename Order , typename Argument >

auto BubbleProfiler::BesselY	(	Order	v,
		Argument	z
	)		-> decltype(boost::math::cyl_neumann(v, z))

Definition at line 67 of file math_wrappers.hpp.

References sm_plus_singlet::type.

double BubbleProfiler::calculate_action	(	const Potential &	potential,
		const Field_profiles &	profiles,
		std::size_t	max_intervals = `1000`,
		double	rel_tol = `1.e-4`,
		double	abs_tol = `1.e-4`,
		Integration_rule	rule = `Integration_rule::GK31`,
		bool	use_kinetic = `true`
	)

Calculates the action using either the kinetic or potential terms.

Parameters

potential	the potential associated with the bounce solution
profiles	the field profiles representing the bounce solution
max_intervals	the maximum allowed number of subintervals for adaptive quadrature routine
rel_tol	the relative error goal
abs_tol	the absolute error goal
rule	the quadrature rule to use
use_kinetic	flag selecting whether the kinetic or potential terms should be used to compute the action

Returns: numerical estimate for the Euclidean action

The method used to evaluate the action is chosen based on the value of use_kinetic, with a value of true indicating that the action should be evaluated using only the contribution from the field kinetic terms. If use_kinetic is false, the action is evaluated using the contribution from the potential.

Internally, this simply function calls BubbleProfiler::calculate_kinetic_action or BubbleProfiler::calculate_potential_action, as appropriate.

See also: calculate_kinetic_action, calculate_potential_action

Definition at line 257 of file euclidean_action.cpp.

References calculate_kinetic_action(), and calculate_potential_action().

Referenced by BubbleProfiler::Perturbative_profiler< Integration_policy >::calculate_bubble_profile(), BubbleProfiler::Relative_convergence_tester::is_converged(), and BubbleProfiler::Profile_observer::write_action_to_file().

double BubbleProfiler::calculate_full_action	(	const Potential &	potential,
		const Field_profiles &	profiles,
		std::size_t	max_intervals = `1000`,
		double	rel_tol = `1.e-4`,
		double	abs_tol = `1.e-4`,
		Integration_rule	rule = `Integration_rule::GK31`
	)

Calculates the action using all terms in the action integrand.

Parameters

potential	the potential associated with the bounce solution
profiles	the field profiles representing the bounce solution
max_intervals	the maximum allowed number of subintervals for adaptive quadrature routine
rel_tol	the relative error goal
abs_tol	the absolute error goal
rule	the quadrature rule to use

Returns: numerical estimate for the Euclidean action

Given the bounce solution for \(n\) scalar fields in \(d\) dimensions defined on a finite domain, an approximate value for the full Euclidean action

\[ S_E \equiv S_{d-1} \int_0^\infty d\rho \rho^{d-1} \left ( \sum_{i=1}^n \frac{1}{2} \dot{\phi}_i^2 + V(\phi_i) \right ) , \]

where \(S_{d-1}\) is the surface area of the \(d\)-sphere and the potential is assumed to vanish at the false vacuum, is calculated using numerical quadrature, with the quadrature rule chosen according to the value of rule. The adaptive quadrature routine attempts to compute an estimate \(\tilde{I}\) for the integral \(I\) appearing above that satisfies

\[ | \tilde{I} - I | \leq \max ( \epsilon_{\text{abs}}, \epsilon_{\text{rel}} |I|) , \]

with \(\epsilon_{\text{abs}}\) and \(\epsilon_{\text{rel}}\) given by abs_tol and rel_tol, respectively. The maximum allowed number of subintervals used in this integration is set by the value of max_intervals.

See also: integrate_gsl_qag

Definition at line 198 of file euclidean_action.cpp.

References area_n_sphere(), BubbleProfiler::Field_profiles::derivative_at(), BubbleProfiler::Field_profiles::evaluate_at(), BubbleProfiler::Field_profiles::get_domain_end(), BubbleProfiler::Field_profiles::get_domain_start(), BubbleProfiler::Field_profiles::get_number_of_dimensions(), BubbleProfiler::Field_profiles::get_number_of_fields(), integrate_gsl_qag(), and gaussian_alpha_tests::n_fields.

double BubbleProfiler::calculate_kinetic_action	(	const Potential &	potential,
		const Field_profiles &	profiles,
		std::size_t	max_intervals = `1000`,
		double	rel_tol = `1.e-4`,
		double	abs_tol = `1.e-4`,
		Integration_rule	rule = `Integration_rule::GK31`
	)

Calculates the action using only the kinetic term contributions.

Parameters

potential	the potential associated with the bounce solution
profiles	the field profiles representing the bounce solution
max_intervals	the maximum allowed number of subintervals for adaptive quadrature routine
rel_tol	the relative error goal
abs_tol	the absolute error goal
rule	the quadrature rule to use

Returns: numerical estimate for the Euclidean action

Given the bounce solution for \(n\) scalar fields in \(d\) dimensions defined on a finite domain, the contribution to the action due to the field kinetic terms,

\[ S_T \equiv S_{d-1} \int_0^\infty d\rho \rho^{d-1} \sum_{i=1}^n \frac{1}{2} \dot{\phi}_i^2 , \]

where \(S_{d-1}\) is the surface area of the \(d\)-sphere, is first calculated using numerical quadrature, with the quadrature rule chosen according to the value of rule. The adaptive quadrature routine attempts to compute an estimate \(\tilde{I}\) for the integral \(I\) appearing above that satisfies

\[ | \tilde{I} - I | \leq \max ( \epsilon_{\text{abs}}, \epsilon_{\text{rel}} |I|) , \]

with \(\epsilon_{\text{abs}}\) and \(\epsilon_{\text{rel}}\) given by abs_tol and rel_tol, respectively. The maximum allowed number of subintervals used in this integration is set by the value of max_intervals. The full value of the action to be returned is then obtained from the value of \(S_T\) using the relation

\[ S_E = \frac{2}{d} S_T . \]

See also: integrate_gsl_qag

Definition at line 63 of file euclidean_action.cpp.

References area_n_sphere(), BubbleProfiler::Field_profiles::derivative_at(), BubbleProfiler::Field_profiles::get_domain_end(), BubbleProfiler::Field_profiles::get_domain_start(), BubbleProfiler::Field_profiles::get_number_of_dimensions(), BubbleProfiler::Field_profiles::get_number_of_fields(), integrate_gsl_qag(), and gaussian_alpha_tests::n_fields.

Referenced by calculate_action().

double BubbleProfiler::calculate_potential_action	(	const Potential &	potential,
		const Field_profiles &	profiles,
		std::size_t	max_intervals = `1000`,
		double	rel_tol = `1.e-4`,
		double	abs_tol = `1.e-4`,
		Integration_rule	rule = `Integration_rule::GK31`
	)

Calculates the action using only the potential term contributions.

Parameters

potential	the potential associated with the bounce solution
profiles	the field profiles representing the bounce solution
max_intervals	the maximum allowed number of subintervals for adaptive quadrature routine
rel_tol	the relative error goal
abs_tol	the absolute error goal
rule	the quadrature rule to use

Returns: numerical estimate for the Euclidean action

Given the bounce solution for \(n\) scalar fields in \(d\) dimensions defined on a finite domain, the contribution to the action due to the field potential terms,

\[ S_V \equiv S_{d-1} \int_0^\infty d\rho \rho^{d-1} V(\phi_i) , \]

where \(S_{d-1}\) is the surface area of the \(d\)-sphere and the potential is assumed to vanish at the false vacuum, is first calculated using numerical quadrature, with the quadrature rule chosen according to the value of rule. The adaptive quadrature routine attempts to compute an estimate \(\tilde{I}\) for the integral \(I\) appearing above that satisfies

\[ | \tilde{I} - I | \leq \max ( \epsilon_{\text{abs}}, \epsilon_{\text{rel}} |I|) , \]

with \(\epsilon_{\text{abs}}\) and \(\epsilon_{\text{rel}}\) given by abs_tol and rel_tol, respectively. The maximum allowed number of subintervals used in this integration is set by the value of max_intervals. The full value of the action to be returned is then obtained from the value of \(S_V\) using the relation

\[ S_E = \frac{2}{2 - d} S_V . \]

See also: integrate_gsl_qag

Definition at line 138 of file euclidean_action.cpp.

References area_n_sphere(), BubbleProfiler::Field_profiles::evaluate_at(), BubbleProfiler::Field_profiles::get_domain_end(), BubbleProfiler::Field_profiles::get_domain_start(), BubbleProfiler::Field_profiles::get_number_of_dimensions(), and integrate_gsl_qag().

Referenced by calculate_action().

Eigen::MatrixXd BubbleProfiler::calculate_rotation_to_target ( const Eigen::VectorXd & target )

Calculate the rotation matrix for a rotation to the target vector.

Given a target vector, this method computes the rotation matrix to transform the current coordinate system to one in which the first basis vector is aligned with the target vector.

Notes:

this change of coordinates is not uniquely specified, and may involve a reflection.
Right multiplication will take coordinates in the rotated system to coordinates in the unrotated system. Take the transpose for the opposite effect.

Parameters

target the target vector to align with

Returns: the rotation matrix

Definition at line 36 of file rotation.cpp.

Referenced by BubbleProfiler::Shooting_profile_guesser::calculate_potential_parameters(), and BubbleProfiler::Kink_profile_guesser::calculate_potential_parameters().

void BubbleProfiler::configure_logging ( const Bubble_profiler_inputs & input )

Definition at line 720 of file run_cmd_line_potential.cpp.

References BubbleProfiler::logging::Logging_manager::get_manager(), BubbleProfiler::logging::Trace, BubbleProfiler::Bubble_profiler_inputs::verbose, and BubbleProfiler::logging::Warning.

Referenced by main().

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::Cos ( T x )

noexcept

Definition at line 126 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Referenced by BubbleProfiler::Shooting::calculate_roll_velocity(), BubbleProfiler::Shooting::interior(), and Sec().

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::Cos ( T n )

noexcept

Definition at line 134 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::Cos ( const std::complex< T > & z )

noexcept

Definition at line 140 of file math_wrappers.hpp.

References sm_plus_singlet::type.

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::Cosh ( T x )

noexcept

Definition at line 276 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Referenced by BubbleProfiler::Shooting::calculate_roll_velocity(), BubbleProfiler::Shooting::interior(), and Sech().

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::Cosh ( T n )

noexcept

Definition at line 284 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::Cosh ( const std::complex< T > & z )

noexcept

Definition at line 290 of file math_wrappers.hpp.

References sm_plus_singlet::type.

template<typename T >

auto BubbleProfiler::Cot ( T x ) -> decltype(Tan(x))

noexcept

Definition at line 190 of file math_wrappers.hpp.

References Tan().

template<typename T >

auto BubbleProfiler::Coth ( T x ) -> decltype(Tanh(x))

noexcept

Definition at line 340 of file math_wrappers.hpp.

References Tanh().

template<typename T >

auto BubbleProfiler::Csc ( T x ) -> decltype(Sin(x))

noexcept

Definition at line 196 of file math_wrappers.hpp.

References Sin().

template<typename T >

auto BubbleProfiler::Csch ( T x ) -> decltype(Sinh(x))

noexcept

Definition at line 346 of file math_wrappers.hpp.

References Sinh().

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::Exp ( T x )

noexcept

Definition at line 76 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Referenced by BubbleProfiler::Kink_profile_guesser::evaluate_ansatz_at(), BubbleProfiler::Kink_profile_guesser::evaluate_ansatz_deriv_at(), BubbleProfiler::Logarithmic_potential::get_action(), BubbleProfiler::Logarithmic_potential::get_bounce_solution_at(), BubbleProfiler::Shooting_profile_guesser::get_large_distance_solution(), and BubbleProfiler::Shooting::unmap().

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::Exp ( T n )

noexcept

Definition at line 84 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::Exp ( const std::complex< T > & z )

noexcept

Definition at line 90 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Eigen::VectorXd BubbleProfiler::find_global_min	(	const Potential &	potential,
		double	opt_timeout
	)

Find the global minimum of the given potential.

Parameters

potential	the potential to minimize
opt_timeout	the allowed maximum amount of time to run for

Returns: the obtained location of the minimum

Definition at line 340 of file run_cmd_line_potential.cpp.

References BubbleProfiler::NLopt_optimizer::get_extremum_location(), BubbleProfiler::Potential::get_number_of_fields(), BubbleProfiler::NLopt_optimizer::MIN, gaussian_alpha_tests::n_fields, optimization_succeeded(), BubbleProfiler::NLopt_optimizer::optimize(), BubbleProfiler::NLopt_optimizer::set_extremum_type(), BubbleProfiler::NLopt_optimizer::set_lower_bounds(), BubbleProfiler::NLopt_optimizer::set_max_time(), and BubbleProfiler::NLopt_optimizer::set_upper_bounds().

Referenced by initialize_extrema().

Eigen::VectorXd BubbleProfiler::find_one_dimensional_barrier	(	const Potential &	potential,
		const Eigen::VectorXd &	true_vacuum_loc,
		const Eigen::VectorXd &	false_vacuum_loc,
		double	opt_timeout
	)

Find barrier directly between two minima of a 1D potential.

In the one-dimensional case, this function attempts to find the location of the barrier between two given minima, taken to be the location of the maximum value of the potential between the two minima.

Parameters

potential	the potential to locate the barrier for
true_vacuum_loc	the location of the global minimum
false_vacuum_loc	the location of the local minimum
opt_timeout	the allowed maximum amount of time to run for

Returns: the obtained location of the maximum

Definition at line 377 of file run_cmd_line_potential.cpp.

Referenced by initialize_extrema().

int BubbleProfiler::get_integration_rule_key ( Integration_rule rule )

Definition at line 22 of file integration_utils.cpp.

References GK15, GK21, GK31, GK41, GK51, and GK61.

Referenced by integrate_gsl_qag().

std::string BubbleProfiler::get_option_value	(	const std::string &	option,
		const std::string &	sep = `"="`
	)

Examples:: general_fubini.cpp, logarithmic.cpp, and thin_wall.cpp.

Definition at line 88 of file general_fubini.cpp.

Referenced by parse_global_min(), and parse_positional_args().

template<typename T , typename = typename std::enable_if< std::is_arithmetic<T>::value,T>::type>

T BubbleProfiler::Im ( T )

noexcept

Definition at line 426 of file math_wrappers.hpp.

template<typename T >

T BubbleProfiler::Im ( const std::complex< T > & z )

noexcept

Definition at line 432 of file math_wrappers.hpp.

References sm_plus_singlet::type.

void BubbleProfiler::initialize_extrema	(	const Potential &	potential,
		const Bubble_profiler_inputs &	input,
		Eigen::VectorXd &	true_vacuum_loc,
		Eigen::VectorXd &	false_vacuum_loc
	)

Locate the requested critical points if not already provided.

If not empty, the values of input.global_min and input.local_min are used to set the values of the global minimum and local minimum, respectively.

If input.global_min is empty, the function attempts to locate the true vacuum by numerically optimizing the potential. By default, the function will not attempt to find the local minimum if input.local_min is empty, and will exit with an error. However, if input.local_min is empty and input.assume_origin_false_vacuum is set to true, then the location of the false vacuum will be set to the origin in field space.

Parameters

potential	the potential to find the critical points of
input	settings to be used to configure the potential and solvers
true_vacuum_loc	the vector in which to store the obtained global minimum
false_vacuum_loc	the vector in which to store the obtained local minimum

Definition at line 440 of file run_cmd_line_potential.cpp.

References BubbleProfiler::Bubble_profiler_inputs::assume_origin_false_vacuum, find_global_min(), BubbleProfiler::Potential::get_number_of_fields(), BubbleProfiler::Bubble_profiler_inputs::global_min, BubbleProfiler::Bubble_profiler_inputs::local_min, gaussian_alpha_tests::n_fields, and BubbleProfiler::Bubble_profiler_inputs::opt_timeout.

Referenced by initialize_extrema(), run_perturbative_profiler(), and run_shooting_profiler().

void BubbleProfiler::initialize_extrema	(	const Potential &	potential,
		const Bubble_profiler_inputs &	input,
		Eigen::VectorXd &	true_vacuum_loc,
		Eigen::VectorXd &	false_vacuum_loc,
		Eigen::VectorXd &	barrier_loc
	)

Locate the necessary critical points if not already provided.

If not empty, the values of input.global_min , input.local_min , and input.barrier are used to set the values of the global minimum, local minimum, and barrier, respectively.

If input.global_min is empty, the function attempts to locate the true vacuum by numerically optimizing the potential. By default, the function will not attempt to find the local minimum if input.local_min is empty, and will exit with an error. However, if input.local_min is empty and input.assume_origin_false_vacuum is set to true, then the location of the false vacuum will be set to the origin in field space.

Locating the position of the barrier between two minima is only supported for one-field potentials. In these cases, if input.barrier is empty, the local maximum of the potential is obtained numerically; otherwise, the given value is used.

Parameters

potential	the potential to find the critical points of
input	settings to be used to configure the potential and solvers
true_vacuum_loc	the vector in which to store the obtained global minimum
false_vacuum_loc	the vector in which to store the obtained local minimum
barrier_loc	the vector in which to store the obtained barrier location

Definition at line 505 of file run_cmd_line_potential.cpp.

References BubbleProfiler::Bubble_profiler_inputs::barrier, find_one_dimensional_barrier(), BubbleProfiler::Potential::get_number_of_fields(), initialize_extrema(), gaussian_alpha_tests::n_fields, and BubbleProfiler::Bubble_profiler_inputs::opt_timeout.

template<typename F >

std::tuple<int,double,double,int> BubbleProfiler::integrate_gsl_cquad	(	F	f,
		double	a,
		double	b,
		double	abs_tol,
		double	rel_tol,
		std::size_t	n_intervals
	)

Definition at line 110 of file integration_utils.hpp.

References make_raii_guard().

template<typename F >

std::tuple<int,double,double> BubbleProfiler::integrate_gsl_qag	(	F	f,
		double	a,
		double	b,
		double	abs_tol,
		double	rel_tol,
		std::size_t	max_intervals,
		Integration_rule	rule
	)

Definition at line 38 of file integration_utils.hpp.

References get_integration_rule_key(), and make_raii_guard().

Referenced by calculate_full_action(), calculate_kinetic_action(), and calculate_potential_action().

template<typename F >

std::tuple<int,double,double> BubbleProfiler::integrate_gsl_qags	(	F	f,
		double	a,
		double	b,
		double	abs_tol,
		double	rel_tol,
		std::size_t	max_intervals
	)

Definition at line 75 of file integration_utils.hpp.

References make_raii_guard().

Eigen::VectorXd BubbleProfiler::interpolate_f_at	(	const Eigen::VectorXd &	x_old,
		const Eigen::VectorXd &	y_old,
		const Eigen::VectorXd &	x_new
	)

Computes interpolated function values at a new set of grid points.

Parameters

[in]	x_old	the initial set of x values at which the function is known
[in]	y_old	the initial set of y values
[in]	x_new	the x values at which to interpolate the function

Returns: a vector of the interpolated values at each point in x_new

The cubic spline used to obtain the interpolated function values is computed using all of the given (x_old, y_old) values, of which there must be at least two. The vectors x_old and y_old must have the same lengths. Default parabolic boundary conditions, with unknown derivatives, are used at the left and right ends of the domain. The obtained spline interpolant is evaluated at all points in x_new .

Definition at line 93 of file gsl_interpolator.cpp.

Referenced by BubbleProfiler::Perturbative_profiler< Integration_policy >::update_field_profiles().

Eigen::VectorXd BubbleProfiler::interpolate_f_at	(	const Eigen::VectorXd &	x_old,
		const Eigen::VectorXd &	y_old,
		int	n_old,
		const Eigen::VectorXd &	x_new,
		int	n_new
	)

Computes interpolated function values at a new set of grid points.

Parameters

[in]	x_old	the initial set of x values at which the function is known
[in]	y_old	the initial set of y values
[in]	n_old	the number of values to use from `x_old` and `y_old`
[in]	x_new	the x values at which to interpolate the function
[in]	n_new	the number of values in `x_new` to evaluate at

Returns: a vector of the interpolated values at the values in x_new

The cubic spline used to obtain the interpolated function values is computed using the first n_old values from x_old and y_old, with n_old between 2 and the minimum of the number of values in x_old and y_old . The obtained spline interpolant is evaluated at the first n_new points in x_new.

Definition at line 114 of file gsl_interpolator.cpp.

References make_raii_guard().

template<typename Scalar , typename Data >

Scalar BubbleProfiler::linear_lagrange_interpolation_at_point	(	Scalar	x,
		const Data &	xdata,
		const Data &	ydata
	)

Assumes data sorted in order of ascending x-values

Definition at line 29 of file univariate_interpolation.hpp.

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::Log ( T x )

noexcept

Definition at line 98 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Referenced by BubbleProfiler::Shooting::calculate_roll_time(), BubbleProfiler::Logarithmic_potential::first_deriv(), BubbleProfiler::Logarithmic_potential::operator()(), BubbleProfiler::Logarithmic_potential::second_deriv(), and Wm1().

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::Log ( T n )

noexcept

Definition at line 106 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::Log ( const std::complex< T > & z )

noexcept

Definition at line 112 of file math_wrappers.hpp.

template<typename F >

constexpr RAII_guard<F> BubbleProfiler::make_raii_guard ( F f )

Definition at line 43 of file raii_guard.hpp.

Referenced by BubbleProfiler::GSL_interpolator::evaluate_at(), BubbleProfiler::GSL_interpolator::evaluate_deriv_at(), BubbleProfiler::GSL_interpolator::evaluate_second_deriv_at(), integrate_gsl_cquad(), integrate_gsl_qag(), integrate_gsl_qags(), interpolate_f_at(), and BubbleProfiler::GSL_root_finder< N >::solve().

bool BubbleProfiler::optimization_succeeded ( nlopt::result r )

Helper function to check NLopt status code

Definition at line 30 of file nlopt_optimizer.cpp.

References SUCCESS.

Referenced by find_global_min(), and find_one_dimensional_barrier().

Thin_wall_options BubbleProfiler::parse_cmd_line_args	(	int	argc,
		const char *	argv[]
	)

Examples:: action.cpp, general_fubini.cpp, logarithmic.cpp, scale.cpp, tabulate.cpp, and thin_wall.cpp.

Definition at line 160 of file run_cmd_line_potential.cpp.

Referenced by main(), parse_global_min(), and parse_positional_args().

double BubbleProfiler::parse_global_min ( const std::string & value )

Examples:: general_fubini.cpp, and logarithmic.cpp.

Definition at line 143 of file general_fubini.cpp.

References BubbleProfiler::Fubini_options::calculate_profile, get_option_value(), BubbleProfiler::Fubini_options::global_min, BubbleProfiler::Fubini_options::output_file, parse_cmd_line_args(), parse_positional_args(), BubbleProfiler::Fubini_options::perturbations_file, print_usage(), starts_with(), BubbleProfiler::Fubini_options::use_perturbative, and BubbleProfiler::Fubini_options::verbose.

Referenced by parse_positional_args().

void BubbleProfiler::parse_positional_args	(	const std::vector< std::string > &	args,
		Scale_options &	options
	)

Definition at line 65 of file scale.cpp.

References BubbleProfiler::Scale_options::alpha, BubbleProfiler::Scale_options::E, parse_cmd_line_args(), parse_positional_args(), print_usage(), BubbleProfiler::Scale_options::scale, starts_with(), and BubbleProfiler::Scale_options::verbose.

void BubbleProfiler::parse_positional_args	(	const std::vector< std::string > &	args,
		Action_options &	options
	)

Definition at line 70 of file action.cpp.

References BubbleProfiler::Action_options::alpha, BubbleProfiler::Action_options::dim, BubbleProfiler::Action_options::E, parse_cmd_line_args(), parse_positional_args(), print_usage(), starts_with(), and BubbleProfiler::Action_options::verbose.

void BubbleProfiler::parse_positional_args	(	const std::vector< std::string > &	args,
		Tabulate_options &	options
	)

Definition at line 99 of file tabulate.cpp.

References BubbleProfiler::Tabulate_options::alpha_step, BubbleProfiler::Tabulate_options::dim, BubbleProfiler::Tabulate_options::max_alpha, BubbleProfiler::Tabulate_options::min_alpha, parse_cmd_line_args(), parse_positional_args(), print_usage(), starts_with(), BubbleProfiler::Tabulate_options::use_perturbative, BubbleProfiler::Tabulate_options::use_shooting, and BubbleProfiler::Tabulate_options::verbose.

void BubbleProfiler::parse_positional_args	(	const std::vector< std::string > &	args,
		Fubini_options &	options
	)

Examples:: action.cpp, general_fubini.cpp, logarithmic.cpp, scale.cpp, tabulate.cpp, and thin_wall.cpp.

Definition at line 101 of file general_fubini.cpp.

References BubbleProfiler::Fubini_options::m, BubbleProfiler::Fubini_options::u, and BubbleProfiler::Fubini_options::v.

Referenced by parse_global_min(), and parse_positional_args().

void BubbleProfiler::parse_positional_args	(	const std::vector< std::string > &	args,
		Logarithmic_options &	options
	)

Definition at line 101 of file logarithmic.cpp.

void BubbleProfiler::parse_positional_args	(	const std::vector< std::string > &	args,
		Thin_wall_options &	options
	)

Definition at line 102 of file thin_wall.cpp.

void BubbleProfiler::print_usage ( )

Examples:: action.cpp, general_fubini.cpp, logarithmic.cpp, scale.cpp, tabulate.cpp, and thin_wall.cpp.

Definition at line 65 of file general_fubini.cpp.

Referenced by parse_global_min(), and parse_positional_args().

template<typename Scalar , typename Data >

Scalar BubbleProfiler::quadratic_lagrange_interpolation_at_point	(	Scalar	x,
		const Data &	xdata,
		const Data &	ydata
	)

Definition at line 61 of file univariate_interpolation.hpp.

Referenced by BubbleProfiler::Kink_profile_guesser::fit_ansatz_parameters().

template<typename T , typename = typename std::enable_if< std::is_arithmetic<T>::value,T>::type>

T BubbleProfiler::Re ( T x )

noexcept

Definition at line 440 of file math_wrappers.hpp.

Referenced by Wm1().

template<typename T >

T BubbleProfiler::Re ( const std::complex< T > & z )

noexcept

Definition at line 446 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Profiler_result BubbleProfiler::run_perturbative_profiler	(	Restricted_quartic_potential	potential,
		int	dim
	)

Definition at line 237 of file tabulate.cpp.

template<class Profiler >

std::tuple<double, Field_profiles> BubbleProfiler::run_perturbative_profiler	(	const Bubble_profiler_inputs &	input,
		Profiler &	profiler
	)

Calculates the action and bubble profile using the perturbative method.

The provided BVP solver is used to solve the system of ODEs that must be integrated to compute successive perturbations to the initial solution ansatz.

Parameters

input settings to be used to configure the potential and solver

Returns: a tuple containing the calculation action and, optionally, the field profiles

Examples:: tabulate.cpp.

Definition at line 599 of file run_cmd_line_potential.cpp.

Referenced by run_perturbative_profiler(), and run_profiler().

std::tuple<double, Field_profiles> BubbleProfiler::run_perturbative_profiler ( const Bubble_profiler_inputs & input )

Calculates the action and bubble profile using the perturbative method.

The BVP solver used in the calculation is determined from the provided setting for the integration algorithm.

Parameters

input	settings to be used to configure the potential and solver
bvp_solver	the BVP solver to be used

Returns: a tuple containing the calculation action and, optionally, the field profiles

Definition at line 670 of file run_cmd_line_potential.cpp.

References BubbleProfiler::Bubble_profiler_inputs::algorithm, Euler, run_perturbative_profiler(), and Runge_kutta_4.

Profiler_result BubbleProfiler::run_profiler	(	const std::string &	profiler,
		const Restricted_quartic_potential &	potential,
		int	dim
	)

Definition at line 284 of file tabulate.cpp.

References run_perturbative_profiler(), and run_shooting_profiler().

void BubbleProfiler::run_profiler ( const Bubble_profiler_inputs & input )

Calculates the action and bubble profile for the given potential.

Parameters

input settings to be used to configure the potential and solver

Examples:: tabulate.cpp.

Definition at line 693 of file run_cmd_line_potential.cpp.

References BubbleProfiler::Bubble_profiler_inputs::fields, gaussian_alpha_tests::n_fields, BubbleProfiler::Bubble_profiler_inputs::output_file, run_perturbative_profiler(), run_shooting_profiler(), BubbleProfiler::Bubble_profiler_inputs::use_perturbative, write_action(), BubbleProfiler::Bubble_profiler_inputs::write_profiles, and write_profiles().

Referenced by main().

Profiler_result BubbleProfiler::run_shooting_profiler	(	const Restricted_quartic_potential &	potential,
		int	dim
	)

Definition at line 196 of file tabulate.cpp.

std::tuple<double, Field_profiles> BubbleProfiler::run_shooting_profiler ( const Bubble_profiler_inputs & input )

Calculates the action and bubble profile using the shooting method.

Parameters

input settings to be used to configure the potential and solver

Returns: a tuple containing the calculation action and, optionally, the field profiles

Examples:: tabulate.cpp.

Definition at line 542 of file run_cmd_line_potential.cpp.

Referenced by run_profiler().

template<typename T >

auto BubbleProfiler::Sec ( T x ) -> decltype(Cos(x))

noexcept

Definition at line 202 of file math_wrappers.hpp.

References Cos(), and sm_plus_singlet::type.

template<typename T >

auto BubbleProfiler::Sech ( T x ) -> decltype(Cosh(x))

noexcept

Definition at line 352 of file math_wrappers.hpp.

References Cosh(), and sm_plus_singlet::type.

Referenced by BubbleProfiler::Kink_profile_guesser::evaluate_ansatz_at(), and BubbleProfiler::Kink_profile_guesser::evaluate_ansatz_deriv_at().

double BubbleProfiler::series ( double a )

Helper function for approximate inverse of \(\sinc x\)

See in Mathematica,

Simplify[Normal[InverseSeries[1 - Series[Sin[x]/x, {x, 0, 20}]]]/Sqrt[3/2] /. x -> x^2, x > 0]

and this link for further information.

Definition at line 73 of file numeric.cpp.

Referenced by asinc().

template<typename T >

int BubbleProfiler::Sign ( const T & x )

Definition at line 118 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Referenced by BubbleProfiler::Shooting::initialize_potential_parameters().

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::Sin ( T x )

noexcept

Definition at line 148 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Referenced by Csc(), BubbleProfiler::Thin_wall_potential::get_global_minimum_location(), BubbleProfiler::Thin_wall_potential::get_local_maximum_location(), BubbleProfiler::Thin_wall_potential::get_local_minimum_location(), BubbleProfiler::Shooting::interior(), and BubbleProfiler::Shooting::quadratic_potential_solution().

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::Sin ( T n )

noexcept

Definition at line 156 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::Sin ( const std::complex< T > & z )

noexcept

Definition at line 162 of file math_wrappers.hpp.

References sm_plus_singlet::type.

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::Sinh ( T x )

noexcept

Definition at line 298 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Referenced by Csch(), BubbleProfiler::Shooting::interior(), and BubbleProfiler::Shooting::quadratic_potential_solution().

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::Sinh ( T n )

noexcept

Definition at line 306 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::Sinh ( const std::complex< T > & z )

noexcept

Definition at line 312 of file math_wrappers.hpp.

References sm_plus_singlet::type.

std::tuple<double, Field_profiles> BubbleProfiler::solve_perturbative	(	Thin_wall_potential &	potential,
		int	dim,
		const std::string &	observer_file
	)

Definition at line 279 of file thin_wall.cpp.

std::tuple<double, Field_profiles> BubbleProfiler::solve_perturbative	(	Logarithmic_potential &	potential,
		double	true_min,
		const std::string &	observer_file
	)

Definition at line 296 of file logarithmic.cpp.

std::tuple<double, Field_profiles> BubbleProfiler::solve_perturbative	(	Generalized_fubini_potential &	potential,
		double	true_min,
		const std::string &	observer_file
	)

Examples:: general_fubini.cpp, logarithmic.cpp, and thin_wall.cpp.

Definition at line 306 of file general_fubini.cpp.

Referenced by main().

std::tuple<double, Field_profiles> BubbleProfiler::solve_shooting	(	const Thin_wall_potential &	potential,
		int	dim,
		bool	calculate_profile
	)

Definition at line 240 of file thin_wall.cpp.

References gaussian_alpha_tests::action, BubbleProfiler::Thin_wall_potential::get_global_minimum_location(), BubbleProfiler::Thin_wall_potential::get_local_maximum_location(), BubbleProfiler::Thin_wall_potential::get_local_minimum_location(), and BubbleProfiler::Shooting::set_bisection_precision_bits().

std::tuple<double, Field_profiles> BubbleProfiler::solve_shooting	(	const Logarithmic_potential &	potential,
		double	true_min,
		bool	calculate_profile
	)

Definition at line 263 of file logarithmic.cpp.

References gaussian_alpha_tests::action, plot_tabulate_results::dim, BubbleProfiler::Shooting::get_bubble_profile(), BubbleProfiler::Shooting::get_euclidean_action(), BubbleProfiler::Logarithmic_potential::get_local_maximum_location(), BubbleProfiler::Logarithmic_potential::get_local_minimum_location(), and BubbleProfiler::Shooting::solve().

std::tuple<double, Field_profiles> BubbleProfiler::solve_shooting	(	const Generalized_fubini_potential &	potential,
		double	true_min,
		bool	calculate_profile
	)

Examples:: general_fubini.cpp, logarithmic.cpp, and thin_wall.cpp.

Definition at line 273 of file general_fubini.cpp.

References gaussian_alpha_tests::action, plot_tabulate_results::dim, BubbleProfiler::Shooting::get_bubble_profile(), BubbleProfiler::Shooting::get_euclidean_action(), BubbleProfiler::Generalized_fubini_potential::get_local_maximum_location(), BubbleProfiler::Generalized_fubini_potential::get_local_minimum_location(), and BubbleProfiler::Shooting::solve().

Referenced by main().

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::Sqrt ( T x )

noexcept

Definition at line 454 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Referenced by approx_root_neg_4(), approx_root_pos_4(), asinc(), asinch(), BubbleProfiler::Shooting::bubble_scale(), BubbleProfiler::Shooting::calculate_roll_velocity(), BubbleProfiler::Kink_profile_guesser::evaluate_ansatz_at(), BubbleProfiler::Kink_profile_guesser::evaluate_ansatz_deriv_at(), BubbleProfiler::Shooting::evolve(), BubbleProfiler::Thin_wall_potential::get_global_minimum_location(), BubbleProfiler::Shooting_profile_guesser::get_large_distance_solution(), BubbleProfiler::Thin_wall_potential::get_local_maximum_location(), BubbleProfiler::Thin_wall_potential::get_local_minimum_location(), BubbleProfiler::Kink_profile_guesser::guess_domain_end(), BubbleProfiler::Shooting::interior(), BubbleProfiler::Shooting::quadratic_potential_solution(), and BubbleProfiler::Thin_wall_potential::Thin_wall_potential().

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::Sqrt ( T n )

noexcept

Definition at line 462 of file math_wrappers.hpp.

bool BubbleProfiler::starts_with	(	const std::string &	option,
		const std::string &	prefix
	)

Examples:: action.cpp, general_fubini.cpp, logarithmic.cpp, scale.cpp, tabulate.cpp, and thin_wall.cpp.

Definition at line 83 of file general_fubini.cpp.

Referenced by parse_global_min(), and parse_positional_args().

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::Tan ( T x )

noexcept

Definition at line 170 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Referenced by Cot().

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::Tan ( T n )

noexcept

Definition at line 178 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::Tan ( const std::complex< T > & z )

noexcept

Definition at line 184 of file math_wrappers.hpp.

template<typename T , typename = typename std::enable_if< std::is_floating_point<T>::value,T>::type>

T BubbleProfiler::Tanh ( T x )

noexcept

Definition at line 320 of file math_wrappers.hpp.

References sm_plus_singlet::type.

Referenced by Coth(), and BubbleProfiler::Kink_profile_guesser::evaluate_ansatz_at().

template<typename T , typename = typename std::enable_if< std::is_integral<T>::value,T>::type>

double BubbleProfiler::Tanh ( T n )

noexcept

Definition at line 328 of file math_wrappers.hpp.

template<typename T >

std::complex<T> BubbleProfiler::Tanh ( const std::complex< T > & z )

noexcept

Definition at line 334 of file math_wrappers.hpp.

void BubbleProfiler::validate	(	boost::any &	v,
		const std::vector< std::string > &	values,
		Integration_algorithm *	,
		int
	)

Definition at line 141 of file run_cmd_line_potential.cpp.

References Euler, and Runge_kutta_4.

double BubbleProfiler::Wm1 ( double a )

Approximation to negative branch of the Lambert- \(W\) function.

See Eq. 4.19 of this paper

This is correct up to order \((\log \log a / \log a)^5\).

Returns: Negative branch of Lambert- \(W\) function

Parameters

a

Definition at line 41 of file numeric.cpp.

References Log(), and Re().

Referenced by approx_root_pos_4(), and asinch().

void BubbleProfiler::write_action	(	double	action,
		std::ostream &	ostr
	)

Write the value of the action to requested output stream.

Parameters

action	the value of the action
ostr	the output stream to write to

Examples:: general_fubini.cpp, logarithmic.cpp, and thin_wall.cpp.

Definition at line 292 of file run_cmd_line_potential.cpp.

Referenced by main(), run_profiler(), solve_perturbative(), and write_profile().

void BubbleProfiler::write_action	(	std::ostream &	ostr,
		double	numerical_action,
		double	exact_action
	)

Definition at line 383 of file general_fubini.cpp.

void BubbleProfiler::write_profile	(	std::ostream &	ostr,
		const Field_profiles &	numerical_profile
	)

Definition at line 325 of file thin_wall.cpp.

References BubbleProfiler::Field_profiles::get_field_profiles(), BubbleProfiler::Field_profiles::get_number_of_grid_points(), BubbleProfiler::Field_profiles::get_spatial_grid(), and write_action().

void BubbleProfiler::write_profile	(	std::ostream &	ostr,
		const Field_profiles &	numerical_profile,
		const Field_profiles &	exact_profile
	)

Examples:: general_fubini.cpp, logarithmic.cpp, and thin_wall.cpp.

Definition at line 354 of file general_fubini.cpp.

References BubbleProfiler::Field_profiles::get_field_profiles(), BubbleProfiler::Field_profiles::get_number_of_grid_points(), and BubbleProfiler::Field_profiles::get_spatial_grid().

Referenced by main(), and solve_perturbative().

void BubbleProfiler::write_profiles	(	const std::vector< std::string > &	fields,
		const Field_profiles &	profiles,
		std::ostream &	ostr
	)

Write the given field profiles to requested output stream.

Parameters

fields	the names of the fields
profiles	the values of the field profiles
ostr	the output stream to write to

Definition at line 304 of file run_cmd_line_potential.cpp.

References BubbleProfiler::Field_profiles::get_field_profiles(), BubbleProfiler::Field_profiles::get_spatial_grid(), and gaussian_alpha_tests::n_fields.

Referenced by run_profiler().

void BubbleProfiler::write_table	(	int	dim,
		double	E,
		const std::vector< double > &	alpha_data,
		const Profiler_data &	profiler_data
	)

Examples:: tabulate.cpp.

Definition at line 313 of file tabulate.cpp.

References write_table_header().

Referenced by main().

void BubbleProfiler::write_table_header ( const std::vector< std::string > & profiler_labels )

Examples:: tabulate.cpp.

Definition at line 298 of file tabulate.cpp.

Referenced by write_table().

Variable Documentation

const double BubbleProfiler::default_action_arrived_rel = 1.e-3

Definition at line 81 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_action_ode_abs = 1.e-6

Definition at line 84 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_action_ode_rel = 1.e-6

Definition at line 85 of file run_cmd_line_potential.cpp.

const Integration_algorithm BubbleProfiler::default_algorithm

Initial value:

=

Integration_algorithm::Runge_kutta_4

Definition at line 64 of file run_cmd_line_potential.cpp.

const std::string BubbleProfiler::default_ansatz_file = ""

Definition at line 59 of file run_cmd_line_potential.cpp.

const bool BubbleProfiler::default_assume_origin_false_vacuum = false

Definition at line 73 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_bisect_lambda_max = 5.0

Definition at line 88 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_domain_end = -1.

Definition at line 61 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_domain_start = -1.

Definition at line 60 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_drho_frac = 1.e-3

Definition at line 86 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_evolve_change_rel = 1.e-2

Definition at line 87 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_f_y_max = 1.e6

Definition at line 91 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_f_y_min = 1.e-3

Definition at line 92 of file run_cmd_line_potential.cpp.

const bool BubbleProfiler::default_force_output = false

Definition at line 70 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_initial_step_size = 1.e-2

Definition at line 62 of file run_cmd_line_potential.cpp.

const int BubbleProfiler::default_interp_fraction = 1.0

Definition at line 63 of file run_cmd_line_potential.cpp.

const int BubbleProfiler::default_iter_max = 100000

Definition at line 89 of file run_cmd_line_potential.cpp.

const int BubbleProfiler::default_max_iterations = -1

Definition at line 72 of file run_cmd_line_potential.cpp.

Referenced by parse_cmd_line_args().

const double BubbleProfiler::default_opt_timeout = 10.

Definition at line 71 of file run_cmd_line_potential.cpp.

const std::string BubbleProfiler::default_output_file = "-"

Definition at line 68 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_periods_max = 1.e2

Definition at line 90 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_rtol_action = 1.e-3

Definition at line 66 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_rtol_fields = 1.e-3

Definition at line 67 of file run_cmd_line_potential.cpp.

const int BubbleProfiler::default_shoot_bisect_bits = 5

Definition at line 80 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_shoot_ode_abs = 1.e-4

Definition at line 82 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_shoot_ode_rel = 1.e-4

Definition at line 83 of file run_cmd_line_potential.cpp.

const bool BubbleProfiler::default_shooting_ansatz = false

Definition at line 76 of file run_cmd_line_potential.cpp.

const bool BubbleProfiler::default_use_perturbative = false

Definition at line 74 of file run_cmd_line_potential.cpp.

const bool BubbleProfiler::default_verbose = false

Definition at line 77 of file run_cmd_line_potential.cpp.

const bool BubbleProfiler::default_write_perturbations = true

Definition at line 69 of file run_cmd_line_potential.cpp.

const bool BubbleProfiler::default_write_profiles = false

Definition at line 75 of file run_cmd_line_potential.cpp.

const double BubbleProfiler::default_y_max = 1.e1

Definition at line 93 of file run_cmd_line_potential.cpp.

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