lsst::gauss2d::fit Namespace Reference

Classes
class	CentroidParameters
	A Centroid with Parameters for x and y. More...
struct	CentroidXParameterD
struct	CentroidYParameterD
class	Channel
	An observational channel, usually representing some range of wavelengths of light. More...
class	Chromatic
class	Component
	An atomic constituent of a source. More...
class	ComponentMixture
	A list of related Component instances. More...
class	Data
	A list of Observation instances that can be modelled. More...
class	EllipticalComponent
	A Component with an elliptically-symmetric intensity profile. More...
class	FractionalIntegralModel
	An IntegralModel that returns a Parameter-dependent fraction of the flux of another IntegralModel. More...
class	GaussianComponent
	A Component consisting of a 2D Gaussian. More...
class	GaussianModelIntegral
	A single-channel GaussianIntegral referencing a Parametric IntegralModel. More...
class	GaussianParametricEllipse
	A Parameter-based implementation of lsst::gauss2d::EllipseData and ParametricEllipse. More...
class	GaussianParametricEllipseHolder
class	GaussianPrior
	A 1D Gaussian prior for a single Parameter. More...
struct	HessianOptions
class	IntegralModel
	A Parametric model for the integral of a 2D distribution. More...
struct	IntegralParameterD
class	IntegralSize
	A pair of integral - size values for a Gaussian (sub)Component. More...
struct	InverseTransform
struct	IsCloseResult
	The result of an isclose() check. More...
struct	JanskyToABMagTransform
class	LinearIntegralModel
	An IntegralModel with a single linear IntegralParameterD per Channel. More...
class	LinearSersicMixInterpolator
	A SersicMixInterpolator that uses linear interpolation between knots. More...
struct	Log10Transform
class	LogitLimitedTransform
struct	LogitTransform
struct	LogTransform
struct	MeanParameterD
class	Model
	A collection of Sources comprising a ParametricModel of Data. More...
struct	MoffatConcentrationParameterD
struct	NanojanskyToABMagTransform
class	Observation
	An observed single-channel image with an associated variance and mask. More...
class	Parametric
	A parametric object that can return and filter its Parameter instances. More...
class	ParametricEllipse
	A Parametric QuasiEllipse. More...
class	ParametricGaussian1D
class	ParametricModel
	A Parametric that can manage Parameter gradients and return Gaussians. More...
struct	ParamFilter
	Options for filtering Parameter instances. More...
class	Prior
	Interface for a prior probability function. More...
class	PriorEvaluation
	Results from the evaluation of a prior probability function. More...
struct	ProperFractionParameterD
class	PsfModel
	A Gaussian mixture model of a point spread function. More...
class	QuasiEllipse
	A Parametric ellipse with two scale sizes. More...
struct	RadiusScaleParameterD
	A generic scale radius, for profiles without specific names like "effective radius". More...
struct	ReffXParameterD
struct	ReffYParameterD
struct	RhoParameterD
class	SersicEllipseData
struct	SersicIndexParameterD
class	SersicMixComponent
	A Gaussian mixture approximation to a Sersic profile Component. More...
class	SersicMixComponentIndexParameterD
	A SersicIndexParameter for a Gaussian mixture Component. More...
class	SersicMixInterpolator
	An interpolator that returns IntegralSize vectors for a given Sersic index. More...
class	SersicMixValues
	A vector of IntegralSize values for a given Sersic index. More...
class	SersicModelIntegral
class	SersicParametricEllipse
	A ParametericEllipse with effective radius Parameters. More...
class	SersicParametricEllipseHolder
	A workaround class to store a SersicParametricEllipse. More...
class	ShapePrior
	A two-part prior on the shape of a parametric ellipse. More...
class	ShapePriorOptions
	Options for a ShapePrior. More...
struct	SigmaXParameterD
struct	SigmaYParameterD
struct	SizeParameterD
	A Parameter representing a size (i.e. a physical length) More...
struct	SizeXParameterD
struct	SizeYParameterD
class	Source
	An association of physically-related Component instances. More...
struct	StdDevParameterD
class	UnitNone

Typedefs
typedef std::vector< std::shared_ptr< Component > >	Components
typedef std::vector< std::shared_ptr< PsfModel > >	PsfModels
typedef std::vector< std::shared_ptr< Source > >	Sources
typedef std::vector< std::shared_ptr< Prior > >	Priors
using	ParamBase = lsst::modelfit::parameters::ParameterBase<double>
using	ParamBaseCRef = std::reference_wrapper<const ParamBase>
using	ParamCRefs = std::vector<ParamBaseCRef>
using	ParamBaseRef = std::reference_wrapper<ParamBase>
using	ParamRefs = std::vector<ParamBaseRef>
template<typename T >
using	Param = parameters::Parameter<double, T>
typedef std::vector< std::array< size_t, lsst::gauss2d::N_EXTRA_MAP > >	ExtraParamMap
typedef std::array< double, lsst::gauss2d::N_EXTRA_FACTOR >	ExtraParamFactorValues
typedef std::vector< ExtraParamFactorValues >	ExtraParamFactors
typedef std::vector< std::array< size_t, lsst::gauss2d::N_PARAMS_GAUSS2D > >	GradParamMap
typedef std::vector< std::array< double, lsst::gauss2d::N_PARAMS_GAUSS2D > >	GradParamFactors
typedef std::map< ParamBaseCRef, size_t >	ParameterMap
typedef parameters::Transform< double >	Transform

Enumerations
enum class	InterpType { linear , polynomial , cspline , akima }
enum class	EvaluatorMode {   image , loglike , loglike_image , loglike_grad ,   jacobian }
	Valid modes to initialize lsst::gauss2d::GaussianEvaluator instances for. More...

Functions
bool	operator< (const std::reference_wrapper< const Channel > &lhs, const std::reference_wrapper< const Channel > &rhs)
bool	operator== (const std::reference_wrapper< const Channel > &lhs, const std::reference_wrapper< const Channel > &rhs)
bool	operator< (const IntegralModel &lhs, const IntegralModel &rhs)
template<typename T >
T	logit (T p)
template<typename T >
double	logpdf_norm (T residual, T sigma)
template<template< typename... > class Container, class Value >
Value	sum_iter (const Container< Value > &container)
double	finite_difference_param (ParamBase &param, double delta)
template<typename t >
void	insert_param (g2f::ParamBase &param, t &params, ParamFilter *filter=nullptr)
	Add a Parameter to a vector thereof, if it meets conditions.
template<typename t >
void	insert_param_channel (const lsst::gauss2d::fit::Channel &channel, g2f::ParamBase &param, t &params, ParamFilter *filter)
	Same as insert_param, but only inserting if filter has a null or matching Channel.
template<typename t >
void	insert_params_ref (const t &params_in, t &params_out, ParamFilter *filter=nullptr)
	Same as insert_param, but inserting from a (ref to a) collection of Parameter instances.
template<typename t >
void	insert_params (const t params_in, t &params_out, ParamFilter *filter=nullptr)
	Same as insert_param, but inserting from a collection of Parameter instances.
const std::shared_ptr< const SersicMixInterpolator >	get_sersic_mix_interpolator_default (unsigned short order=SERSICMIX_ORDER_DEFAULT)
bool	operator< (const SersicMixValues &lhs, const SersicMixValues &rhs)
bool	operator< (const SersicMixValues &lhs, double x)
bool	operator< (double x, const SersicMixValues &rhs)
std::vector< SersicMixValues >	get_sersic_mix_knots_copy (unsigned short order)
const std::vector< SersicMixValues > &	get_sersic_mix_knots (unsigned short order)
const std::vector< SersicMixValues > &	get_sersic_mix_knots_order4 ()
const std::vector< SersicMixValues > &	get_sersic_mix_knots_order8 ()
template<class T >
std::shared_ptr< T >	get_transform_default ()
template<typename T >
IsCloseResult< T >	isclose (T a, T b, T rtol=1e-5, T atol=1e-8)
	Check if two values are close, within some tolerances.
template<template< typename... > class Map, class Key , class Value >
std::set< Key >	map_keys (const Map< Key, Value > &map)
template<template< typename... > class Map, class Key , class Value >
std::set< std::reference_wrapper< const Key > >	map_keys_ref_const (const Map< std::reference_wrapper< const Key >, Value, std::less< const Key > > &map)
template<template< typename... > class Map, class Key , class Value >
std::set< std::shared_ptr< const Value > >	map_values_shared_ptr_const (const Map< Key, std::shared_ptr< const Value > > &map)
template<template< typename... > class Map, class Key , class Value >
std::set< std::reference_wrapper< const Value > >	map_values_ref_const (const Map< Key, std::reference_wrapper< const Value > > &map)
template<typename T >
std::vector< T >	nonconsecutive_unique (const std::vector< T > &vec)
template<template< typename... > class Container, class Value >
Container< Value >	head_iter (const Container< Value > &container, size_t n)
template<template< typename... > class Container, class Value >
Container< Value >	tail_iter (const Container< Value > &container, size_t n)
template<typename T >
constexpr std::string_view	suffix_type ()
template<>
constexpr std::string_view	suffix_type< double > ()
template<typename T >
std::string	suffix_type_str ()
template<typename t >
t &	_get_parameters (t &params, ParamFilter *filter, CentroidXParameterD &x, CentroidYParameterD &y)
double	_get_integral_remainder (const FractionalIntegralModel *frac, const IntegralModel &model, const Channel &channel)
template<typename t >
t &	_get_parameters (t &params, ParamFilter *filter, SigmaXParameterD &x, SigmaYParameterD &y, RhoParameterD &r)
std::string	str_jacobians (const std::map< ParamBaseCRef, std::vector< double > > &jacobians, bool python_style=true)
template<typename t >
t &	_get_parameters (t &params, ParamFilter *filter, ReffXParameterD &x, ReffYParameterD &y, RhoParameterD &r)

Variables
const double	LOG_1 = log(1)
const double	SQRT_2_PI = sqrt(2. * M_PI)
const double	LOG_1_M_LOG_SQRT_2_PI = LOG_1 - log(SQRT_2_PI)

Typedef Documentation

Components

typedef std::vector<std::shared_ptr<Component> > lsst::gauss2d::fit::Components

Definition at line 14 of file componentmixture.h.

ExtraParamFactors

typedef std::vector<ExtraParamFactorValues> lsst::gauss2d::fit::ExtraParamFactors

Definition at line 13 of file parametricmodel.h.

ExtraParamFactorValues

typedef std::array<double, lsst::gauss2d::N_EXTRA_FACTOR> lsst::gauss2d::fit::ExtraParamFactorValues

Definition at line 12 of file parametricmodel.h.

ExtraParamMap

typedef std::vector<std::array<size_t, lsst::gauss2d::N_EXTRA_MAP> > lsst::gauss2d::fit::ExtraParamMap

Definition at line 11 of file parametricmodel.h.

GradParamFactors

typedef std::vector<std::array<double, lsst::gauss2d::N_PARAMS_GAUSS2D> > lsst::gauss2d::fit::GradParamFactors

Definition at line 15 of file parametricmodel.h.

GradParamMap

typedef std::vector<std::array<size_t, lsst::gauss2d::N_PARAMS_GAUSS2D> > lsst::gauss2d::fit::GradParamMap

Definition at line 14 of file parametricmodel.h.

Param

template<typename T >

using lsst::gauss2d::fit::Param = parameters::Parameter<double, T>

Definition at line 44 of file parameters.h.

ParamBase

using lsst::gauss2d::fit::ParamBase = lsst::modelfit::parameters::ParameterBase<double>

Definition at line 9 of file param_defs.h.

ParamBaseCRef

using lsst::gauss2d::fit::ParamBaseCRef = std::reference_wrapper<const ParamBase>

Definition at line 10 of file param_defs.h.

ParamBaseRef

using lsst::gauss2d::fit::ParamBaseRef = std::reference_wrapper<ParamBase>

Definition at line 12 of file param_defs.h.

ParamCRefs

using lsst::gauss2d::fit::ParamCRefs = std::vector<ParamBaseCRef>

Definition at line 11 of file param_defs.h.

ParameterMap

typedef std::map<ParamBaseCRef, size_t> lsst::gauss2d::fit::ParameterMap

Definition at line 17 of file parametricmodel.h.

ParamRefs

using lsst::gauss2d::fit::ParamRefs = std::vector<ParamBaseRef>

Definition at line 13 of file param_defs.h.

Priors

typedef std::vector<std::shared_ptr<Prior> > lsst::gauss2d::fit::Priors

Definition at line 54 of file model.h.

PsfModels

typedef std::vector<std::shared_ptr<PsfModel> > lsst::gauss2d::fit::PsfModels

Definition at line 52 of file model.h.

Sources

typedef std::vector<std::shared_ptr<Source> > lsst::gauss2d::fit::Sources

Definition at line 53 of file model.h.

Transform

typedef parameters::Transform<double> lsst::gauss2d::fit::Transform

Definition at line 15 of file transforms.h.

Enumeration Type Documentation

EvaluatorMode

enum class lsst::gauss2d::fit::EvaluatorMode

strong

Valid modes to initialize lsst::gauss2d::GaussianEvaluator instances for.

Enumerator
image	Compute the model images only.
loglike	Compute the log likelihood only.
loglike_image	Compute the model images and log likelihood.
loglike_grad	Compute the gradients of the log likelihood.
jacobian	Compute the model Jacobian.

Definition at line 32 of file model.h.

                         {
    image,          
    loglike,        
    loglike_image,  
    loglike_grad,   
    jacobian        
};

InterpType

enum class lsst::gauss2d::fit::InterpType

strong

Enumerator
linear	Linear interpolation.
polynomial	Polynomial interpolation.
cspline	Cubic spline interpolation.
akima	Akima spline with natural boundary conditions.

Definition at line 6 of file interpolation.h.

                      {
    linear,      
    polynomial,  
    cspline,     
    akima,       
};

Function Documentation

_get_integral_remainder()

double lsst::gauss2d::fit::_get_integral_remainder ( const FractionalIntegralModel * frac, const IntegralModel & model, const Channel & channel )

inline

Definition at line 110 of file fractionalintegralmodel.cc.

                                                              {
    return (frac == nullptr ? model.get_integral(channel) : frac->get_integral_remainder(channel));
}

_get_parameters() [1/3]

template<typename t >

t & lsst::gauss2d::fit::_get_parameters	(	t &	params,
		ParamFilter *	filter,
		CentroidXParameterD &	x,
		CentroidYParameterD &	y )

Definition at line 9 of file centroidparameters.cc.

                                                                                                   {
    insert_param(x, params, filter);
    insert_param(y, params, filter);
    return params;
}

_get_parameters() [2/3]

template<typename t >

t & lsst::gauss2d::fit::_get_parameters	(	t &	params,
		ParamFilter *	filter,
		ReffXParameterD &	x,
		ReffYParameterD &	y,
		RhoParameterD &	r )

Definition at line 7 of file sersicparametricellipse.cc.

                                                                                                             {
    insert_param(x, params, filter);
    insert_param(y, params, filter);
    insert_param(r, params, filter);
    return params;
}

_get_parameters() [3/3]

template<typename t >

t & lsst::gauss2d::fit::_get_parameters	(	t &	params,
		ParamFilter *	filter,
		SigmaXParameterD &	x,
		SigmaYParameterD &	y,
		RhoParameterD &	r )

Definition at line 9 of file gaussianparametricellipse.cc.

                                     {
    insert_param(x, params, filter);
    insert_param(y, params, filter);
    insert_param(r, params, filter);
    return params;
}

finite_difference_param()

double lsst::gauss2d::fit::finite_difference_param	(	ParamBase &	param,
		double	delta )

Definition at line 6 of file param_defs.cc.

                                                               {
    const double value = param.get_value_transformed();
    double value_new = value + delta;
    try {
        param.set_value_transformed(value_new);
        // If the param is near an upper limit, this might fail: try -delta then
        if (param.get_value_transformed() != value_new) {
            delta = -delta;
            value_new = value + delta;
            param.set_value_transformed(value_new);
        }
    } catch (const std::runtime_error& err) {
        delta = -delta;
        value_new = value + delta;
        try {
            param.set_value_transformed(value_new);
        } catch (const std::runtime_error& err2) {
            throw std::runtime_error("Couldn't set param=" + param.str()
                                     + " to new value_transformed=" + std::to_string(value_new) + " due to "
                                     + err2.what() + "; are limits too restrictive?");
        }
    }
    return delta;
}

get_sersic_mix_interpolator_default()

const std::shared_ptr< const SersicMixInterpolator > lsst::gauss2d::fit::get_sersic_mix_interpolator_default

(

unsigned short

order = SERSICMIX_ORDER_DEFAULT

)

Definition at line 38 of file sersicmix.cc.

                                                                                                           {
#ifdef LSST_GAUSS2D_FIT_HAS_GSL
    static auto interpolator = std::make_shared<GSLSersicMixInterpolator>(order);
#else
    static auto interpolator = std::make_shared<LinearSersicMixInterpolator>(order);
#endif
    return interpolator;
}

get_sersic_mix_knots()

const std::vector< SersicMixValues > & lsst::gauss2d::fit::get_sersic_mix_knots

(

unsigned short

order

)

Definition at line 50 of file sersicmix.cc.

                                                                             {
    if (order == 4)
        return get_sersic_mix_knots_order4();
    else if (order == 8)
        return get_sersic_mix_knots_order8();
    throw std::invalid_argument("Unsupported Sersic mixture knot order=" + std::to_string(order));
}

get_sersic_mix_knots_copy()

std::vector< SersicMixValues > lsst::gauss2d::fit::get_sersic_mix_knots_copy

(

unsigned short

order

)

Definition at line 68 of file sersicmix.cc.

                                                                           {
    if (order == 4) {
        return {
                SersicMixValues(0.5, {IntegralSize(1.000000000000000e+00, 1.1774100225154747),
                                      IntegralSize(0.000000000000000e+00, 1.021991899543432),
                                      IntegralSize(0.000000000000000e+00, 0.654639972518604),
                                      IntegralSize(0.000000000000000e+00, 0.32025552612420916)}),
                SersicMixValues(0.501, {IntegralSize(9.894570026400000e-01, 1.179547276262387),
                                        IntegralSize(9.934070038799999e-03, 1.0223438473444877),
                                        IntegralSize(5.965425654400000e-04, 0.6546532125531775),
                                        IntegralSize(1.238475576004205e-05, 0.3201924396121452)}),
                SersicMixValues(0.502, {IntegralSize(9.791584531999999e-01, 1.1816845300092997),
                                        IntegralSize(1.962344016000000e-02, 1.0226957951337692),
                                        IntegralSize(1.192748593700000e-03, 0.6546664525877514),
                                        IntegralSize(2.535804630010574e-05, 0.32012935308830726)}),
                SersicMixValues(0.503, {IntegralSize(9.690961475500000e-01, 1.183821783873953),
                                        IntegralSize(2.907633669100000e-02, 1.0230477429348248),
                                        IntegralSize(1.788607694200000e-03, 0.654679692622325),
                                        IntegralSize(3.890806480011388e-05, 0.3200662665762433)}),
                SersicMixValues(0.504, {IntegralSize(9.592621979300000e-01, 1.1859590376208655),
                                        IntegralSize(3.830068423900000e-02, 1.0233996907358804),
                                        IntegralSize(2.384080407200000e-03, 0.6546929326568988),
                                        IntegralSize(5.303742380002863e-05, 0.3200031800524053)}),
                SersicMixValues(0.505, {IntegralSize(9.496490795500000e-01, 1.1880962913677777),
                                        IntegralSize(4.730403460100000e-02, 1.0237516385251622),
                                        IntegralSize(2.979145776600000e-03, 0.6547061726914724),
                                        IntegralSize(6.774007240006874e-05, 0.3199400935403414)}),
                SersicMixValues(0.506, {IntegralSize(9.402495735700001e-01, 1.1902335451146904),
                                        IntegralSize(5.609364092700000e-02, 1.0241035863262178),
                                        IntegralSize(3.573769507900000e-03, 0.6547194127260461),
                                        IntegralSize(8.301599509996649e-05, 0.3198770070165034)}),
                SersicMixValues(0.507, {IntegralSize(9.310567887700000e-01, 1.1923707989793437),
                                        IntegralSize(6.467642103700000e-02, 1.0244555341154993),
                                        IntegralSize(4.167929228400000e-03, 0.6547326527606196),
                                        IntegralSize(9.886096459998939e-05, 0.3198139205044395)}),
                SersicMixValues(0.508, {IntegralSize(9.220641492100000e-01, 1.1945080527262564),
                                        IntegralSize(7.305896672300000e-02, 1.024807481916555),
                                        IntegralSize(4.761618540600000e-03, 0.6547458927951935),
                                        IntegralSize(1.152655263999547e-04, 0.3197508339806015)}),
                SersicMixValues(0.509, {IntegralSize(9.132652912100000e-01, 1.1966453064731688),
                                        IntegralSize(8.124768267700000e-02, 1.0251594297176105),
                                        IntegralSize(5.354791879400000e-03, 0.654759132829767),
                                        IntegralSize(1.322342335999815e-04, 0.3196877474685376)}),
                SersicMixValues(0.51, {IntegralSize(9.046541594000000e-01, 1.1987825602200812),
                                       IntegralSize(8.924864580300000e-02, 1.0255113775068923),
                                       IntegralSize(5.947434228300000e-03, 0.6547723728643409),
                                       IntegralSize(1.497605686999748e-04, 0.31962466095647374)}),
                SersicMixValues(0.512, {IntegralSize(8.879720516100000e-01, 1.2030570678316472),
                                        IntegralSize(1.047104342300000e-01, 1.0262152731090035),
                                        IntegralSize(7.131042455900000e-03, 0.6547988529217141),
                                        IntegralSize(1.864717040999109e-04, 0.3194984879205719)}),
                SersicMixValues(0.514, {IntegralSize(8.719740293300000e-01, 1.2073315753254719),
                                        IntegralSize(1.194883334100000e-01, 1.0269191686993409),
                                        IntegralSize(8.312260525900001e-03, 0.6548253329908614),
                                        IntegralSize(2.253767341000579e-04, 0.31937231488467)}),
                SersicMixValues(0.516, {IntegralSize(8.566197309400000e-01, 1.2116060829370379),
                                        IntegralSize(1.336228931600000e-01, 1.0276230642896778),
                                        IntegralSize(9.490927177900000e-03, 0.6548518130600088),
                                        IntegralSize(2.664487221000211e-04, 0.3192461418487681)}),
                SersicMixValues(0.518, {IntegralSize(8.418719103100000e-01, 1.215880590430863),
                                        IntegralSize(1.471515280900000e-01, 1.0283269598917892),
                                        IntegralSize(1.066690570800000e-02, 0.6548782931291562),
                                        IntegralSize(3.096558920000492e-04, 0.3191199688128662)}),
                SersicMixValues(0.52, {IntegralSize(8.276960586500000e-01, 1.2201550979246878),
                                       IntegralSize(1.601089337500000e-01, 1.0290308554821264),
                                       IntegralSize(1.184002696500000e-02, 0.6549047731983035),
                                       IntegralSize(3.549806350000573e-04, 0.3189937957769643)}),
                SersicMixValues(0.525, {IntegralSize(7.945549774900000e-01, 1.230841366894732),
                                        IntegralSize(1.902081582400000e-01, 1.0307905944638567),
                                        IntegralSize(1.475949528400000e-02, 0.654970973371172),
                                        IntegralSize(4.773689859999264e-04, 0.3186783631930966)}),
                SersicMixValues(0.53, {IntegralSize(7.643558574400000e-01, 1.2415276357470353),
                                       IntegralSize(2.173733639900000e-01, 1.0325503334455866),
                                       IntegralSize(1.765836612400000e-02, 0.6550371735440405),
                                       IntegralSize(6.124124460000768e-04, 0.3183629305974548)}),
                SersicMixValues(0.535, {IntegralSize(7.367315034800000e-01, 1.2522139045993386),
                                        IntegralSize(2.419738283500000e-01, 1.0343100724273167),
                                        IntegralSize(2.053494838800000e-02, 0.6551033737051348),
                                        IntegralSize(7.597197819999568e-04, 0.3180474980135871)}),
                SersicMixValues(0.54, {IntegralSize(7.113728840900000e-01, 1.2629001734516418),
                                       IntegralSize(2.643204328100000e-01, 1.0360698114208209),
                                       IntegralSize(2.338777378400000e-02, 0.6551695738780032),
                                       IntegralSize(9.189093160000272e-04, 0.3177320654297195)}),
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                                      IntegralSize(2.295454518800000e-01, 0.44721200855929333),
                                      IntegralSize(1.159685891500000e-01, 0.15186432106918743)}),
                SersicMixValues(5.2, {IntegralSize(3.220845076300000e-01, 4.5373147240459),
                                      IntegralSize(3.292888060000000e-01, 1.3278163704470598),
                                      IntegralSize(2.303343245300000e-01, 0.45211274779451427),
                                      IntegralSize(1.182923618400000e-01, 0.15421232731290296)}),
                SersicMixValues(5.3, {IntegralSize(3.210064675900000e-01, 4.586047793638561),
                                      IntegralSize(3.277457186600000e-01, 1.339107878915049),
                                      IntegralSize(2.309179255900000e-01, 0.455963004397949),
                                      IntegralSize(1.203298881599999e-01, 0.15606241214466773)}),
                SersicMixValues(5.4, {IntegralSize(3.202789632100000e-01, 4.629088010300377),
                                      IntegralSize(3.263140603100000e-01, 1.3480796586308363),
                                      IntegralSize(2.313141472000000e-01, 0.45876476829850243),
                                      IntegralSize(1.220928292800001e-01, 0.157417468107684)}),
                SersicMixValues(5.5, {IntegralSize(3.192633606400000e-01, 4.676683232377911),
                                      IntegralSize(3.248434367700000e-01, 1.3594826233218587),
                                      IntegralSize(2.318431931600000e-01, 0.46274015782559924),
                                      IntegralSize(1.240500094300000e-01, 0.15931314749499514)}),
                SersicMixValues(5.6, {IntegralSize(3.185825067000000e-01, 4.718596826834015),
                                      IntegralSize(3.234811850800000e-01, 1.3685523066826153),
                                      IntegralSize(2.321963688200000e-01, 0.4656609444451806),
                                      IntegralSize(1.257399394000001e-01, 0.16071290372354932)}),
                SersicMixValues(5.7, {IntegralSize(3.179221779600000e-01, 4.7599421800182755),
                                      IntegralSize(3.221514634000000e-01, 1.3776591442763013),
                                      IntegralSize(2.325312351100000e-01, 0.4686349368107874),
                                      IntegralSize(1.273951235299999e-01, 0.16213299339932472)}),
                SersicMixValues(5.8, {IntegralSize(3.172826124600000e-01, 4.800717521930206),
                                      IntegralSize(3.208531497900000e-01, 1.386796673770267),
                                      IntegralSize(2.328483549600000e-01, 0.47165816845176173),
                                      IntegralSize(1.290158827900000e-01, 0.16357190065401378)}),
                SersicMixValues(5.9, {IntegralSize(3.166640855600000e-01, 4.840922072653407),
                                      IntegralSize(3.195851752500000e-01, 1.3959584348334604),
                                      IntegralSize(2.331482900400000e-01, 0.47472674758056327),
                                      IntegralSize(1.306024491500000e-01, 0.16502824071214084)}),
                SersicMixValues(6.0, {IntegralSize(3.163378845100000e-01, 4.875543891132607),
                                      IntegralSize(3.184191997800000e-01, 1.4027751892109375),
                                      IntegralSize(2.332998231900000e-01, 0.4767359942988522),
                                      IntegralSize(1.319430925200000e-01, 0.16599035845093296)}),
                SersicMixValues(6.15, {IntegralSize(3.159963566000000e-01, 4.923987695808347),
                                       IntegralSize(3.167577172900000e-01, 1.4118530514504155),
                                       IntegralSize(2.334469498300000e-01, 0.47927772307499805),
                                       IntegralSize(1.337989762800000e-01, 0.16721064630843122)}),
                SersicMixValues(6.3, {IntegralSize(3.156665947400000e-01, 4.971293186125886),
                                      IntegralSize(3.151544390000000e-01, 1.4209662774354015),
                                      IntegralSize(2.335797880700000e-01, 0.4819072955518174),
                                      IntegralSize(1.355991781900000e-01, 0.16846726122122171)}),
                SersicMixValues(6.45, {IntegralSize(3.155985344300000e-01, 5.012518368133609),
                                       IntegralSize(3.136774796100000e-01, 1.4277394220762778),
                                       IntegralSize(2.335799727600000e-01, 0.4835176097219425),
                                       IntegralSize(1.371440132000000e-01, 0.16924955098438885)}),
                SersicMixValues(6.6, {IntegralSize(3.157745357300000e-01, 5.04771490870264),
                                      IntegralSize(3.123222798200000e-01, 1.4321555562185169),
                                      IntegralSize(2.334585919600000e-01, 0.48410148341955844),
                                      IntegralSize(1.384445924900001e-01, 0.16955677921038223)}),
                SersicMixValues(6.8, {IntegralSize(3.161516246500000e-01, 5.089778956379133),
                                      IntegralSize(3.106355860500000e-01, 1.4364656594076244),
                                      IntegralSize(2.332238340200000e-01, 0.4842498615725239),
                                      IntegralSize(1.399889552799999e-01, 0.16967587466980136)}),
                SersicMixValues(7.0, {IntegralSize(3.167381326500000e-01, 5.125153155993239),
                                      IntegralSize(3.090960248300000e-01, 1.4383737931673495),
                                      IntegralSize(2.328861111000000e-01, 0.48339942354096144),
                                      IntegralSize(1.412797314200001e-01, 0.169337768218392)}),
                SersicMixValues(7.2, {IntegralSize(3.177563577200000e-01, 5.148765319243021),
                                      IntegralSize(3.077654530100000e-01, 1.435402469813652),
                                      IntegralSize(2.323436482000000e-01, 0.48041416256080033),
                                      IntegralSize(1.421345410700000e-01, 0.16802853741844914)}),
                SersicMixValues(7.4, {IntegralSize(3.189649423600000e-01, 5.165566538751529),
                                      IntegralSize(3.065675687400000e-01, 1.429874585567177),
                                      IntegralSize(2.317124418400000e-01, 0.47637256992908417),
                                      IntegralSize(1.427550470599999e-01, 0.16624860052116552)}),
                SersicMixValues(7.6, {IntegralSize(3.203656186400000e-01, 5.175439069866539),
                                      IntegralSize(3.054966299600000e-01, 1.421708147948776),
                                      IntegralSize(2.309930734600000e-01, 0.4712451642878735),
                                      IntegralSize(1.431446779400000e-01, 0.16399036546897494)}),
                SersicMixValues(7.8, {IntegralSize(3.219644493700000e-01, 5.178201270835836),
                                      IntegralSize(3.045475859400000e-01, 1.4108049451852775),
                                      IntegralSize(2.301838048000000e-01, 0.46499847934678185),
                                      IntegralSize(1.433041598900000e-01, 0.1612453381080743)}),
                SersicMixValues(8.0, {IntegralSize(3.240152894900000e-01, 5.168013248702098),
                                      IntegralSize(3.037829008200000e-01, 1.3944405343161739),
                                      IntegralSize(2.291682052300000e-01, 0.4564297828909366),
                                      IntegralSize(1.430336044599999e-01, 0.15748506377045932)}),
        };
    } else if (order == 8) {
        return {SersicMixValues(0.5, {IntegralSize(1.000000000000000e+00, 1.1774100225154747),
                                      IntegralSize(0.000000000000000e+00, 1.070350124913453),
                                      IntegralSize(0.000000000000000e+00, 0.9191071563749802),
                                      IntegralSize(0.000000000000000e+00, 0.6668004503333704),
                                      IntegralSize(0.000000000000000e+00, 0.47920409257360413),
                                      IntegralSize(0.000000000000000e+00, 0.32294197416925663),
                                      IntegralSize(0.000000000000000e+00, 0.19624403248977948),
                                      IntegralSize(0.000000000000000e+00, 0.09647324497759727)}),
                SersicMixValues(0.501, {IntegralSize(9.830908106200000e-01, 1.1800430212201372),
                                        IntegralSize(1.408700923700000e-02, 1.071848165938149),
                                        IntegralSize(2.491640616300000e-03, 0.9197501136496137),
                                        IntegralSize(2.466802366100000e-04, 0.6670669573980934),
                                        IntegralSize(7.374589951499999e-05, 0.47920409257360413),
                                        IntegralSize(7.323307590200000e-06, 0.3228129521660974),
                                        IntegralSize(2.682888719100000e-06, 0.19608725670708457),
                                        IntegralSize(1.071942655750391e-07, 0.09635766199130548)}),
                SersicMixValues(0.502, {IntegralSize(9.666302814500000e-01, 1.1826766373586155),
                                        IntegralSize(2.770059206800000e-02, 1.073345310188501),
                                        IntegralSize(4.999009878400000e-03, 0.9203922372826289),
                                        IntegralSize(5.027356046800000e-04, 0.6673330392294127),
                                        IntegralSize(1.467597930800000e-04, 0.47920409257360413),
                                        IntegralSize(1.505550242700000e-05, 0.3226842388327496),
                                        IntegralSize(5.350576848500000e-06, 0.19593091840285765),
                                        IntegralSize(2.151265646732625e-07, 0.09624244754494744)}),
                SersicMixValues(0.503, {IntegralSize(9.506030525300000e-01, 1.1853108725792836),
                                        IntegralSize(4.085776923300000e-02, 1.0748415599957815),
                                        IntegralSize(7.520758136900000e-03, 0.9210335300291653),
                                        IntegralSize(7.677381641400000e-04, 0.6675986973697353),
                                        IntegralSize(2.192138525600000e-04, 0.47920409257360413),
                                        IntegralSize(2.312065278500000e-05, 0.3225558328034177),
                                        IntegralSize(8.024799753900000e-06, 0.19577501550485701),
                                        IntegralSize(3.226308611381512e-07, 0.0961275997311189)}),
                SersicMixValues(0.504, {IntegralSize(9.349933060500000e-01, 1.1879457259402137),
                                        IntegralSize(5.357709371600000e-02, 1.076336917679488),
                                        IntegralSize(1.005404066200000e-02, 0.9216739945972661),
                                        IntegralSize(1.041949557200000e-03, 0.6678639333379203),
                                        IntegralSize(2.908251496200000e-04, 0.47920409257360413),
                                        IntegralSize(3.171250718700000e-05, 0.3224277327476283),
                                        IntegralSize(1.063178511700000e-05, 0.1956195459172929),
                                        IntegralSize(4.405728759593330e-07, 0.09601311665889936)}),
                SersicMixValues(0.505, {IntegralSize(9.197866380200000e-01, 1.1905811962639956),
                                        IntegralSize(6.587500921099999e-02, 1.0778313855355697),
                                        IntegralSize(1.259688973600000e-02, 0.9223136336949741),
                                        IntegralSize(1.325295593300000e-03, 0.6681287486175042),
                                        IntegralSize(3.616277926400000e-04, 0.47920409257360413),
                                        IntegralSize(4.077717135400000e-05, 0.32229993733490825),
                                        IntegralSize(1.318402214500000e-05, 0.1954645076032459),
                                        IntegralSize(5.784535609398844e-07, 0.09589899644914245)}),
                SersicMixValues(0.506, {IntegralSize(9.049702475400000e-01, 1.193217282373219),
                                        IntegralSize(7.776489544200001e-02, 1.0793249658482025),
                                        IntegralSize(1.514936661900000e-02, 0.9229524500303325),
                                        IntegralSize(1.616828031500000e-03, 0.668393144715572),
                                        IntegralSize(4.320606280100000e-04, 0.47920409257360413),
                                        IntegralSize(5.014068206100000e-05, 0.322172445234784),
                                        IntegralSize(1.575534967400000e-05, 0.19530989849047442),
                                        IntegralSize(7.057077548999757e-07, 0.09578523723565323)}),
                SersicMixValues(0.507, {IntegralSize(8.905298892200000e-01, 1.1958539833259565),
                                        IntegralSize(8.926392245000001e-02, 1.0808176609015616),
                                        IntegralSize(1.770823107000000e-02, 0.9235904462760621),
                                        IntegralSize(1.917102295600000e-03, 0.6686571231392083),
                                        IntegralSize(5.017617604300000e-04, 0.47920409257360413),
                                        IntegralSize(5.997028326100000e-05, 0.3220452551167824),
                                        IntegralSize(1.827533833100000e-05, 0.19515571656560732),
                                        IntegralSize(8.475823779496849e-07, 0.0956718371675432)}),
                SersicMixValues(0.508, {IntegralSize(8.764537693900000e-01, 1.1984912980625384),
                                        IntegralSize(1.003845154900000e-01, 1.0823094729680485),
                                        IntegralSize(2.027336730400000e-02, 0.9242276251048835),
                                        IntegralSize(2.225362311300000e-03, 0.6689206853484017),
                                        IntegralSize(5.710740416100000e-04, 0.47920409257360413),
                                        IntegralSize(7.012559913200000e-05, 0.3219183656975264),
                                        IntegralSize(2.079362649300000e-05, 0.19500195981527346),
                                        IntegralSize(9.922374649695698e-07, 0.09555879440687527)}),
                SersicMixValues(0.509, {IntegralSize(8.627290863000000e-01, 1.2011292254055552),
                                        IntegralSize(1.111418294200000e-01, 1.0838004042965161),
                                        IntegralSize(2.284224920600000e-02, 0.9248639891659693),
                                        IntegralSize(2.541974524900000e-03, 0.6691838328266887),
                                        IntegralSize(6.396887688500000e-04, 0.47920409257360413),
                                        IntegralSize(8.077413038799999e-05, 0.32179177565831685),
                                        IntegralSize(2.324651406400000e-05, 0.1948486262025535),
                                        IntegralSize(1.151135797905489e-06, 0.09544610712630913)}),
                SersicMixValues(0.51, {IntegralSize(8.493446962900000e-01, 1.2037677642953377),
                                       IntegralSize(1.215479013800000e-01, 1.0852904571475919),
                                       IntegralSize(2.541436244000000e-02, 0.925499541096718),
                                       IntegralSize(2.866364591500000e-03, 0.6694465670458319),
                                       IntegralSize(7.079066530400000e-04, 0.47920409257360413),
                                       IntegralSize(9.176608484000000e-05, 0.3216654837157768),
                                       IntegralSize(2.568975552800000e-05, 0.19469571376117265),
                                       IntegralSize(1.312805092079650e-06, 0.09533377351263332)}),
                SersicMixValues(0.512, {IntegralSize(8.235524985200000e-01, 1.2090466728297466),
                                        IntegralSize(1.413561232900000e-01, 1.0882679363305618),
                                        IntegralSize(3.056341000600000e-02, 0.9267682190697014),
                                        IntegralSize(3.537750218000000e-03, 0.6699708014877702),
                                        IntegralSize(8.432215242500000e-04, 0.47920409257360413),
                                        IntegralSize(1.148196346800000e-04, 0.3214137889754234),
                                        IntegralSize(3.052266768400000e-05, 0.194391144468459),
                                        IntegralSize(1.654139386020326e-06, 0.09511016010139674)}),
                SersicMixValues(0.514, {IntegralSize(7.989931692100000e-01, 1.2143280151884133),
                                        IntegralSize(1.599038064700000e-01, 1.0912419283193973),
                                        IntegralSize(3.571088717100000e-02, 0.9280336798522169),
                                        IntegralSize(4.238418902400000e-03, 0.670493400248157),
                                        IntegralSize(9.771160470799999e-04, 0.47920409257360413),
                                        IntegralSize(1.393114832100000e-04, 0.32116327130364347),
                                        IntegralSize(3.527127016300000e-05, 0.19408823624225693),
                                        IntegralSize(2.019446147083492e-06, 0.09488793992061721)}),
                SersicMixValues(0.516, {IntegralSize(7.755894316300000e-01, 1.219611782893985),
                                        IntegralSize(1.772773877600000e-01, 1.094212450739927),
                                        IntegralSize(4.084885408100000e-02, 0.9292959440960364),
                                        IntegralSize(4.966899216500000e-03, 0.6710143747714178),
                                        IntegralSize(1.109903573100000e-03, 0.47920409257360413),
                                        IntegralSize(1.651634209200000e-04, 0.32091392063358165),
                                        IntegralSize(3.995171679100000e-05, 0.19378697362317282),
                                        IntegralSize(2.408601688874690e-06, 0.09466709892143835)}),
                SersicMixValues(0.518, {IntegralSize(7.532701365800000e-01, 1.2248979677045921),
                                        IntegralSize(1.935561952300000e-01, 1.097179521064915),
                                        IntegralSize(4.597032490300000e-02, 0.9305550322174497),
                                        IntegralSize(5.721759593100000e-03, 0.6715337363724627),
                                        IntegralSize(1.241874810300000e-03, 0.47920409257360413),
                                        IntegralSize(1.923184154900000e-04, 0.3206657270514452),
                                        IntegralSize(4.456980917800000e-05, 0.1934873413519728),
                                        IntegralSize(2.820658932090048e-06, 0.09444762324574418)}),
                SersicMixValues(0.52, {IntegralSize(7.319691923200000e-01, 1.2301865614961052),
                                       IntegralSize(2.088140719200000e-01, 1.1001431566022888),
                                       IntegralSize(5.106857451500000e-02, 0.9318109643972646),
                                       IntegralSize(6.501810606800000e-03, 0.672051496224913),
                                       IntegralSize(1.373230568000000e-03, 0.47920409257360413),
                                       IntegralSize(2.207287306300000e-04, 0.32041868073763474),
                                       IntegralSize(4.913899414000000e-05, 0.19318932434603445),
                                       IntegralSize(3.252345429971548e-06, 0.09422949923204621)}),
                SersicMixValues(0.525, {IntegralSize(6.827830146500000e-01, 1.2434185313998436),
                                        IntegralSize(2.429240961500000e-01, 1.10753733055128),
                                        IntegralSize(6.367678377000000e-02, 0.9349371184876218),
                                        IntegralSize(8.553975233700000e-03, 0.673338960634315),
                                        IntegralSize(1.700359140800000e-03, 0.47920409257360413),
                                        IntegralSize(2.969830817300000e-04, 0.31980602103689054),
                                        IntegralSize(6.035644554900000e-05, 0.19245125152159095),
                                        IntegralSize(4.431528220938397e-06, 0.09369001473883691)}),
                SersicMixValues(0.53, {IntegralSize(6.387550734000000e-01, 1.2566653798808136),
                                       IntegralSize(2.719891439700000e-01, 1.1149104080795813),
                                       IntegralSize(7.603306482900000e-02, 0.9380439795844466),
                                       IntegralSize(1.073713740600000e-02, 0.6746166528702049),
                                       IntegralSize(2.028392270300000e-03, 0.47920409257360413),
                                       IntegralSize(3.800413636800000e-04, 0.31920032346757643),
                                       IntegralSize(7.141788662300000e-05, 0.1917229546030493),
                                       IntegralSize(5.728874396981887e-06, 0.09315868886583216)}),
                SersicMixValues(0.535, {IntegralSize(5.991880819600000e-01, 1.2699269831932218),
                                        IntegralSize(2.967754215900000e-01, 1.122262647546274),
                                        IntegralSize(8.808289301100000e-02, 0.9411318470913335),
                                        IntegralSize(1.303475165500000e-02, 0.6758847382409497),
                                        IntegralSize(2.359992883100000e-03, 0.47920409257360413),
                                        IntegralSize(4.693072439300000e-04, 0.31860144433857307),
                                        IntegralSize(8.241092227300000e-05, 0.19100421370908782),
                                        IntegralSize(7.140734696986506e-06, 0.09263532299102561)}),
                SersicMixValues(0.54, {IntegralSize(5.634984962800000e-01, 1.2832032193573897),
                                       IntegralSize(3.179186791600000e-01, 1.129594301788386),
                                       IntegralSize(9.978737713700001e-02, 0.9442010130295162),
                                       IntegralSize(1.543166988700000e-02, 0.6771433777573704),
                                       IntegralSize(2.697463030000000e-03, 0.47920409257360413),
                                       IntegralSize(5.642325765800000e-04, 0.3180092442563081),
                                       IntegralSize(9.342342505800000e-05, 0.1902948158697816),
                                       IntegralSize(8.658504362046848e-06, 0.09211972512829385)}),
                SersicMixValues(0.545, {IntegralSize(5.311950333900000e-01, 1.296493969101682),
                                        IntegralSize(3.359490979700000e-01, 1.1369056182504083),
                                        IntegralSize(1.111199551400000e-01, 0.9472517622615755),
                                        IntegralSize(1.791396160900000e-02, 0.6783927282740299),
                                        IntegralSize(3.042852702300000e-03, 0.47920409257360413),
                                        IntegralSize(6.642728186200000e-04, 0.3174235878892735),
                                        IntegralSize(1.045564361300000e-04, 0.18959455480289467),
                                        IntegralSize(1.026993395003561e-05, 0.09161170964364046)}),
                SersicMixValues(0.55, {IntegralSize(5.018614264000000e-01, 1.3097991148028376),
                                       IntegralSize(3.513116940300000e-01, 1.144196839160904),
                                       IntegralSize(1.220630720100000e-01, 0.950284372762244),
                                       IntegralSize(2.046921709200000e-02, 0.6796329426422973),
                                       IntegralSize(3.397724672300000e-03, 0.47920409257360413),
                                       IntegralSize(7.690260526600000e-04, 0.3168443439091553),
                                       IntegralSize(1.158666861400000e-04, 0.18890323060775346),
                                       IntegralSize(1.197305689992767e-05, 0.09111109698674669)}),
                SersicMixValues(0.56, {IntegralSize(4.507379039200000e-01, 1.3364521340616435),
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                                      IntegralSize(1.815920358300000e-01, 1.788573727513949),
                                      IntegralSize(1.675845126600000e-01, 0.9540942341821471),
                                      IntegralSize(1.357631567600000e-01, 0.5168447420060793),
                                      IntegralSize(9.789393526900000e-02, 0.28068960669460746),
                                      IntegralSize(6.335709147900000e-02, 0.15125243777616024),
                                      IntegralSize(3.743088737199995e-02, 0.07970930363502056)}),
                SersicMixValues(5.3, {IntegralSize(1.460427167800000e-01, 8.054256101609804),
                                      IntegralSize(1.703938981100000e-01, 3.516444900021637),
                                      IntegralSize(1.799422696900000e-01, 1.7999354143289201),
                                      IntegralSize(1.664334748800000e-01, 0.9610296716547311),
                                      IntegralSize(1.355617819800000e-01, 0.5212530458300602),
                                      IntegralSize(9.853922795099999e-02, 0.28359630708680605),
                                      IntegralSize(6.446123474800000e-02, 0.15322086713877997),
                                      IntegralSize(3.862539586100000e-02, 0.08104661418988306)}),
                SersicMixValues(5.4, {IntegralSize(1.472241201000000e-01, 8.104585311793157),
                                      IntegralSize(1.694936612200000e-01, 3.5331461575369745),
                                      IntegralSize(1.784631898200000e-01, 1.8088616428767204),
                                      IntegralSize(1.653513944200000e-01, 0.966274464898575),
                                      IntegralSize(1.353081019100000e-01, 0.5245207040122225),
                                      IntegralSize(9.905334229300000e-02, 0.2857472929197147),
                                      IntegralSize(6.541494416000000e-02, 0.15469638194315097),
                                      IntegralSize(3.969124607699992e-02, 0.0820704266702705)}),
                SersicMixValues(5.5, {IntegralSize(1.482963711100000e-01, 8.157998300350163),
                                      IntegralSize(1.684936809100000e-01, 3.5526214820775555),
                                      IntegralSize(1.769193968500000e-01, 1.8200893112313608),
                                      IntegralSize(1.642568530800000e-01, 0.9732222429586682),
                                      IntegralSize(1.350881729400000e-01, 0.5289666833438721),
                                      IntegralSize(9.963501702300000e-02, 0.28868225280082765),
                                      IntegralSize(6.645610619099999e-02, 0.15667865291444724),
                                      IntegralSize(4.085440189600009e-02, 0.08341094265916177)}),
                SersicMixValues(5.6, {IntegralSize(1.494216577100000e-01, 8.206038634633545),
                                      IntegralSize(1.676512182400000e-01, 3.568745913471352),
                                      IntegralSize(1.755368510500000e-01, 1.8288955890137792),
                                      IntegralSize(1.632299275500000e-01, 0.9784823842837643),
                                      IntegralSize(1.348230809500000e-01, 0.5322729918821055),
                                      IntegralSize(1.000949517600000e-01, 0.29086197600983066),
                                      IntegralSize(6.735311827400001e-02, 0.1581682701355888),
                                      IntegralSize(4.188919446599992e-02, 0.08443812380970346)}),
                SersicMixValues(5.7, {IntegralSize(1.505179972200000e-01, 8.253088141765527),
                                      IntegralSize(1.668332885500000e-01, 3.584649586137495),
                                      IntegralSize(1.741976284100000e-01, 1.8376722076022485),
                                      IntegralSize(1.622296935600000e-01, 0.9837649687864564),
                                      IntegralSize(1.345552579800000e-01, 0.5356060719455632),
                                      IntegralSize(1.005321347700000e-01, 0.29306037679192154),
                                      IntegralSize(6.822469380500000e-02, 0.15966780616488666),
                                      IntegralSize(4.290930570499996e-02, 0.0854688506021903)}),
                SersicMixValues(5.8, {IntegralSize(1.515879272500000e-01, 8.299142402455335),
                                      IntegralSize(1.660400547300000e-01, 3.6003105860029048),
                                      IntegralSize(1.728998930900000e-01, 1.8464016506678635),
                                      IntegralSize(1.612547251600000e-01, 0.9890592370113803),
                                      IntegralSize(1.342848426400000e-01, 0.5389596618204895),
                                      IntegralSize(1.009474823600000e-01, 0.2952735553178496),
                                      IntegralSize(6.907123243400000e-02, 0.16117467858893839),
                                      IntegralSize(4.391384233599993e-02, 0.08650176611278063)}),
                SersicMixValues(5.9, {IntegralSize(1.526327958200000e-01, 8.34422551063296),
                                      IntegralSize(1.652706114400000e-01, 3.615735680584908),
                                      IntegralSize(1.716424885700000e-01, 1.8550812038095585),
                                      IntegralSize(1.603048214800000e-01, 0.9943594050730895),
                                      IntegralSize(1.340119131100000e-01, 0.5423294487834868),
                                      IntegralSize(1.013413302800000e-01, 0.2974998397831239),
                                      IntegralSize(6.989331157700000e-02, 0.16268848721785148),
                                      IntegralSize(4.490272772299997e-02, 0.08753684056124277)}),
                SersicMixValues(6.0, {IntegralSize(1.537171389800000e-01, 8.384362091359415),
                                      IntegralSize(1.646310001100000e-01, 3.6280605151722813),
                                      IntegralSize(1.705224381100000e-01, 1.8614764777777508),
                                      IntegralSize(1.594194804800000e-01, 0.99804852006924),
                                      IntegralSize(1.337115424200000e-01, 0.5446026166326404),
                                      IntegralSize(1.016382102200000e-01, 0.29899499492875814),
                                      IntegralSize(7.058963559700000e-02, 0.1637239535978523),
                                      IntegralSize(4.577055408299990e-02, 0.08826675518346225)}),
                SersicMixValues(6.15, {IntegralSize(1.553219926000000e-01, 8.441014582539653),
                                       IntegralSize(1.637522910100000e-01, 3.64481587785716),
                                       IntegralSize(1.689514167800000e-01, 1.8699314093449904),
                                       IntegralSize(1.581551069500000e-01, 1.0028217018463064),
                                       IntegralSize(1.332531374400000e-01, 0.5475069152025859),
                                       IntegralSize(1.020207149700000e-01, 0.3009023776775003),
                                       IntegralSize(7.155031538800000e-02, 0.16505421807430498),
                                       IntegralSize(4.699502486199991e-02, 0.08921555769356705)}),
                SersicMixValues(6.3, {IntegralSize(1.568660317900000e-01, 8.495918425092837),
                                      IntegralSize(1.629052106300000e-01, 3.6612181682437677),
                                      IntegralSize(1.674465993900000e-01, 1.8783509624490966),
                                      IntegralSize(1.569397119200000e-01, 1.0076434259191034),
                                      IntegralSize(1.328024313800000e-01, 0.5504647776042669),
                                      IntegralSize(1.023769030800000e-01, 0.3028470110772787),
                                      IntegralSize(7.247272794700001e-02, 0.16640498028199932),
                                      IntegralSize(4.819038386300001e-02, 0.09017262629786325)}),
                SersicMixValues(6.45, {IntegralSize(1.584076580300000e-01, 8.54518367412543),
                                       IntegralSize(1.621834605900000e-01, 3.6744872956771832),
                                       IntegralSize(1.660956620500000e-01, 1.8845450508361086),
                                       IntegralSize(1.558110805500000e-01, 1.0109181572035904),
                                       IntegralSize(1.323394201700000e-01, 0.5523764398734438),
                                       IntegralSize(1.026408969900000e-01, 0.30409508873128516),
                                       IntegralSize(7.326585608699999e-02, 0.1672969445995797),
                                       IntegralSize(4.925596553299993e-02, 0.09083361738605814)}),
                SersicMixValues(6.6, {IntegralSize(1.599430618700000e-01, 8.5889306051325),
                                      IntegralSize(1.615775399000000e-01, 3.68467590274822),
                                      IntegralSize(1.648885950300000e-01, 1.8885333328969849),
                                      IntegralSize(1.547661931400000e-01, 1.0126537471525356),
                                      IntegralSize(1.318691205700000e-01, 0.5532459985728079),
                                      IntegralSize(1.028219238300000e-01, 0.3046492190736835),
                                      IntegralSize(7.393782679999999e-02, 0.16773223824195957),
                                      IntegralSize(5.019573886000006e-02, 0.09120010405918302)}),
                SersicMixValues(6.75, {IntegralSize(1.614191029400000e-01, 8.631228209983592),
                                       IntegralSize(1.609876728200000e-01, 3.694626910831533),
                                       IntegralSize(1.637289864800000e-01, 1.8925235188298677),
                                       IntegralSize(1.537618822900000e-01, 1.014446128543763),
                                       IntegralSize(1.314130542500000e-01, 0.5541700416383855),
                                       IntegralSize(1.029913679300000e-01, 0.30524103311852435),
                                       IntegralSize(7.458548783700000e-02, 0.16818880612926504),
                                       IntegralSize(5.111244545299998e-02, 0.09157590396434473)}),
                SersicMixValues(7.0, {IntegralSize(1.638666208300000e-01, 8.689369708274644),
                                      IntegralSize(1.602454109400000e-01, 3.70416707240192),
                                      IntegralSize(1.620943369900000e-01, 1.894043171921973),
                                      IntegralSize(1.522656837200000e-01, 1.0138258652350602),
                                      IntegralSize(1.306463137600000e-01, 0.5532634092762597),
                                      IntegralSize(1.031084588500000e-01, 0.3046005860349625),
                                      IntegralSize(7.541083002100001e-02, 0.16788230600185547),
                                      IntegralSize(5.236234488899993e-02, 0.09151619758687649)}),
                SersicMixValues(7.25, {IntegralSize(1.662504589200000e-01, 8.73581497187982),
                                       IntegralSize(1.597037092400000e-01, 3.7074506543128685),
                                       IntegralSize(1.607315629000000e-01, 1.8911066090088884),
                                       IntegralSize(1.509457568900000e-01, 1.0101086993517292),
                                       IntegralSize(1.298942407600000e-01, 0.5502728440874953),
                                       IntegralSize(1.030937651300000e-01, 0.3025811417449203),
                                       IntegralSize(7.601705187799999e-02, 0.1666726510399181),
                                       IntegralSize(5.336345428199996e-02, 0.0908753687540178)}),
                SersicMixValues(7.5, {IntegralSize(1.685717366200000e-01, 8.77054653545207),
                                      IntegralSize(1.593527049100000e-01, 3.704366651524866),
                                      IntegralSize(1.596246730900000e-01, 1.8835921147408314),
                                      IntegralSize(1.497927684200000e-01, 1.0032092600367217),
                                      IntegralSize(1.291600397800000e-01, 0.5451494536734917),
                                      IntegralSize(1.029593245100000e-01, 0.2991583640074194),
                                      IntegralSize(7.641670405900000e-02, 0.16454959592772325),
                                      IntegralSize(5.412204861100001e-02, 0.08965025802255285)}),
                SersicMixValues(7.75, {IntegralSize(1.708343542400000e-01, 8.793377487269655),
                                       IntegralSize(1.591895879800000e-01, 3.69467937316087),
                                       IntegralSize(1.587642427300000e-01, 1.871293619875331),
                                       IntegralSize(1.487993446900000e-01, 0.9929942424108256),
                                       IntegralSize(1.284444032600000e-01, 0.5378177971825264),
                                       IntegralSize(1.027117028900000e-01, 0.29429337459045307),
                                       IntegralSize(7.661663656999999e-02, 0.16149551145806715),
                                       IntegralSize(5.463972764000002e-02, 0.08783447554825745)}),
                SersicMixValues(8.0, {IntegralSize(1.730482518700000e-01, 8.803779630482044),
                                      IntegralSize(1.592189247800000e-01, 3.677941365381982),
                                      IntegralSize(1.581466945200000e-01, 1.8538906624862852),
                                      IntegralSize(1.479602725900000e-01, 0.9792646139048276),
                                      IntegralSize(1.277443118400000e-01, 0.528167613474513),
                                      IntegralSize(1.023504400300000e-01, 0.28793204614207485),
                                      IntegralSize(7.661713173100000e-02, 0.15748674336940466),
                                      IntegralSize(5.491397263899989e-02, 0.08541952853723707)})};
    }
    throw std::invalid_argument("No knots available for Sersic mixture of order " + std::to_string(order));
};

get_sersic_mix_knots_order4()

const std::vector< SersicMixValues > & lsst::gauss2d::fit::get_sersic_mix_knots_order4

(

)

Definition at line 58 of file sersicmix.cc.

                                                                {
    static const std::vector<SersicMixValues> values = get_sersic_mix_knots_copy(4);
    return values;
}

get_sersic_mix_knots_order8()

const std::vector< SersicMixValues > & lsst::gauss2d::fit::get_sersic_mix_knots_order8

(

)

Definition at line 63 of file sersicmix.cc.

                                                                {
    static const std::vector<SersicMixValues> values = get_sersic_mix_knots_copy(8);
    return values;
}

get_transform_default()

template<class T >

std::shared_ptr< T > lsst::gauss2d::fit::get_transform_default

(

)

Definition at line 159 of file transforms.h.

                                         {
    static T transform_default{};
    static std::shared_ptr<T> ptr{std::shared_ptr<T>{}, &transform_default};
    return ptr;
}

head_iter()

template<template< typename... > class Container, class Value >

Container< Value > lsst::gauss2d::fit::head_iter	(	const Container< Value > &	container,
		size_t	n )

Definition at line 118 of file util.h.

                                                                        {
    return Container<Value>(container.begin(), container.begin() + n);
}

insert_param()

template<typename t >

void lsst::gauss2d::fit::insert_param ( g2f::ParamBase & param, t & params, ParamFilter * filter = nullptr )

inline

Add a Parameter to a vector thereof, if it meets conditions.

Template Parameters

t	The type of the Parameter class (usually double or float).

Parameters

param	The Parameter to add (or not).
params	The vector to add to.
filter	The filter to apply.

Definition at line 34 of file param_filter.h.

                                                                                        {
    bool is_fixed = param.get_fixed();
    bool is_linear = param.get_linear();
    if ((filter == nullptr)
        || (((is_fixed == filter->fixed) || (is_fixed != filter->free))
            && ((is_linear == filter->linear) || (is_linear != filter->nonlinear)))) {
        params.insert(params.end(), param);
    }
}

insert_param_channel()

template<typename t >

void lsst::gauss2d::fit::insert_param_channel	(	const lsst::gauss2d::fit::Channel &	channel,
		g2f::ParamBase &	param,
		t &	params,
		ParamFilter *	filter )

Same as insert_param, but only inserting if filter has a null or matching Channel.

Definition at line 46 of file param_filter.h.

                                               {
    if ((filter == nullptr) || (filter->channel == std::nullopt) || (filter->channel == channel)) {
        insert_param(param, params, filter);
    }
}

insert_params()

template<typename t >

void lsst::gauss2d::fit::insert_params ( const t params_in, t & params_out, ParamFilter * filter = nullptr )

inline

Same as insert_param, but inserting from a collection of Parameter instances.

Definition at line 64 of file param_filter.h.

                                                                                           {
    insert_params_ref<t>(params_in, params_out, filter);
}

insert_params_ref()

template<typename t >

void lsst::gauss2d::fit::insert_params_ref ( const t & params_in, t & params_out, ParamFilter * filter = nullptr )

inline

Same as insert_param, but inserting from a (ref to a) collection of Parameter instances.

Definition at line 55 of file param_filter.h.

                                                                                                {
    if (filter != nullptr)
        for (auto& p : params_in) insert_param<t>(p.get(), params_out, filter);
    else
        for (auto& p : params_in) params_out.push_back(p);
}

isclose()

template<typename T >

IsCloseResult< T > lsst::gauss2d::fit::isclose	(	T	a,
		T	b,
		T	rtol = 1e-5,
		T	atol = 1e-8 )

Check if two values are close, within some tolerances.

This function mimics the behaviour of numpy.isclose as of v1.7.0

Note

See https://numpy.org/doc/stable/reference/generated/numpy.isclose.html

Template Parameters

T	The type of value being checked (usually float/double).

Parameters

a	The (measured) value to check.
b	The (reference) value to check against.
rtol	The relative tolerance.
atol	The absolute tolerance.

Returns

An IsCloseResult object with the result and some metadata.

Definition at line 48 of file util.h.

                                                                 {
    const T diff_abs = std::abs(a - b);
    const T margin = atol + rtol * std::abs(b);
    return IsCloseResult<T>{diff_abs <= margin, diff_abs, margin};
}

logit()

template<typename T >

T lsst::gauss2d::fit::logit

(

T

p

)

Definition at line 13 of file math.h.

             {
    return log(p / (1 + p));
}

logpdf_norm()

template<typename T >

double lsst::gauss2d::fit::logpdf_norm	(	T	residual,
		T	sigma )

Definition at line 18 of file math.h.

                                        {
    return LOG_1_M_LOG_SQRT_2_PI - log(sigma) - residual * residual / 2;
}

map_keys()

template<template< typename... > class Map, class Key , class Value >

std::set< Key > lsst::gauss2d::fit::map_keys

(

const Map< Key, Value > &

map

)

Definition at line 56 of file util.h.

                                                 {
    std::set<Key> result;
    for (const auto& it : map) {
        result.insert(it.first);
    }
    return result;
}

map_keys_ref_const()

template<template< typename... > class Map, class Key , class Value >

std::set< std::reference_wrapper< const Key > > lsst::gauss2d::fit::map_keys_ref_const

(

const Map< std::reference_wrapper< const Key >, Value, std::less< const Key > > &

map

)

Definition at line 65 of file util.h.

                                                                                    {
    std::set<std::reference_wrapper<const Key>> result;
    for (const auto& it : map) result.insert(it.first.get());
    return result;
}

map_values_ref_const()

template<template< typename... > class Map, class Key , class Value >

std::set< std::reference_wrapper< const Value > > lsst::gauss2d::fit::map_values_ref_const

(

const Map< Key, std::reference_wrapper< const Value > > &

map

)

Definition at line 81 of file util.h.

                                                                {
    std::set<std::reference_wrapper<const Value>> result;
    for (const auto& it : map) result.insert(it.second);
    return result;
}

map_values_shared_ptr_const()

template<template< typename... > class Map, class Key , class Value >

std::set< std::shared_ptr< const Value > > lsst::gauss2d::fit::map_values_shared_ptr_const

(

const Map< Key, std::shared_ptr< const Value > > &

map

)

Definition at line 73 of file util.h.

                                                         {
    std::set<std::shared_ptr<const Value>> result;
    for (const auto& it : map) result.insert(it.second);
    return result;
}

nonconsecutive_unique()

template<typename T >

std::vector< T > lsst::gauss2d::fit::nonconsecutive_unique

(

const std::vector< T > &

vec

)

Definition at line 92 of file util.h.

                                                            {
    std::set<T> set{};
    std::vector<T> rval{};
    rval.reserve(vec.size());
    for (const auto& elem : vec) {
        auto result = set.insert(elem);
        if (result.second) rval.push_back(elem);
    }
    return rval;
}

operator<() [1/5]

bool lsst::gauss2d::fit::operator< ( const IntegralModel & lhs, const IntegralModel & rhs )

inline

Definition at line 41 of file integralmodel.h.

{ return &lhs < &rhs; }

operator<() [2/5]

bool lsst::gauss2d::fit::operator< ( const SersicMixValues & lhs, const SersicMixValues & rhs )

inline

Definition at line 73 of file sersicmix.h.

                                                                              {
    return lhs.sersicindex < rhs.sersicindex;
}

operator<() [3/5]

bool lsst::gauss2d::fit::operator< ( const SersicMixValues & lhs, double x )

inline

Definition at line 76 of file sersicmix.h.

{ return lhs.sersicindex < x; }

operator<() [4/5]

bool lsst::gauss2d::fit::operator< ( const std::reference_wrapper< const Channel > & lhs, const std::reference_wrapper< const Channel > & rhs )

inline

Definition at line 104 of file channel.h.

                                                                      {
    return (lhs.get() < rhs.get());
}

operator<() [5/5]

bool lsst::gauss2d::fit::operator< ( double x, const SersicMixValues & rhs )

inline

Definition at line 77 of file sersicmix.h.

{ return x < rhs.sersicindex; }

operator==()

bool lsst::gauss2d::fit::operator== ( const std::reference_wrapper< const Channel > & lhs, const std::reference_wrapper< const Channel > & rhs )

inline

Definition at line 109 of file channel.h.

                                                                       {
    return (lhs.get() == rhs.get());
}

str_jacobians()

std::string lsst::gauss2d::fit::str_jacobians	(	const std::map< ParamBaseCRef, std::vector< double > > &	jacobians,
		bool	python_style = true )

Definition at line 35 of file prior.cc.

                                                    {
    std::string str = "{";
    const std::string prefix = python_style ? "" : "{ ";
    const std::string separator = python_style ? ": " : ", ";
    for (const auto& [obj, value] : jacobians) {
        str += obj.get().str() + separator + to_string_float_iter(value) + ", ";
    }
    return str.substr(0, str.size() - 2 * (jacobians.size() > 0)) + "}";
}

suffix_type()

template<typename T >

constexpr std::string_view lsst::gauss2d::fit::suffix_type ( )

constexpr

suffix_type< double >()

template<>

constexpr std::string_view lsst::gauss2d::fit::suffix_type< double > ( )

constexpr

Definition at line 12 of file utils.h.

                                               {
    return "D";
}

suffix_type_str()

template<typename T >

std::string lsst::gauss2d::fit::suffix_type_str

(

)

Definition at line 17 of file utils.h.

                            {
    return std::string(suffix_type<T>());
}

sum_iter()

template<template< typename... > class Container, class Value >

Value lsst::gauss2d::fit::sum_iter

(

const Container< Value > &

container

)

Definition at line 23 of file math.h.

                                                  {
    Value sum = 0;
    for (const auto& value : container) sum += value;
    return sum;
}

tail_iter()

template<template< typename... > class Container, class Value >

Container< Value > lsst::gauss2d::fit::tail_iter	(	const Container< Value > &	container,
		size_t	n )

Definition at line 123 of file util.h.

                                                                        {
    return Container<Value>(container.end() - n, container.end());
}

Variable Documentation

LOG_1

const double lsst::gauss2d::fit::LOG_1 = log(1)

Definition at line 8 of file math.h.

LOG_1_M_LOG_SQRT_2_PI

const double lsst::gauss2d::fit::LOG_1_M_LOG_SQRT_2_PI = LOG_1 - log(SQRT_2_PI)

Definition at line 10 of file math.h.

SQRT_2_PI

const double lsst::gauss2d::fit::SQRT_2_PI = sqrt(2. * M_PI)

Definition at line 9 of file math.h.