cvspline Class Reference

Constructs a spline \( s(l) \) with constant velocity, i.e. \( \frac{ds(l)}{dl} \equiv 1\). \( l \) acts as the length alongisde the spline. It works by using tk::spline to construct a cubic spline which depends on another arbitrary parameter \( x \) and then construct an additional spline to convert from \( x \to l \equiv l(x) \). More...

#include <BSMPT/utility/const_velocity_spline.h>

Public Member Functions
	cvspline ()
	Default constructor.
	cvspline (const std::vector< std::vector< double > > &phipath_in)
	Construct a new cvspline object.
	cvspline (const std::vector< std::vector< double > > &phipath_in, int input_num_inter)
	Construct a new cvspline object.
void	initialize ()
	initialize the constant velocity spline using the given path
void	add_point (const double &p, const std::vector< double > &new_vev, const bool &compile=true)
	introduce a new point on the knot list
std::vector< double >	deriv (int order, double x)
	derivative of the constant velocity spline in \( x \)
std::vector< double >	dl (double l)
	first derivative of the constant velocity spline in \( l \)
std::vector< double >	d2l (double l)
	second derivative of the constant velocity spline in \( l \)
std::vector< double >	operator() (double l) const
	value of the constant velocity spline at \( l \)
void	print_path () const
	print the current knots of the spline
void	save_path (const std::string &file_name, const bool &header=true)
	save the knots of the splien into a file

Public Attributes
int	dim
	Dimension of the VEV space.
int	num_points
	Number of points in the path (knots)
int	num_inter
	Number of point from x to l (and viceversa)
tk::spline	x_to_l
	Spline to convert from linear length to spline length.
tk::spline	l_to_x
	Spline to convert from spline length to linear length.
float	linL
	Linear length of the (spline) path.
float	L
	True length of the (spline) path.
std::vector< double >	lin_lengths
	We need a parameter, so I used the linear lengths (not the path spline length) as parameter, this is not optimal as the velocity will not be 1.
std::vector< double >	vev_position
	Position of the VEV list "lin_lengths" using spline length.
std::vector< tk::spline >	splines
	Vector of each 2D splines (x = linear length (not important, must be increasing), y = vev_i)
std::vector< std::vector< double > >	transposed_phi
	Transpose of the path given, easier for calculations.
std::vector< std::vector< double > >	phipath
	// List of VEVs paths

Private Member Functions
double	lin_abs_deriv (double x)
	derivative in \( x \)
double	Simpson_step (double t0, double t1)
	Integrates from \( t_0 \) to \( t_1 \) using a single Simposons' 3/8 integration step.

Private Attributes
std::vector< double >	list_x
	List of x for linear lengths division.
std::vector< double >	list_l
	// List of l for spline lengths division

Detailed Description

Constructs a spline \( s(l) \) with constant velocity, i.e. \( \frac{ds(l)}{dl} \equiv 1\). \( l \) acts as the length alongisde the spline. It works by using tk::spline to construct a cubic spline which depends on another arbitrary parameter \( x \) and then construct an additional spline to convert from \( x \to l \equiv l(x) \).

Constructor & Destructor Documentation

cvspline() [1/2]

cvspline::cvspline

(

const std::vector< std::vector< double > > &

phipath_in

)

Construct a new cvspline object.

Parameters

phipath_in

knots of the path

cvspline() [2/2]

cvspline::cvspline	(	const std::vector< std::vector< double > > &	phipath_in,
		int	input_num_inter
	)

Construct a new cvspline object.

Parameters

phipath_in	knots of the path
input_num_inter	number of interpolations between \( x \) and \( l \)

Member Function Documentation

add_point()

void cvspline::add_point	(	const double &	p,
		const std::vector< double > &	new_vev,
		const bool &	compile = true
	)

introduce a new point on the knot list

Parameters

p	parameter of the point
new_vev	value of the knot
compile	initialize after point is added?

d2l()

std::vector< double > cvspline::d2l

(

double

l

)

second derivative of the constant velocity spline in \( l \)

Parameters

l	where to calculate the derivative

Returns

std::vector<double> result

deriv()

std::vector< double > cvspline::deriv	(	int	order,
		double	x
	)

derivative of the constant velocity spline in \( x \)

Parameters

order	order of the derivative
x	where to calculate the derivative

Returns

std::vector<double> result

dl()

std::vector< double > cvspline::dl

(

double

l

)

first derivative of the constant velocity spline in \( l \)

Parameters

l	where to calculate the derivative

Returns

std::vector<double> result

lin_abs_deriv()

double cvspline::lin_abs_deriv ( double  x )

private

derivative in \( x \)

Parameters

x

Returns

double

operator()()

std::vector< double > cvspline::operator()

(

double

l

)

const

value of the constant velocity spline at \( l \)

Parameters

l

Returns

std::vector<double>

save_path()

void cvspline::save_path	(	const std::string &	file_name,
		const bool &	header = true
	)

save the knots of the splien into a file

Parameters

file_name	name of the file
header	print the names of the VEVs in the first column?

Simpson_step()

double cvspline::Simpson_step ( double  t0, double  t1  )

private

Integrates from \( t_0 \) to \( t_1 \) using a single Simposons' 3/8 integration step.

Parameters

t0	lower limit
t1	upper limit

Returns

double value of the integral

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

• include/BSMPT/utility/const_velocity_spline.h
• src/utility/const_velocity_spline.cpp