Mathematical functions for signal modelling: Gaussian and Woods-Saxon profiles, ellipse geometry, and thin wrappers around the <cmath> functions. More...

Namespaces
namespace	Gaussian
	Normalized Gaussian profiles.

namespace	GeometryCalc
	Ellipse radii and plane angles used by the Woods-Saxon profiles.

namespace	WoodSaxon
	Woods-Saxon (Fermi-function) profiles.

Functions
double	Sqrt (const double &x)
	std::sqrt wrapper.

double	Power (const double &x, const double &exponent)
	std::pow wrapper.

double	Sin (const double &x)
	std::sin wrapper.

double	Cos (const double &x)
	std::cos wrapper.

double	ATan (const double &x)
	std::atan wrapper.

double	ATan2 (const double &y, const double &x)
	Quadrant-aware arctangent with swapped argument forwarding.

double	Exp (const double &x)
	std::exp wrapper.

double	Gaus (const double &x, const double &mean, const double &sigma, const bool &norm)
	Gaussian kernel $e^{-(x-\mu)^2/(2\sigma^2)}$ , divided by $\sqrt{2\pi}\,\sigma$ when `norm` is true.

QPMatrix	RotationMatrix (double theta)
	Counterclockwise 2D rotation matrix.

Variables
const double	InvPi = 0.3183098861837906715377675267450287240689192
	$1/\pi$

const double	InvSqrtPi = 0.5641895835477562869480794515607725858440506
	$1/\sqrt{\pi}$

const double	InvSqrt2Pi = 0.3989422804014326779399460599343818684758586
	$1/\sqrt{2\pi}$

const double	Degree = 0.01745329251994329576923690768488612713442871
	one degree in radians, $\pi/180$

const double	Pi = 3.1415926535897932384626433832795028841971693
	$\pi$

Detailed Description

Mathematical functions for signal modelling: Gaussian and Woods-Saxon profiles, ellipse geometry, and thin wrappers around the <cmath> functions.

Angles are in radians throughout.

Function Documentation

◆ Sqrt()

double QPMath::Sqrt ( const double & x )

std::sqrt wrapper.

Parameters

x operand

Returns: $\sqrt{x}$

Definition at line 192 of file QPMath.cpp.

Referenced by QPMath::GeometryCalc::EllipseRotAxis(), QPMath::Gaussian::MatrixForm2D(), QPMath::Gaussian::RotAxis2D(), QPMath::WoodSaxon::RotAxis2D(), QPMath::WoodSaxon::RotAxis2DUnsync(), QPMath::Gaussian::Simple2D(), QPMath::WoodSaxon::Simple2D(), QPMath::Gaussian::UniAxis2D(), and QPMath::WoodSaxon::UniAxis2D().

◆ Power()

double QPMath::Power	(	const double &	x,
		const double &	exponent
	)

std::pow wrapper.

Parameters

x	base
exponent	exponent

Returns: $x^{\mathrm{exponent}}$

Definition at line 196 of file QPMath.cpp.

Referenced by QPMath::GeometryCalc::EllipseRotAxis(), QPMath::Gaussian::RotAxis2D(), QPMath::WoodSaxon::RotAxis2D(), QPMath::WoodSaxon::RotAxis2DUnsync(), QPMath::Gaussian::Simple2D(), QPMath::WoodSaxon::Simple2D(), QPMath::Gaussian::UniAxis2D(), and QPMath::WoodSaxon::UniAxis2D().

◆ Sin()

double QPMath::Sin ( const double & x )

std::sin wrapper.

Parameters

x	angle, radians

Returns: $\sin x$

Definition at line 200 of file QPMath.cpp.

Referenced by QPMath::Gaussian::Assymetry2D(), QPMath::GeometryCalc::EllipseRotAxis(), RotationMatrix(), and QPMath::Gaussian::RotAxis2D().

◆ Cos()

double QPMath::Cos ( const double & x )

std::cos wrapper.

Parameters

x	angle, radians

Returns: $\cos x$

Definition at line 204 of file QPMath.cpp.

Referenced by QPMath::Gaussian::Assymetry2D(), QPMath::GeometryCalc::EllipseRotAxis(), RotationMatrix(), and QPMath::Gaussian::RotAxis2D().

◆ ATan()

double QPMath::ATan ( const double & x )

std::atan wrapper.

Parameters

x operand

Returns: $\arctan x \in (-\pi/2, \pi/2)$ , radians

Definition at line 208 of file QPMath.cpp.

◆ ATan2()

double QPMath::ATan2	(	const double &	y,
		const double &	x
	)

Quadrant-aware arctangent with swapped argument forwarding.

Warning: Forwards its parameters to std::atan2 in reversed order: ATan2(y, x) returns std::atan2(x, y), i.e. the quadrant-aware $\arctan(x/y)$ — the angle measured from the +y axis — instead of the conventional $\arctan(y/x)$ . GeometryCalc::Angle depends on this behavior.