dg::Cauchy Struct Reference

\( f(x,y) = \begin{cases} Ae^{1 + \left(\frac{(x-x_0)^2}{\sigma_x^2} + \frac{(y-y_0)^2}{\sigma_y^2} - 1\right)^{-1}} \text{ if } \frac{(x-x_0)^2}{\sigma_x^2} + \frac{(y-y_0)^2}{\sigma_y^2} < 1\\ 0 \text{ else} \end{cases} \) More...

Public Member Functions
	Cauchy (double x0, double y0, double sigma_x, double sigma_y, double amp)
	A blob that drops to zero.
DG_DEVICE double	operator() (double x, double y) const
bool	inside (double x, double y) const
double	dx (double x, double y) const
double	dxx (double x, double y) const
double	dy (double x, double y) const
double	dyy (double x, double y) const
double	dxy (double x, double y) const

Detailed Description

\( f(x,y) = \begin{cases} Ae^{1 + \left(\frac{(x-x_0)^2}{\sigma_x^2} + \frac{(y-y_0)^2}{\sigma_y^2} - 1\right)^{-1}} \text{ if } \frac{(x-x_0)^2}{\sigma_x^2} + \frac{(y-y_0)^2}{\sigma_y^2} < 1\\ 0 \text{ else} \end{cases} \)

A bump that drops to zero and is infinitely continuously differentiable

Constructor & Destructor Documentation

Cauchy()

dg::Cauchy::Cauchy ( double x0, double y0, double sigma_x, double sigma_y, double amp )

inline

A blob that drops to zero.

Parameters

x0	x-center-coordinate
y0	y-center-coordinate
sigma_x	radius in x (must be !=0)
sigma_y	radius in y (must be !=0)
amp	Amplitude

Member Function Documentation

dx()

double dg::Cauchy::dx ( double x, double y ) const

inline

dxx()

double dg::Cauchy::dxx ( double x, double y ) const

inline

dxy()

double dg::Cauchy::dxy ( double x, double y ) const

inline

dy()

double dg::Cauchy::dy ( double x, double y ) const

inline

dyy()

double dg::Cauchy::dyy ( double x, double y ) const

inline

inside()

bool dg::Cauchy::inside ( double x, double y ) const

inline

operator()()

DG_DEVICE double dg::Cauchy::operator() ( double x, double y ) const

inline

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

• functors.h