CGCoordinates::Base_XY_XZ_YZ Class Reference

Contains common member functions of the XY, XZ, and YZ classes. More...

#include <Base_XY_XZ_YZ.h>

Inheritance diagram for CGCoordinates::Base_XY_XZ_YZ:

Static Public Member Functions
static Mdouble	getGaussPrefactor (Mdouble width, Mdouble cutoff)
	Computes the prefactor of the Gauss CGFunction, which is dependent on the number of non-averaged dimensions. More...
static Mdouble	getGaussIntegralPrefactor (Mdouble distance, Mdouble width, Mdouble cutoff)
	Computes the prefactor of the Gauss line integral, which is dependent on the number of non-averaged dimensions. More...
static void	normalisePolynomialCoefficients (std::vector< Mdouble > &coefficients, Mdouble cutoff)
	Normalises the coefficients of Polynomial CGFunction such that the integral over all non-averaged dimensions is unity. More...
static const unsigned	countVariables ()
Static Public Member Functions inherited from CGCoordinates::BaseCoordinates
static Mdouble	getDomainVolume (const Vec3D &min, const Vec3D &max)

Additional Inherited Members
Public Member Functions inherited from CGCoordinates::BaseCoordinates
virtual Mdouble	getWeight ()

Detailed Description

Contains common member functions of the XY, XZ, and YZ classes.

As XY, XZ, and YZ share a lot of functionality, the shared functions are stored in this common base class.

Member Function Documentation

countVariables()

const unsigned Base_XY_XZ_YZ::countVariables ( )

static

returns the number of variables (in this case two)

{
    return 2;
}

getGaussIntegralPrefactor()

Mdouble Base_XY_XZ_YZ::getGaussIntegralPrefactor ( Mdouble  distance, Mdouble  width, Mdouble  cutoff  )

static

Computes the prefactor of the Gauss line integral, which is dependent on the number of non-averaged dimensions.

{
    Mdouble widthSqrt2 = width * constants::sqrt_2;
    Mdouble a = -cutoff;
    Mdouble b = cutoff + distance;
    //1D prefactor
    Mdouble prefactor_ = 1.0 / (widthSqrt2 * constants::sqrt_pi);
    prefactor_ /= erf(cutoff / (widthSqrt2));
    return prefactor_ * 0.5 / (
            +erf(b / widthSqrt2) * b
            + widthSqrt2 / constants::sqrt_pi * exp(-mathsFunc::square(b / widthSqrt2))
            - erf(a / widthSqrt2) * a
            - widthSqrt2 / constants::sqrt_pi * exp(-mathsFunc::square(a / widthSqrt2))
    );
}

References a, b, Eigen::bfloat16_impl::exp(), constants::sqrt_2, constants::sqrt_pi, and mathsFunc::square().

getGaussPrefactor()

Mdouble Base_XY_XZ_YZ::getGaussPrefactor ( Mdouble  width, Mdouble  cutoff  )

static

Computes the prefactor of the Gauss CGFunction, which is dependent on the number of non-averaged dimensions.

{
    //Wolfram alpha: integrate(x*exp(-x^2/(2w^2)),{x,0,c})/integrate(x*exp(-x^2/(2w^2)),{x,0,inf})=1-e^(-c^2/(2 w^2))
    Mdouble prefactor = 1.0 / (constants::sqrt_2 * constants::sqrt_pi * width);
    return mathsFunc::square(prefactor) / (1.0 - exp(-0.5 * mathsFunc::square(cutoff / width)));
}

References Eigen::bfloat16_impl::exp(), constants::sqrt_2, constants::sqrt_pi, and mathsFunc::square().

normalisePolynomialCoefficients()

void Base_XY_XZ_YZ::normalisePolynomialCoefficients ( std::vector< Mdouble > &  coefficients, Mdouble  cutoff  )

static

Normalises the coefficients of Polynomial CGFunction such that the integral over all non-averaged dimensions is unity.

The volume is computed as

\[volume=\int_0^1\sum_{i=1}^n c_i r^i 2 pi r dr = 2 pi \sum_{i=1}^n c_i/(i+2) \]

with 2 pi r the circumference of a circle.

{
    Mdouble volume = 0.0;
    for (std::size_t i = 0; i < coefficients.size(); i++)
        volume += coefficients[i] / static_cast<Mdouble>(i + 2);
    volume *= 2.0 * constants::pi * mathsFunc::square(cutoff);
    for (double& coefficient : coefficients)
        coefficient /= volume;
}

References i, constants::pi, and mathsFunc::square().

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

• Base_XY_XZ_YZ.h
• Base_XY_XZ_YZ.cc