Marmot::Math Namespace Reference

Functions
template<typename T >
bool	isNaN (T x)
double	linearInterpolation (double x, double x0, double x1, double y0, double y1)
double	exp (double x)
int	getExponentPowerTen (const double x)
constexpr double	radToDeg (const double alpha)
constexpr double	degToRad (const double alpha)
constexpr double	macauly (double scalar)
constexpr int	heaviside (double scalar)
template<typename T >
constexpr T	sgn (T val)
double	makeReal (const double &value)
double	makeReal (const std::complex< double > &value)
double	makeReal (const autodiff::real &value)
template<typename T , typename G >
double	makeReal (const autodiff::detail::Dual< T, G > &number)
template<int nRows, int nCols>
Eigen::Matrix< double, nRows, nCols >	macaulyMatrix (const Eigen::Matrix< double, nRows, nCols > &mat)
template<typename functionType , typename yType , typename... Args>
yType	explicitEuler (yType yN, const double dt, functionType fRate, Args &&... fRateArgs)
template<int ySize, typename functionType , typename... Args>
Eigen::Matrix< double, ySize, 1 >	semiImplicitEuler (Eigen::Matrix< double, ySize, 1 > yN, const double dt, functionType fRate, Args &&... fRateArgs)
template<int nRows, int nCols, typename functionType >
Eigen::Matrix< double, nRows, nCols >	centralDiff (functionType f, const Eigen::Matrix< double, nCols, 1 > &X)
template<typename functionType , typename yType , typename... Args>
yType	explicitEulerRichardson (yType yN, const double dt, functionType fRate, Args &&... fRateArgs)
template<int ySize, typename functionType , typename... Args>
std::tuple< Eigen::Matrix< double, ySize, 1 >, double >	explicitEulerRichardsonWithErrorEstimator (Eigen::Matrix< double, ySize, 1 > yN, const double dt, const double TOL, functionType fRate, Args &&... fRateArgs)
Matrix3d	directionCosines (const Matrix3d &transformedCoordinateSystem)
Matrix3d	orthonormalCoordinateSystem (Vector3d &normalVector)
double	makeReal (const autodiff::dual &value)

Function Documentation

isNaN()

template<typename T >

bool Marmot::Math::isNaN

(

T

x

)

Check if value x is a valid floating point number

linearInterpolation()

double Marmot::Math::linearInterpolation	(	double	x,
		double	x0,
		double	x1,
		double	y0,
		double	y1
	)

Linear interpolation at location x between two points (x0|y0) and (x1|y1)

exp()

double Marmot::Math::exp

(

double

x

)

exponential of value x with numerical limits check

getExponentPowerTen()

int Marmot::Math::getExponentPowerTen

(

const double

x

)

compute the exponent to the power of ten of an expression, e.g., 5*10^5 --> return 5

radToDeg()

constexpr double Marmot::Math::radToDeg ( const double  alpha )

constexpr

convert angle alpha in radiant to degree

degToRad()

constexpr double Marmot::Math::degToRad ( const double  alpha )

constexpr

convert angle alpha in degree to radiant

macauly()

constexpr double Marmot::Math::macauly ( double  scalar )

constexpr

Macaulay function applied to scalar

heaviside()

constexpr int Marmot::Math::heaviside ( double  scalar )

constexpr

Heaviside function applied to scalar

sgn()

template<typename T >

constexpr T Marmot::Math::sgn ( T  val )

constexpr

Extract sign of value val

makeReal() [1/5]

double Marmot::Math::makeReal

(

const double &

value

)

makeReal() [2/5]

double Marmot::Math::makeReal

(

const std::complex< double > &

value

)

makeReal() [3/5]

double Marmot::Math::makeReal

(

const autodiff::real &

value

)

makeReal() [4/5]

template<typename T , typename G >

double Marmot::Math::makeReal

(

const autodiff::detail::Dual< T, G > &

number

)

macaulyMatrix()

template<int nRows, int nCols>

Eigen::Matrix< double, nRows, nCols > Marmot::Math::macaulyMatrix

(

const Eigen::Matrix< double, nRows, nCols > &

mat

)

apply Macaulay function to a matrix

Todo:

: Can be replaced easily with Eigen's array() functionality ???

explicitEuler()

template<typename functionType , typename yType , typename... Args>

yType Marmot::Math::explicitEuler	(	yType	yN,
		const double	dt,
		functionType	fRate,
		Args &&...	fRateArgs
	)

Explicit Euler integration of function fRate taking arguments fRateArgs and initial value a yN

semiImplicitEuler()

template<int ySize, typename functionType , typename... Args>

Eigen::Matrix< double, ySize, 1 > Marmot::Math::semiImplicitEuler	(	Eigen::Matrix< double, ySize, 1 >	yN,
		const double	dt,
		functionType	fRate,
		Args &&...	fRateArgs
	)

Semi-implicit Euler integration of function fRate taking arguments fRateArgs and initial value yN using central difference scheme for computing

Todo:

: Replace inverse bei solving equation system?

: Use external central difference function?

centralDiff()

template<int nRows, int nCols, typename functionType >

Eigen::Matrix< double, nRows, nCols > Marmot::Math::centralDiff	(	functionType	f,
		const Eigen::Matrix< double, nCols, 1 > &	X
	)

returns central numerical differentiation of a vector-valued function f with respect to vector X --> use std::bind to create function f(x) from function with multiple arguments

explicitEulerRichardson()

template<typename functionType , typename yType , typename... Args>

yType Marmot::Math::explicitEulerRichardson	(	yType	yN,
		const double	dt,
		functionType	fRate,
		Args &&...	fRateArgs
	)

Explicit Euler integration with Richardson extrapolation of function fRate taking arguments fRateArgs and initial value yN

explicitEulerRichardsonWithErrorEstimator()

template<int ySize, typename functionType , typename... Args>

std::tuple< Eigen::Matrix< double, ySize, 1 >, double > Marmot::Math::explicitEulerRichardsonWithErrorEstimator	(	Eigen::Matrix< double, ySize, 1 >	yN,
		const double	dt,
		const double	TOL,
		functionType	fRate,
		Args &&...	fRateArgs
	)

Explicit Euler integration with error estimation based on Richardson extrapolation of function fRate taking arguments fRateArgs and initial value yN .

directionCosines()

Matrix3d Marmot::Math::directionCosines

(

const Matrix3d &

transformedCoordinateSystem

)

Computes the directional cosines between a transformed and the global cartesian coordinate system.

orthonormalCoordinateSystem()

Matrix3d Marmot::Math::orthonormalCoordinateSystem

(

Vector3d &

normalVector

)

Computes an orthonormal coordinate system from an unit normal vector as \( x_1 \) - axis.

makeReal() [5/5]

double Marmot::Math::makeReal

(

const autodiff::dual &

value

)