Provides geometrical methods such as point inside rectangle. More...

Functions
double	derLinearStepFunc (const double &x, const double &x1, const double &x2)
	Compute derivative of linear step function. More...

double	doubleGaussian2d (const util::Point3 &x, const size_t &dof, const std::vector< double > &params)
	Compute sum of two Gaussian function in 2-d. More...

double	gaussian (const double &r, const double &a, const double &beta)
	Compute Gaussian function in 1-d. More...

double	gaussian2d (const util::Point3 &x, const size_t &dof, const std::vector< double > &params)
	Compute Gaussian function in 2-d. More...

double	getDeterminant (const std::vector< util::Point3 > &rows)
	Get determinant of 3-d matrix. More...

double	hatFunction (const double &x, const double &x_min, const double &x_max)
	Computes hat function at given point. More...

double	hatFunctionQuick (const double &x, const double &x_min, const double &x_max)
	Computes hat function at given point. More...

double	linearStepFunc (const double &x, const double &x1, const double &x2)
	Compute linear step function. More...

util::Point3	signVector (const util::Point3 &v)
	Get vector with plus or minus 1 depending on the sign of component of another vector. More...

Detailed Description

Provides geometrical methods such as point inside rectangle.

Function Documentation

◆ derLinearStepFunc()

double util::function::derLinearStepFunc	(	const double &	x,
		const double &	x1,
		const double &	x2
	)

Compute derivative of linear step function.

Parameters

x	Point in real line
x1	Point such that function is linear with slope 1 in [0, x1)
x2	Point such that function is constant in [x1, x1 + x2)

Returns: value Derivative of step function at x

Referenced by loading::ULoading::apply().

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◆ doubleGaussian2d()

double util::function::doubleGaussian2d	(	const util::Point3 &	x,
		const size_t &	dof,
		const std::vector< double > &	params
	)

Compute sum of two Gaussian function in 2-d.

Double Gaussian (2-d) function:

$f(x,y) = (f_1(x,y), f_2(x,y)) + (g_1(x,y), g_2(x,y)),$

where $ (f_1,f_2)$ and $(g_1, g_2)$ are two Gaussian 2-d function as described in Gaussian2d() with different values of $ (x_c, y_c), a, (d_1, d_2)$ .

Parameters

x	Coordinates of point
params	List of parameters
dof	Component of Gaussian function

Returns: value Component of Gaussian 2-d vector function along dof

Referenced by loading::InitialCondition::getICFormula().

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◆ gaussian()

double util::function::gaussian	(	const double &	r,
		const double &	a,
		const double &	beta
	)

Compute Gaussian function in 1-d.

Gaussian (1-d) function: $f(r) = a \exp(-\frac{r^2}{\beta}).$

Here $ a$ is the amplitude and $\beta$ is the exponential factor.

Parameters

r	Distance from origin
a	Amplitude
beta	Factor in exponential function

Returns: value Component of Gaussian 1-d function

Referenced by doubleGaussian2d(), and gaussian2d().

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◆ gaussian2d()

double util::function::gaussian2d	(	const util::Point3 &	x,
		const size_t &	dof,
		const std::vector< double > &	params
	)

Compute Gaussian function in 2-d.

Gaussian (2-d) function:

$f(x,y) = (f_1(x,y), f_2(x,y)),$

where

$f_1(x,y) = a \exp(-\frac{(x-x_c)^2 + (y-y_c)^2}{\beta}) d_1, \quad f_1(x,y) = a \exp(-\frac{(x-x_c)^2 + (y-y_c)^2}{\beta}) d_2.$

Here $ (x_c,y_c) $ is the center of the pulse, $ a$ is the amplitude, $\beta$ is the exponential factor, and $ (d_1,d_2)$ is the direction of the pulse.

Parameters

x	Coordinates of point
params	List of parameters
dof	Component of Gaussian function

Returns: value Component of Gaussian 2-d vector function along dof

Referenced by loading::InitialCondition::getICFormula().

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◆ getDeterminant()

double util::function::getDeterminant ( const std::vector< util::Point3 > & rows )

Get determinant of 3-d matrix.

Parameters

rows	Three rows of matrix

Returns: det Determinant

Referenced by util::geometry::getTetVolume().

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◆ hatFunction()

double util::function::hatFunction	(	const double &	x,
		const double &	x_min,
		const double &	x_max
	)

Computes hat function at given point.

Hat function: f ^ | | 1 o | /|\ | / | \ | / | \ | / | \ | / | \ | / | \ o____________o____________o______\ x / x_min x_max

Parameters

x	Point in real line
x_min	Left side point in real line
x_max	Right side point in real line

Returns: value Evaluation of hat function at x

Referenced by loading::FLoading::apply().

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◆ hatFunctionQuick()

double util::function::hatFunctionQuick	(	const double &	x,
		const double &	x_min,
		const double &	x_max
	)

Computes hat function at given point.

This version does not test if point x is in valid interval.

Hat function: f ^ | | 1 o | /|\ | / | \ | / | \ | / | \ | / | \ | / | \ o____________o____________o______\ x / x_min x_max

Parameters

x	Point in real line
x_min	Left side point in real line
x_max	Right side point in real line

Returns: value Evaluation of hat function at x

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◆ linearStepFunc()

double util::function::linearStepFunc	(	const double &	x,
		const double &	x1,
		const double &	x2
	)

Compute linear step function.

Step function:

f ^ | __________ | / | / | _______/ | / | / |/_________________________ t x1 x1+x2

Linear (with slope 1) in [0,l1), constant in [l1,l1+l2)
Periodic with periodicity l1+l2

Parameters

x	Point in real line
x1	Point such that function is linear with slope 1 in [0, x1)
x2	Point such that function is constant in [x1, x1 + x2)

Returns: value Evaluation of step function at x

Referenced by loading::FLoading::apply(), and loading::ULoading::apply().

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◆ signVector()

util::Point3 util::function::signVector ( const util::Point3 & v )

Get vector with plus or minus 1 depending on the sign of component of another vector.

Parameters

v	Vector from which a new vector is created

Returns: vec Vector

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Functions

Detailed Description

Function Documentation

◆ derLinearStepFunc()

◆ doubleGaussian2d()

◆ gaussian()

◆ gaussian2d()

◆ getDeterminant()

◆ hatFunction()

◆ hatFunctionQuick()

◆ linearStepFunc()

◆ signVector()