Enumerations
enum class	Type { GENERAL , UNIFORM , QUADRATIC , CUBIC , CHEBYSHEV , CHEBYSHEV_STRETCHED , CHEBYSHEV_AUGMENTED , CHEBYSHEV_2 , CHEBYSHEV_3 , CHEBYSHEV_3_STRETCHED , CHEBYSHEV_4 , CHEBYSHEV_4_STRETCHED , CHEBYSHEV_ELLIPSE , CHEBYSHEV_ELLIPSE_STRETCHED , CHEBYSHEV_ELLIPSE_AUGMENTED , CHEBYSHEV_ELLIPSE_2 , CHEBYSHEV_ELLIPSE_3 , CHEBYSHEV_ELLIPSE_3_STRETCHED , CHEBYSHEV_ELLIPSE_4 , CHEBYSHEV_ELLIPSE_4_STRETCHED , LOGISTIC , LOGISTIC_STRETCHED , ERF , ERF_STRETCHED }

Functions
template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	uniform (SizeT n, const Number &a, const Number &b)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	quadratic (SizeT n, const Number &a, const Number &b)
	Generates a distribution of `n` points on the segment `[a, b]` using two quadratic polynomials.

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	cubic (SizeT n, const Number &a, const Number &b)
	Generates a distribution of `n` points on the segment `[a, b]` using cubic polynomial.

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev (SizeT n, const Number &a, const Number &b)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_stretched (SizeT n, const Number &a, const Number &b)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_augmented (SizeT n, const Number &a, const Number &b)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_2 (SizeT n, const Number &a, const Number &b)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_3 (SizeT n, const Number &a, const Number &b)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_3_stretched (SizeT n, const Number &a, const Number &b)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_4 (SizeT n, const Number &a, const Number &b)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_4_stretched (SizeT n, const Number &a, const Number &b)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_ellipse (SizeT n, const Number &a, const Number &b, const Number &ratio)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_ellipse_stretched (SizeT n, const Number &a, const Number &b, const Number &ratio)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_ellipse_augmented (SizeT n, const Number &a, const Number &b, const Number &ratio)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_ellipse_2 (SizeT n, const Number &a, const Number &b, const Number &ratio)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_ellipse_3 (SizeT n, const Number &a, const Number &b, const Number &ratio)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_ellipse_3_stretched (SizeT n, const Number &a, const Number &b, const Number &ratio)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_ellipse_4 (SizeT n, const Number &a, const Number &b, const Number &ratio)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	chebyshev_ellipse_4_stretched (SizeT n, const Number &a, const Number &b, const Number &ratio)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	logistic (SizeT n, const Number &a, const Number &b, const Number &steepness)
	Generates a distribution of `n` points on the interval `(a, b)` using the logistic function.

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	logistic_stretched (SizeT n, const Number &a, const Number &b, const Number &steepness)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	erf (SizeT n, const Number &a, const Number &b, const Number &steepness)
	Generates a distribution of `n` points on the interval `(a, b)` using the error function.

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	erf_stretched (SizeT n, const Number &a, const Number &b, const Number &steepness)

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>
Container< Number >	of_type (Type type, SizeT n, const Number &a, const Number &b, const Number &parameter=NAN)

Enumeration Type Documentation

◆ Type

enum class alfi::dist::Type

strong

Enumerator
GENERAL
UNIFORM
QUADRATIC
CUBIC
CHEBYSHEV
CHEBYSHEV_STRETCHED
CHEBYSHEV_AUGMENTED
CHEBYSHEV_2
CHEBYSHEV_3
CHEBYSHEV_3_STRETCHED
CHEBYSHEV_4
CHEBYSHEV_4_STRETCHED
CHEBYSHEV_ELLIPSE
CHEBYSHEV_ELLIPSE_STRETCHED
CHEBYSHEV_ELLIPSE_AUGMENTED
CHEBYSHEV_ELLIPSE_2
CHEBYSHEV_ELLIPSE_3
CHEBYSHEV_ELLIPSE_3_STRETCHED
CHEBYSHEV_ELLIPSE_4
CHEBYSHEV_ELLIPSE_4_STRETCHED
LOGISTIC
LOGISTIC_STRETCHED
ERF
ERF_STRETCHED

Function Documentation

◆ uniform()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::uniform	(	SizeT	n,
		const Number &	a,
		const Number &	b )

◆ quadratic()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::quadratic	(	SizeT	n,
		const Number &	a,
		const Number &	b )

Generates a distribution of n points on the segment [a, b] using two quadratic polynomials.

The following transform function \(f\):

\[ f(x) = \begin{cases} (x+1)^2 - 1, & x \leq 0 \\ -(x-1)^2 + 1, & x > 0 \end{cases} \]

is applied to n points uniformly distributed on the segment [-1, 1], mapping them onto the same segment.
The resulting points are then linearly mapped to the target segment [a, b].

Parameters

n	number of points
a	left boundary of the segment
b	right boundary of the segment

Returns: a container with n points distributed on the segment [a, b] according to the transform function

◆ cubic()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::cubic	(	SizeT	n,
		const Number &	a,
		const Number &	b )

Generates a distribution of n points on the segment [a, b] using cubic polynomial.

The following transform function \(f\):

\[ f(x) = -0.5x^3 + 1.5x \]

is applied to n points uniformly distributed on the segment [-1, 1], mapping them onto the same segment.
The resulting points are then linearly mapped to the target segment [a, b].

Parameters

n	number of points
a	left boundary of the segment
b	right boundary of the segment

Returns: a container with n points distributed on the segment [a, b] according to the transform function

◆ chebyshev()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev	(	SizeT	n,
		const Number &	a,
		const Number &	b )

◆ chebyshev_stretched()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_stretched	(	SizeT	n,
		const Number &	a,
		const Number &	b )

◆ chebyshev_augmented()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_augmented	(	SizeT	n,
		const Number &	a,
		const Number &	b )

◆ chebyshev_2()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_2	(	SizeT	n,
		const Number &	a,
		const Number &	b )

◆ chebyshev_3()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_3	(	SizeT	n,
		const Number &	a,
		const Number &	b )

◆ chebyshev_3_stretched()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_3_stretched	(	SizeT	n,
		const Number &	a,
		const Number &	b )

◆ chebyshev_4()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_4	(	SizeT	n,
		const Number &	a,
		const Number &	b )

◆ chebyshev_4_stretched()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_4_stretched	(	SizeT	n,
		const Number &	a,
		const Number &	b )

◆ chebyshev_ellipse()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_ellipse	(	SizeT	n,
		const Number &	a,
		const Number &	b,
		const Number &	ratio )

◆ chebyshev_ellipse_stretched()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_ellipse_stretched	(	SizeT	n,
		const Number &	a,
		const Number &	b,
		const Number &	ratio )

◆ chebyshev_ellipse_augmented()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_ellipse_augmented	(	SizeT	n,
		const Number &	a,
		const Number &	b,
		const Number &	ratio )

◆ chebyshev_ellipse_2()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_ellipse_2	(	SizeT	n,
		const Number &	a,
		const Number &	b,
		const Number &	ratio )

◆ chebyshev_ellipse_3()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_ellipse_3	(	SizeT	n,
		const Number &	a,
		const Number &	b,
		const Number &	ratio )

◆ chebyshev_ellipse_3_stretched()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_ellipse_3_stretched	(	SizeT	n,
		const Number &	a,
		const Number &	b,
		const Number &	ratio )

◆ chebyshev_ellipse_4()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_ellipse_4	(	SizeT	n,
		const Number &	a,
		const Number &	b,
		const Number &	ratio )

◆ chebyshev_ellipse_4_stretched()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::chebyshev_ellipse_4_stretched	(	SizeT	n,
		const Number &	a,
		const Number &	b,
		const Number &	ratio )

◆ logistic()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::logistic	(	SizeT	n,
		const Number &	a,
		const Number &	b,
		const Number &	steepness )

Generates a distribution of n points on the interval (a, b) using the logistic function.

The following transform function \(f\):

\[ f(x) = \frac{1}{1 + e^{-steepness \cdot x}} \]

is applied to n points uniformly distributed on the interval (-1, 1), mapping them onto the (0, 1) interval.
The resulting points are then linearly mapped to the target interval (a, b).

The slope of the transform function \(f\) at x = 0 is determined by steepness and is given by:

\[ \left. \dv{f}{x} \right\vert_{x=0} = \frac14 \cdot steepness \]

Note: Extreme points don't lie on the interval (a, b) boundaries.

Parameters

n	number of points
a	left boundary of the interval
b	right boundary of the interval
steepness	determines the slope of the transform function at `x = 0`

Returns: a container with n points distributed on the interval (a, b) according to the transform function

◆ logistic_stretched()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::logistic_stretched	(	SizeT	n,
		const Number &	a,
		const Number &	b,
		const Number &	steepness )

◆ erf()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::erf	(	SizeT	n,
		const Number &	a,
		const Number &	b,
		const Number &	steepness )

Generates a distribution of n points on the interval (a, b) using the error function.

The following transform function \(f\):

\[ f(x) = \operatorname{erf}(steepness \cdot x) \]

is applied to n points uniformly distributed on the interval (-1, 1), mapping them onto the same interval.
The resulting points are then linearly mapped to the target interval (a, b).

The slope of the transform function \(f\) at x = 0 is determined by steepness and is given by:

\[ \left. \dv{f}{x} \right\vert_{x=0} = \frac2\pi \cdot steepness \]

Note: Extreme points don't lie on the interval (a, b) boundaries.

Parameters

n	number of points
a	left boundary of the interval
b	right boundary of the interval
steepness	determines the slope of the transform function at `x = 0`

Returns: a container with n points distributed on the interval (a, b) according to the transform function

◆ erf_stretched()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::erf_stretched	(	SizeT	n,
		const Number &	a,
		const Number &	b,
		const Number &	steepness )

◆ of_type()

template<typename Number = DefaultNumber, template< typename, typename... > class Container = DefaultContainer>

Container< Number > alfi::dist::of_type	(	Type	type,
		SizeT	n,
		const Number &	a,
		const Number &	b,
		const Number &	parameter = NAN )

Enumerations

Functions

Enumeration Type Documentation

◆ Type

Function Documentation

◆ uniform()

◆ quadratic()

◆ cubic()

◆ chebyshev()

◆ chebyshev_stretched()

◆ chebyshev_augmented()

◆ chebyshev_2()

◆ chebyshev_3()

◆ chebyshev_3_stretched()

◆ chebyshev_4()

◆ chebyshev_4_stretched()

◆ chebyshev_ellipse()

◆ chebyshev_ellipse_stretched()

◆ chebyshev_ellipse_augmented()

◆ chebyshev_ellipse_2()

◆ chebyshev_ellipse_3()

◆ chebyshev_ellipse_3_stretched()

◆ chebyshev_ellipse_4()

◆ chebyshev_ellipse_4_stretched()

◆ logistic()

◆ logistic_stretched()

◆ erf()

◆ erf_stretched()

◆ of_type()