cmp::grid::LatinHypercubeGrid Class Reference

Latin Hypercube Sampling (LHS) grid generator. More...

#include <grid.h>

Inheritance diagram for cmp::grid::LatinHypercubeGrid:

Collaboration diagram for cmp::grid::LatinHypercubeGrid:

Public Member Functions
	LatinHypercubeGrid (const Eigen::Ref< const Eigen::VectorXd > &lowerBound, const Eigen::Ref< const Eigen::VectorXd > &upperBound, unsigned int seed=42)
	Constructs a LatinHypercubeGrid generator.
Eigen::MatrixXd	construct (const size_t &nPoints) override
	Constructs a Latin Hypercube matrix of samples.
size_t	dim () const override
	Returns the dimension of the domain.
Public Member Functions inherited from cmp::grid::Grid
virtual	~Grid ()=default

Private Attributes
size_t	dimension_
	Number of dimensions.
std::default_random_engine	rng_
	Pseudo-random number generator.
Eigen::VectorXd	lowerBound_
	Lower bounds vector.
Eigen::VectorXd	upperBound_
	Upper bounds vector.

Detailed Description

Latin Hypercube Sampling (LHS) grid generator.

Mathematical Formulation For each dimension \(d \in \{1,\dots,D\}\), LHS divides the domain range \([a_d, b_d]\) into \(N\) equal-probability bins. The coordinate values for the \(i\)-th sample is placed inside the \(\pi_d(i)\)-th bin:

\[ x_{i, d} = a_d + \frac{b_d - a_d}{N} \left( \pi_d(i) - 1 + u_{i,d} \right) \]

where \(\pi_d\) is a random permutation of the set \(\{1,\dots,N\}\) chosen independently for each dimension, and \(u_{i,d} \sim \mathcal{U}(0, 1)\) is a random jitter.

Implementation Algorithm

1. Allocates \(N \times D\) matrix.
2. For each dimension \(d\), generates a vector of indices \(\{0, \dots, N-1\}\) and shuffles it.
3. Draws a random uniform offset \(u\) inside each bin and maps the resulting value to the target hyperrectangle bounds.

Constructor & Destructor Documentation

LatinHypercubeGrid()

cmp::grid::LatinHypercubeGrid::LatinHypercubeGrid ( const Eigen::Ref< const Eigen::VectorXd > &  lowerBound, const Eigen::Ref< const Eigen::VectorXd > &  upperBound, unsigned int  seed = 42  )

inline

Constructs a LatinHypercubeGrid generator.

Parameters

lowerBound	The lower bounds of the hyperrectangle.
upperBound	The upper bounds of the hyperrectangle.
seed	Seed for the random number generator.

Member Function Documentation

construct()

Eigen::MatrixXd cmp::grid::LatinHypercubeGrid::construct ( const size_t &  nPoints )

inlineoverridevirtual

Constructs a Latin Hypercube matrix of samples.

Parameters

nPoints

Number of points to generate.

Implements cmp::grid::Grid.

dim()

size_t cmp::grid::LatinHypercubeGrid::dim ( ) const

inlineoverridevirtual

Returns the dimension of the domain.

Implements cmp::grid::Grid.

Member Data Documentation

dimension_

size_t cmp::grid::LatinHypercubeGrid::dimension_

private

Number of dimensions.

lowerBound_

Eigen::VectorXd cmp::grid::LatinHypercubeGrid::lowerBound_

private

Lower bounds vector.

rng_

std::default_random_engine cmp::grid::LatinHypercubeGrid::rng_

private

Pseudo-random number generator.

upperBound_

Eigen::VectorXd cmp::grid::LatinHypercubeGrid::upperBound_

private

Upper bounds vector.

---

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

• include/grid.h