cmp::grid::SobolGrid Class Reference

Sobol low-discrepancy sequence grid generator. More...

#include <grid.h>

Inheritance diagram for cmp::grid::SobolGrid:

Collaboration diagram for cmp::grid::SobolGrid:

Public Member Functions
	SobolGrid (const Eigen::Ref< const Eigen::VectorXd > &lowerBound, const Eigen::Ref< const Eigen::VectorXd > &upperBound)
Eigen::MatrixXd	construct (const size_t &nPoints) override
Eigen::VectorXd	operator() ()
size_t	dim () const override
Public Member Functions inherited from cmp::grid::Grid
virtual	~Grid ()=default

Private Attributes
boost::random::sobol	gen_
	Boost Sobol sequence generator.
size_t	dimension_
	Number of dimensions.
Eigen::VectorXd	lowerBound_
	Lower bounds vector.
Eigen::VectorXd	upperBound_
	Upper bounds vector.

Detailed Description

Sobol low-discrepancy sequence grid generator.

Mathematical Formulation Generates points using the quasi-random Sobol sequence to minimize star discrepancy:

\[ D_N^*(\mathcal{P}) = O\left( \frac{\log^D N}{N} \right) \]

ensuring faster convergence of multi-dimensional integrals compared to standard Monte Carlo.

Implementation Algorithm

1. Invokes Boost's Sobol generator.
2. Multiplies generated uniform fractions by dimension bounds \([a_d, b_d]\).
3. Shuffles output coordinates to break spatial correlations in short prefixes.

Constructor & Destructor Documentation

SobolGrid()

cmp::grid::SobolGrid::SobolGrid ( const Eigen::Ref< const Eigen::VectorXd > &  lowerBound, const Eigen::Ref< const Eigen::VectorXd > &  upperBound  )

inline

Member Function Documentation

construct()

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

inlineoverridevirtual

Implements cmp::grid::Grid.

dim()

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

inlineoverridevirtual

Implements cmp::grid::Grid.

operator()()

Eigen::VectorXd cmp::grid::SobolGrid::operator() ( )

inline

Member Data Documentation

dimension_

size_t cmp::grid::SobolGrid::dimension_

private

Number of dimensions.

gen_

boost::random::sobol cmp::grid::SobolGrid::gen_

private

Boost Sobol sequence generator.

lowerBound_

Eigen::VectorXd cmp::grid::SobolGrid::lowerBound_

private

Lower bounds vector.

upperBound_

Eigen::VectorXd cmp::grid::SobolGrid::upperBound_

private

Upper bounds vector.

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

• include/grid.h