cmp::grid::ScrambledSobolGrid Class Reference

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

#include <grid.h>

Inheritance diagram for cmp::grid::ScrambledSobolGrid:

Collaboration diagram for cmp::grid::ScrambledSobolGrid:

Public Member Functions
	ScrambledSobolGrid (const Eigen::Ref< const Eigen::VectorXd > &lowerBound, const Eigen::Ref< const Eigen::VectorXd > &upperBound, unsigned int seed=42)
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

Static Private Member Functions
static uint64_t	hash_prefix (uint64_t prefix, uint64_t seed)
static uint64_t	owen_scramble (uint64_t val, uint64_t seed)

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.
std::vector< uint64_t >	dim_seeds_
	Seeds used to initialize scrambling for each coordinate dimension.

Detailed Description

Owen-scrambled Sobol low-discrepancy sequence grid generator.

Mathematical Formulation Owen scrambling randomized digital nets by applying random permutations on the digital trees. It preserves the low-discrepancy property:

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

while providing unbiased estimates and improving the numerical integration variance rate to \(o(N^{-1})\).

Implementation Algorithm

1. Obtains Sobol sequences from the underlying Boost generator.
2. Maps values to 64-bit unsigned integers representing fractional components.
3. Applies a recursive bitwise Owen scrambled hash permutation using the prefix history.
4. Maps the scrambled values back to floating point space and scales them to the boundaries.

Constructor & Destructor Documentation

ScrambledSobolGrid()

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

inline

Member Function Documentation

construct()

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

inlineoverridevirtual

Implements cmp::grid::Grid.

dim()

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

inlineoverridevirtual

Implements cmp::grid::Grid.

hash_prefix()

static uint64_t cmp::grid::ScrambledSobolGrid::hash_prefix ( uint64_t  prefix, uint64_t  seed  )

inlinestaticprivate

operator()()

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

inline

owen_scramble()

static uint64_t cmp::grid::ScrambledSobolGrid::owen_scramble ( uint64_t  val, uint64_t  seed  )

inlinestaticprivate

Member Data Documentation

dim_seeds_

std::vector<uint64_t> cmp::grid::ScrambledSobolGrid::dim_seeds_

private

Seeds used to initialize scrambling for each coordinate dimension.

dimension_

size_t cmp::grid::ScrambledSobolGrid::dimension_

private

Number of dimensions.

gen_

boost::random::sobol cmp::grid::ScrambledSobolGrid::gen_

private

Boost Sobol sequence generator.

lowerBound_

Eigen::VectorXd cmp::grid::ScrambledSobolGrid::lowerBound_

private

Lower bounds vector.

upperBound_

Eigen::VectorXd cmp::grid::ScrambledSobolGrid::upperBound_

private

Upper bounds vector.

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

• include/grid.h