This class implements a generating matrix of a digital net in base 2. More...

#include <GeneratingMatrix.h>

Public Types
typedef boost::dynamic_bitset	Row
	Type for the rows of the matrices.
typedef Row::reference	reference
	Type for references to rows.
typedef unsigned long	uInteger
	Type for unsigned long.

Public Member Functions
	GeneratingMatrix (unsigned int nRows=0, unsigned int nCols=0)
	Constructs a generating matrix with all entries set to zero.
	GeneratingMatrix (unsigned int nRows, unsigned int nCols, std::vector< uInteger > init)
	Constructs a generating matrix with rows initialized using the given integers.
unsigned int	nCols () const
	Returns the number of columns of the matrix.
unsigned int	nRows () const
	Returns the number of rows of the matrix.
void	resize (unsigned int nRows, unsigned int nCols)
	Resizes the matrix to the given shape.
bool	operator() (unsigned int i, unsigned j) const
	Returns the element at position `i`, `j` of the matrix.
reference	operator() (unsigned int i, unsigned int j)
	Returns a reference to the element at position `i`, `j` of the matrix.
void	flip (unsigned int i, unsigned int j)
	Flip the element at at position `i`, `j` of the matrix.
Row	operator[] (unsigned int i) const
	Returns the row at position `i` of the matrix.
Row &	operator[] (unsigned int i)
	Returns a reference to the row at position `i` of the matrix.
GeneratingMatrix	upperLeftSubMatrix (unsigned int nRows, unsigned int nCols) const
	Returns the upper-left submatrix with `nRows` rows and `nCols` columns.
GeneratingMatrix	subMatrix (unsigned int startingRow, unsigned int startingCol, unsigned nRows, unsigned nCols) const
	Returns the submatrix with upper-left corner at position `startingRow`, `startingCol` with `nRows` rows and `nCols` columns.
GeneratingMatrix	operator* (const GeneratingMatrix &m) const
	Computes the product of the matrix by matrix `m`.
void	swapRows (unsigned int i1, unsigned int i2)
	Swap the rows at position i1 and i2 of the matrix.
void	stackRight (const GeneratingMatrix &block)
	Extends the matrix by stacking on the right the matrix `block`.
void	stackBelow (GeneratingMatrix block)
	Extends the matrix by stacking below the matrix `block`.
std::string	formatToColumnsReverse (unsigned int nBits=31) const
std::vector< unsigned long >	getColsReverse () const
	Returns an integer representation of the columns of the matrix.

Static Public Member Functions
static GeneratingMatrix	fromColsReverse (unsigned int nInputBits, unsigned int nOutputRows, std::vector< unsigned long > columns)
	Creates a matrix from its reversed column representation.
template<typename RAND>
static GeneratingMatrix	createRandomLowerTriangularMatrix (unsigned int nRows, unsigned int nCols, RAND &randomGen)
	Creates a matrix with ones on the main diagonal, random bits below the main diagonal, and zeros above.

Friends
std::ostream &	operator<< (std::ostream &os, const GeneratingMatrix &mat)
	Overloads of << operator to print matrices.

Detailed Description

This class implements a generating matrix of a digital net in base 2.

Internally, a matrix is represented as a std::vector of rows implemented by boost::dynamic_bitset. This internal representation allows to work with arbitrarly large matrices. The choice of representing the matrix by its rows and not its columns comes from the rank computation algorithm, which is the most complicated algorithm handling matrices in the software. For this algorithm, it is more convenient to handle matrices by rows.

For now, we did not implement an algorithm to compute directly the points generated by a given matrix. However, the Stride associated with a matrix, i.e. the permutation of \({i/n, 0 <= i <= n}\), is computed in latbuilder/Storage-SIMPLE-DIGITAL.h. For more information, see Section 4.3.2 of Maxime’s report (https://github.com/umontreal-simul/latnetbuilder/blob/dev/reports/report_godin.pdf), and the documentation of netbuilder/DigitalNet.n.

Constructor & Destructor Documentation

◆ GeneratingMatrix() [1/2]

NetBuilder::GeneratingMatrix::GeneratingMatrix	(	unsigned int	nRows = 0,
		unsigned int	nCols = 0 )

Constructs a generating matrix with all entries set to zero.

Parameters

nRows	Number of rows.
nCols	Number of columns.

References nCols(), and nRows().

Referenced by createRandomLowerTriangularMatrix(), fromColsReverse(), operator*(), operator<<, stackBelow(), stackRight(), subMatrix(), and upperLeftSubMatrix().

◆ GeneratingMatrix() [2/2]

NetBuilder::GeneratingMatrix::GeneratingMatrix	(	unsigned int	nRows,
		unsigned int	nCols,
		std::vector< uInteger >	init )

Constructs a generating matrix with rows initialized using the given integers.

The elements of a row are the binary digits of the corresponding integer, with the least significant bit on the left.

Parameters

nRows	Number of rows.
nCols	Number of columns.
init	Vector of uInteger of length nRows

References nCols(), and nRows().

Member Function Documentation

◆ createRandomLowerTriangularMatrix()

template<typename RAND>

GeneratingMatrix NetBuilder::GeneratingMatrix::createRandomLowerTriangularMatrix	(	unsigned int	nRows,
		unsigned int	nCols,
		RAND &	randomGen )

inlinestatic

Creates a matrix with ones on the main diagonal, random bits below the main diagonal, and zeros above.

This is done by sampling one unsigned long integer for each row, so it works only if the number of columns is smaller than the number of bits of an unsigned long (usually 32).

Parameters

nRows	Number of rows of the matrix.
nCols	Number of columns of the matrix.
randomGen	Random Number Generator. By default it is the LFSR258 generator by L'Ecuyer [18].

References GeneratingMatrix(), nCols(), and nRows().

◆ flip()

void NetBuilder::GeneratingMatrix::flip	(	unsigned int	i,
		unsigned int	j )

Flip the element at at position i, j of the matrix.

Parameters

i	Row index.
j	Column index.

◆ fromColsReverse()

GeneratingMatrix NetBuilder::GeneratingMatrix::fromColsReverse	(	unsigned int	nInputBits,
		unsigned int	nOutputRows,
		std::vector< unsigned long >	columns )

static

Creates a matrix from its reversed column representation.

Parameters

nInputRows	Number of bits in the integer representation of the columns. Typically equals 31.
nOutputRows	Number of rows of the matrix returned by the function. Rows below are ignored. Typically equals the number of columns.
columns	Integer representation of the columns of the matrix.

References GeneratingMatrix().

◆ getColsReverse()

std::vector< unsigned long > NetBuilder::GeneratingMatrix::getColsReverse ( ) const

Returns an integer representation of the columns of the matrix.

A column is read as a bit string with highest bit in first position. This function is used to generate the points from the digital net.

◆ operator()() [1/2]

reference NetBuilder::GeneratingMatrix::operator()	(	unsigned int	i,
		unsigned int	j )

Returns a reference to the element at position i, j of the matrix.

Parameters

i	Row index.
j	Column index.

◆ operator()() [2/2]

bool NetBuilder::GeneratingMatrix::operator()	(	unsigned int	i,
		unsigned	j ) const

Returns the element at position i, j of the matrix.

Parameters

i	Row index.
j	Column index.

◆ operator*()

GeneratingMatrix NetBuilder::GeneratingMatrix::operator* ( const GeneratingMatrix & m ) const

Computes the product of the matrix by matrix m.

Parameters

m	Right multiplier.

References GeneratingMatrix().

◆ operator[]() [1/2]

Row & NetBuilder::GeneratingMatrix::operator[] ( unsigned int i )

Returns a reference to the row at position i of the matrix.

Parameters

i	Position of the row.

◆ operator[]() [2/2]

Row NetBuilder::GeneratingMatrix::operator[] ( unsigned int i ) const

Returns the row at position i of the matrix.

Parameters

i	Position of the row.

◆ resize()

void NetBuilder::GeneratingMatrix::resize	(	unsigned int	nRows,
		unsigned int	nCols )

Resizes the matrix to the given shape.

Potential new elements are set to zero.

Parameters

nRows	is the new number of rows of the matrix
nCols	is the new number of columns of the matrix

References nCols(), and nRows().

◆ stackBelow()

void NetBuilder::GeneratingMatrix::stackBelow ( GeneratingMatrix block )

Extends the matrix by stacking below the matrix block.

Parameters

block The matrix to stack. Should have the same number of columns as the base matrix.

References GeneratingMatrix().

◆ stackRight()

void NetBuilder::GeneratingMatrix::stackRight ( const GeneratingMatrix & block )

Extends the matrix by stacking on the right the matrix block.

Parameters

block The matrix to stack. Should have the same number of rows as the base matrix.

References GeneratingMatrix().

◆ subMatrix()

GeneratingMatrix NetBuilder::GeneratingMatrix::subMatrix	(	unsigned int	startingRow,
		unsigned int	startingCol,
		unsigned	nRows,
		unsigned	nCols ) const

Returns the submatrix with upper-left corner at position startingRow, startingCol with nRows rows and nCols columns.

Parameters

startingRow	Row position of the upper-left corner.
startingCol	Column position of the upper-left corner.
nRows	Number of rows.
nCols	Number of columns.

Returns: A copy of the submatrix.

References GeneratingMatrix(), nCols(), and nRows().

Referenced by NetBuilder::FigureOfMerit::ResolutionGapProjMerit< EmbeddingType::MULTILEVEL >::operator()(), and NetBuilder::FigureOfMerit::ResolutionGapProjMerit< EmbeddingType::UNILEVEL >::operator()().

◆ swapRows()

void NetBuilder::GeneratingMatrix::swapRows	(	unsigned int	i1,
		unsigned int	i2 )

Swap the rows at position i1 and i2 of the matrix.

Parameters

i1	Position of the first row.
i2	Position of the second row.

◆ upperLeftSubMatrix()

GeneratingMatrix NetBuilder::GeneratingMatrix::upperLeftSubMatrix	(	unsigned int	nRows,
		unsigned int	nCols ) const

Returns the upper-left submatrix with nRows rows and nCols columns.

Parameters

nRows	Number of rows.
nCols	Number of columns.

Returns: A copy of the submatrix.

References GeneratingMatrix(), nCols(), and nRows().

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

include/netbuilder/GeneratingMatrix.h

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ GeneratingMatrix() [1/2]

◆ GeneratingMatrix() [2/2]

Member Function Documentation

◆ createRandomLowerTriangularMatrix()

◆ flip()

◆ fromColsReverse()

◆ getColsReverse()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ resize()

◆ stackBelow()

◆ stackRight()

◆ subMatrix()

◆ swapRows()

◆ upperLeftSubMatrix()