Nilpotent< S > Class Template Reference

A class which determines the information of a nilpotent matrix. More...

#include <nilpotent.hpp>

Public Member Functions
	Nilpotent (S nbOne, S size)
	A constructor of class `Nilpotent`. More...
	Nilpotent (S nbOne, S diag, S size)
	A constructor of class `Nilpotent`. More...
	Nilpotent (std::vector< S > nilpvec, S size)
	A constructor of class `Nilpotent`. More...
	Nilpotent (std::vector< S > nilpvec, S diag, S size)
	A constructor of class `Nilpotent`. More...
	~Nilpotent ()
	A destructor of class `Nilpotent`.
S	computeDegree (std::vector< S > nilpvec)
	compute the degree of a nilpotent with its off-diagonal entries stored in a vector `nilpvec`. More...
S	getProbSize ()
	Get the size of nilpotent matrix. More...
S	getDegree ()
	Get the nilpotency of nilpotent matrix. More...
S	getOffset ()
	Get off-diagonal offset of nilpotent matrix. More...
std::vector< S >	getIndOfZeros ()
	Get indices of all zeros entries on the off-diagonal. More...
void	show ()
	Display the information of a nilpotent matrix. More...

Private Attributes
S	probSize
	size of nilpotent matrix More...
S	degree
	nilpotency of nilpotent matrix More...
S	offset
	offset of off-diagonal More...
std::vector< S >	indOfZeros
	indices of all zeros entries on the off-diagonal. More...

Detailed Description

template<typename S>
class Nilpotent< S >

A class which determines the information of a nilpotent matrix.

This class determines a special subset of nilpotent matrix, in which only one single off-diagonal on the upper-triangular part of a square matrix has non-zeros entries. These non-zeros entries are fixed to be `1`.

This types of nilpotent matrix is determined by the four variables: Nilpotent<S>::probSize, Nilpotent<S>::degree, Nilpotent<S>::offset and Nilpotent<S>::indOfZeros.

Template Parameters

S	type of integer to describes the dimension of matrices to be generated.

Member Function Documentation

getDegree()

template<typename S >

S Nilpotent< S >::getDegree ( )

inline

Get the nilpotency of nilpotent matrix.

return Nilpotent<S>::degree

getIndOfZeros()

template<typename S >

std::vector<S> Nilpotent< S >::getIndOfZeros ( )

inline

Get indices of all zeros entries on the off-diagonal.

return Nilpotent<S>::indOfZeros

getOffset()

template<typename S >

S Nilpotent< S >::getOffset ( )

inline

Get off-diagonal offset of nilpotent matrix.

return Nilpotent<S>::offset

return Nilpotent<S>::offset

getProbSize()

template<typename S >

S Nilpotent< S >::getProbSize ( )

inline

Get the size of nilpotent matrix.

return Nilpotent<S>::probSize

Member Data Documentation

degree

template<typename S >

S Nilpotent< S >::degree

private

nilpotency of nilpotent matrix

Nipotency of the determined nilpotent matrix. For a nilpotent matrix `A`, it is the minimal integer `k` which makes .

indOfZeros

template<typename S >

std::vector<S> Nilpotent< S >::indOfZeros

private

indices of all zeros entries on the off-diagonal.

Indices of all zero entries on the only off-diagonal of a nilpotent matrix

offset

template<typename S >

S Nilpotent< S >::offset

private

offset of off-diagonal

Offset of the the off-diagonal on the upper-triangular part of nilpotent matrix. It is `0`-indexed, which means that the offset of main diagonal is `0`.

• Currently, the maximum degree supported is `80`

probSize

template<typename S >

S Nilpotent< S >::probSize

private

size of nilpotent matrix

size of nilpotent matrix (square matrix with number of rows = number of columns = probSize)

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

• include/smg2s/nilpotent.hpp