Nilpotent

This module relates to the nilpotent matrix used by SMG2S. More...

Classes
class	Nilpotent< S >
	A class which determines the information of a nilpotent matrix. More...

Functions
	Nilpotent< S >::Nilpotent (S nbOne, S size)
	A constructor of class `Nilpotent`. More...
	Nilpotent< S >::Nilpotent (S nbOne, S diag, S size)
	A constructor of class `Nilpotent`. More...
	Nilpotent< S >::Nilpotent (std::vector< S > nilpvec, S size)
	A constructor of class `Nilpotent`. More...
	Nilpotent< S >::Nilpotent (std::vector< S > nilpvec, S diag, S size)
	A constructor of class `Nilpotent`. More...
S	Nilpotent< S >::computeDegree (std::vector< S > nilpvec)
	compute the degree of a nilpotent with its off-diagonal entries stored in a vector `nilpvec`. More...
void	Nilpotent< S >::show ()
	Display the information of a nilpotent matrix. More...
	Nilpotent< S >::~Nilpotent ()
	A destructor of class `Nilpotent`.

Detailed Description

This module relates to the nilpotent matrix used by SMG2S.

Function Documentation

computeDegree()

template<typename S >

S Nilpotent< S >::computeDegree

(

std::vector< S >

nilpvec

)

compute the degree of a nilpotent with its off-diagonal entries stored in a vector `nilpvec`.

This is a member function of class `Nilpotent`, which computes the degree of a nilpotent with its off-diagonal entries stored in a vector `nilpvec`.

• Attention, the size of nilpotent matrix and the offset of diagonal should already be provided.

Parameters

[in]

nilpvec

user provided vector

Nilpotent() [1/4]

template<typename S >

Nilpotent< S >::Nilpotent	(	S	nbOne,
		S	diag,
		S	size
	)

A constructor of class `Nilpotent`.

This is a constructor of class `Nilpotent`. With this constructor, the nilpotent has single off-diagonal with index `diag`. On this diagonal, the entries starts with a number `k` of continuous `1`, in which `k` is randomly generated as an integer between `0` and `nbOne`. Then a new `k` is re-generated, for a continuous `k` of zero-entries.

In this pattern, the nilpotency is not trivial and it can be computed by Nilpotent<S>::computeDegree.

• Currently, the maximum degree supported is `80`, there's risk that SMG2S fails with

Parameters

[in]	nbOne	determines the maximum lengths of continous `1` and `0` on the off-diagonal. The lengths are randomly generated between `0` and `nbOne`, step by step.
[in]	diag	offset of the single off-diagonal of nilpotent matrix
[in]	size	size of nilpotent matrix

Nilpotent() [2/4]

template<typename S >

Nilpotent< S >::Nilpotent	(	S	nbOne,
		S	size
	)

A constructor of class `Nilpotent`.

This is a constructor of class `Nilpotent`. With this constructor, the nilpotent has single off-diagonal with index `1`. On this diagonal, the entries starts with `nbOne` number of continuous `1`, then one single entry to be `0`, then `nbOne` number of continuous `1`. The pattern repeats until to the end.

In this pattern, the nilpotency is easy to be determined as .

• Currently, the maximum degree supported is `80`, there's risk that SMG2S fails with

Parameters

[in]	nbOne	number of continuous `1` on the single off-diagonal
[in]	size	size of nilpotent matrix

Nilpotent() [3/4]

template<typename S >

Nilpotent< S >::Nilpotent	(	std::vector< S >	nilpvec,
		S	diag,
		S	size
	)

A constructor of class `Nilpotent`.

This is a constructor of class `Nilpotent`. It determines a nilpotent with user provided vector `nilpvec`, and set it onto the off-diagonal indexing `diag`.

In this pattern, the nilpotency is not trivial and it can be computed by Nilpotent<S>::computeDegree.

• Currently, the maximum degree supported is `80`, there's risk that SMG2S fails with user-given `nilpvec`.

Parameters

[in]	nilpvec	user provided vector
[in]	diag	offset of the single off-diagonal of nilpotent matrix
[in]	size	size of nilpotent matrix

Nilpotent() [4/4]

template<typename S >

Nilpotent< S >::Nilpotent	(	std::vector< S >	nilpvec,
		S	size
	)

A constructor of class `Nilpotent`.

This is a constructor of class `Nilpotent`. It determines a nilpotent with user provided vector `nilpvec`, and set it onto the off-diagonal indexing `1`.

In this pattern, the nilpotency is not trivial and it can be computed by Nilpotent<S>::computeDegree.

• Currently, the maximum degree supported is `80`, there's risk that SMG2S fails with user-given `nilpvec`.

Parameters

[in]	nilpvec	user provided vector
[in]	size	size of nilpotent matrix

show()

template<typename S >

void Nilpotent< S >::show

Display the information of a nilpotent matrix.

print Nilpotent<S>::probSize, Nilpotent<S>::degree, Nilpotent<S>::offset, and Nilpotent<S>::indOfZeros