The Smith Normal Form and its coefficient matrices. More...

#include <Smith.hpp>

Inheritance diagram for SmithNormalForm< _S, _R, _C >:

Collaboration diagram for SmithNormalForm< _S, _R, _C >:

Public Member Functions
	SmithNormalForm (const _S &S, bool do_P=1, bool do_Q=1, bool do_sort=1, bool do_verify=0)
	Constructor computes the Smith Normal Form. More...

Public Attributes
row_vector_t< _S >	diagonal
	The diagonal of the Smith normal form. More...

_R	P
	One of the coefficient matrices (S=PAQ) More...

_R	Qi
	One of the coefficient matrices (A=PiSQi) More...

_C	Q
	One of the coefficient matrices (S=PAQ) More...

_C	Pi
	One of the coefficient matrices (A=PiSQi) More...

Detailed Description

template<typename _S, typename _R, typename _C>
struct mackey::SmithNormalForm< _S, _R, _C >

The Smith Normal Form and its coefficient matrices.

The SNF of \(A\) is a diagonal matrix \(S\) and invertible coefficient matrices \(P,Q\) s.t. \(PAQ=S\)
S is stored as a diagonal vector diagonal. In addition to P,Q we also store their inverses Pi,Qi.
All are computed simultaneously through row-column elimination

Template Parameters

_S	The type of the original matrix.
_R	Row major version of `_S`
_C	Column major version of `_S`

Constructor & Destructor Documentation

◆ SmithNormalForm()

SmithNormalForm	(	const _S &	S,
		bool	do_P = `1`,
		bool	do_Q = `1`,
		bool	do_sort = `1`,
		bool	do_verify = `0`
	)

Constructor computes the Smith Normal Form.

Parameters

S	The given matrix to diagonalize
do_P	Set to 1 if P,Pi are wanted
do_Q	Set to 1 if Q,Qi are wanted
do_sort	Set to 1 if we want the diagonal of the SNF to be ordered and increasing, excluding any units
do_verify	Set to 1 to verify the SNF was computed correctly (for debugging).