Matrix< T, NumberTraits > Class Template Reference

#include <Matrix.h>

List of all members.

Public Types
typedef Matrix< T, NumberTraits >	matrix_type
	A shorthand for Matrix< T, NumberTraits >.
typedef T	number_type
	The type of the elements the matrix holds.
typedef NumberTraits	traits_type
	The AlgebraicTraits type associated to the type of matrix elements.
typedef NumberTraits::norm_type	norm_type
	A type for the norm of a matrix.
Public Member Functions
	Matrix ()
	operator const number_type *const * () const
	operator number_type ** ()
const matrix_type	zero () const
const matrix_type	one () const
unsigned int	rows () const
unsigned int	cols () const
bool	isNull () const
bool	resize (unsigned int r, unsigned int c)
void	swapRows (unsigned int i, unsigned int j)
void	swapCols (unsigned int i, unsigned int j)
void	multiplyRow (unsigned int row, const number_type &value)
void	multiplyRowAndAddToRow (unsigned int source, unsigned int dest, const number_type &value)
void	multiplyCol (unsigned int col, const number_type &value)
void	multiplyColAndAddToCol (unsigned int source, unsigned int dest, const number_type &value)
void	fill (const number_type &value)
	Matrix (unsigned int nRows, unsigned int nCols)
	Matrix (unsigned int dim)
	Matrix (const matrix_type &other)
	~Matrix ()
matrix_type &	operator= (const matrix_type &other)
number_type	determinant () const
void	getCofactor (unsigned int i, unsigned int j, matrix_type &cofactor) const
void	getMinor (const IndexSet &keep_rows, const IndexSet &keep_cols, matrix_type &minor) const
matrix_type &	transpose ()
matrix_type	operator * (const matrix_type &rhs) const
matrix_type	operator- () const
matrix_type	operator+ (const matrix_type &rhs) const
matrix_type	operator- (const matrix_type &rhs) const
matrix_type	operator/ (const matrix_type &rhs) const
matrix_type &	operator+= (const matrix_type &rhs)
matrix_type &	operator-= (const matrix_type &rhs)
matrix_type &	operator *= (const matrix_type &rhs)
matrix_type &	operator/= (const matrix_type &rhs)
bool	operator== (const matrix_type &rhs) const
bool	operator!= (const matrix_type &rhs) const
bool	operator< (const matrix_type &rhs) const
matrix_type	inverse () const
number_type	getNorm () const
number_type	getEuclideanNorm () const
void	display (std::ostream &os=std::cout) const
void	load (std::istream &is)
void	save (std::ostream &os) const
Classes
struct	Int2Type

---

Detailed Description

template<class T, class NumberTraits = AlgebraicTraits< T >>
class Matrix< T, NumberTraits >

Is represented as a pointer to an array containing pointers to arrays containing the elements of each row of the matrix, and two integers representing the number of rows and the number of columns in the matrix. The matrix class provides the following public type definitions that are used throughout the implementation of the class "Matrix"

Definition at line 30 of file Matrix.h.

---

Constructor & Destructor Documentation

template<class T, class NumberTraits = AlgebraicTraits< T >>

Matrix< T, NumberTraits >::Matrix

(

)

[inline]

Default constructor, constructs an empty matrix

Definition at line 48 of file Matrix.h.

template<class T, class NumberTraits = AlgebraicTraits< T >>

Matrix< T, NumberTraits >::Matrix	(	unsigned int	nRows,
		unsigned int	nCols
	)			[inline]

Constructor

Parameters:

	nRows	no. of matrix rows
	nCols	no. of matrix columns

Definition at line 375 of file Matrix.h.

template<class T, class NumberTraits = AlgebraicTraits< T >>

Matrix< T, NumberTraits >::Matrix

(

unsigned int

dim

)

[inline, explicit]

Constructs a square matrix

Parameters:

dim

no. of matrix rows and columns

Definition at line 384 of file Matrix.h.

template<class T, class NumberTraits = AlgebraicTraits< T >>

Matrix< T, NumberTraits >::Matrix

(

const matrix_type &

other

)

[inline]

Copy constructor

Parameters:

other

matrix to copy

Definition at line 393 of file Matrix.h.

References Matrix< T, NumberTraits >::m_nCols, and Matrix< T, NumberTraits >::m_nRows.

template<class T, class NumberTraits = AlgebraicTraits< T >>

Matrix< T, NumberTraits >::~Matrix

(

)

[inline]

Destructor

Definition at line 417 of file Matrix.h.

---

Member Function Documentation

template<class T, class NumberTraits = AlgebraicTraits< T >>

Matrix< T, NumberTraits >::operator const number_type *const *

(

)

const [inline]

Provides read-only access to the elements of the matrix in the same way as accessing a C 2 dimensional array. e.g. M[0][0]

Returns:

const pointer to an array of const pointers pointing to the rows of the matrix

Definition at line 57 of file Matrix.h.

template<class T, class NumberTraits = AlgebraicTraits< T >>

Matrix< T, NumberTraits >::operator number_type **

(

)

[inline]

Provides read-write access to the elements of the matrix in the same way as accessing a C 2 dimensional array. e.g. M[0][0]

Returns:

pointer to an array of pointers pointing to the rows of the matrix

Definition at line 67 of file Matrix.h.

template<class T, class NumberTraits = AlgebraicTraits< T >>

const matrix_type Matrix< T, NumberTraits >::zero

(

)

const [inline]

Create the zero matrix having the same dimensions as this matrix. This matrix can not be empty.

Definition at line 79 of file Matrix.h.

Referenced by Matrix< T, NumberTraits >::one().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

const matrix_type Matrix< T, NumberTraits >::one

(

)

const [inline]

Create the identity matrix having the same dimensions as this matrix. This matrix can not be empty.

Definition at line 101 of file Matrix.h.

References Matrix< T, NumberTraits >::zero().

Referenced by Matrix< T, NumberTraits >::inverse().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

unsigned int Matrix< T, NumberTraits >::rows

(

)

const [inline]

Get the count of rows of this matrix

Returns:

the number of rows this matrix has

Definition at line 129 of file Matrix.h.

Referenced by checkColumn(), checkSmithForm(), getMinimumDegreeElemIndexesInMatrix(), processColumn3(), processRow3(), recursiveSmithNormalForm3(), and smithNormalForm3().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

unsigned int Matrix< T, NumberTraits >::cols

(

)

const [inline]

Get the count of columns of this matrix

Returns:

the number of columns this matrix has

Definition at line 137 of file Matrix.h.

Referenced by checkRow(), checkSmithForm(), getMinimumDegreeElemIndexesInMatrix(), processColumn3(), processRow3(), recursiveSmithNormalForm3(), and smithNormalForm3().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

bool Matrix< T, NumberTraits >::isNull

(

)

const [inline]

Determine if this matrix is empty

Returns:

true if this is an empty matrix, and false otherwise

Definition at line 145 of file Matrix.h.

Referenced by Matrix< T, NumberTraits >::operator=().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

bool Matrix< T, NumberTraits >::resize	(	unsigned int	r,
		unsigned int	c
	)			[inline]

Resize the matrix to have the given number of rows and columns. The original data in the matrix will be lost if either the number of rows or the number of columns is increased.

Parameters:

	r	new number of rows
	c	new number of columns

Returns:

true if the function succeeded

Definition at line 247 of file Matrix.h.

Referenced by Matrix< T, NumberTraits >::getCofactor(), Matrix< T, NumberTraits >::getMinor(), and smithNormalForm3().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

void Matrix< T, NumberTraits >::swapRows	(	unsigned int	i,
		unsigned int	j
	)			[inline]

Swap two rows in this matrix.

Parameters:

	i	row to swap
	j	the other row to swap

Definition at line 272 of file Matrix.h.

Referenced by Matrix< T, NumberTraits >::inverse(), and processColumn3().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

void Matrix< T, NumberTraits >::swapCols	(	unsigned int	i,
		unsigned int	j
	)			[inline]

Swap two columns in this matrix.

Parameters:

	i	column to swap
	j	the other column to swap

Definition at line 284 of file Matrix.h.

Referenced by processRow3(), and recursiveSmithNormalForm3().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

void Matrix< T, NumberTraits >::multiplyRow	(	unsigned int	row,
		const number_type &	value
	)			[inline]

Multiply all elements of a row by a constant

Parameters:

	row	row index
	value	multiplier

Definition at line 298 of file Matrix.h.

template<class T, class NumberTraits = AlgebraicTraits< T >>

void Matrix< T, NumberTraits >::multiplyRowAndAddToRow	(	unsigned int	source,
		unsigned int	dest,
		const number_type &	value
	)			[inline]

Multiply all elements of a row by a constant and add to another row

Parameters:

	source	source row index
	dest	destination row index
	value	multiplier

Definition at line 311 of file Matrix.h.

template<class T, class NumberTraits = AlgebraicTraits< T >>

void Matrix< T, NumberTraits >::multiplyCol	(	unsigned int	col,
		const number_type &	value
	)			[inline]

Multiply all elements of a column by a constant

Parameters:

	col	column index
	value	multiplier

Definition at line 329 of file Matrix.h.

template<class T, class NumberTraits = AlgebraicTraits< T >>

void Matrix< T, NumberTraits >::multiplyColAndAddToCol	(	unsigned int	source,
		unsigned int	dest,
		const number_type &	value
	)			[inline]

Multiply all elements of a column by a constant and add to another column

Parameters:

	source	source column index
	dest	destination column index
	value	multiplier

Definition at line 342 of file Matrix.h.

Referenced by recursiveSmithNormalForm3().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

void Matrix< T, NumberTraits >::fill

(

const number_type &

value

)

[inline]

Set all elements of this matrix to the given value

Parameters:

value

value to set all matrix elements

Definition at line 362 of file Matrix.h.

Referenced by smithNormalForm3().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

matrix_type& Matrix< T, NumberTraits >::operator=

(

const matrix_type &

other

)

[inline]

Assignment operator.

If the matrices don't have the same dimensions it's probably a user mistake so the function report an error and return this matrix unchanged. If this matrix is null it allocates memory and copies source matrix

Parameters:

other

matrix to copy

Returns:

reference to this matrix

Definition at line 431 of file Matrix.h.

References Matrix< T, NumberTraits >::isNull(), Matrix< T, NumberTraits >::m_nCols, and Matrix< T, NumberTraits >::m_nRows.

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template<class T, class NumberTraits = AlgebraicTraits< T >>

number_type Matrix< T, NumberTraits >::determinant

(

)

const [inline]

Computes the determinant of this matrix

Returns:

The value of the determinant

Remarks:

If the matrix elements are from a field algebraic structure it uses Gaussian elimination to compute the determinant, complexity = O(n^3). Else it uses laplace minors (cofactors). It is used with rings (algebraic structures where usually elements don't have a reciprocal with regard to the * operation e.g. the ring of polynomials with real coefficients). This is highly inefficient complexity = O(n!)

Definition at line 485 of file Matrix.h.

template<class T, class NumberTraits = AlgebraicTraits< T >>

void Matrix< T, NumberTraits >::getCofactor	(	unsigned int	i,
		unsigned int	j,
		matrix_type &	cofactor
	)			const [inline]

Computes a cofactor for this matrix by removing line i and col j

Parameters:

	i	the line no. we remove from this matrix
	j	the column no. we remove from this matrix
	cofactor	a reference to the matrix that will contain the cofactor

Definition at line 627 of file Matrix.h.

References Matrix< T, NumberTraits >::resize().

Referenced by recursiveSmithNormalForm3().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

void Matrix< T, NumberTraits >::getMinor	(	const IndexSet &	keep_rows,
		const IndexSet &	keep_cols,
		matrix_type &	minor
	)			const [inline]

Computes a minor for this matrix

Minors are always square matrices so keep_rows and keep_cols must contain the same number of indexes

Parameters:

	keep_rows	a set of row indexes to keep
	keep_cols	a set of column indexes to keep
	minor	a reference to the matrix that will contain the minor

Definition at line 667 of file Matrix.h.

References IndexSet::find(), Matrix< T, NumberTraits >::m_nCols, Matrix< T, NumberTraits >::m_nRows, Matrix< T, NumberTraits >::resize(), and IndexSet::size().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

matrix_type& Matrix< T, NumberTraits >::transpose

(

)

[inline]

Transposes this matrix.Replaces element [i][j] with element [j][i]

Returns:

A refference to this matrix.

Remarks:

If the matrix is not square the matrix dimmensions will change after this operation

Definition at line 784 of file Matrix.h.

template<class T, class NumberTraits = AlgebraicTraits< T >>

matrix_type Matrix< T, NumberTraits >::operator *

(

const matrix_type &

rhs

)

const [inline]

Matrix multiplication.

Complexity = O(n^3)

Parameters:

rhs

right hand side matrix

Returns:

the result of the multiplication

Definition at line 826 of file Matrix.h.

References Matrix< T, NumberTraits >::m_nCols, and Matrix< T, NumberTraits >::m_nRows.

template<class T, class NumberTraits = AlgebraicTraits< T >>

matrix_type Matrix< T, NumberTraits >::operator-

(

)

const [inline]

Unary minus

Returns:

zero minus this matrix

Definition at line 861 of file Matrix.h.

References Matrix< T, NumberTraits >::m_nCols, and Matrix< T, NumberTraits >::m_nRows.

template<class T, class NumberTraits = AlgebraicTraits< T >>

matrix_type Matrix< T, NumberTraits >::operator+

(

const matrix_type &

rhs

)

const [inline]

Matrix addition

Matrices must have the same number of rows and columns to perform addition

Parameters:

rhs

right hand side matrix

Returns:

the result of the addition

Definition at line 882 of file Matrix.h.

References Matrix< T, NumberTraits >::m_nCols, and Matrix< T, NumberTraits >::m_nRows.

template<class T, class NumberTraits = AlgebraicTraits< T >>

matrix_type Matrix< T, NumberTraits >::operator-

(

const matrix_type &

rhs

)

const [inline]

Matrix subtraction

Matrices must have the same number of rows and columns to perform subtraction

Parameters:

rhs

right hand side matrix

Returns:

the result of the subtraction

Definition at line 912 of file Matrix.h.

References Matrix< T, NumberTraits >::m_nCols, and Matrix< T, NumberTraits >::m_nRows.

template<class T, class NumberTraits = AlgebraicTraits< T >>

matrix_type Matrix< T, NumberTraits >::operator/

(

const matrix_type &

rhs

)

const [inline]

Matrix division

Matrices must have the same number of rows and columns to perform division. If the right hand side matrix is not inversable an exception is thrown

Parameters:

rhs

right hand side matrix

Returns:

the result of the addition

Definition at line 941 of file Matrix.h.

References Matrix< T, NumberTraits >::inverse(), Matrix< T, NumberTraits >::m_nCols, and Matrix< T, NumberTraits >::m_nRows.

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template<class T, class NumberTraits = AlgebraicTraits< T >>

matrix_type& Matrix< T, NumberTraits >::operator+=

(

const matrix_type &

rhs

)

[inline]

Addition assignment

Matrices must have the same number of rows and columns to perform addition.

Parameters:

rhs

right hand side matrix

Returns:

refference to the result of the addition

Definition at line 960 of file Matrix.h.

References Matrix< T, NumberTraits >::m_nCols, and Matrix< T, NumberTraits >::m_nRows.

template<class T, class NumberTraits = AlgebraicTraits< T >>

matrix_type& Matrix< T, NumberTraits >::operator-=

(

const matrix_type &

rhs

)

[inline]

Subtraction assignment

Matrices must have the same number of rows and columns to perform subtraction.

Parameters:

rhs

right hand side matrix

Returns:

refference to the result of the subtraction

Definition at line 986 of file Matrix.h.

References Matrix< T, NumberTraits >::m_nCols, and Matrix< T, NumberTraits >::m_nRows.

template<class T, class NumberTraits = AlgebraicTraits< T >>

matrix_type& Matrix< T, NumberTraits >::operator *=

(

const matrix_type &

rhs

)

[inline]

Multiplication assignment

Matrices should be compatible to perform multiplication i.e. the number of columns of the first matrix should be equal to the number of rows of the second matrix.

Parameters:

rhs

right hand side matrix

Returns:

refference to the result of the multiplication

Definition at line 1014 of file Matrix.h.

References Matrix< T, NumberTraits >::m_nRows.

template<class T, class NumberTraits = AlgebraicTraits< T >>

matrix_type& Matrix< T, NumberTraits >::operator/=

(

const matrix_type &

rhs

)

[inline]

Division assignment

Matrices should be square and have the same dimensions. If the second matrix is not inversable an exception is thrown.

Parameters:

rhs

right hand side matrix

Returns:

refference to the result of the division

Definition at line 1034 of file Matrix.h.

References Matrix< T, NumberTraits >::m_nCols, and Matrix< T, NumberTraits >::m_nRows.

template<class T, class NumberTraits = AlgebraicTraits< T >>

bool Matrix< T, NumberTraits >::operator==

(

const matrix_type &

rhs

)

const [inline]

Equality operator

Matrices should have the same number of columns and rows.

Parameters:

rhs

right hand side matrix

Returns:

true if matrices are equal, false otherwise

Definition at line 1055 of file Matrix.h.

References Matrix< T, NumberTraits >::m_nCols, and Matrix< T, NumberTraits >::m_nRows.

Referenced by Matrix< T, NumberTraits >::operator!=().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

bool Matrix< T, NumberTraits >::operator!=

(

const matrix_type &

rhs

)

const [inline]

Inequality operator

Matrices should have the same number of columns and rows.

Parameters:

rhs

right hand side matrix

Returns:

true if matrices are different, false otherwise

Definition at line 1083 of file Matrix.h.

References Matrix< T, NumberTraits >::operator==().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

bool Matrix< T, NumberTraits >::operator<

(

const matrix_type &

rhs

)

const [inline]

Comparison operator

This function merely compares the norms of the matrices.

Parameters:

rhs

right hand side matrix

Returns:

true if the norm of this matrix is less than the norm of the other matrix

Definition at line 1096 of file Matrix.h.

References Matrix< T, NumberTraits >::getNorm(), and Matrix< T, NumberTraits >::m_nRows.

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template<class T, class NumberTraits = AlgebraicTraits< T >>

matrix_type Matrix< T, NumberTraits >::inverse

(

)

const [inline]

Compute the inverse of this matrix

Algorithm uses the relation obtained through elementary transformations) between the composed matrices [A:I] and [I:A^-1]. Complexity = O(n^3). This matrix must be a square matrix. If this matrix is not inversable an exception is thrown

Returns:

the inverse of this matrix

Definition at line 1114 of file Matrix.h.

References Matrix< T, NumberTraits >::m_nCols, Matrix< T, NumberTraits >::m_nRows, Matrix< T, NumberTraits >::one(), Matrix< T, NumberTraits >::swapRows(), and AlgebraicTraits< T >::zero().

Referenced by Matrix< T, NumberTraits >::operator/().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

number_type Matrix< T, NumberTraits >::getNorm

(

)

const [inline]

Compute the euclidean norm of this matrix

Returns:

the value of the norm

Definition at line 1234 of file Matrix.h.

Referenced by Matrix< T, NumberTraits >::operator<().

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template<class T, class NumberTraits = AlgebraicTraits< T >>

number_type Matrix< T, NumberTraits >::getEuclideanNorm

(

)

const [inline]

Compute the euclidean norm of this matrix

Returns:

the value of the norm

Definition at line 1248 of file Matrix.h.

template<class T, class NumberTraits = AlgebraicTraits< T >>

void Matrix< T, NumberTraits >::display

(

std::ostream &

os = std::cout

)

const [inline]

Display this matrix to a stream

Parameters:

os

stream to display this matrix

Definition at line 1283 of file Matrix.h.

template<class T, class NumberTraits = AlgebraicTraits< T >>

void Matrix< T, NumberTraits >::load

(

std::istream &

is

)

[inline]

Load this from a stream

Parameters:

is

stream to load from

Definition at line 1298 of file Matrix.h.

template<class T, class NumberTraits = AlgebraicTraits< T >>

void Matrix< T, NumberTraits >::save

(

std::ostream &

os

)

const [inline]

Save this to a stream

Parameters:

os

stream to save to

Definition at line 1320 of file Matrix.h.

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

• Matrix.h

---