Matrix used in linear algebra. More...

#include <ql/math/matrix.hpp>

Inheritance diagram for Matrix:

Public Types
typedef Real *	iterator

typedef const Real *	const_iterator

typedef boost::reverse_iterator< iterator >	reverse_iterator

typedef boost::reverse_iterator< const_iterator >	const_reverse_iterator

typedef Real *	row_iterator

typedef const Real *	const_row_iterator

typedef boost::reverse_iterator< row_iterator >	reverse_row_iterator

typedef boost::reverse_iterator< const_row_iterator >	const_reverse_row_iterator

typedef step_iterator< iterator >	column_iterator

typedef step_iterator< const_iterator >	const_column_iterator

typedef boost::reverse_iterator< column_iterator >	reverse_column_iterator

typedef boost::reverse_iterator< const_column_iterator >	const_reverse_column_iterator

Public Member Functions
Constructors, destructor, and assignment
	Matrix ()
	creates a null matrix

	Matrix (Size rows, Size columns)
	creates a matrix with the given dimensions

	Matrix (Size rows, Size columns, Real value)
	creates the matrix and fills it with `value`

	Matrix (const Matrix &)

	Matrix (const Disposable< Matrix > &)

Matrix &	operator= (const Matrix &)

Matrix &	operator= (const Disposable< Matrix > &)

Algebraic operators
const Matrix &	operator+= (const Matrix &)

const Matrix &	operator-= (const Matrix &)

const Matrix &	*operator=** (Real)

const Matrix &	operator/= (Real)

Iterator access
const_iterator	begin () const

iterator	begin ()

const_iterator	end () const

iterator	end ()

const_reverse_iterator	rbegin () const

reverse_iterator	rbegin ()

const_reverse_iterator	rend () const

reverse_iterator	rend ()

const_row_iterator	row_begin (Size i) const

row_iterator	row_begin (Size i)

const_row_iterator	row_end (Size i) const

row_iterator	row_end (Size i)

const_reverse_row_iterator	row_rbegin (Size i) const

reverse_row_iterator	row_rbegin (Size i)

const_reverse_row_iterator	row_rend (Size i) const

reverse_row_iterator	row_rend (Size i)

const_column_iterator	column_begin (Size i) const

column_iterator	column_begin (Size i)

const_column_iterator	column_end (Size i) const

column_iterator	column_end (Size i)

const_reverse_column_iterator	column_rbegin (Size i) const

reverse_column_iterator	column_rbegin (Size i)

const_reverse_column_iterator	column_rend (Size i) const

reverse_column_iterator	column_rend (Size i)

Element access
const_row_iterator	operator[] (Size) const

const_row_iterator	at (Size) const

row_iterator	operator[] (Size)

row_iterator	at (Size)

Disposable< Array >	diagonal (void) const

Real &	operator() (Size i, Size j) const

Inspectors
Size	rows () const

Size	columns () const

bool	empty () const

Size	size1 () const

Size	size2 () const

Utilities
void	swap (Matrix &)

Related Functions
(Note that these are not member functions.)
const Disposable< Matrix >	operator+ (const Matrix &, const Matrix &)

const Disposable< Matrix >	operator- (const Matrix &, const Matrix &)

const Disposable< Matrix >	operator* (const Matrix &, Real)

const Disposable< Matrix >	operator* (Real, const Matrix &)

const Disposable< Matrix >	operator/ (const Matrix &, Real)

const Disposable< Array >	operator* (const Array &, const Matrix &)

const Disposable< Array >	operator* (const Matrix &, const Array &)

const Disposable< Matrix >	operator* (const Matrix &, const Matrix &)

const Disposable< Matrix >	transpose (const Matrix &)

const Disposable< Matrix >	outerProduct (const Array &v1, const Array &v2)

template<class Iterator1 , class Iterator2 >
const Disposable< Matrix >	outerProduct (Iterator1 v1begin, Iterator1 v1end, Iterator2 v2begin, Iterator2 v2end)

void	swap (Matrix &, Matrix &)

std::ostream &	operator<< (std::ostream &, const Matrix &)

Disposable< Matrix >	inverse (const Matrix &m)

Real	determinant (const Matrix &m)

const Disposable< Matrix >	CholeskyDecomposition (const Matrix &m, bool flexible=false)

const Disposable< Matrix >	pseudoSqrt (const Matrix &, SalvagingAlgorithm::Type=SalvagingAlgorithm::None)
	Returns the pseudo square root of a real symmetric matrix. More...

const Disposable< Matrix >	rankReducedSqrt (const Matrix &, Size maxRank, Real componentRetainedPercentage, SalvagingAlgorithm::Type)
	Returns the rank-reduced pseudo square root of a real symmetric matrix. More...

Detailed Description

Matrix used in linear algebra.

This class implements the concept of Matrix as used in linear algebra. As such, it is not meant to be used as a container.

Member Function Documentation

const Matrix & operator+= ( const Matrix & m )

Precondition: all matrices involved in an algebraic expression must have the same size.

Friends And Related Function Documentation

const Disposable< Matrix > operator+	(	const Matrix &	,
		const Matrix &
	)

const Disposable< Matrix > operator-	(	const Matrix &	,
		const Matrix &
	)

const Disposable< Matrix > operator*	(	const Matrix &	,
		Real
	)

const Disposable< Matrix > operator*	(	Real	,
		const Matrix &
	)

const Disposable< Matrix > operator/	(	const Matrix &	,
		Real
	)

const Disposable< Array > operator*	(	const Array &	,
		const Matrix &
	)

const Disposable< Array > operator*	(	const Matrix &	,
		const Array &
	)

const Disposable< Matrix > operator*	(	const Matrix &	,
		const Matrix &
	)

const Disposable< Matrix > outerProduct	(	const Array &	v1,
		const Array &	v2
	)

const Disposable< Matrix > outerProduct	(	Iterator1	v1begin,
		Iterator1	v1end,
		Iterator2	v2begin,
		Iterator2	v2end
	)

void swap	(	Matrix &	,
		Matrix &
	)

std::ostream & operator<<	(	std::ostream &	,
		const Matrix &
	)

const Disposable< Matrix > CholeskyDecomposition	(	const Matrix &	m,
		bool	flexible = `false`
	)

const Disposable< Matrix > pseudoSqrt	(	const Matrix &	,
		SalvagingAlgorithm::Type	= `SalvagingAlgorithm::None`
	)

Given a matrix \( M \), the result \( S \) is defined as the matrix such that \( S S^T = M. \) If the matrix is not positive semi definite, it can return an approximation of the pseudo square root using a (user selected) salvaging algorithm.

For more information see: R. Rebonato and P. J�ckel, The most general methodology to create a valid correlation matrix for risk management and option pricing purposes, The Journal of Risk, 2(2), Winter 1999/2000. http://www.rebonato.com/correlationmatrix.pdf

Revised and extended in "Monte Carlo Methods in Finance", by Peter J�ckel, Chapter 6.

Precondition: the given matrix must be symmetric.

Warning:: Higham algorithm only works for correlation matrices.

Tests:

the correctness of the results is tested by reproducing known good data.
the correctness of the results is tested by checking returned values against numerical calculations.

const Disposable< Matrix > rankReducedSqrt	(	const Matrix &	,
		Size	maxRank,
		Real	componentRetainedPercentage,
		SalvagingAlgorithm::Type
	)

The result matrix has rank<=maxRank. If maxRank>=size, then the specified percentage of eigenvalues out of the eigenvalues' sum is retained.

If the input matrix is not positive semi definite, it can return an approximation of the pseudo square root using a (user selected) salvaging algorithm.

Precondition: the given matrix must be symmetric.

Public Types

Public Member Functions

Related Functions

Detailed Description

Member Function Documentation

Friends And Related Function Documentation