QuantLib: Matrix Class Reference

Matrix used in linear algebra. More...

#include <ql/math/matrix.hpp>

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
template<class Iterator>
	Matrix (Size rows, Size columns, Iterator begin, Iterator end)
	creates the matrix and fills it with data from a range.
	Matrix (const Matrix &)
	Matrix (Matrix &&) noexcept
	Matrix (std::initializer_list< std::initializer_list< Real > >)
Matrix &	operator= (const Matrix &)
Matrix &	operator= (Matrix &&) noexcept
bool	operator== (const Matrix &) const
bool	operator!= (const Matrix &) const
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)
Array	diagonal () const
Real &	operator() (Size i, Size j) const
Inspectors
Size	rows () const
Size	columns () const
bool	empty () const
Size	size1 () const
Size	size2 () const

Related Symbols
(Note that these are not member symbols.)
Matrix	operator+ (const Matrix &, const Matrix &)
Matrix	operator+ (const Matrix &, Matrix &&)
Matrix	operator+ (Matrix &&, const Matrix &)
Matrix	operator+ (Matrix &&, Matrix &&)
Matrix	operator- (const Matrix &)
Matrix	operator- (Matrix &&)
Matrix	operator- (const Matrix &, const Matrix &)
Matrix	operator- (const Matrix &, Matrix &&)
Matrix	operator- (Matrix &&, const Matrix &)
Matrix	operator- (Matrix &&, Matrix &&)
Matrix	operator* (const Matrix &, Real)
Matrix	operator* (Matrix &&, Real)
Matrix	operator* (Real, const Matrix &)
Matrix	operator* (Real, Matrix &&)
Matrix	operator/ (const Matrix &, Real)
Matrix	operator/ (Matrix &&, Real)
Array	operator* (const Array &, const Matrix &)
Array	operator* (const Matrix &, const Array &)
Matrix	operator* (const Matrix &, const Matrix &)
Matrix	transpose (const Matrix &)
Matrix	outerProduct (const Array &v1, const Array &v2)
template<class Iterator1, class Iterator2>
Matrix	outerProduct (Iterator1 v1begin, Iterator1 v1end, Iterator2 v2begin, Iterator2 v2end)
void	swap (Matrix &, Matrix &) noexcept
std::ostream &	operator<< (std::ostream &, const Matrix &)
Matrix	inverse (const Matrix &m)
Real	determinant (const Matrix &m)
Matrix	CholeskyDecomposition (const Matrix &m, bool flexible=false)
Matrix	pseudoSqrt (const Matrix &, SalvagingAlgorithm::Type=SalvagingAlgorithm::None)
	Returns the pseudo square root of a real symmetric matrix.
Matrix	rankReducedSqrt (const Matrix &, Size maxRank, Real componentRetainedPercentage, SalvagingAlgorithm::Type)
	Returns the rank-reduced pseudo square root of a real symmetric matrix.

Algebraic operators
typedef Real *	iterator
typedef const Real *	const_iterator
typedef std::reverse_iterator< iterator >	reverse_iterator
typedef std::reverse_iterator< const_iterator >	const_reverse_iterator
typedef Real *	row_iterator
typedef const Real *	const_row_iterator
typedef std::reverse_iterator< row_iterator >	reverse_row_iterator
typedef std::reverse_iterator< const_row_iterator >	const_reverse_row_iterator
typedef step_iterator< iterator >	column_iterator
typedef step_iterator< const_iterator >	const_column_iterator
typedef std::reverse_iterator< column_iterator >	reverse_column_iterator
typedef std::reverse_iterator< const_column_iterator >	const_reverse_column_iterator
const Matrix &	operator+= (const Matrix &)
const Matrix &	operator-= (const Matrix &)
const Matrix &	*operator=** (Real)
const Matrix &	operator/= (Real)

Utilities
void	swap (Matrix &) noexcept

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.

Constructor & Destructor Documentation

◆ Matrix()

template<class Iterator>

Matrix	(	Size	rows,
		Size	columns,
		Iterator	begin,
		Iterator	end )

creates the matrix and fills it with data from a range.

Warning: if the range defined by [begin, end) is larger than the size of the matrix, a memory access violation might occur. It is up to the user to avoid this.

Member Function Documentation

◆ operator+=()

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

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

◆ pseudoSqrt()

Matrix pseudoSqrt	(	const Matrix &	,
		SalvagingAlgorithm::Type	= SalvagingAlgorithm::None )

Returns the pseudo square root of a real symmetric matrix.

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. Jäckel, 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 Jäckel, 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.

◆ rankReducedSqrt()

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

Returns the rank-reduced pseudo square root of a real symmetric matrix.

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 Member Functions

Related Symbols

Algebraic operators

Utilities