Matrix used in linear algebra. More...

#include <ql/math/matrix.hpp>

Collaboration diagram for Matrix:

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

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

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

template<class Iterator >
	Matrix (Size rows, Size columns, Iterator begin, Iterator end)
	creates the matrix and fills it with data from a range. More...

	Matrix (const Matrix &)

	Matrix (Matrix &&) noexcept

	Matrix (std::initializer_list< std::initializer_list< Real > >)

	~Matrix ()=default

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 Functions
(Note that these are not member functions.)
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. More...

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

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
std::unique_ptr< Real[]>	data_

Size	rows_ = 0

Size	columns_ = 0

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.

Definition at line 41 of file matrix.hpp.

Member Typedef Documentation

◆ iterator

typedef Real* iterator

Definition at line 81 of file matrix.hpp.

◆ const_iterator

typedef const Real* const_iterator

Definition at line 82 of file matrix.hpp.

◆ reverse_iterator

typedef std::reverse_iterator<iterator> reverse_iterator

Definition at line 83 of file matrix.hpp.

◆ const_reverse_iterator

typedef std::reverse_iterator<const_iterator> const_reverse_iterator

Definition at line 84 of file matrix.hpp.

◆ row_iterator

typedef Real* row_iterator

Definition at line 85 of file matrix.hpp.

◆ const_row_iterator

typedef const Real* const_row_iterator

Definition at line 86 of file matrix.hpp.

◆ reverse_row_iterator

typedef std::reverse_iterator<row_iterator> reverse_row_iterator

Definition at line 87 of file matrix.hpp.

◆ const_reverse_row_iterator

typedef std::reverse_iterator<const_row_iterator> const_reverse_row_iterator

Definition at line 89 of file matrix.hpp.

◆ column_iterator

typedef step_iterator<iterator> column_iterator

Definition at line 90 of file matrix.hpp.

◆ const_column_iterator

typedef step_iterator<const_iterator> const_column_iterator

Definition at line 91 of file matrix.hpp.

◆ reverse_column_iterator

typedef std::reverse_iterator<column_iterator> reverse_column_iterator

Definition at line 93 of file matrix.hpp.

◆ const_reverse_column_iterator

typedef std::reverse_iterator<const_column_iterator> const_reverse_column_iterator

Definition at line 95 of file matrix.hpp.

Constructor & Destructor Documentation

◆ Matrix() [1/7]

Matrix ( )

creates a null matrix

Definition at line 222 of file matrix.hpp.

◆ Matrix() [2/7]

Matrix	(	Size	rows,
		Size	columns
	)

creates a matrix with the given dimensions

Definition at line 224 of file matrix.hpp.

◆ Matrix() [3/7]

Matrix	(	Size	rows,
		Size	columns,
		Real	value
	)

creates the matrix and fills it with value

Definition at line 228 of file matrix.hpp.

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◆ Matrix() [4/7]

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.

Definition at line 235 of file matrix.hpp.

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◆ Matrix() [5/7]

Matrix ( const Matrix & from )

Definition at line 241 of file matrix.hpp.

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◆ Matrix() [6/7]

Matrix ( Matrix && from )

noexcept

Definition at line 250 of file matrix.hpp.

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◆ Matrix() [7/7]

Matrix ( std::initializer_list< std::initializer_list< Real > > data )

Definition at line 255 of file matrix.hpp.

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◆ ~Matrix()

~Matrix ( )

default

Member Function Documentation

◆ operator=() [1/2]

Matrix & operator= ( const Matrix & from )

Definition at line 270 of file matrix.hpp.

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◆ operator=() [2/2]

Matrix & operator= ( Matrix && from )

noexcept

Definition at line 277 of file matrix.hpp.

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◆ operator==()

bool operator== ( const Matrix & to ) const

Definition at line 282 of file matrix.hpp.

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◆ operator!=()

bool operator!= ( const Matrix & to ) const

Definition at line 287 of file matrix.hpp.

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◆ operator+=()

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

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

Definition at line 297 of file matrix.hpp.

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◆ operator-=()

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

Definition at line 307 of file matrix.hpp.

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◆ operator*=()

const Matrix & operator*= ( Real x )

Definition at line 317 of file matrix.hpp.

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◆ operator/=()

const Matrix & operator/= ( Real x )

Definition at line 322 of file matrix.hpp.

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◆ begin() [1/2]

Matrix::const_iterator begin ( ) const

Definition at line 327 of file matrix.hpp.

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◆ begin() [2/2]

Matrix::iterator begin ( )

Definition at line 331 of file matrix.hpp.

◆ end() [1/2]

Matrix::const_iterator end ( ) const

Definition at line 335 of file matrix.hpp.

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◆ end() [2/2]

Matrix::iterator end ( )

Definition at line 339 of file matrix.hpp.

◆ rbegin() [1/2]

Matrix::const_reverse_iterator rbegin ( ) const

Definition at line 343 of file matrix.hpp.

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◆ rbegin() [2/2]

Matrix::reverse_iterator rbegin ( )

Definition at line 347 of file matrix.hpp.

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◆ rend() [1/2]

Matrix::const_reverse_iterator rend ( ) const

Definition at line 351 of file matrix.hpp.

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◆ rend() [2/2]

Matrix::reverse_iterator rend ( )

Definition at line 355 of file matrix.hpp.

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◆ row_begin() [1/2]

Matrix::const_row_iterator row_begin ( Size i ) const

Definition at line 360 of file matrix.hpp.

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◆ row_begin() [2/2]

Matrix::row_iterator row_begin ( Size i )

Definition at line 369 of file matrix.hpp.

◆ row_end() [1/2]

Matrix::const_row_iterator row_end ( Size i ) const

Definition at line 378 of file matrix.hpp.

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◆ row_end() [2/2]

Matrix::row_iterator row_end ( Size i )

Definition at line 387 of file matrix.hpp.

◆ row_rbegin() [1/2]

Matrix::const_reverse_row_iterator row_rbegin ( Size i ) const

Definition at line 397 of file matrix.hpp.

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◆ row_rbegin() [2/2]

Matrix::reverse_row_iterator row_rbegin ( Size i )

Definition at line 401 of file matrix.hpp.

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◆ row_rend() [1/2]

Matrix::const_reverse_row_iterator row_rend ( Size i ) const

Definition at line 406 of file matrix.hpp.

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◆ row_rend() [2/2]

Matrix::reverse_row_iterator row_rend ( Size i )

Definition at line 410 of file matrix.hpp.

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◆ column_begin() [1/2]

Matrix::const_column_iterator column_begin ( Size i ) const

Definition at line 415 of file matrix.hpp.

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◆ column_begin() [2/2]

Matrix::column_iterator column_begin ( Size i )

Definition at line 424 of file matrix.hpp.

◆ column_end() [1/2]

Matrix::const_column_iterator column_end ( Size i ) const

Definition at line 434 of file matrix.hpp.

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◆ column_end() [2/2]

Matrix::column_iterator column_end ( Size i )

Definition at line 443 of file matrix.hpp.

◆ column_rbegin() [1/2]

Matrix::const_reverse_column_iterator column_rbegin ( Size i ) const

Definition at line 453 of file matrix.hpp.

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◆ column_rbegin() [2/2]

Matrix::reverse_column_iterator column_rbegin ( Size i )

Definition at line 458 of file matrix.hpp.

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◆ column_rend() [1/2]

Matrix::const_reverse_column_iterator column_rend ( Size i ) const

Definition at line 463 of file matrix.hpp.

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◆ column_rend() [2/2]

Matrix::reverse_column_iterator column_rend ( Size i )

Definition at line 468 of file matrix.hpp.

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◆ operator[]() [1/2]

Matrix::const_row_iterator operator[] ( Size i ) const

Definition at line 473 of file matrix.hpp.

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◆ at() [1/2]

Matrix::const_row_iterator at ( Size i ) const

Definition at line 478 of file matrix.hpp.

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◆ operator[]() [2/2]

Matrix::row_iterator operator[] ( Size i )

Definition at line 483 of file matrix.hpp.

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◆ at() [2/2]

Matrix::row_iterator at ( Size i )

Definition at line 487 of file matrix.hpp.

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◆ diagonal()

Array diagonal ( ) const

Definition at line 492 of file matrix.hpp.

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◆ operator()()

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

Definition at line 500 of file matrix.hpp.

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◆ rows()

Size rows ( ) const

Definition at line 504 of file matrix.hpp.

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◆ columns()

Size columns ( ) const

Definition at line 508 of file matrix.hpp.

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◆ empty()

bool empty ( ) const

Definition at line 520 of file matrix.hpp.

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◆ size1()

Size size1 ( ) const

Definition at line 512 of file matrix.hpp.

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◆ size2()

Size size2 ( ) const

Definition at line 516 of file matrix.hpp.

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◆ swap()

void swap ( Matrix & from )

noexcept

Definition at line 291 of file matrix.hpp.

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Friends And Related Function Documentation

◆ operator+() [1/4]

Matrix operator+	(	const Matrix &	,
		const Matrix &
	)

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◆ operator+() [2/4]

Matrix operator+	(	const Matrix &	,
		Matrix &&
	)

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◆ operator+() [3/4]

Matrix operator+	(	Matrix &&	,
		const Matrix &
	)

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◆ operator+() [4/4]

Matrix operator+	(	Matrix &&	,
		Matrix &&
	)

◆ operator-() [1/6]

Matrix operator- ( const Matrix & )

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◆ operator-() [2/6]

Matrix operator- ( Matrix && )

◆ operator-() [3/6]

Matrix operator-	(	const Matrix &	,
		const Matrix &
	)

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◆ operator-() [4/6]

Matrix operator-	(	const Matrix &	,
		Matrix &&
	)

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◆ operator-() [5/6]

Matrix operator-	(	Matrix &&	,
		const Matrix &
	)

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◆ operator-() [6/6]

Matrix operator-	(	Matrix &&	,
		Matrix &&
	)

◆ operator*() [1/7]

Matrix operator*	(	const Matrix &	,
		Real
	)

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◆ operator*() [2/7]

Matrix operator*	(	Matrix &&	,
		Real
	)

◆ operator*() [3/7]

Matrix operator*	(	Real	,
		const Matrix &
	)

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◆ operator*() [4/7]

Matrix operator*	(	Real	,
		Matrix &&
	)

◆ operator/() [1/2]

Matrix operator/	(	const Matrix &	,
		Real
	)

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◆ operator/() [2/2]

Matrix operator/	(	Matrix &&	,
		Real
	)

◆ operator*() [5/7]

Array operator*	(	const Array &	,
		const Matrix &
	)

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◆ operator*() [6/7]

Array operator*	(	const Matrix &	,
		const Array &
	)

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◆ operator*() [7/7]

Matrix operator*	(	const Matrix &	,
		const Matrix &
	)

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◆ transpose()

Matrix transpose ( const Matrix & )

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◆ outerProduct() [1/2]

Matrix outerProduct	(	const Array &	v1,
		const Array &	v2
	)

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◆ outerProduct() [2/2]

Matrix outerProduct	(	Iterator1	v1begin,
		Iterator1	v1end,
		Iterator2	v2begin,
		Iterator2	v2end
	)

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◆ swap()

void swap	(	Matrix &	,
		Matrix &
	)

◆ operator<<()

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

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◆ inverse()

Matrix inverse ( const Matrix & m )

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◆ determinant()

Real determinant ( const Matrix & m )

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◆ CholeskyDecomposition()

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

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◆ pseudoSqrt()

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. 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.

Definition at line 347 of file pseudosqrt.cpp.

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◆ rankReducedSqrt()

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.

Definition at line 427 of file pseudosqrt.cpp.

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Member Data Documentation

◆ data_

std::unique_ptr<Real[]> data_

private

Definition at line 148 of file matrix.hpp.

◆ rows_

Size rows_ = 0

private

Definition at line 149 of file matrix.hpp.

◆ columns_

Size columns_ = 0

private

Definition at line 149 of file matrix.hpp.

Public Member Functions

Related Functions

Algebraic operators

Utilities

Detailed Description

Member Typedef Documentation

◆ iterator

◆ const_iterator

◆ reverse_iterator

◆ const_reverse_iterator

◆ row_iterator

◆ const_row_iterator

◆ reverse_row_iterator

◆ const_reverse_row_iterator

◆ column_iterator

◆ const_column_iterator

◆ reverse_column_iterator

◆ const_reverse_column_iterator

Constructor & Destructor Documentation

◆ Matrix() [1/7]

◆ Matrix() [2/7]

◆ Matrix() [3/7]

◆ Matrix() [4/7]

◆ Matrix() [5/7]

◆ Matrix() [6/7]

◆ Matrix() [7/7]

◆ ~Matrix()

Member Function Documentation

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator!=()

◆ operator+=()

◆ operator-=()

◆ operator*=()

◆ operator/=()

◆ begin() [1/2]

◆ begin() [2/2]

◆ end() [1/2]

◆ end() [2/2]

◆ rbegin() [1/2]

◆ rbegin() [2/2]

◆ rend() [1/2]

◆ rend() [2/2]

◆ row_begin() [1/2]

◆ row_begin() [2/2]

◆ row_end() [1/2]

◆ row_end() [2/2]

◆ row_rbegin() [1/2]

◆ row_rbegin() [2/2]

◆ row_rend() [1/2]

◆ row_rend() [2/2]

◆ column_begin() [1/2]

◆ column_begin() [2/2]

◆ column_end() [1/2]

◆ column_end() [2/2]

◆ column_rbegin() [1/2]

◆ column_rbegin() [2/2]

◆ column_rend() [1/2]

◆ column_rend() [2/2]

◆ operator[]() [1/2]

◆ at() [1/2]

◆ operator[]() [2/2]

◆ at() [2/2]

◆ diagonal()

◆ operator()()

◆ rows()

◆ columns()

◆ empty()

◆ size1()

◆ size2()

◆ swap()

Friends And Related Function Documentation

◆ operator+() [1/4]

◆ operator+() [2/4]

◆ operator+() [3/4]

◆ operator+() [4/4]

◆ operator-() [1/6]

◆ operator-() [2/6]

◆ operator-() [3/6]