Functions dealing with matrices. More...

#include <Bpp/Numeric/Matrix/MatrixTools.h>

Public Member Functions
	MatrixTools ()

	~MatrixTools ()

Static Public Member Functions
template<class MatrixA , class MatrixO >
static void	copy (const MatrixA &A, MatrixO &O)
	Copy operation. This function supplies the lack of inheritence of the assigment operator :D . More...

template<class MatrixA , class MatrixO >
static void	copyUp (const MatrixA &A, MatrixO &O)
	O(i,j)=A(i+1,j) and O(nbRow,j)=0. More...

template<class MatrixA , class MatrixO >
static void	copyDown (const MatrixA &A, MatrixO &O)
	O(i,j)=A(i-1,j) and O(0,j)=0. More...

template<class Matrix >
static void	getId (size_t n, Matrix &O)
	Get a identity matrix of a given size. More...

template<class Scalar >
static void	diag (const std::vector< Scalar > &D, Matrix< Scalar > &O)

template<class Scalar >
static void	diag (const Scalar x, size_t n, Matrix< Scalar > &O)

template<class Scalar >
static void	diag (const Matrix< Scalar > &M, std::vector< Scalar > &O)

template<class Matrix , class Scalar >
static void	fill (Matrix &M, Scalar x)
	Set all elements in M to value x. More...

template<class Matrix , class Scalar >
static void	fillDiag (Matrix &M, Scalar x)
	Set all diagonal elements in M to value x. More...

template<class Matrix , class Scalar >
static void	scale (Matrix &A, Scalar a, Scalar b=0)
	Multiply all elements of a matrix by a given value, and add a constant. More...

template<class Scalar >
static void	mult (const Matrix< Scalar > &A, const Matrix< Scalar > &B, Matrix< Scalar > &O)

template<class Scalar >
static void	mult (const Matrix< Scalar > &A, const Matrix< Scalar > &iA, const Matrix< Scalar > &B, const Matrix< Scalar > &iB, Matrix< Scalar > &O, Matrix< Scalar > &iO)
	Product of complex matrices as couples of matrices. More...

template<class Scalar >
static void	mult (const Matrix< Scalar > &A, const std::vector< Scalar > &D, const Matrix< Scalar > &B, Matrix< Scalar > &O)
	Compute A . D . B where D is a diagonal matrix in O(n^3). More...

template<class Scalar >
static void	mult (const Matrix< Scalar > &A, const Matrix< Scalar > &iA, const std::vector< Scalar > &D, const std::vector< Scalar > &iD, const Matrix< Scalar > &B, const Matrix< Scalar > &iB, Matrix< Scalar > &O, Matrix< Scalar > &iO)
	Compute A . D . B where D is a diagonal matrix in O(n^3). More...

template<class Scalar >
static void	mult (const Matrix< Scalar > &A, const std::vector< Scalar > &D, const std::vector< Scalar > &U, const std::vector< Scalar > &L, const Matrix< Scalar > &B, Matrix< Scalar > &O)
	Compute A . (U+D+L) . B where D is a diagonal matrix, U (resp. L) is a matrix in which the only non-zero terms are on the diagonal that is over (resp. under) the main diagonal, in O(n^3). More...

template<class MatrixA , class MatrixB >
static void	add (MatrixA &A, const MatrixB &B)
	Add matrix B to matrix A. More...

template<class MatrixA , class MatrixB , class Scalar >
static void	add (MatrixA &A, Scalar &x, const MatrixB &B)
	Add matrix x.B to matrix A. More...

template<class Matrix >
static void	pow (const Matrix &A, size_t p, Matrix &O)
	Compute the power of a given matrix. More...

template<class Scalar >
static void	pow (const Matrix< Scalar > &A, double p, Matrix< Scalar > &O)
	Compute the power of a given matrix, using eigen value decomposition. More...

template<class Scalar >
static void	exp (const Matrix< Scalar > &A, Matrix< Scalar > &O)
	Perform matrix exponentiation using diagonalization. More...

template<class Matrix , class Scalar >
static void	Taylor (const Matrix &A, size_t p, std::vector< RowMatrix< Scalar >> &vO)
	Compute a vector of the first powers of a given matrix. More...

template<class Matrix >
static std::vector< size_t >	whichMax (const Matrix &m)

template<class Matrix >
static std::vector< size_t >	whichMin (const Matrix &m)

template<class Real >
static Real	max (const Matrix< Real > &m)

template<class Real >
static Real	min (const Matrix< Real > &m)

template<class Matrix >
static void	print (const Matrix &m, std::ostream &out=std::cout)
	Print a matrix to a stream. More...

template<class Matrix >
static void	print (const Matrix &m, bpp::OutputStream &out, char pIn='(', char pOut=')')
	Print a matrix to a stream. More...

template<class Matrix >
static void	printForR (const Matrix &m, const std::string &variableName="x", std::ostream &out=std::cout)
	Print a matrix to a stream, so that it is read by R. More...

template<class Real >
static void	print (const std::vector< Real > &v, std::ostream &out=std::cout)
	Print a vector to a stream. More...

template<class Matrix >
static bool	isSquare (const Matrix &A)

template<class Scalar >
static Scalar	inv (const Matrix< Scalar > &A, Matrix< Scalar > &O)

template<class Scalar >
static double	det (const Matrix< Scalar > &A)
	Get determinant of a square matrix. More...

template<class MatrixA , class MatrixO >
static void	transpose (const MatrixA &A, MatrixO &O)

template<class MatrixA >
static bool	isSymmetric (const MatrixA &A)

template<class Scalar >
static void	covar (const Matrix< Scalar > &A, Matrix< Scalar > &O)
	Compute the variance-covariance matrix of an input matrix. More...

template<class Scalar >
static void	kroneckerMult (const Matrix< Scalar > &A, const Matrix< Scalar > &B, Matrix< Scalar > &O, bool check=true)
	Compute the Kronecker product of two row matrices. More...

template<class Scalar >
static void	kroneckerMult (const Matrix< Scalar > &A, size_t dim, const Scalar &v, Matrix< Scalar > &O, bool check=true)
	Compute the Kronecker product of one Matrice with a diagonal matrix, which main term and dimension are given. More...

template<class Scalar >
static void	kroneckerMult (const Matrix< Scalar > &A, const Matrix< Scalar > &B, const Scalar &dA, const Scalar &dB, Matrix< Scalar > &O, bool check=true)
	Compute the Kronecker product of two row matrices in which the diagonal element is changed. More...

template<class Scalar >
static void	hadamardMult (const Matrix< Scalar > &A, const Matrix< Scalar > &B, Matrix< Scalar > &O)
	Compute the Hadamard product of two row matrices with same dimensions. More...

template<class Scalar >
static void	hadamardMult (const Matrix< Scalar > &A, const Matrix< Scalar > &iA, const Matrix< Scalar > &B, const Matrix< Scalar > &iB, Matrix< Scalar > &O, Matrix< Scalar > &iO)
	Compute the Hadamard product of two row matrices with same dimensions. More...

template<class Scalar >
static void	hadamardMult (const Matrix< Scalar > &A, const std::vector< Scalar > &B, Matrix< Scalar > &O, bool row=true)
	Compute the "Hadamard" product of a row matrix and a vector containing weights, according to rows or columns. More...

template<class Scalar >
static void	directSum (const Matrix< Scalar > &A, const Matrix< Scalar > &B, Matrix< Scalar > &O)
	Compute the direct sum of two row matrices. More...

template<class Scalar >
static void	directSum (const std::vector< Matrix< Scalar > *> &vA, Matrix< Scalar > &O)
	Compute the direct sum of n row matrices. More...

template<class Scalar >
static void	toVVdouble (const Matrix< Scalar > &M, std::vector< std::vector< Scalar >> &vO)
	Convert to a vector of vector. More...

template<class Scalar >
static Scalar	sumElements (const Matrix< Scalar > &M)
	Sum all elements in M. More...

template<class Scalar >
static Scalar	lap (Matrix< Scalar > &assignCost, std::vector< int > &rowSol, std::vector< int > &colSol, std::vector< Scalar > &u, std::vector< Scalar > &v)
	Linear Assignment Problem. More...

Detailed Description

Functions dealing with matrices.

Definition at line 22 of file MatrixTools.h.

Constructor & Destructor Documentation

◆ MatrixTools()

bpp::MatrixTools::MatrixTools ( )

inline

Definition at line 25 of file MatrixTools.h.

◆ ~MatrixTools()

bpp::MatrixTools::~MatrixTools ( )

inline

Definition at line 26 of file MatrixTools.h.

Member Function Documentation

◆ add() [1/2]

template<class MatrixA , class MatrixB >

static void bpp::MatrixTools::add	(	MatrixA &	A,
		const MatrixB &	B
	)

inlinestatic

Add matrix B to matrix A.

Parameters

A	[in, out] Matrix A
B	[in] Matrix B

Exceptions

DimensionException If A and B have note the same size.

Definition at line 414 of file MatrixTools.h.

Referenced by covar().

◆ add() [2/2]

template<class MatrixA , class MatrixB , class Scalar >

static void bpp::MatrixTools::add	(	MatrixA &	A,
		Scalar &	x,
		const MatrixB &	B
	)

inlinestatic

Add matrix x.B to matrix A.

Parameters

A	[in,out] Matrix A
x	[in] Scalar x
B	[in] Matrix B

Exceptions

DimensionException If A and B have note the same size.

Definition at line 442 of file MatrixTools.h.

◆ copy()

template<class MatrixA , class MatrixO >

static void bpp::MatrixTools::copy	(	const MatrixA &	A,
		MatrixO &	O
	)

inlinestatic

Copy operation. This function supplies the lack of inheritence of the assigment operator :D .

Parameters

A	[in] Original matrix.
O	[out] A copy of the given matrix.

Definition at line 36 of file MatrixTools.h.

Referenced by pow(), and Taylor().

◆ copyDown()

template<class MatrixA , class MatrixO >

static void bpp::MatrixTools::copyDown	(	const MatrixA &	A,
		MatrixO &	O
	)

inlinestatic

O(i,j)=A(i-1,j) and O(0,j)=0.

Parameters

A	[in] Original matrix.
O	[out] A copy of the given matrix.

Definition at line 79 of file MatrixTools.h.

◆ copyUp()

template<class MatrixA , class MatrixO >

static void bpp::MatrixTools::copyUp	(	const MatrixA &	A,
		MatrixO &	O
	)

inlinestatic

O(i,j)=A(i+1,j) and O(nbRow,j)=0.

Parameters

A	[in] Original matrix.
O	[out] A copy of the given matrix.

Definition at line 55 of file MatrixTools.h.

◆ covar()

template<class Scalar >

static void bpp::MatrixTools::covar	(	const Matrix< Scalar > &	A,
		Matrix< Scalar > &	O
	)

inlinestatic

Compute the variance-covariance matrix of an input matrix.

The input matrix represent a n-sample of a random vector of dimension r. It is assumed to have r rows and n columns. The variance matrix is then computed as

$V = A\cdot A^T - \mu\cdot\mu^T$

, where $\mu$ is the mean vector of the sample. the output matrix is a square matrix of size r.

Parameters

A	[in] The intput matrix.
O	[out] The resulting variance covariance matrix.

Definition at line 874 of file MatrixTools.h.

References add(), bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), mult(), bpp::Matrix< Scalar >::resize(), scale(), and transpose().

Referenced by bpp::AdaptiveKernelDensityEstimation::init_().

◆ det()

template<class Scalar >

static double bpp::MatrixTools::det ( const Matrix< Scalar > & A )

inlinestatic

Get determinant of a square matrix.

This implementation is in $o(n^3)$ and uses the LU decomposition method.

Parameters

A	[in] The input matrix.

Returns: The determinant of A.

Exceptions

DimensionException If A is not a square matrix.

Definition at line 816 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and isSquare().

Referenced by bpp::AdaptiveKernelDensityEstimation::init_().

◆ diag() [1/3]

template<class Scalar >

static void bpp::MatrixTools::diag	(	const std::vector< Scalar > &	D,
		Matrix< Scalar > &	O
	)

inlinestatic

Parameters

D	[in] A vector of diagonal elements.
O	[out] A diagonal matrix with diagonal elements taken from a vector.

Definition at line 120 of file MatrixTools.h.

References bpp::Matrix< Scalar >::resize().

◆ diag() [2/3]

template<class Scalar >

static void bpp::MatrixTools::diag	(	const Scalar	x,
		size_t	n,
		Matrix< Scalar > &	O
	)

inlinestatic

Parameters

x	[in] A scalar
n	[in] the dimension of the output matrix
O	[out] A diagonal matrix with diagonal elements equal to x

Definition at line 136 of file MatrixTools.h.

References bpp::Matrix< Scalar >::resize().

◆ diag() [3/3]

template<class Scalar >

static void bpp::MatrixTools::diag	(	const Matrix< Scalar > &	M,
		std::vector< Scalar > &	O
	)

inlinestatic

Parameters

M	[in] The matrix.
O	[out] The diagonal elements of a square matrix as a vector.

Exceptions

DimensionException If M is not a square matrix.

Definition at line 151 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), and bpp::Matrix< Scalar >::getNumberOfRows().

◆ directSum() [1/2]

template<class Scalar >

static void bpp::MatrixTools::directSum	(	const Matrix< Scalar > &	A,
		const Matrix< Scalar > &	B,
		Matrix< Scalar > &	O
	)

inlinestatic

Compute the direct sum of two row matrices.

Parameters

A	[in] The first row matrix.
B	[in] The second row matrix.
O	[out] The sum $A \oplus B$ .

Definition at line 1113 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and bpp::Matrix< Scalar >::resize().

◆ directSum() [2/2]

template<class Scalar >

static void bpp::MatrixTools::directSum	(	const std::vector< Matrix< Scalar > *> &	vA,
		Matrix< Scalar > &	O
	)

inlinestatic

Compute the direct sum of n row matrices.

Parameters

vA	[in] A vector of row matrices of any size.
O	[out] The sum $\bigoplus_i A_i$ .

Definition at line 1161 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and bpp::Matrix< Scalar >::resize().

◆ exp()

template<class Scalar >

static void bpp::MatrixTools::exp	(	const Matrix< Scalar > &	A,
		Matrix< Scalar > &	O
	)

inlinestatic

Perform matrix exponentiation using diagonalization.

Warning: This method currently relies only on diagonalization, so it won't work if your matrix is not diagonalizable. The function may be extended later to deal with other cases.

Parameters

A	[in] The matrix.
O	[out] $\prod_{i=1}^p m$ .

Exceptions

DimensionException If m is not a square matrix.

Definition at line 536 of file MatrixTools.h.

References bpp::VectorTools::exp(), bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), bpp::EigenValue< Real >::getRealEigenValues(), bpp::EigenValue< Real >::getV(), inv(), and mult().

◆ fill()

template<class Matrix , class Scalar >

static void bpp::MatrixTools::fill	(	Matrix &	M,
		Scalar	x
	)

inlinestatic

Set all elements in M to value x.

Parameters

M	A matrix.
x	The value to use.

Definition at line 166 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), and bpp::Matrix< Scalar >::getNumberOfRows().

◆ fillDiag()

template<class Matrix , class Scalar >

static void bpp::MatrixTools::fillDiag	(	Matrix &	M,
		Scalar	x
	)

inlinestatic

Set all diagonal elements in M to value x.

Parameters

M	A matrix.
x	The value to use.

Definition at line 183 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfRows().

◆ getId()

template<class Matrix >

static void bpp::MatrixTools::getId	(	size_t	n,
		Matrix &	O
	)

inlinestatic

Get a identity matrix of a given size.

Parameters

n	the size of the matrix.
O	[out] A identity matrix of size n.

Definition at line 103 of file MatrixTools.h.

References bpp::Matrix< Scalar >::resize().

Referenced by inv().

◆ hadamardMult() [1/3]

template<class Scalar >

static void bpp::MatrixTools::hadamardMult	(	const Matrix< Scalar > &	A,
		const Matrix< Scalar > &	B,
		Matrix< Scalar > &	O
	)

inlinestatic

Compute the Hadamard product of two row matrices with same dimensions.

Parameters

A	[in] The first row matrix.
B	[in] The second row matrix.
O	[out] The Hadamard product.

Definition at line 1017 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and bpp::Matrix< Scalar >::resize().

Referenced by bpp::DualityDiagram::compute_(), and bpp::CorrespondenceAnalysis::CorrespondenceAnalysis().

◆ hadamardMult() [2/3]

template<class Scalar >

static void bpp::MatrixTools::hadamardMult	(	const Matrix< Scalar > &	A,
		const Matrix< Scalar > &	iA,
		const Matrix< Scalar > &	B,
		const Matrix< Scalar > &	iB,
		Matrix< Scalar > &	O,
		Matrix< Scalar > &	iO
	)

inlinestatic

Compute the Hadamard product of two row matrices with same dimensions.

Parameters

A	[in] First matrix (real part)
iA	[in] First matrix (imaginary part)
B	[in] Second matrix (real part)
iB	[in] Second matrix(imaginary part)
O	[out] The 'Hadamard' product (real part)
iO	[out] The 'Hadamard' product(imaginary part)

Definition at line 1046 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and bpp::Matrix< Scalar >::resize().

◆ hadamardMult() [3/3]

template<class Scalar >

static void bpp::MatrixTools::hadamardMult	(	const Matrix< Scalar > &	A,
		const std::vector< Scalar > &	B,
		Matrix< Scalar > &	O,
		bool	row = `true`
	)

inlinestatic

Compute the "Hadamard" product of a row matrix and a vector containing weights, according to rows or columns.

Parameters

A	[in] The row matrix.
B	[in] The vector of row or column weights.
O	[out] The 'Hadamard' product.
row	Boolean. If row is set to 'true', the vector contains weights for rows. Otherwise the vector contains weights for columns.

Definition at line 1075 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and bpp::Matrix< Scalar >::resize().

◆ inv()

template<class Scalar >

static Scalar bpp::MatrixTools::inv	(	const Matrix< Scalar > &	A,
		Matrix< Scalar > &	O
	)

inlinestatic

Parameters

A	[in] The matrix to inverse.
O	[out] The inverse matrix of A.

Returns: x the minimum absolute value of the diagonal of the LU decomposition

Exceptions

DimensionException If A is not a square matrix.

Definition at line 797 of file MatrixTools.h.

References getId(), bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and isSquare().

Referenced by exp(), and pow().

◆ isSquare()

template<class Matrix >

static bool bpp::MatrixTools::isSquare ( const Matrix & A )

inlinestatic

Returns: True if the matrix is a square matrix.

Parameters

A A matrix.

Definition at line 788 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), and bpp::Matrix< Scalar >::getNumberOfRows().

Referenced by det(), and inv().

◆ isSymmetric()

template<class MatrixA >

static bool bpp::MatrixTools::isSymmetric ( const MatrixA & A )

inlinestatic

Parameters

A	[in] The matrix to transpose.

Returns: if symmetric

Definition at line 845 of file MatrixTools.h.

◆ kroneckerMult() [1/3]

template<class Scalar >

static void bpp::MatrixTools::kroneckerMult	(	const Matrix< Scalar > &	A,
		const Matrix< Scalar > &	B,
		Matrix< Scalar > &	O,
		bool	check = `true`
	)

inlinestatic

Compute the Kronecker product of two row matrices.

Parameters

A	[in] The first row matrix.
B	[in] The second row matrix.
O	[out] The product $A \otimes B$ .
check	[optional] if resize of 0 (default: true)

Definition at line 909 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and bpp::Matrix< Scalar >::resize().

◆ kroneckerMult() [2/3]

template<class Scalar >

static void bpp::MatrixTools::kroneckerMult	(	const Matrix< Scalar > &	A,
		size_t	dim,
		const Scalar &	v,
		Matrix< Scalar > &	O,
		bool	check = `true`
	)

inlinestatic

Compute the Kronecker product of one Matrice with a diagonal matrix, which main term and dimension are given.

Parameters

A	[in] The first row matrix.
dim	[in] The dimension of the diagonal matrix.
v	[in] The diagonal value of the diagonal matrix.
O	[out] The product $A \otimes B$ .
check	[optional] if resize of 0 (default: true)

Definition at line 946 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and bpp::Matrix< Scalar >::resize().

◆ kroneckerMult() [3/3]

template<class Scalar >

static void bpp::MatrixTools::kroneckerMult	(	const Matrix< Scalar > &	A,
		const Matrix< Scalar > &	B,
		const Scalar &	dA,
		const Scalar &	dB,
		Matrix< Scalar > &	O,
		bool	check = `true`
	)

inlinestatic

Compute the Kronecker product of two row matrices in which the diagonal element is changed.

Parameters

A	[in] The first row matrix.
B	[in] The second row matrix.
dA	[in] The replaced diagonal element of A
dB	[in] The replaced diagonal element of B
O	[out] The product $A \otimes B$ .
check	[optional] if resize of 0 (default: true)

Definition at line 982 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and bpp::Matrix< Scalar >::resize().

◆ lap()

template<class Scalar >

static Scalar bpp::MatrixTools::lap	(	Matrix< Scalar > &	assignCost,
		std::vector< int > &	rowSol,
		std::vector< int > &	colSol,
		std::vector< Scalar > &	u,
		std::vector< Scalar > &	v
	)

inlinestatic

Linear Assignment Problem.

The algorithm coded here is described in

A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems, Computing 38, 325-340, 1987 by R. Jonker and A. Volgenant, University of Amsterdam.

Parameters

assignCost	[input/output] Cost matrix
rowSol	[output] Column assigned to row in solution
colSol	[output] Row assigned to column in solution
u	[output] Dual variables, row reduction numbers
v	[output] Dual variables, column reduction numbers

Returns: The optimal cost.

Definition at line 1253 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and min().

◆ max()

template<class Real >

static Real bpp::MatrixTools::max ( const Matrix< Real > & m )

inlinestatic

Returns: The maximum value in the matrix.

Parameters

m	The matrix.

Definition at line 640 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), and bpp::Matrix< Scalar >::getNumberOfRows().

◆ min()

template<class Real >

static Real bpp::MatrixTools::min ( const Matrix< Real > & m )

inlinestatic

Returns: The minimum value in the matrix.

Parameters

m	The matrix.

Definition at line 666 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), and bpp::Matrix< Scalar >::getNumberOfRows().

Referenced by lap().

◆ mult() [1/5]

template<class Scalar >

static void bpp::MatrixTools::mult	(	const Matrix< Scalar > &	A,
		const Matrix< Scalar > &	B,
		Matrix< Scalar > &	O
	)

inlinestatic

Parameters

A	[in] First matrix.
B	[in] Second matrix.
O	[out] The product of two matrices.

Definition at line 221 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and bpp::Matrix< Scalar >::resize().

Referenced by bpp::DualityDiagram::compute_(), covar(), exp(), bpp::AdaptiveKernelDensityEstimation::init_(), bpp::AdaptiveKernelDensityEstimation::kDensity(), pow(), and Taylor().

◆ mult() [2/5]

template<class Scalar >

static void bpp::MatrixTools::mult	(	const Matrix< Scalar > &	A,
		const Matrix< Scalar > &	iA,
		const Matrix< Scalar > &	B,
		const Matrix< Scalar > &	iB,
		Matrix< Scalar > &	O,
		Matrix< Scalar > &	iO
	)

inlinestatic

Product of complex matrices as couples of matrices.

Parameters

A	[in] First matrix (real part)
iA	[in] First matrix (imaginary part)
B	[in] Second matrix (real part)
iB	[in] Second matrix(imaginary part)
O	[out] The dot product of two matrices (real part)
iO	[out] The dot product of two matrices(imaginary part)

Definition at line 253 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and bpp::Matrix< Scalar >::resize().

◆ mult() [3/5]

template<class Scalar >

static void bpp::MatrixTools::mult	(	const Matrix< Scalar > &	A,
		const std::vector< Scalar > &	D,
		const Matrix< Scalar > &	B,
		Matrix< Scalar > &	O
	)

inlinestatic

Compute A . D . B where D is a diagonal matrix in O(n^3).

Since D is a diagonal matrix, this function is more efficient than doing mult(mult(A, diag(D)), B), which involves two 0(n^3) operations.

Parameters

A	[in] The first matrix.
D	[in] The diagonal matrix (only diagonal elements in a vector)
B	[in] The second matrix.
O	[out] The result matrix.

Exceptions

DimensionException If matrices have not the appropriate size.

Definition at line 290 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and bpp::Matrix< Scalar >::resize().

◆ mult() [4/5]

template<class Scalar >

static void bpp::MatrixTools::mult	(	const Matrix< Scalar > &	A,
		const Matrix< Scalar > &	iA,
		const std::vector< Scalar > &	D,
		const std::vector< Scalar > &	iD,
		const Matrix< Scalar > &	B,
		const Matrix< Scalar > &	iB,
		Matrix< Scalar > &	O,
		Matrix< Scalar > &	iO
	)

inlinestatic

Compute A . D . B where D is a diagonal matrix in O(n^3).

Since D is a diagonal matrix, this function is more efficient than doing mult(mult(A, diag(D)), B), which involves two 0(n^3) operations.

Parameters

A	[in] First matrix (real part)
iA	[in] First matrix (imaginary part)
D	[in] The diagonal matrix (only diagonal elements in a vector) (real part)
iD	[in] The diagonal matrix (only diagonal elements in a vector) (imaginary part)
B	[in] Second matrix (real part)
iB	[in] Second matrix(imaginary part)
O	[out] The dot product of two matrices (real part)
iO	[out] The dot product of two matrices(imaginary part)

Exceptions

DimensionException If matrices have not the appropriate size.

Definition at line 331 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and bpp::Matrix< Scalar >::resize().

◆ mult() [5/5]

template<class Scalar >

static void bpp::MatrixTools::mult	(	const Matrix< Scalar > &	A,
		const std::vector< Scalar > &	D,
		const std::vector< Scalar > &	U,
		const std::vector< Scalar > &	L,
		const Matrix< Scalar > &	B,
		Matrix< Scalar > &	O
	)

inlinestatic

Compute A . (U+D+L) . B where D is a diagonal matrix, U (resp. L) is a matrix in which the only non-zero terms are on the diagonal that is over (resp. under) the main diagonal, in O(n^3).

Since D is a diagonal matrix, this function is more efficient than doing mult(mult(A, diag(D)), B), which involves two 0(n^3) operations.

Parameters

A	[in] The first matrix.
D	[in] The diagonal matrix (only diagonal elements in a vector)
U	[in] The upper diagonal matrix (only upper diagonal elements in a vector)
L	[in] The lower diagonal matrix (only lower diagonal elements in a vector)
B	[in] The second matrix.
O	[out] The result matrix.

Exceptions

DimensionException If matrices have not the appropriate size.

Definition at line 377 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and bpp::Matrix< Scalar >::resize().

◆ pow() [1/2]

template<class Matrix >

static void bpp::MatrixTools::pow	(	const Matrix &	A,
		size_t	p,
		Matrix &	O
	)

inlinestatic

Compute the power of a given matrix.

Parameters

A	[in] The matrix.
p	The number of multiplications.
O	[out] computed recursively: $A^{2n} = (A^n)^2$ $A^{2n+1} = A*(A^n)^2$ If p = 0, sends the identity matrix.

Exceptions

DimensionException If m is not a square matrix.

Definition at line 472 of file MatrixTools.h.

References copy(), bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and mult().

Referenced by bpp::FullHmmTransitionMatrix::getEquilibriumFrequencies().

◆ pow() [2/2]

template<class Scalar >

static void bpp::MatrixTools::pow	(	const Matrix< Scalar > &	A,
		double	p,
		Matrix< Scalar > &	O
	)

inlinestatic

Compute the power of a given matrix, using eigen value decomposition.

Parameters

A	[in] The matrix.
p	The power of the matrix.
O	[out] $\prod_{i=1}^p m$ . If p = 0, sends the identity matrix.

Exceptions

DimensionException If m is not a square matrix.

Definition at line 514 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), bpp::EigenValue< Real >::getRealEigenValues(), bpp::EigenValue< Real >::getV(), inv(), mult(), and bpp::VectorTools::pow().

◆ print() [1/3]

template<class Matrix >

static void bpp::MatrixTools::print	(	const Matrix &	m,
		std::ostream &	out = `std::cout`
	)

inlinestatic

Print a matrix to a stream.

Parameters

m	The matrix to print.
out	The stream to use.

Definition at line 692 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), and bpp::Matrix< Scalar >::getNumberOfRows().

◆ print() [2/3]

template<class Matrix >

static void bpp::MatrixTools::print	(	const Matrix &	m,
		bpp::OutputStream &	out,
		char	pIn = `'('`,
		char	pOut = `')'`
	)

inlinestatic

Print a matrix to a stream.

Parameters

m	The matrix to print.
out	The stream to use.
pIn	left delimiter (default: "(")
pOut	right delimiter (default: ")")

Definition at line 717 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), and bpp::Matrix< Scalar >::getNumberOfRows().

◆ print() [3/3]

template<class Real >

static void bpp::MatrixTools::print	(	const std::vector< Real > &	v,
		std::ostream &	out = `std::cout`
	)

inlinestatic

Print a vector to a stream.

Parameters

v	The vector to print.
out	The stream to use.

Definition at line 771 of file MatrixTools.h.

◆ printForR()

template<class Matrix >

static void bpp::MatrixTools::printForR	(	const Matrix &	m,
		const std::string &	variableName = `"x"`,
		std::ostream &	out = `std::cout`
	)

inlinestatic

Print a matrix to a stream, so that it is read by R.

Parameters

m	The matrix to print.
variableName	The name of the R variable handeling the matrix
out	The stream to use.

Definition at line 744 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), and bpp::Matrix< Scalar >::getNumberOfRows().

◆ scale()

template<class Matrix , class Scalar >

static void bpp::MatrixTools::scale	(	Matrix &	A,
		Scalar	a,
		Scalar	b = `0`
	)

inlinestatic

Multiply all elements of a matrix by a given value, and add a constant.

Performs $\forall i \forall j m_{i,j} = a.m_{i,j}+b$ .

Parameters

A	A matrix.
a	Multiplicator.
b	Constant.

Definition at line 201 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), and bpp::Matrix< Scalar >::getNumberOfRows().

Referenced by bpp::CorrespondenceAnalysis::CorrespondenceAnalysis(), covar(), bpp::AdaptiveKernelDensityEstimation::init_(), and bpp::AdaptiveKernelDensityEstimation::kDensity().

◆ sumElements()

template<class Scalar >

static Scalar bpp::MatrixTools::sumElements ( const Matrix< Scalar > & M )

inlinestatic

Sum all elements in M.

Parameters

M A matrix.

Returns: The sum of all elements.

Definition at line 1224 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), and bpp::Matrix< Scalar >::getNumberOfRows().

◆ Taylor()

template<class Matrix , class Scalar >

static void bpp::MatrixTools::Taylor	(	const Matrix &	A,
		size_t	p,
		std::vector< RowMatrix< Scalar >> &	vO
	)

inlinestatic

Compute a vector of the first powers of a given matrix.

Parameters

A	[in] The matrix.
p	The number of powers.
vO	[out] the vector of the powers (from 0 to p)

Exceptions

DimensionException If m is not a square matrix.

Definition at line 557 of file MatrixTools.h.

References copy(), bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), and mult().

◆ toVVdouble()

template<class Scalar >

static void bpp::MatrixTools::toVVdouble	(	const Matrix< Scalar > &	M,
		std::vector< std::vector< Scalar >> &	vO
	)

inlinestatic

Convert to a vector of vector.

Parameters

M	[in] A matrix object.
vO	[out] The output vector of vector (will be resized accordingly).

Definition at line 1203 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), and bpp::Matrix< Scalar >::getNumberOfRows().

◆ transpose()

template<class MatrixA , class MatrixO >

static void bpp::MatrixTools::transpose	(	const MatrixA &	A,
		MatrixO &	O
	)

inlinestatic

Parameters

A	[in] The matrix to transpose.
O	[out] The transposition of A.

Definition at line 828 of file MatrixTools.h.

Referenced by bpp::DualityDiagram::compute_(), and covar().

◆ whichMax()

template<class Matrix >

static std::vector<size_t> bpp::MatrixTools::whichMax ( const Matrix & m )

inlinestatic

Returns: The position of the maximum value in the matrix.

Parameters

m	The matrix.

Definition at line 577 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), and bpp::Matrix< Scalar >::getNumberOfRows().

◆ whichMin()

template<class Matrix >

static std::vector<size_t> bpp::MatrixTools::whichMin ( const Matrix & m )

inlinestatic

Returns: The position of the minimum value in the matrix.

Parameters

m	The matrix.

Definition at line 609 of file MatrixTools.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), and bpp::Matrix< Scalar >::getNumberOfRows().

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

Bpp/Numeric/Matrix/MatrixTools.h

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ MatrixTools()

◆ ~MatrixTools()

Member Function Documentation

◆ add() [1/2]

◆ add() [2/2]

◆ copy()

◆ copyDown()

◆ copyUp()

◆ covar()

◆ det()

◆ diag() [1/3]

◆ diag() [2/3]

◆ diag() [3/3]

◆ directSum() [1/2]

◆ directSum() [2/2]

◆ exp()

◆ fill()

◆ fillDiag()

◆ getId()

◆ hadamardMult() [1/3]

◆ hadamardMult() [2/3]

◆ hadamardMult() [3/3]

◆ inv()

◆ isSquare()

◆ isSymmetric()

◆ kroneckerMult() [1/3]

◆ kroneckerMult() [2/3]

◆ kroneckerMult() [3/3]

◆ lap()

◆ max()

◆ min()

◆ mult() [1/5]

◆ mult() [2/5]

◆ mult() [3/5]

◆ mult() [4/5]

◆ mult() [5/5]

◆ pow() [1/2]

◆ pow() [2/2]

◆ print() [1/3]

◆ print() [2/3]

◆ print() [3/3]

◆ printForR()

◆ scale()

◆ sumElements()

◆ Taylor()

◆ toVVdouble()

◆ transpose()

◆ whichMax()

◆ whichMin()