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 .
template<class Matrix >
static void	getId (size_t n, Matrix &O)
	Get a identity matrix of a given size.
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) throw (DimensionException)
template<class Matrix , class Scalar >
static void	fill (Matrix &M, Scalar x)
	Set all elements in M to value x.
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.
template<class Scalar >
static void	mult (const Matrix< Scalar > &A, const Matrix< Scalar > &B, Matrix< Scalar > &O) throw (DimensionException)
template<class Scalar >
static void	mult (const Matrix< Scalar > &A, const std::vector< Scalar > &D, const Matrix< Scalar > &B, Matrix< Scalar > &O) throw (DimensionException)
	Compute A . D . B where D is a diagonal matrix in O(n^3).
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) throw (DimensionException)
	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).
template<class MatrixA , class MatrixB >
static void	add (MatrixA &A, const MatrixB &B) throw (DimensionException)
	Add matrix B to matrix A.
template<class MatrixA , class MatrixB , class Scalar >
static void	add (MatrixA &A, Scalar &x, const MatrixB &B) throw (DimensionException)
	Add matrix x.B to matrix A.
template<class Matrix >
static void	pow (const Matrix &A, size_t p, Matrix &O) throw (DimensionException)
	Compute the power of a given matrix.
template<class Scalar >
static void	pow (const Matrix< Scalar > &A, double p, Matrix< Scalar > &O) throw (DimensionException)
	Compute the power of a given matrix, using eigen value decomposition.
template<class Scalar >
static void	exp (const Matrix< Scalar > &A, Matrix< Scalar > &O) throw (DimensionException)
	Perform matrix exponentiation using diagonalization.
template<class Matrix , class Scalar >
static void	Taylor (const Matrix &A, size_t p, std::vector< RowMatrix< Scalar > > &vO) throw (DimensionException)
	Compute a vector of the first powers of a given matrix.
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.
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.
template<class Real >
static void	print (const std::vector< Real > &v, std::ostream &out=std::cout)
	Print a vector to a stream.
template<class Matrix >
static bool	isSquare (const Matrix &A)
template<class Scalar >
static Scalar	inv (const Matrix< Scalar > &A, Matrix< Scalar > &O) throw (DimensionException, ZeroDivisionException)
template<class Scalar >
static double	det (const Matrix< Scalar > &A) throw (DimensionException)
	Get determinant of a square matrix.
template<class MatrixA , class MatrixO >
static void	transpose (const MatrixA &A, MatrixO &O)
template<class Scalar >
static void	covar (const Matrix< Scalar > &A, Matrix< Scalar > &O)
	Compute the variance-covariance matrix of an input matrix.
template<class Scalar >
static void	kroneckerMult (const Matrix< Scalar > &A, const Matrix< Scalar > &B, Matrix< Scalar > &O)
	Compute the Kronecker product of two row matrices.
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.
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.
template<class Scalar >
static void	kroneckerSum (const Matrix< Scalar > &A, const Matrix< Scalar > &B, Matrix< Scalar > &O)
	Compute the Kronecker sum of two row matrices.
template<class Scalar >
static void	kroneckerSum (const std::vector< Matrix< Scalar > * > &vA, Matrix< Scalar > &O)
	Compute the Kronecker sum of n row matrices.
template<class Scalar >
static void	toVVdouble (const Matrix< Scalar > &M, std::vector< std::vector< Scalar > > &vO)
	Convert to a vector of vector.
template<class Scalar >
static Scalar	sumElements (const Matrix< Scalar > &M)
	Sum all elements in M.
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) throw (Exception)
	Linear Assignment Problem.

Detailed Description

Functions dealing with matrices.

Definition at line 56 of file MatrixTools.h.

Constructor & Destructor Documentation

bpp::MatrixTools::MatrixTools ( ) [inline]

Definition at line 59 of file MatrixTools.h.

bpp::MatrixTools::~MatrixTools ( ) [inline]

Definition at line 60 of file MatrixTools.h.

Member Function Documentation

template<class MatrixA , class MatrixB >

static void bpp::MatrixTools::add	(	MatrixA &	A,
		const MatrixB &	B
	)		throw (DimensionException) `[inline, static]`

Add matrix B to matrix A.

Parameters:

A	[in] Matrix A
B	[in] Matrix B

Exceptions:

DimensionException If A and B have note the same size.

Definition at line 299 of file MatrixTools.h.

Referenced by covar().

template<class MatrixA , class MatrixB , class Scalar >

static void bpp::MatrixTools::add	(	MatrixA &	A,
		Scalar &	x,
		const MatrixB &	B
	)		throw (DimensionException) `[inline, static]`

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 325 of file MatrixTools.h.

template<class MatrixA , class MatrixO >

static void bpp::MatrixTools::copy	(	const MatrixA &	A,
		MatrixO &	O
	)		`[inline, static]`

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 70 of file MatrixTools.h.

Referenced by pow(), and Taylor().

template<class Scalar >

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

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 702 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_().

template<class Scalar >

static double bpp::MatrixTools::det ( const Matrix< Scalar > & A ) throw (DimensionException) [inline, static]

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 665 of file MatrixTools.h.

References isSquare().

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

template<class Scalar >

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

Parameters:

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

Definition at line 105 of file MatrixTools.h.

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

template<class Scalar >

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

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 121 of file MatrixTools.h.

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

template<class Scalar >

static void bpp::MatrixTools::diag	(	const Matrix< Scalar > &	M,
		std::vector< Scalar > &	O
	)		throw (DimensionException) `[inline, static]`

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 136 of file MatrixTools.h.

template<class Scalar >

static void bpp::MatrixTools::exp	(	const Matrix< Scalar > &	A,
		Matrix< Scalar > &	O
	)		throw (DimensionException) `[inline, static]`

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 415 of file MatrixTools.h.

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

template<class Matrix , class Scalar >

static void bpp::MatrixTools::fill	(	Matrix &	M,
		Scalar	x
	)		`[inline, static]`

Set all elements in M to value x.

Parameters:

M	A matrix.
x	The value to use.

Definition at line 151 of file MatrixTools.h.

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

template<class Matrix >

static void bpp::MatrixTools::getId	(	size_t	n,
		Matrix &	O
	)		`[inline, static]`

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 89 of file MatrixTools.h.

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

Referenced by inv().

template<class Scalar >

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

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 767 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().

template<class Scalar >

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

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 794 of file MatrixTools.h.

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

template<class Scalar >

static Scalar bpp::MatrixTools::inv	(	const Matrix< Scalar > &	A,
		Matrix< Scalar > &	O
	)		throw (DimensionException, ZeroDivisionException) `[inline, static]`

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 646 of file MatrixTools.h.

References getId(), and isSquare().

Referenced by exp(), and pow().

template<class Matrix >

static bool bpp::MatrixTools::isSquare ( const Matrix & A ) [inline, static]

Returns:: True if the matrix is a square matrix.

Parameters:

A A matrix.

Definition at line 637 of file MatrixTools.h.

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

Referenced by det(), and inv().

template<class Scalar >

static void bpp::MatrixTools::kroneckerMult	(	const Matrix< Scalar > &	A,
		const Matrix< Scalar > &	B,
		Matrix< Scalar > &	O
	)		`[inline, static]`

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 $A \otimes B$ .

Definition at line 736 of file MatrixTools.h.

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

template<class Scalar >

static void bpp::MatrixTools::kroneckerSum	(	const Matrix< Scalar > &	A,
		const Matrix< Scalar > &	B,
		Matrix< Scalar > &	O
	)		`[inline, static]`

Compute the Kronecker sum of two row matrices.

Parameters:

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

Definition at line 832 of file MatrixTools.h.

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

template<class Scalar >

static void bpp::MatrixTools::kroneckerSum	(	const std::vector< Matrix< Scalar > * > &	vA,
		Matrix< Scalar > &	O
	)		`[inline, static]`

Compute the Kronecker sum of n row matrices.

Parameters:

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

Definition at line 862 of file MatrixTools.h.

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

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
	)		throw (Exception) `[inline, static]`

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 947 of file MatrixTools.h.

References min().

template<class Real >

static Real bpp::MatrixTools::max ( const Matrix< Real > & m ) [inline, static]

Returns:: The maximum value in the matrix.

Parameters:

m	The matrix.

Definition at line 520 of file MatrixTools.h.

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

template<class Real >

static Real bpp::MatrixTools::min ( const Matrix< Real > & m ) [inline, static]

Returns:: The minimum value in the matrix.

Parameters:

m	The matrix.

Definition at line 546 of file MatrixTools.h.

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

Referenced by lap().

template<class Scalar >

static void bpp::MatrixTools::mult	(	const Matrix< Scalar > &	A,
		const Matrix< Scalar > &	B,
		Matrix< Scalar > &	O
	)		throw (DimensionException) `[inline, static]`

Parameters:

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

Definition at line 189 of file MatrixTools.h.

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

template<class Scalar >

static void bpp::MatrixTools::mult	(	const Matrix< Scalar > &	A,
		const std::vector< Scalar > &	D,
		const Matrix< Scalar > &	B,
		Matrix< Scalar > &	O
	)		throw (DimensionException) `[inline, static]`

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 223 of file MatrixTools.h.

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
	)		throw (DimensionException) `[inline, static]`

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 262 of file MatrixTools.h.

template<class Matrix >

static void bpp::MatrixTools::pow	(	const Matrix &	A,
		size_t	p,
		Matrix &	O
	)		throw (DimensionException) `[inline, static]`

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 354 of file MatrixTools.h.

References copy(), and mult().

template<class Scalar >

static void bpp::MatrixTools::pow	(	const Matrix< Scalar > &	A,
		double	p,
		Matrix< Scalar > &	O
	)		throw (DimensionException) `[inline, static]`

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 393 of file MatrixTools.h.

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

template<class Matrix >

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

Print a matrix to a stream.

Parameters:

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

Definition at line 572 of file MatrixTools.h.

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

template<class Real >

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

Print a vector to a stream.

Parameters:

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

Definition at line 620 of file MatrixTools.h.

template<class Matrix >

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

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 596 of file MatrixTools.h.

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

template<class Matrix , class Scalar >

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

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 172 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().

template<class Scalar >

static Scalar bpp::MatrixTools::sumElements ( const Matrix< Scalar > & M ) [inline, static]

Sum all elements in M.

Parameters:

M A matrix.

Returns:: The sum of all elements.

Definition at line 917 of file MatrixTools.h.

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

template<class Matrix , class Scalar >

static void bpp::MatrixTools::Taylor	(	const Matrix &	A,
		size_t	p,
		std::vector< RowMatrix< Scalar > > &	vO
	)		throw (DimensionException) `[inline, static]`

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 437 of file MatrixTools.h.

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

template<class Scalar >

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

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 896 of file MatrixTools.h.

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

template<class MatrixA , class MatrixO >

static void bpp::MatrixTools::transpose	(	const MatrixA &	A,
		MatrixO &	O
	)		`[inline, static]`

Parameters:

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

Definition at line 677 of file MatrixTools.h.

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

template<class Matrix >

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

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

Parameters:

m	The matrix.

Definition at line 457 of file MatrixTools.h.

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

template<class Matrix >

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

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

Parameters:

m	The matrix.

Definition at line 489 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

Member Function Documentation