LAPACK_utilities Namespace Reference

Classes
struct	QR_Factorization

Functions
void	MGS (const Eigen::MatrixXd &X, Eigen::MatrixXd &Q, Eigen::MatrixXd &R)
	Compute the modified Gram-Schmidt factorization of matrix X.
double	rcondest (const Eigen::SparseMatrix< double > &sparseA)
Eigen::MatrixXd	triu (const Eigen::MatrixXd &X, const unsigned int &i)
	Extract upper triangular part of matrix X.
void	svd (Eigen::MatrixXd A, Eigen::MatrixXd &V, Eigen::VectorXd &S)
	Given A = U * S * V' returns only S and V'.
void	inverseTri (const Eigen::MatrixXd A, Eigen::MatrixXd &InvA, const char &UPLO, const char &DIAG)
	Compute inverse of triangular matrix.
void	eig (const Eigen::MatrixXd A, Eigen::VectorXd &D, Eigen::MatrixXd &R)
	Compute eigenvalues and eigenvectors of A = R * D * R'.
Eigen::VectorXd	svd (Eigen::MatrixXd A)
	Given A = U * S * V' returns only S.
void	svd (Eigen::MatrixXd A, Eigen::MatrixXd &U, Eigen::MatrixXd &V, Eigen::VectorXd &S)
	Given A = U * S * V' returns U, S and V'.
QR_Factorization	MGS (const Eigen::MatrixXd &X, const double &tolerance=std::numeric_limits< double >::epsilon())
	Compute the modified Gram-Schmidt factorization of matrix X with no maximum rank.
QR_Factorization	QR (const Eigen::MatrixXd &X, const double &tolerance=std::numeric_limits< double >::epsilon())
	Compute the QR matrix based on Householder reflectors.
QR_Factorization	QRP (const Eigen::MatrixXd &X, const double &tolerance=std::numeric_limits< double >::epsilon())
	Compute the QR with pivoting matrix based on Householder reflectors.
unsigned int	rank (const Eigen::VectorXd &s, const double &tolerance)
double	cond (const Eigen::VectorXd &s)
	Compute condition number in norm 2 given singular values.

Function Documentation

cond()

double LAPACK_utilities::cond ( const Eigen::VectorXd &  s )

inline

Compute condition number in norm 2 given singular values.

Parameters

s	the singular values of matrix

eig()

void LAPACK_utilities::eig	(	const Eigen::MatrixXd	A,
		Eigen::VectorXd &	D,
		Eigen::MatrixXd &	R
	)

Compute eigenvalues and eigenvectors of A = R * D * R'.

inverseTri()

void LAPACK_utilities::inverseTri	(	const Eigen::MatrixXd	A,
		Eigen::MatrixXd &	InvA,
		const char &	UPLO,
		const char &	DIAG
	)

Compute inverse of triangular matrix.

UPLO is CHARACTER*1 = 'U': A is upper triangular or = 'L': A is lower triangular. DIAG is CHARACTER*1 = 'N': A is non-unit triangular; or = 'U': A is unit triangular.

MGS() [1/2]

QR_Factorization LAPACK_utilities::MGS	(	const Eigen::MatrixXd &	X,
		const double &	tolerance
	)

Compute the modified Gram-Schmidt factorization of matrix X with no maximum rank.

MGS() [2/2]

void LAPACK_utilities::MGS	(	const Eigen::MatrixXd &	X,
		Eigen::MatrixXd &	Q,
		Eigen::MatrixXd &	R
	)

Compute the modified Gram-Schmidt factorization of matrix X.

QR()

QR_Factorization LAPACK_utilities::QR	(	const Eigen::MatrixXd &	X,
		const double &	tolerance
	)

Compute the QR matrix based on Householder reflectors.

QRP()

QR_Factorization LAPACK_utilities::QRP	(	const Eigen::MatrixXd &	X,
		const double &	tolerance
	)

Compute the QR with pivoting matrix based on Householder reflectors.

rank()

unsigned int LAPACK_utilities::rank	(	const Eigen::VectorXd &	s,
		const double &	tolerance = std::numeric_limits< double >::epsilon()
	)

Parameters

s	the singular values of matrix

rcondest()

double LAPACK_utilities::rcondest

(

const Eigen::SparseMatrix< double > &

sparseA

)

svd() [1/3]

Eigen::VectorXd LAPACK_utilities::svd

(

Eigen::MatrixXd

A

)

Given A = U * S * V' returns only S.

Compute SVD: A = U * S * V'. It returns and computes only S.

svd() [2/3]

void LAPACK_utilities::svd	(	Eigen::MatrixXd	A,
		Eigen::MatrixXd &	U,
		Eigen::MatrixXd &	V,
		Eigen::VectorXd &	S
	)

Given A = U * S * V' returns U, S and V'.

Compute SVD: A = U * S * V'. It returns U, S and V'.

svd() [3/3]

void LAPACK_utilities::svd	(	Eigen::MatrixXd	A,
		Eigen::MatrixXd &	V,
		Eigen::VectorXd &	S
	)

Given A = U * S * V' returns only S and V'.

Compute SVD: A = U * S * V'. It returns and computes only S and V'.

triu()

Eigen::MatrixXd LAPACK_utilities::triu	(	const Eigen::MatrixXd &	X,
		const unsigned int &	i
	)

Extract upper triangular part of matrix X.

Extract the upper triangular matrix of matrix X. If i > 0, it returns the elements on and above the ith diagonal of A.