DenseLinAlgLAPack Namespace Reference

Classes
class	FactorizationException
	Exception for factorization error. More...

Typedefs
typedef DenseLinAlgPack::value_type	value_type
typedef DenseLinAlgPack::index_type	index_type
typedef DenseLinAlgPack::size_type	size_type

Functions
void	potrf (DMatrixSliceTriEle *A)
	Calls xPOTRF to compute the cholesky factorization of a symmetric positive definte matrix. More...
void	geqrf (DMatrixSlice *A, DVectorSlice *tau, DVectorSlice *work)
	Calls xGEQRF to compute the QR factorization of a matrix A. More...
void	ormrq (BLAS_Cpp::Side side, BLAS_Cpp::Transp trans, const DMatrixSlice &A, const DVectorSlice &tau, DMatrixSlice *C, DVectorSlice *work)
	Calls xORMRQ to compute a matrix matrix op(C)=op(Q)*op(C) where Q is stored in A and tau computed from geqrf(..). More...
void	sytrf (DMatrixSliceTriEle *A, FortranTypes::f_int ipiv[], DVectorSlice *work)
	Calls xSYTRF to compute the P*A*P' = L'*D*L factorization of a symmetric possibly indefinite matrix. More...
void	sytrs (const DMatrixSliceTriEle &A, FortranTypes::f_int ipiv[], DMatrixSlice *B, DVectorSlice *work)
	Calls xSYTRS(...) to compute the solution of the factorized system A * X = B where A was factorized by xSYTRF(...). More...
void	getrf (DMatrixSlice *A, FortranTypes::f_int ipiv[], FortranTypes::f_int *rank)
	Calls xGETRF to compute the P'*A = L*U factorization of a general rectuangular matrix. More...
void	getrs (const DMatrixSlice &LU, const FortranTypes::f_int ipiv[], BLAS_Cpp::Transp transp, DMatrixSlice *B)
	Calls xGETRS to solve linear systems with the factors of P'*A = L*U generated by xGETRF. More...

Typedef Documentation

typedef DenseLinAlgPack::value_type DenseLinAlgLAPack::value_type

Definition at line 16 of file DenseLinAlgLAPack_Types.hpp.

typedef DenseLinAlgPack::index_type DenseLinAlgLAPack::index_type

Definition at line 17 of file DenseLinAlgLAPack_Types.hpp.

typedef DenseLinAlgPack::size_type DenseLinAlgLAPack::size_type

Definition at line 18 of file DenseLinAlgLAPack_Types.hpp.

Function Documentation

void DenseLinAlgLAPack::potrf

(

DMatrixSliceTriEle *

A

)

Calls xPOTRF to compute the cholesky factorization of a symmetric positive definte matrix.

On input A contains the upper or lower trianagular elements of a symmetric positive definite matrix. On output it contians the cholesky factor U (A = U'*U) if #A.uplo() == upper# and L (A=L*L') if #A.uplo() == lower# of the matrix.

If the matrix is not positive definite a #FactorizationException# will be thrown with an error message.

Definition at line 53 of file DenseLinAlgLAPack.cpp.

void DenseLinAlgLAPack::geqrf	(	DMatrixSlice *	A,
		DVectorSlice *	tau,
		DVectorSlice *	work
	)

Calls xGEQRF to compute the QR factorization of a matrix A.

The factors A = Q*R are stored in the storage space for A and in an extra vector tau of length k = min(A.rows(),A.cols()). The matrix R is stored in the upper diagonal of A on exit and Q is stored as a set of elementary reflectors in the elements of A below the diagonal and in the extra vector tau.

See LAPACK documentation of xGEQRF for more detail of these parameters.

If there is a problem with one of the arguments a std::invalid_argument exception will be thrown.

Parameters

A	[in/out] The mxn matrix to be factorized on input. On output contains R and part of Q.
tau	[out] DVector of length min(m,n) for the other part of Q.
work	[work] Workspace vector of length > N.

Definition at line 73 of file DenseLinAlgLAPack.cpp.

void DenseLinAlgLAPack::ormrq	(	BLAS_Cpp::Side	side,
		BLAS_Cpp::Transp	trans,
		const DMatrixSlice &	A,
		const DVectorSlice &	tau,
		DMatrixSlice *	C,
		DVectorSlice *	work
	)

Calls xORMRQ to compute a matrix matrix op(C)=op(Q)*op(C) where Q is stored in A and tau computed from geqrf(..).

See the LAPACK documentation for xQRMRQ to see a description of the parameters.

Parameters

side	[in] Determines if op(Q) is on the right (C=op(Q)*C) or on the left (C=C*op(Q)).
trans	[in] Determines if op(Q) = Q or Q'.
A	[in] Contains part of Q stored in the lower diagonal elements as set by geqrf(...).
tau	[in] Contains the other part of Q as set by geqrf(...).
C	[in/out] On input contains C and on output contains op(Q)*C (left) or C*op(Q) (right).
work	[work] Workspace vector of length > N if side==left or > M if side==right.

Definition at line 91 of file DenseLinAlgLAPack.cpp.

void DenseLinAlgLAPack::sytrf	(	DMatrixSliceTriEle *	A,
		FortranTypes::f_int	ipiv[],
		DVectorSlice *	work
	)

Calls xSYTRF to compute the P*A*P' = L'*D*L factorization of a symmetric possibly indefinite matrix.

See LAPACK documentation for xSYTRF so see a description of the function.

This factorization can be used to solve linear systems by calling sytrs(...). This function will throw #FactorizationException# if the matrix is singular.

Parameters

A	[in/out] On input contains the elements of the symmetric matrix to be factorized. On output contains the factorization.
ipiv	[out] Array of length >= A.rows(). On output contains permutation matrix P.
work	[work] Workspace used to compute factoization. The length must be greater than 0 but optimal is n * NB. NB is the optimal block size (64?), n = A.rows().

Definition at line 111 of file DenseLinAlgLAPack.cpp.

void DenseLinAlgLAPack::sytrs	(	const DMatrixSliceTriEle &	A,
		FortranTypes::f_int	ipiv[],
		DMatrixSlice *	B,
		DVectorSlice *	work
	)

Calls xSYTRS(...) to compute the solution of the factorized system A * X = B where A was factorized by xSYTRF(...).

See LAPACK documentation for xSYTRS so see a description of the function.

This factorization can be used to solve linear systems by calling sytrs(...).

Parameters

A	[in] Factorization of A computed by sytrf(...).
ipiv	[out] Array of length >= A.rows() computed by sytrf(...).
B	[in/out] On input contains the rhs matrix B. On output contiains the solution matrix X.
work	[work] Workspace used to compute factoization. The length must be greater than 0 but optimal is n * NB. NB is the optimal block size (64?), n = A.rows().

Definition at line 131 of file DenseLinAlgLAPack.cpp.

void DenseLinAlgLAPack::getrf	(	DMatrixSlice *	A,
		FortranTypes::f_int	ipiv[],
		FortranTypes::f_int *	rank
	)

Calls xGETRF to compute the P'*A = L*U factorization of a general rectuangular matrix.

See LAPACK documentation for xGETRF so see a description of the function.

This factorization can be used to solve linear systems by calling getrs(...). This function will throw #FactorizationException# if the matrix is singular.

Parameters

A	[in/out] On input contains the elements of the general matrix to be factorized. On output contains the factorization.
ipiv	[out] Array of length >= A.rows(). On output contains permutation matrix P.
rank	[out] Returns the rank of the matrix.

Definition at line 151 of file DenseLinAlgLAPack.cpp.

void DenseLinAlgLAPack::getrs	(	const DMatrixSlice &	LU,
		const FortranTypes::f_int	ipiv[],
		BLAS_Cpp::Transp	transp,
		DMatrixSlice *	B
	)

Calls xGETRS to solve linear systems with the factors of P'*A = L*U generated by xGETRF.

See LAPACK documentation for xGETRS so see a description of the function.

This factorization can be used to solve linear systems by calling getrs(...). This function will throw #FactorizationException# if the matrix is singular.

Parameters

LU	[in] On input contains the elements of the LU factors.
ipiv	[out] Array of length >= LU.rows() that contains permutation matrix P.
tranp	[in] Determines of (P*L*U) * X = Y (no_trans) is solved or (P*L*U)' * X = Y (trans) is solved.
B	[in/out] On input, contains the rhs matrix Y, on output, contains the solution matix X.

Definition at line 169 of file DenseLinAlgLAPack.cpp.