Functions
void	dgetrf_ (int m, int n, double A, int lda, int ipiv, int info)
	LU decomposition. More...

void	zgetrf_ (int m, int n, std::complex< double > A, int lda, int ipiv, int info)

void	dgetrs_ (char trans, int n, int nrhs, double A, int lda, int ipiv, double b, int ldb, int *info)
	Solve linear system of equations. More...

void	dgetri_ (int n, double A, int lda, int ipiv, double work, int lwork, int *info)
	Matrix inversion. More...

void	zgetri_ (int n, std::complex< double > A, int lda, int ipiv, std::complex< double > work, int lwork, int *info)

void	ilaenv_ (int ispec, char name, char opts, int n1, int n2, int n3, int *n4)
	Optimal parameters for computation. More...

void	dgesvx_ (char fact, char trans, int n, int nrhs, double A, int lda, double AF, int ldaf, int ipiv, char equed, double R, double C, double B, int ldb, double X, int ldx, double RCOND, double FERR, double BERR, double WORK, int IWORK, int info)
	Solve linear system. More...

void	dgeev_ (char jobvl, char jobvr, int n, double A, int lda, double WR, double WI, double VL, int ldvl, double VR, int ldvr, double work, int lwork, double rwork, int *info)

void	zgeev_ (char jobvl, char jobvr, int n, std::complex< double > A, int lda, std::complex< double > W, std::complex< double > VL, int ldvl, std::complex< double > VR, int ldvr, std::complex< double > work, int lwork, double rwork, int info)

Function Documentation

◆ dgeev_()

void lapack::dgeev_	(	char *	jobvl,
		char *	jobvr,
		int *	n,
		double *	A,
		int *	lda,
		double *	WR,
		double *	WI,
		double *	VL,
		int *	ldvl,
		double *	VR,
		int *	ldvr,
		double *	work,
		int *	lwork,
		double *	rwork,
		int *	info
	)

Referenced by diagonalize().

◆ dgesvx_()

void lapack::dgesvx_	(	char *	fact,
		char *	trans,
		int *	n,
		int *	nrhs,
		double *	A,
		int *	lda,
		double *	AF,
		int *	ldaf,
		int *	ipiv,
		char *	equed,
		double *	R,
		double *	C,
		double *	B,
		int *	ldb,
		double *	X,
		int *	ldx,
		double *	RCOND,
		double *	FERR,
		double *	BERR,
		double *	WORK,
		int *	IWORK,
		int *	info
	)

Solve linear system.

Solves the linear system A*X = B using LAPACK's dgesv function. The use of the expert function is necessary since we need to solve the system for the inverse matrix due to the different memory layouts in arts and BLAS. Since most of the parameters are unused they are not fully documented. See LAPACK documentation.

Parameters

[in]	fact	Specifies whether or not the factored form of the matrix A is provided and whether the matrix A should be equilibrated.
[in]	trans	Specifies the form of the linear system = 'N': A * x = B = 'N': A^T * x = B = 'N': A^H * x = B
[in]	n	Dimensionality of the system.
[in]	nrhs	Number of right-hand side columns.
[in]	A	The double array (column-major order) representing the matrix a A that describes the linear system.
[in]	lda	The leading dimension of A.
[in,out]	AF	If a is given in factored form AF must contain the factored form of A on input. On output contains the factored form of A.
[in]	ldaf	The leading dimension of AF.
[in,out]	ipiv	The pivot vector from the LU decomposition.
[in]	equed	Specifies the form of equilibration that was done.
[in]	R	The low scale factors for A.
[in]	C	The column scale factors for A.
[in]	B	The right hand-side matrix of the system.
[in]	ldb	The leading dimension of B.
[out]	X	The solution matrix.
[in]	ldx	The leading dimension of x.
[out]	RCOND	The estimate of the reciprocal condition number of the matrix A after equilibration (if done).
[out]	FERR	The estimates error bound for each solution.
[out]	BERR	The componentwise relative backward error.
[out]	WORK
[out]	IWORK
[out]	info

◆ dgetrf_()

void lapack::dgetrf_	(	int *	m,
		int *	n,
		double *	A,
		int *	lda,
		int *	ipiv,
		int *	info
	)

LU decomposition.

Performs an LU decomposition of a genereal m-by-n matrix using partial pivoting with row interchanges. See LAPACK reference.

Parameters

[in]	m	The number of rows of the matrix A.
[in]	n	The number of column of the matrix A.
[out]	A	The matrix A.
[in]	lda	The leading dimension of the matrix A.
[out]	ipiv	Integer array to hold the pivoting indices.
[out]	info	Integer indicating if operation was successful: 0 if success, otherwise failure.

Referenced by inv(), and ludcmp().

◆ dgetri_()

void lapack::dgetri_	(	int *	n,
		double *	A,
		int *	lda,
		int *	ipiv,
		double *	work,
		int *	lwork,
		int *	info
	)

Matrix inversion.

Inverts a given matrix using LU decompositions. See LAPACK reference.

Parameters

[in]	n	The number of rows and columns of the matrix A.
[in,out]	A	The matrix to be inverted.
[in]	lda	The leading dimension of A.
[in]	ipiv	The vector containing the pivoting indices returned from dgetrf_.
[in]	work	Work array for improved performance.
[in]	lwork	Size of the work array.
[out]	info	Integer indicating if operation was successful: 0 if success, otherwise failure.

Referenced by inv().

◆ dgetrs_()

void lapack::dgetrs_	(	char *	trans,
		int *	n,
		int *	nrhs,
		double *	A,
		int *	lda,
		int *	ipiv,
		double *	b,
		int *	ldb,
		int *	info
	)

Solve linear system of equations.

Solves a linear system of equations of the form

trans(A) * x = b

using the QR decomposition obtained using dgetrf_.

Parameters

[in] trans Specifies the form of the system of equations:

trans = 'N' : trans(A) = A trans = 'T' : trans(A) = A^T trans = 'C' : trans(A) = conj( A^T )

Parameters

[in]	n	The size of the system.
[in]	nrhs	The number of right-hand sides.
[in]	A	The matrix describing the system.
[in]	lda	The leading dimension of A.
[in]	ipiv	The pivot vector as returned by dgetrf_.
[in,out]	b	The matrix containing the right-hand side vectors.
[in]	ldb	The leading dimension of b.
[out]	info	Integer indicating succes of the operation.

Referenced by lubacksub().

◆ ilaenv_()

void lapack::ilaenv_	(	int *	ispec,
		char *	name,
		char *	opts,
		int *	n1,
		int *	n2,
		int *	n3,
		int *	n4
	)

Optimal parameters for computation.

This function returns problem-dependent parameters for the computing environment. See LAPACK reference.

Parameters

[in,out]	ispec	On input specifies which parameter to be returned and on output contains the requested parameter.
[in]	name	Name of the functions to be called.
[in]	opts	Character options to the function "Name"
[in]	n1	Problem dimension 1 of "Name".
[in]	n2	Problem dimension 2 of "Name".
[in]	n3	Problem dimension 3 of "Name".
[in]	n4	Problem dimension 4 of "Name".

◆ zgeev_()

void lapack::zgeev_	(	char *	jobvl,
		char *	jobvr,
		int *	n,
		std::complex< double > *	A,
		int *	lda,
		std::complex< double > *	W,
		std::complex< double > *	VL,
		int *	ldvl,
		std::complex< double > *	VR,
		int *	ldvr,
		std::complex< double > *	work,
		int *	lwork,
		double *	rwork,
		int *	info
	)

Referenced by diagonalize().

◆ zgetrf_()

void lapack::zgetrf_	(	int *	m,
		int *	n,
		std::complex< double > *	A,
		int *	lda,
		int *	ipiv,
		int *	info
	)

Referenced by inv(), and ComplexMatrix::inv().

◆ zgetri_()

void lapack::zgetri_	(	int *	n,
		std::complex< double > *	A,
		int *	lda,
		int *	ipiv,
		std::complex< double > *	work,
		int *	lwork,
		int *	info
	)

Referenced by inv(), and ComplexMatrix::inv().

Functions

Function Documentation

◆ dgeev_()

◆ dgesvx_()

◆ dgetrf_()

◆ dgetri_()

◆ dgetrs_()

◆ ilaenv_()

◆ zgeev_()

◆ zgetrf_()

◆ zgetri_()