Symmetric indefinite: Aasen's

Functions
int64_t	lapack::sytrf_aa (lapack::Uplo uplo, int64_t n, double *A, int64_t lda, int64_t *ipiv)
int64_t	lapack::sytrf_aa (lapack::Uplo uplo, int64_t n, float *A, int64_t lda, int64_t *ipiv)
int64_t	lapack::sytrf_aa (lapack::Uplo uplo, int64_t n, std::complex< double > *A, int64_t lda, int64_t *ipiv)
	Computes the factorization of a symmetric matrix A using the Aasen's algorithm.
int64_t	lapack::sytrf_aa (lapack::Uplo uplo, int64_t n, std::complex< float > *A, int64_t lda, int64_t *ipiv)
int64_t	lapack::sytrs_aa (lapack::Uplo uplo, int64_t n, int64_t nrhs, double const *A, int64_t lda, int64_t const *ipiv, double *B, int64_t ldb)
int64_t	lapack::sytrs_aa (lapack::Uplo uplo, int64_t n, int64_t nrhs, float const *A, int64_t lda, int64_t const *ipiv, float *B, int64_t ldb)
int64_t	lapack::sytrs_aa (lapack::Uplo uplo, int64_t n, int64_t nrhs, std::complex< double > const *A, int64_t lda, int64_t const *ipiv, std::complex< double > *B, int64_t ldb)
	Solves a system of linear equations \(A X = B\) with a symmetric matrix A using the factorization \(A = U T U^T\) or \(A = L T L^T\) computed by lapack::sytrf_aa.
int64_t	lapack::sytrs_aa (lapack::Uplo uplo, int64_t n, int64_t nrhs, std::complex< float > const *A, int64_t lda, int64_t const *ipiv, std::complex< float > *B, int64_t ldb)

Detailed Description

Function Documentation

sytrf_aa()

int64_t lapack::sytrf_aa	(	lapack::Uplo	uplo,
		int64_t	n,
		std::complex< double > *	A,
		int64_t	lda,
		int64_t *	ipiv
	)

Computes the factorization of a symmetric matrix A using the Aasen's algorithm.

The form of the factorization is

\[ A = U T U^T \]

or

\[ A = L T L^T \]

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a symmetric tridiagonal matrix.

This is the blocked version of the algorithm, calling Level 3 BLAS.

Overloaded versions are available for float, double, std::complex<float>, and std::complex<double>. For real matrices, lapack::hetrf_aa is an alias for this. For complex Hermitian matrices, see lapack::hetrf_aa.

Parameters

[in]	uplo	lapack::Uplo::Upper: Upper triangle of A is stored; lapack::Uplo::Lower: Lower triangle of A is stored.
[in]	n	The order of the matrix A. n >= 0.
[in,out]	A	The n-by-n matrix A, stored in an lda-by-n array. On entry, the symmetric matrix A. If uplo = Upper, the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo = Lower, the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, the tridiagonal matrix is stored in the diagonals and the subdiagonals of A just below (or above) the diagonals, and L is stored below (or above) the subdiaonals, when uplo is 'L' (or 'U').
[in]	lda	The leading dimension of the array A. lda >= max(1,n).
[out]	ipiv	The vector ipiv of length n. On exit, it contains the details of the interchanges, i.e., the row and column k of A were interchanged with the row and column ipiv(k).

Returns

= 0: successful exit

sytrs_aa()

int64_t lapack::sytrs_aa	(	lapack::Uplo	uplo,
		int64_t	n,
		int64_t	nrhs,
		std::complex< double > const *	A,
		int64_t	lda,
		int64_t const *	ipiv,
		std::complex< double > *	B,
		int64_t	ldb
	)

Solves a system of linear equations \(A X = B\) with a symmetric matrix A using the factorization \(A = U T U^T\) or \(A = L T L^T\) computed by lapack::sytrf_aa.

Overloaded versions are available for float, double, std::complex<float>, and std::complex<double>. For real matrices, lapack::hetrs_aa is an alias for this. For complex Hermitian matrices, see lapack::hetrs_aa.

Parameters

[in]	uplo	Whether the details of the factorization are stored as an upper or lower triangular matrix. lapack::Uplo::Upper: Upper triangular, form is \(A = U T U^T;\) lapack::Uplo::Lower: Lower triangular, form is \(A = L T L^T.\)
[in]	n	The order of the matrix A. n >= 0.
[in]	nrhs	The number of right hand sides, i.e., the number of columns of the matrix B. nrhs >= 0.
[in]	A	The n-by-n matrix A, stored in an lda-by-n array. Details of factors computed by lapack::sytrf_aa.
[in]	lda	The leading dimension of the array A. lda >= max(1,n).
[in]	ipiv	The vector ipiv of length n. Details of the interchanges as computed by lapack::sytrf_aa.
[in,out]	B	The n-by-nrhs matrix B, stored in an ldb-by-nrhs array. On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]	ldb	The leading dimension of the array B. ldb >= max(1,n).

Returns

= 0: successful exit