ssytrf_aa_2stage()

subroutine ssytrf_aa_2stage	(	character	uplo,
		integer	n,
		real, dimension( lda, * )	a,
		integer	lda,
		real, dimension( * )	tb,
		integer	ltb,
		integer, dimension( * )	ipiv,
		integer, dimension( * )	ipiv2,
		real, dimension( * )	work,
		integer	lwork,
		integer	info )

SSYTRF_AA_2STAGE

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Purpose:

!>
!> SSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A
!> using the Aasen's algorithm.  The form of the factorization is
!>
!>    A = U**T*T*U  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 band matrix with the
!> bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is 
!> LU factorized with partial pivoting).
!>
!> This is the blocked version of the algorithm, calling Level 3 BLAS.
!> 

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in,out]	A	!> A is REAL array, dimension (LDA,N) !> On entry, the symmetric matrix A. If UPLO = 'U', 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 = 'L', 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, L is stored below (or above) the subdiagonal blocks, !> when UPLO is 'L' (or 'U'). !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[out]	TB	!> TB is REAL array, dimension (LTB) !> On exit, details of the LU factorization of the band matrix. !>
[in]	LTB	!> LTB is INTEGER !> The size of the array TB. LTB >= MAX(1,4*N), internally !> used to select NB such that LTB >= (3*NB+1)*N. !> !> If LTB = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of LTB, !> returns this value as the first entry of TB, and !> no error message related to LTB is issued by XERBLA. !>
[out]	IPIV	!> IPIV is INTEGER array, dimension (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). !>
[out]	IPIV2	!> IPIV2 is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i.e., !> the row and column k of T were interchanged with the !> row and column IPIV(k). !>
[out]	WORK	!> WORK is REAL workspace of size (MAX(1,LWORK)) !>
[in]	LWORK	!> LWORK is INTEGER !> The size of WORK. LWORK >= MAX(1,N), internally used to !> select NB such that LWORK >= N*NB. !> !> If LWORK = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of the WORK array, !> returns this value as the first entry of the WORK array, and !> no error message related to LWORK is issued by XERBLA. !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value. !> > 0: if INFO = i, band LU factorization failed on i-th column !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.