zsytri_3x()

subroutine zsytri_3x	(	character	uplo,
		integer	n,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( * )	e,
		integer, dimension( * )	ipiv,
		complex*16, dimension( n+nb+1, * )	work,
		integer	nb,
		integer	info )

ZSYTRI_3X

Download ZSYTRI_3X + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!> ZSYTRI_3X computes the inverse of a complex symmetric indefinite
!> matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK:
!>
!>     A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),
!>
!> where U (or L) is unit upper (or lower) triangular matrix,
!> U**T (or L**T) is the transpose of U (or L), P is a permutation
!> matrix, P**T is the transpose of P, and D is symmetric and block
!> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
!>
!> This is the blocked version of the algorithm, calling Level 3 BLAS.
!> 

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are !> stored as an upper or lower triangular matrix. !> = '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 COMPLEX*16 array, dimension (LDA,N) !> On entry, diagonal of the block diagonal matrix D and !> factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK: !> a) ONLY diagonal elements of the symmetric block diagonal !> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); !> (superdiagonal (or subdiagonal) elements of D !> should be provided on entry in array E), and !> b) If UPLO = 'U': factor U in the superdiagonal part of A. !> If UPLO = 'L': factor L in the subdiagonal part of A. !> !> On exit, if INFO = 0, the symmetric inverse of the original !> matrix. !> If UPLO = 'U': the upper triangular part of the inverse !> is formed and the part of A below the diagonal is not !> referenced; !> If UPLO = 'L': the lower triangular part of the inverse !> is formed and the part of A above the diagonal is not !> referenced. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[in]	E	!> E is COMPLEX*16 array, dimension (N) !> On entry, contains the superdiagonal (or subdiagonal) !> elements of the symmetric block diagonal matrix D !> with 1-by-1 or 2-by-2 diagonal blocks, where !> If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) not referenced; !> If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) not referenced. !> !> NOTE: For 1-by-1 diagonal block D(k), where !> 1 <= k <= N, the element E(k) is not referenced in both !> UPLO = 'U' or UPLO = 'L' cases. !>
[in]	IPIV	!> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by ZSYTRF_RK or ZSYTRF_BK. !>
[out]	WORK	!> WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3). !>
[in]	NB	!> NB is INTEGER !> Block size. !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its !> inverse could not be computed. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

!>
!>  June 2017,  Igor Kozachenko,
!>                  Computer Science Division,
!>                  University of California, Berkeley
!>
!>