*> \brief \b ZHETRI_3
*
* =========== DOCUMENTATION ===========
*
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*
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*
* Definition:
* ===========
*
* SUBROUTINE ZHETRI_3( UPLO, N, A, LDA, E, IPIV, WORK, LWORK,
* INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, LDA, LWORK, N
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* COMPLEX*16 A( LDA, * ), E( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*> ZHETRI_3 computes the inverse of a complex Hermitian indefinite
*> matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK:
*>
*> A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),
*>
*> where U (or L) is unit upper (or lower) triangular matrix,
*> U**H (or L**H) is the conjugate of U (or L), P is a permutation
*> matrix, P**T is the transpose of P, and D is Hermitian and block
*> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
*>
*> ZHETRI_3 sets the leading dimension of the workspace before calling
*> ZHETRI_3X that actually computes the inverse. This is the blocked
*> version of the algorithm, calling Level 3 BLAS.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> 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 ZHETRF_RK and ZHETRF_BK:
*> a) ONLY diagonal elements of the Hermitian 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 Hermitian 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*> E is COMPLEX*16 array, dimension (N)
*> On entry, contains the superdiagonal (or subdiagonal)
*> elements of the Hermitian 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 refernced;
*> 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.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> Details of the interchanges and the block structure of D
*> as determined by ZHETRF_RK or ZHETRF_BK.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3).
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of WORK. LWORK >= (N+NB+1)*(NB+3).
*>
*> If LDWORK = -1, then a workspace query is assumed;
*> the routine only calculates the optimal size of 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.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> 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.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16HEcomputational
*
*> \par Contributors:
* ==================
*> \verbatim
*>
*> December 2016, Igor Kozachenko,
*> Computer Science Division,
*> University of California, Berkeley
*>
*> \endverbatim
*
* =====================================================================
SUBROUTINE ZHETRI_3( UPLO, N, A, LDA, E, IPIV, WORK, LWORK,
$ INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, LWORK, N
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX*16 A( LDA, * ), E( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL UPPER, LQUERY
INTEGER LWKOPT, NB
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL ZHETRI_3X
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
LQUERY = ( LWORK.EQ.-1 )
*
* Determine the block size
*
NB = MAX( 1, ILAENV( 1, 'ZHETRI_3', UPLO, N, -1, -1, -1 ) )
LWKOPT = ( N+NB+1 ) * ( NB+3 )
*
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -4
ELSE IF ( LWORK .LT. LWKOPT .AND. .NOT.LQUERY ) THEN
INFO = -8
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZHETRI_3', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
WORK( 1 ) = LWKOPT
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
CALL ZHETRI_3X( UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO )
*
WORK( 1 ) = LWKOPT
*
RETURN
*
* End of ZHETRI_3
*
END