zhetri2.f

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*> \brief \b ZHETRI2
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE ZHETRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, LWORK, N
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       COMPLEX*16         A( LDA, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZHETRI2 computes the inverse of a COMPLEX*16 hermitian indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> ZHETRF. ZHETRI2 set the LEADING DIMENSION of the workspace
*> before calling ZHETRI2X that actually computes the inverse.
*> \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 triangular, form is A = U*D*U**T;
*>          = 'L':  Lower triangular, form is A = L*D*L**T.
*> \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, the block diagonal matrix D and the multipliers
*>          used to obtain the factor U or L as computed by ZHETRF.
*>
*>          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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \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.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)).
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The dimension of the array WORK.
*>          If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3).
*>          If LWORK = -1, then a workspace query is assumed; the routine
*>          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.
*> \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.
*
*> \ingroup hetri2
*
*  =====================================================================
      SUBROUTINE zhetri2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, LWORK, N
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX*16         A( LDA, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            UPPER, LQUERY
      INTEGER            MINSIZE, NBMAX
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           lsame, ilaenv
*     ..
*     .. External Subroutines ..
      EXTERNAL           zhetri2x, zhetri, xerbla
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      upper = lsame( uplo, 'U' )
      lquery = ( lwork.EQ.-1 )
*
*     Get blocksize
*
      nbmax = ilaenv( 1, 'ZHETRF', uplo, n, -1, -1, -1 )
      IF( n.EQ.0 ) THEN
         minsize = 1
      ELSE IF( nbmax.GE.n ) THEN
         minsize = n
      ELSE
         minsize = (n+nbmax+1)*(nbmax+3)
      END IF
*
      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.minsize .AND. .NOT.lquery ) THEN
         info = -7
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZHETRI2', -info )
         RETURN
      ELSE IF( lquery ) THEN
         work( 1 ) = minsize
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
 
      IF( nbmax.GE.n ) THEN
         CALL zhetri( uplo, n, a, lda, ipiv, work, info )
      ELSE
         CALL zhetri2x( uplo, n, a, lda, ipiv, work, nbmax, info )
      END IF
*
      RETURN
*
*     End of ZHETRI2
*
      END