zlauu2.f

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*> \brief \b ZLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE ZLAUU2( UPLO, N, A, LDA, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, N
*       ..
*       .. Array Arguments ..
*       COMPLEX*16         A( LDA, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZLAUU2 computes the product U * U**H or L**H * L, where the triangular
*> factor U or L is stored in the upper or lower triangular part of
*> the array A.
*>
*> If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
*> overwriting the factor U in A.
*> If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
*> overwriting the factor L in A.
*>
*> This is the unblocked form of the algorithm, calling Level 2 BLAS.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the triangular factor stored in the array A
*>          is upper or lower triangular:
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the triangular factor U or L.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is COMPLEX*16 array, dimension (LDA,N)
*>          On entry, the triangular factor U or L.
*>          On exit, if UPLO = 'U', the upper triangle of A is
*>          overwritten with the upper triangle of the product U * U**H;
*>          if UPLO = 'L', the lower triangle of A is overwritten with
*>          the lower triangle of the product L**H * L.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0: successful exit
*>          < 0: if INFO = -k, the k-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup lauu2
*
*  =====================================================================
      SUBROUTINE zlauu2( UPLO, N, A, LDA, INFO )
*
*  -- LAPACK auxiliary 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, N
*     ..
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ONE
      parameter( one = ( 1.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I
      DOUBLE PRECISION   AII
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      COMPLEX*16         ZDOTC
      EXTERNAL           lsame, zdotc
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zdscal, zgemv, zlacgv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble, dcmplx, max
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      upper = lsame( uplo, 'U' )
      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
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZLAUU2', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
      IF( upper ) THEN
*
*        Compute the product U * U**H.
*
         DO 10 i = 1, n
            aii = dble( a( i, i ) )
            IF( i.LT.n ) THEN
               a( i, i ) = aii*aii + dble( zdotc( n-i, a( i, i+1 ),
     $            lda,
     $                     a( i, i+1 ), lda ) )
               CALL zlacgv( n-i, a( i, i+1 ), lda )
               CALL zgemv( 'No transpose', i-1, n-i, one, a( 1,
     $                     i+1 ),
     $                     lda, a( i, i+1 ), lda, dcmplx( aii ),
     $                     a( 1, i ), 1 )
               CALL zlacgv( n-i, a( i, i+1 ), lda )
            ELSE
               CALL zdscal( i, aii, a( 1, i ), 1 )
            END IF
   10    CONTINUE
*
      ELSE
*
*        Compute the product L**H * L.
*
         DO 20 i = 1, n
            aii = dble( a( i, i ) )
            IF( i.LT.n ) THEN
               a( i, i ) = aii*aii + dble( zdotc( n-i, a( i+1, i ),
     $            1,
     $                     a( i+1, i ), 1 ) )
               CALL zlacgv( i-1, a( i, 1 ), lda )
               CALL zgemv( 'Conjugate transpose', n-i, i-1, one,
     $                     a( i+1, 1 ), lda, a( i+1, i ), 1,
     $                     dcmplx( aii ), a( i, 1 ), lda )
               CALL zlacgv( i-1, a( i, 1 ), lda )
            ELSE
               CALL zdscal( i, aii, a( i, 1 ), lda )
            END IF
   20    CONTINUE
      END IF
*
      RETURN
*
*     End of ZLAUU2
*
      SUBROUTINE zlauu2( UPLO, N, A, LDA, INFO ) …
      END