OpenBLAS/lapack-netlib/SRC/zupgtr.f

*> \brief \b ZUPGTR
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDQ, N
*       ..
*       .. Array Arguments ..
*       COMPLEX*16         AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZUPGTR generates a complex unitary matrix Q which is defined as the
*> product of n-1 elementary reflectors H(i) of order n, as returned by
*> ZHPTRD using packed storage:
*>
*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U': Upper triangular packed storage used in previous
*>                 call to ZHPTRD;
*>          = 'L': Lower triangular packed storage used in previous
*>                 call to ZHPTRD.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix Q. N >= 0.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
*>          The vectors which define the elementary reflectors, as
*>          returned by ZHPTRD.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is COMPLEX*16 array, dimension (N-1)
*>          TAU(i) must contain the scalar factor of the elementary
*>          reflector H(i), as returned by ZHPTRD.
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*>          Q is COMPLEX*16 array, dimension (LDQ,N)
*>          The N-by-N unitary matrix Q.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*>          LDQ is INTEGER
*>          The leading dimension of the array Q. LDQ >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 array, dimension (N-1)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-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.
*
*> \date December 2016
*
*> \ingroup complex16OTHERcomputational
*
*  =====================================================================
      SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, 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, LDQ, N
*     ..
*     .. Array Arguments ..
      COMPLEX*16         AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         CZERO, CONE
      PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
     $                   CONE = ( 1.0D+0, 0.0D+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, IINFO, IJ, J
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA, ZUNG2L, ZUNG2R
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      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( LDQ.LT.MAX( 1, N ) ) THEN
         INFO = -6
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'ZUPGTR', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
      IF( UPPER ) THEN
*
*        Q was determined by a call to ZHPTRD with UPLO = 'U'
*
*        Unpack the vectors which define the elementary reflectors and
*        set the last row and column of Q equal to those of the unit
*        matrix
*
         IJ = 2
         DO 20 J = 1, N - 1
            DO 10 I = 1, J - 1
               Q( I, J ) = AP( IJ )
               IJ = IJ + 1
   10       CONTINUE
            IJ = IJ + 2
            Q( N, J ) = CZERO
   20    CONTINUE
         DO 30 I = 1, N - 1
            Q( I, N ) = CZERO
   30    CONTINUE
         Q( N, N ) = CONE
*
*        Generate Q(1:n-1,1:n-1)
*
         CALL ZUNG2L( N-1, N-1, N-1, Q, LDQ, TAU, WORK, IINFO )
*
      ELSE
*
*        Q was determined by a call to ZHPTRD with UPLO = 'L'.
*
*        Unpack the vectors which define the elementary reflectors and
*        set the first row and column of Q equal to those of the unit
*        matrix
*
         Q( 1, 1 ) = CONE
         DO 40 I = 2, N
            Q( I, 1 ) = CZERO
   40    CONTINUE
         IJ = 3
         DO 60 J = 2, N
            Q( 1, J ) = CZERO
            DO 50 I = J + 1, N
               Q( I, J ) = AP( IJ )
               IJ = IJ + 1
   50       CONTINUE
            IJ = IJ + 2
   60    CONTINUE
         IF( N.GT.1 ) THEN
*
*           Generate Q(2:n,2:n)
*
            CALL ZUNG2R( N-1, N-1, N-1, Q( 2, 2 ), LDQ, TAU, WORK,
     $                   IINFO )
         END IF
      END IF
      RETURN
*
*     End of ZUPGTR
*
      END