dopgtr.f

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*> \brief \b DOPGTR
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDQ, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DOPGTR generates a real orthogonal matrix Q which is defined as the
*> product of n-1 elementary reflectors H(i) of order n, as returned by
*> DSPTRD 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 DSPTRD;
*>          = 'L': Lower triangular packed storage used in previous
*>                 call to DSPTRD.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix Q. N >= 0.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
*>          The vectors which define the elementary reflectors, as
*>          returned by DSPTRD.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is DOUBLE PRECISION array, dimension (N-1)
*>          TAU(i) must contain the scalar factor of the elementary
*>          reflector H(i), as returned by DSPTRD.
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
*>          The N-by-N orthogonal 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 DOUBLE PRECISION 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.
*
*> \ingroup upgtr
*
*  =====================================================================
      SUBROUTINE dopgtr( UPLO, N, AP, TAU, Q, LDQ, WORK, 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, LDQ, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, IINFO, IJ, J
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           dorg2l, dorg2r, xerbla
*     ..
*     .. 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( 'DOPGTR', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
      IF( upper ) THEN
*
*        Q was determined by a call to DSPTRD 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 ) = zero
   20    CONTINUE
         DO 30 i = 1, n - 1
            q( i, n ) = zero
   30    CONTINUE
         q( n, n ) = one
*
*        Generate Q(1:n-1,1:n-1)
*
         CALL dorg2l( n-1, n-1, n-1, q, ldq, tau, work, iinfo )
*
      ELSE
*
*        Q was determined by a call to DSPTRD 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 ) = one
         DO 40 i = 2, n
            q( i, 1 ) = zero
   40    CONTINUE
         ij = 3
         DO 60 j = 2, n
            q( 1, j ) = zero
            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 dorg2r( n-1, n-1, n-1, q( 2, 2 ), ldq, tau, work,
     $                   iinfo )
         END IF
      END IF
      RETURN
*
*     End of DOPGTR
*
      END