dorgtr.f

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*> \brief \b DORGTR
*
*  =========== DOCUMENTATION ===========
*
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*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, LWORK, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DORGTR generates a real orthogonal matrix Q which is defined as the
*> product of n-1 elementary reflectors of order N, as returned by
*> DSYTRD:
*>
*> 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 triangle of A contains elementary reflectors
*>                 from DSYTRD;
*>          = 'L': Lower triangle of A contains elementary reflectors
*>                 from DSYTRD.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix Q. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          On entry, the vectors which define the elementary reflectors,
*>          as returned by DSYTRD.
*>          On exit, the N-by-N orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A. LDA >= max(1,N).
*> \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 DSYTRD.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The dimension of the array WORK. LWORK >= max(1,N-1).
*>          For optimum performance LWORK >= (N-1)*NB, where NB is
*>          the optimal blocksize.
*>
*>          If LWORK = -1, then a workspace query is assumed; the routine
*>          only 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
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup ungtr
*
*  =====================================================================
      SUBROUTINE dorgtr( UPLO, N, A, LDA, TAU, 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 ..
      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, UPPER
      INTEGER            I, IINFO, J, LWKOPT, NB
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           lsame, ilaenv
*     ..
*     .. External Subroutines ..
      EXTERNAL           dorgql, dorgqr, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      lquery = ( lwork.EQ.-1 )
      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
      ELSE IF( lwork.LT.max( 1, n-1 ) .AND. .NOT.lquery ) THEN
         info = -7
      END IF
*
      IF( info.EQ.0 ) THEN
         IF( upper ) THEN
            nb = ilaenv( 1, 'DORGQL', ' ', n-1, n-1, n-1, -1 )
         ELSE
            nb = ilaenv( 1, 'DORGQR', ' ', n-1, n-1, n-1, -1 )
         END IF
         lwkopt = max( 1, n-1 )*nb
         work( 1 ) = lwkopt
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DORGTR', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 ) THEN
         work( 1 ) = 1
         RETURN
      END IF
*
      IF( upper ) THEN
*
*        Q was determined by a call to DSYTRD with UPLO = 'U'
*
*        Shift the vectors which define the elementary reflectors one
*        column to the left, and set the last row and column of Q to
*        those of the unit matrix
*
         DO 20 j = 1, n - 1
            DO 10 i = 1, j - 1
               a( i, j ) = a( i, j+1 )
   10       CONTINUE
            a( n, j ) = zero
   20    CONTINUE
         DO 30 i = 1, n - 1
            a( i, n ) = zero
   30    CONTINUE
         a( n, n ) = one
*
*        Generate Q(1:n-1,1:n-1)
*
         CALL dorgql( n-1, n-1, n-1, a, lda, tau, work, lwork,
     $                iinfo )
*
      ELSE
*
*        Q was determined by a call to DSYTRD with UPLO = 'L'.
*
*        Shift the vectors which define the elementary reflectors one
*        column to the right, and set the first row and column of Q to
*        those of the unit matrix
*
         DO 50 j = n, 2, -1
            a( 1, j ) = zero
            DO 40 i = j + 1, n
               a( i, j ) = a( i, j-1 )
   40       CONTINUE
   50    CONTINUE
         a( 1, 1 ) = one
         DO 60 i = 2, n
            a( i, 1 ) = zero
   60    CONTINUE
         IF( n.GT.1 ) THEN
*
*           Generate Q(2:n,2:n)
*
            CALL dorgqr( n-1, n-1, n-1, a( 2, 2 ), lda, tau, work,
     $                   lwork, iinfo )
         END IF
      END IF
      work( 1 ) = lwkopt
      RETURN
*
*     End of DORGTR
*
      SUBROUTINE dorgtr( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) …
      END