dorgr2.f

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*> \brief \b DORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DORGR2( M, N, K, A, LDA, TAU, WORK, INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            INFO, K, LDA, M, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DORGR2 generates an m by n real matrix Q with orthonormal rows,
*> which is defined as the last m rows of a product of k elementary
*> reflectors of order n
*>
*>       Q  =  H(1) H(2) . . . H(k)
*>
*> as returned by DGERQF.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix Q. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix Q. N >= M.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*>          K is INTEGER
*>          The number of elementary reflectors whose product defines the
*>          matrix Q. M >= K >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          On entry, the (m-k+i)-th row must contain the vector which
*>          defines the elementary reflector H(i), for i = 1,2,...,k, as
*>          returned by DGERQF in the last k rows of its array argument
*>          A.
*>          On exit, the m by n matrix Q.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The first dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is DOUBLE PRECISION array, dimension (K)
*>          TAU(i) must contain the scalar factor of the elementary
*>          reflector H(i), as returned by DGERQF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (M)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0: successful exit
*>          < 0: if INFO = -i, the i-th argument has an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup ungr2
*
*  =====================================================================
      SUBROUTINE dorgr2( M, N, K, A, LDA, TAU, 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 ..
      INTEGER            INFO, K, LDA, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      parameter( one = 1.0d+0, zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, II, J, L
*     ..
*     .. External Subroutines ..
      EXTERNAL           dlarf, dscal, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      IF( m.LT.0 ) THEN
         info = -1
      ELSE IF( n.LT.m ) THEN
         info = -2
      ELSE IF( k.LT.0 .OR. k.GT.m ) THEN
         info = -3
      ELSE IF( lda.LT.max( 1, m ) ) THEN
         info = -5
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DORGR2', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.LE.0 )
     $   RETURN
*
      IF( k.LT.m ) THEN
*
*        Initialise rows 1:m-k to rows of the unit matrix
*
         DO 20 j = 1, n
            DO 10 l = 1, m - k
               a( l, j ) = zero
   10       CONTINUE
            IF( j.GT.n-m .AND. j.LE.n-k )
     $         a( m-n+j, j ) = one
   20    CONTINUE
      END IF
*
      DO 40 i = 1, k
         ii = m - k + i
*
*        Apply H(i) to A(1:m-k+i,1:n-k+i) from the right
*
         a( ii, n-m+ii ) = one
         CALL dlarf( 'Right', ii-1, n-m+ii, a( ii, 1 ), lda, tau( i ),
     $               a, lda, work )
         CALL dscal( n-m+ii-1, -tau( i ), a( ii, 1 ), lda )
         a( ii, n-m+ii ) = one - tau( i )
*
*        Set A(m-k+i,n-k+i+1:n) to zero
*
         DO 30 l = n - m + ii + 1, n
            a( ii, l ) = zero
   30    CONTINUE
   40 CONTINUE
      RETURN
*
*     End of DORGR2
*
      END