dorgl2.f

*> \brief \b DORGL2
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DORGL2( 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
*>
*> DORGL2 generates an m by n real matrix Q with orthonormal rows,
*> which is defined as the first m rows of a product of k elementary
*> reflectors of order n
*>
*>       Q  =  H(k) . . . H(2) H(1)
*>
*> as returned by DGELQF.
*> \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 i-th row must contain the vector which defines
*>          the elementary reflector H(i), for i = 1,2,...,k, as returned
*>          by DGELQF in the first 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 DGELQF.
*> \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 doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DORGL2( 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, 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( 'DORGL2', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( M.LE.0 )
     $   RETURN
*
      IF( K.LT.M ) THEN
*
*        Initialise rows k+1:m to rows of the unit matrix
*
         DO 20 J = 1, N
            DO 10 L = K + 1, M
               A( L, J ) = ZERO
   10       CONTINUE
            IF( J.GT.K .AND. J.LE.M )
     $         A( J, J ) = ONE
   20    CONTINUE
      END IF
*
      DO 40 I = K, 1, -1
*
*        Apply H(i) to A(i:m,i:n) from the right
*
         IF( I.LT.N ) THEN
            IF( I.LT.M ) THEN
               A( I, I ) = ONE
               CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
     $                     TAU( I ), A( I+1, I ), LDA, WORK )
            END IF
            CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
         END IF
         A( I, I ) = ONE - TAU( I )
*
*        Set A(i,1:i-1) to zero
*
         DO 30 L = 1, I - 1
            A( I, L ) = ZERO
   30    CONTINUE
   40 CONTINUE
      RETURN
*
*     End of DORGL2
*
      END