sorg2l.f

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*> \brief \b SORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE SORG2L( M, N, K, A, LDA, TAU, WORK, INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            INFO, K, LDA, M, N
*       ..
*       .. Array Arguments ..
*       REAL               A( LDA, * ), TAU( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SORG2L generates an m by n real matrix Q with orthonormal columns,
*> which is defined as the last n columns of a product of k elementary
*> reflectors of order m
*>
*>       Q  =  H(k) . . . H(2) H(1)
*>
*> as returned by SGEQLF.
*> \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. M >= N >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*>          K is INTEGER
*>          The number of elementary reflectors whose product defines the
*>          matrix Q. N >= K >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is REAL array, dimension (LDA,N)
*>          On entry, the (n-k+i)-th column must contain the vector which
*>          defines the elementary reflector H(i), for i = 1,2,...,k, as
*>          returned by SGEQLF in the last k columns 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 REAL array, dimension (K)
*>          TAU(i) must contain the scalar factor of the elementary
*>          reflector H(i), as returned by SGEQLF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (N)
*> \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 ung2l
*
*  =====================================================================
      SUBROUTINE sorg2l( 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 ..
      REAL               A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      parameter( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, II, J, L
*     ..
*     .. External Subroutines ..
      EXTERNAL           slarf, sscal, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      IF( m.LT.0 ) THEN
         info = -1
      ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
         info = -2
      ELSE IF( k.LT.0 .OR. k.GT.n ) THEN
         info = -3
      ELSE IF( lda.LT.max( 1, m ) ) THEN
         info = -5
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'SORG2L', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.LE.0 )
     $   RETURN
*
*     Initialise columns 1:n-k to columns of the unit matrix
*
      DO 20 j = 1, n - k
         DO 10 l = 1, m
            a( l, j ) = zero
   10    CONTINUE
         a( m-n+j, j ) = one
   20 CONTINUE
*
      DO 40 i = 1, k
         ii = n - k + i
*
*        Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
*
         a( m-n+ii, ii ) = one
         CALL slarf( 'Left', m-n+ii, ii-1, a( 1, ii ), 1, tau( i ), a,
     $               lda, work )
         CALL sscal( m-n+ii-1, -tau( i ), a( 1, ii ), 1 )
         a( m-n+ii, ii ) = one - tau( i )
*
*        Set A(m-k+i+1:m,n-k+i) to zero
*
         DO 30 l = m - n + ii + 1, m
            a( l, ii ) = zero
   30    CONTINUE
   40 CONTINUE
      RETURN
*
*     End of SORG2L
*
      END