dgelqs.f

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*> \brief \b DGELQS
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
*                          INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), TAU( * ),
*      $                   WORK( LWORK )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> Compute a minimum-norm solution
*>     min || A*X - B ||
*> using the LQ factorization
*>     A = L*Q
*> computed by DGELQF.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix A.  M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix A.  N >= M >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of columns of B.  NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          Details of the LQ factorization of the original matrix A as
*>          returned by DGELQF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= M.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is DOUBLE PRECISION array, dimension (M)
*>          Details of the orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
*>          On entry, the m-by-nrhs right hand side matrix B.
*>          On exit, the n-by-nrhs solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B. LDB >= N.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The length of the array WORK.  LWORK must be at least NRHS,
*>          and should be at least NRHS*NB, where NB is the block size
*>          for this environment.
*> \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 double_lin
*
*  =====================================================================
      SUBROUTINE dgelqs( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
     $                   INFO )
*
*  -- LAPACK test 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, LDA, LDB, LWORK, M, N, NRHS
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), TAU( * ),
     $                   work( lwork )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. External Subroutines ..
      EXTERNAL           dlaset, dormlq, dtrsm, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      IF( m.LT.0 ) THEN
         info = -1
      ELSE IF( n.LT.0 .OR. m.GT.n ) THEN
         info = -2
      ELSE IF( nrhs.LT.0 ) THEN
         info = -3
      ELSE IF( lda.LT.max( 1, m ) ) THEN
         info = -5
      ELSE IF( ldb.LT.max( 1, n ) ) THEN
         info = -8
      ELSE IF( lwork.LT.1 .OR. lwork.LT.nrhs .AND. m.GT.0 .AND. n.GT.0 )
     $          THEN
         info = -10
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DGELQS', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 .OR. nrhs.EQ.0 .OR. m.EQ.0 )
     $   RETURN
*
*     Solve L*X = B(1:m,:)
*
      CALL dtrsm( 'Left', 'Lower', 'No transpose', 'Non-unit', m, nrhs,
     $            one, a, lda, b, ldb )
*
*     Set B(m+1:n,:) to zero
*
      IF( m.LT.n )
     $   CALL dlaset( 'Full', n-m, nrhs, zero, zero, b( m+1, 1 ), ldb )
*
*     B := Q' * B
*
      CALL dormlq( 'Left', 'Transpose', n, nrhs, m, a, lda, tau, b, ldb,
     $             work, lwork, info )
*
      RETURN
*
*     End of DGELQS
*
      END