dgemlqt.f

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*> \brief \b DGEMLQT
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DGEMLQT( SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT,
*                          C, LDC, WORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER SIDE, TRANS
*       INTEGER   INFO, K, LDV, LDC, M, N, MB, LDT
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DGEMLQT overwrites the general real M-by-N matrix C with
*>
*>                 SIDE = 'L'     SIDE = 'R'
*> TRANS = 'N':      Q C            C Q
*> TRANS = 'T':   Q**T C            C Q**T
*>
*> where Q is a real orthogonal matrix defined as the product of K
*> elementary reflectors:
*>
*>       Q = H(1) H(2) . . . H(K) = I - V T V**T
*>
*> generated using the compact WY representation as returned by DGELQT.
*>
*> Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] SIDE
*> \verbatim
*>          SIDE is CHARACTER*1
*>          = 'L': apply Q or Q**T from the Left;
*>          = 'R': apply Q or Q**T from the Right.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          = 'N':  No transpose, apply Q;
*>          = 'C':  Transpose, apply Q**T.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix C. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix C. N >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*>          K is INTEGER
*>          The number of elementary reflectors whose product defines
*>          the matrix Q.
*>          If SIDE = 'L', M >= K >= 0;
*>          if SIDE = 'R', N >= K >= 0.
*> \endverbatim
*>
*> \param[in] MB
*> \verbatim
*>          MB is INTEGER
*>          The block size used for the storage of T.  K >= MB >= 1.
*>          This must be the same value of MB used to generate T
*>          in DGELQT.
*> \endverbatim
*>
*> \param[in] V
*> \verbatim
*>          V is DOUBLE PRECISION array, dimension
*>                               (LDV,M) if SIDE = 'L',
*>                               (LDV,N) if SIDE = 'R'
*>          The i-th row must contain the vector which defines the
*>          elementary reflector H(i), for i = 1,2,...,k, as returned by
*>          DGELQT in the first K rows of its array argument A.
*> \endverbatim
*>
*> \param[in] LDV
*> \verbatim
*>          LDV is INTEGER
*>          The leading dimension of the array V. LDV >= max(1,K).
*> \endverbatim
*>
*> \param[in] T
*> \verbatim
*>          T is DOUBLE PRECISION array, dimension (LDT,K)
*>          The upper triangular factors of the block reflectors
*>          as returned by DGELQT, stored as a MB-by-K matrix.
*> \endverbatim
*>
*> \param[in] LDT
*> \verbatim
*>          LDT is INTEGER
*>          The leading dimension of the array T.  LDT >= MB.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*>          C is DOUBLE PRECISION array, dimension (LDC,N)
*>          On entry, the M-by-N matrix C.
*>          On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*>          LDC is INTEGER
*>          The leading dimension of the array C. LDC >= max(1,M).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array. The dimension of
*>          WORK is N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'.
*> \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.
*
*> \date June 2017
*
*> \ingroup doubleGEcomputational
*
*  =====================================================================
      SUBROUTINE dgemlqt( SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT,
     $                   C, LDC, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.7.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2017
*
*     .. Scalar Arguments ..
      CHARACTER SIDE, TRANS
      INTEGER   INFO, K, LDV, LDC, M, N, MB, LDT
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION V( ldv, * ), C( ldc, * ), T( ldt, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     ..
*     .. Local Scalars ..
      LOGICAL            LEFT, RIGHT, TRAN, NOTRAN
      INTEGER            I, IB, LDWORK, KF, Q
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, dlarfb
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     .. Test the input arguments ..
*
      info   = 0
      left   = lsame( side,  'L' )
      right  = lsame( side,  'R' )
      tran   = lsame( trans, 'T' )
      notran = lsame( trans, 'N' )
*
      IF( left ) THEN
         ldwork = max( 1, n )
      ELSE IF ( right ) THEN
         ldwork = max( 1, m )
      END IF
      IF( .NOT.left .AND. .NOT.right ) THEN
         info = -1
      ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
         info = -2
      ELSE IF( m.LT.0 ) THEN
         info = -3
      ELSE IF( n.LT.0 ) THEN
         info = -4
      ELSE IF( k.LT.0) THEN
         info = -5
      ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0)) THEN
         info = -6
      ELSE IF( ldv.LT.max( 1, k ) ) THEN
          info = -8
      ELSE IF( ldt.LT.mb ) THEN
         info = -10
      ELSE IF( ldc.LT.max( 1, m ) ) THEN
         info = -12
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DGEMLQT', -info )
         RETURN
      END IF
*
*     .. Quick return if possible ..
*
      IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
*
      IF( left .AND. notran ) THEN
*
         DO i = 1, k, mb
            ib = min( mb, k-i+1 )
            CALL dlarfb( 'L', 'T', 'F', 'R', m-i+1, n, ib,
     $                   v( i, i ), ldv, t( 1, i ), ldt,
     $                   c( i, 1 ), ldc, work, ldwork )
         END DO
*
      ELSE IF( right .AND. tran ) THEN
*
         DO i = 1, k, mb
            ib = min( mb, k-i+1 )
            CALL dlarfb( 'R', 'N', 'F', 'R', m, n-i+1, ib,
     $                   v( i, i ), ldv, t( 1, i ), ldt,
     $                   c( 1, i ), ldc, work, ldwork )
         END DO
*
      ELSE IF( left .AND. tran ) THEN
*
         kf = ((k-1)/mb)*mb+1
         DO i = kf, 1, -mb
            ib = min( mb, k-i+1 )
            CALL dlarfb( 'L', 'N', 'F', 'R', m-i+1, n, ib,
     $                   v( i, i ), ldv, t( 1, i ), ldt,
     $                   c( i, 1 ), ldc, work, ldwork )
         END DO
*
      ELSE IF( right .AND. notran ) THEN
*
         kf = ((k-1)/mb)*mb+1
         DO i = kf, 1, -mb
            ib = min( mb, k-i+1 )
            CALL dlarfb( 'R', 'T', 'F', 'R', m, n-i+1, ib,
     $                   v( i, i ), ldv, t( 1, i ), ldt,
     $                   c( 1, i ), ldc, work, ldwork )
         END DO
*
      END IF
*
      RETURN
*
*     End of DGEMLQT
*
      END