dormrq.f

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*> \brief \b DORMRQ
*
*  =========== DOCUMENTATION ===========
*
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*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DORMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
*                          WORK, LWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          SIDE, TRANS
*       INTEGER            INFO, K, LDA, LDC, LWORK, M, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DORMRQ 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)
*>
*> as returned by DGERQF. 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;
*>          = 'T':  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] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension
*>                               (LDA,M) if SIDE = 'L',
*>                               (LDA,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
*>          DGERQF in the last k rows of its array argument A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A. LDA >= max(1,K).
*> \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[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 or Q**T*C or 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, dimension (MAX(1,LWORK))
*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The dimension of the array WORK.
*>          If SIDE = 'L', LWORK >= max(1,N);
*>          if SIDE = 'R', LWORK >= max(1,M).
*>          For good performance, LWORK should generally be larger.
*>
*>          If LWORK = -1, then a workspace query is assumed; the routine
*>          only calculates the optimal size of the WORK array, returns
*>          this value as the first entry of the WORK array, and no error
*>          message related to LWORK is issued by XERBLA.
*> \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 December 2016
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE dormrq( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
     $                   WORK, LWORK, INFO )
*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE, TRANS
      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( lda, * ), C( ldc, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            NBMAX, LDT, TSIZE
      parameter( nbmax = 64, ldt = nbmax+1,
     $                     tsize = ldt*nbmax )
*     ..
*     .. Local Scalars ..
      LOGICAL            LEFT, LQUERY, NOTRAN
      CHARACTER          TRANST
      INTEGER            I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT,
     $                   mi, nb, nbmin, ni, nq, nw
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           lsame, ilaenv
*     ..
*     .. External Subroutines ..
      EXTERNAL           dlarfb, dlarft, dormr2, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      left = lsame( side, 'L' )
      notran = lsame( trans, 'N' )
      lquery = ( lwork.EQ.-1 )
*
*     NQ is the order of Q and NW is the minimum dimension of WORK
*
      IF( left ) THEN
         nq = m
         nw = max( 1, n )
      ELSE
         nq = n
         nw = max( 1, m )
      END IF
      IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
         info = -1
      ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
         info = -2
      ELSE IF( m.LT.0 ) THEN
         info = -3
      ELSE IF( n.LT.0 ) THEN
         info = -4
      ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
         info = -5
      ELSE IF( lda.LT.max( 1, k ) ) THEN
         info = -7
      ELSE IF( ldc.LT.max( 1, m ) ) THEN
         info = -10
      ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
         info = -12
      END IF
*
      IF( info.EQ.0 ) THEN
*
*        Compute the workspace requirements
*
         IF( m.EQ.0 .OR. n.EQ.0 ) THEN
            lwkopt = 1
         ELSE
            nb = min( nbmax, ilaenv( 1, 'DORMRQ', side // trans, m, n,
     $                               k, -1 ) )
            lwkopt = nw*nb + tsize
         END IF
         work( 1 ) = lwkopt
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DORMRQ', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.EQ.0 .OR. n.EQ.0 ) THEN
         RETURN
      END IF
*
      nbmin = 2
      ldwork = nw
      IF( nb.GT.1 .AND. nb.LT.k ) THEN
         IF( lwork.LT.nw*nb+tsize ) THEN
            nb = (lwork-tsize) / ldwork
            nbmin = max( 2, ilaenv( 2, 'DORMRQ', side // trans, m, n, k,
     $              -1 ) )
         END IF
      END IF
*
      IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
*
*        Use unblocked code
*
         CALL dormr2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
     $                iinfo )
      ELSE
*
*        Use blocked code
*
         iwt = 1 + nw*nb
         IF( ( left .AND. .NOT.notran ) .OR.
     $       ( .NOT.left .AND. notran ) ) THEN
            i1 = 1
            i2 = k
            i3 = nb
         ELSE
            i1 = ( ( k-1 ) / nb )*nb + 1
            i2 = 1
            i3 = -nb
         END IF
*
         IF( left ) THEN
            ni = n
         ELSE
            mi = m
         END IF
*
         IF( notran ) THEN
            transt = 'T'
         ELSE
            transt = 'N'
         END IF
*
         DO 10 i = i1, i2, i3
            ib = min( nb, k-i+1 )
*
*           Form the triangular factor of the block reflector
*           H = H(i+ib-1) . . . H(i+1) H(i)
*
            CALL dlarft( 'Backward', 'Rowwise', nq-k+i+ib-1, ib,
     $                   a( i, 1 ), lda, tau( i ), work( iwt ), ldt )
            IF( left ) THEN
*
*              H or H**T is applied to C(1:m-k+i+ib-1,1:n)
*
               mi = m - k + i + ib - 1
            ELSE
*
*              H or H**T is applied to C(1:m,1:n-k+i+ib-1)
*
               ni = n - k + i + ib - 1
            END IF
*
*           Apply H or H**T
*
            CALL dlarfb( side, transt, 'Backward', 'Rowwise', mi, ni,
     $                   ib, a( i, 1 ), lda, work( iwt ), ldt, c, ldc,
     $                   work, ldwork )
   10    CONTINUE
      END IF
      work( 1 ) = lwkopt
      RETURN
*
*     End of DORMRQ
*
      END