dgemqr.f

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*
*  Definition:
*  ===========
*
*      SUBROUTINE DGEMQR( SIDE, TRANS, M, N, K, A, LDA, T,
*     $                   TSIZE, C, LDC, WORK, LWORK, INFO )
*
*
*     .. Scalar Arguments ..
*     CHARACTER         SIDE, TRANS
*     INTEGER           INFO, LDA, M, N, K, LDT, TSIZE, LWORK, LDC
*     ..
*     .. Array Arguments ..
*     DOUBLE PRECISION  A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
*     ..
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DGEMQR 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 blocked elementary reflectors computed by tall skinny
*> QR factorization (DGEQR)
*>
*> \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 A.  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,K)
*>          Part of the data structure to represent Q as returned by DGEQR.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.
*>          If SIDE = 'L', LDA >= max(1,M);
*>          if SIDE = 'R', LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] T
*> \verbatim
*>          T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)).
*>          Part of the data structure to represent Q as returned by DGEQR.
*> \endverbatim
*>
*> \param[in] TSIZE
*> \verbatim
*>          TSIZE is INTEGER
*>          The dimension of the array T. TSIZE >= 5.
*> \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
*>         (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The dimension of the array WORK.
*>          If LWORK = -1, then a workspace query is assumed. The routine
*>          only calculates the size of the WORK array, returns this
*>          value as WORK(1), and no error message related to WORK 
*>          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.
*
*> \par Further Details
*  ====================
*>
*> \verbatim
*>
*> These details are particular for this LAPACK implementation. Users should not 
*> take them for granted. These details may change in the future, and are unlikely not
*> true for another LAPACK implementation. These details are relevant if one wants
*> to try to understand the code. They are not part of the interface.
*>
*> In this version,
*>
*>          T(2): row block size (MB)
*>          T(3): column block size (NB)
*>          T(6:TSIZE): data structure needed for Q, computed by
*>                           DLATSQR or DGEQRT
*>
*>  Depending on the matrix dimensions M and N, and row and column
*>  block sizes MB and NB returned by ILAENV, DGEQR will use either
*>  DLATSQR (if the matrix is tall-and-skinny) or DGEQRT to compute
*>  the QR factorization.
*>  This version of DGEMQR will use either DLAMTSQR or DGEMQRT to 
*>  multiply matrix Q by another matrix.
*>  Further Details in DLATMSQR or DGEMQRT.
*>
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE dgemqr( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
     $                   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, LDA, M, N, K, TSIZE, LWORK, LDC
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( lda, * ), T( * ), C( ldc, * ), WORK( * )
*     ..
*
* =====================================================================
*
*     ..
*     .. Local Scalars ..
      LOGICAL            LEFT, RIGHT, TRAN, NOTRAN, LQUERY
      INTEGER            MB, NB, LW, NBLCKS, MN
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           dgemqrt, dlamtsqr, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          int, max, min, mod
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      lquery  = lwork.EQ.-1
      notran  = lsame( trans, 'N' )
      tran    = lsame( trans, 'T' )
      left    = lsame( side, 'L' )
      right   = lsame( side, 'R' )
*
      mb = int( t( 2 ) )
      nb = int( t( 3 ) )
      IF( left ) THEN
        lw = n * nb
        mn = m
      ELSE
        lw = mb * nb
        mn = n
      END IF
*
      IF( ( mb.GT.k ) .AND. ( mn.GT.k ) ) THEN
        IF( mod( mn - k, mb - k ).EQ.0 ) THEN
          nblcks = ( mn - k ) / ( mb - k )
        ELSE
          nblcks = ( mn - k ) / ( mb - k ) + 1
        END IF
      ELSE
        nblcks = 1
      END IF
*
      info = 0
      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 .OR. k.GT.mn ) THEN
        info = -5
      ELSE IF( lda.LT.max( 1, mn ) ) THEN
        info = -7
      ELSE IF( tsize.LT.5 ) THEN
        info = -9
      ELSE IF( ldc.LT.max( 1, m ) ) THEN
        info = -11
      ELSE IF( ( lwork.LT.max( 1, lw ) ) .AND. ( .NOT.lquery ) ) THEN
        info = -13
      END IF
*
      IF( info.EQ.0 ) THEN
        work( 1 ) = lw
      END IF
*
      IF( info.NE.0 ) THEN
        CALL xerbla( 'DGEMQR', -info )
        RETURN
      ELSE IF( lquery ) THEN
        RETURN
      END IF
*
*     Quick return if possible
*
      IF( min( m, n, k ).EQ.0 ) THEN
        RETURN
      END IF
*
      IF( ( left .AND. m.LE.k ) .OR. ( right .AND. n.LE.k )
     $     .OR. ( mb.LE.k ) .OR. ( mb.GE.max( m, n, k ) ) ) THEN
        CALL dgemqrt( side, trans, m, n, k, nb, a, lda, t( 6 ),
     $                nb, c, ldc, work, info )
      ELSE
        CALL dlamtsqr( side, trans, m, n, k, mb, nb, a, lda, t( 6 ),
     $                 nb, c, ldc, work, lwork, info )
      END IF
*
      work( 1 ) = lw
*
      RETURN
*
*     End of DGEMQR
*
      END