cunmqr.f

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*> \brief \b CUNMQR
*
*  =========== DOCUMENTATION ===========
*
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*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE CUNMQR( 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 ..
*       COMPLEX            A( LDA, * ), C( LDC, * ), TAU( * ),
*      $                   WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CUNMQR overwrites the general complex M-by-N matrix C with
*>
*>                 SIDE = 'L'     SIDE = 'R'
*> TRANS = 'N':      Q * C          C * Q
*> TRANS = 'C':      Q**H * C       C * Q**H
*>
*> where Q is a complex unitary matrix defined as the product of k
*> elementary reflectors
*>
*>       Q = H(1) H(2) . . . H(k)
*>
*> as returned by CGEQRF. 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**H from the Left;
*>          = 'R': apply Q or Q**H from the Right.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          = 'N':  No transpose, apply Q;
*>          = 'C':  Conjugate transpose, apply Q**H.
*> \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 COMPLEX array, dimension (LDA,K)
*>          The i-th column must contain the vector which defines the
*>          elementary reflector H(i), for i = 1,2,...,k, as returned by
*>          CGEQRF in the first k columns of its array argument A.
*> \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] TAU
*> \verbatim
*>          TAU is COMPLEX array, dimension (K)
*>          TAU(i) must contain the scalar factor of the elementary
*>          reflector H(i), as returned by CGEQRF.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*>          C is COMPLEX array, dimension (LDC,N)
*>          On entry, the M-by-N matrix C.
*>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H 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 COMPLEX 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.
*
*> \ingroup complexOTHERcomputational
*
*  =====================================================================
      SUBROUTINE cunmqr( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
     $                   WORK, LWORK, 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 ..
      CHARACTER          SIDE, TRANS
      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
*     ..
*     .. Array Arguments ..
      COMPLEX            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
      INTEGER            I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK,
     $                   lwkopt, mi, nb, nbmin, ni, nq, nw
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           lsame, ilaenv
*     ..
*     .. External Subroutines ..
      EXTERNAL           clarfb, clarft, cunm2r, 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, 'C' ) ) 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, nq ) ) 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
*
         nb = min( nbmax, ilaenv( 1, 'CUNMQR', side // trans, m, n, k,
     $        -1 ) )
         lwkopt = nw*nb + tsize
         work( 1 ) = lwkopt
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'cunmqr', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
.EQ..OR..EQ..OR..EQ.      IF( M0  N0  K0 ) THEN
         WORK( 1 ) = 1
         RETURN
      END IF
*
      NBMIN = 2
      LDWORK = NW
.GT..AND..LT.      IF( NB1  NBK ) THEN
.LT.         IF( LWORKLWKOPT ) THEN
            NB = (LWORK-TSIZE) / LDWORK
            NBMIN = MAX( 2, ILAENV( 2, 'cunmqr', SIDE // TRANS, M, N, K,
     $              -1 ) )
         END IF
      END IF
*
.LT..OR..GE.      IF( NBNBMIN  NBK ) THEN
*
*        Use unblocked code
*
         CALL CUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
     $                IINFO )
      ELSE
*
*        Use blocked code
*
         IWT = 1 + NW*NB
.AND..NOT..OR.         IF( ( LEFT  NOTRAN ) 
.NOT..AND.     $       ( LEFT  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
            JC = 1
         ELSE
            MI = M
            IC = 1
         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) H(i+1) . . . H(i+ib-1)
*
            CALL CLARFT( 'forward', 'columnwise', NQ-I+1, IB, A( I, I ),
     $                   LDA, TAU( I ), WORK( IWT ), LDT )
            IF( LEFT ) THEN
*
*              H or H**H is applied to C(i:m,1:n)
*
               MI = M - I + 1
               IC = I
            ELSE
*
*              H or H**H is applied to C(1:m,i:n)
*
               NI = N - I + 1
               JC = I
            END IF
*
*           Apply H or H**H
*
            CALL CLARFB( SIDE, TRANS, 'forward', 'columnwise', MI, NI,
     $                   IB, A( I, I ), LDA, WORK( IWT ), LDT,
     $                   C( IC, JC ), LDC, WORK, LDWORK )
   10    CONTINUE
      END IF
      WORK( 1 ) = LWKOPT
      RETURN
*
*     End of CUNMQR
*
      END