dormbr.f

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*> \brief \b DORMBR
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
*                          LDC, WORK, LWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          SIDE, TRANS, VECT
*       INTEGER            INFO, K, LDA, LDC, LWORK, M, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> If VECT = 'Q', DORMBR 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
*>
*> If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C
*> with
*>                 SIDE = 'L'     SIDE = 'R'
*> TRANS = 'N':      P * C          C * P
*> TRANS = 'T':      P**T * C       C * P**T
*>
*> Here Q and P**T are the orthogonal matrices determined by DGEBRD when
*> reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
*> P**T are defined as products of elementary reflectors H(i) and G(i)
*> respectively.
*>
*> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
*> order of the orthogonal matrix Q or P**T that is applied.
*>
*> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
*> if nq >= k, Q = H(1) H(2) . . . H(k);
*> if nq < k, Q = H(1) H(2) . . . H(nq-1).
*>
*> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
*> if k < nq, P = G(1) G(2) . . . G(k);
*> if k >= nq, P = G(1) G(2) . . . G(nq-1).
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] VECT
*> \verbatim
*>          VECT is CHARACTER*1
*>          = 'Q': apply Q or Q**T;
*>          = 'P': apply P or P**T.
*> \endverbatim
*>
*> \param[in] SIDE
*> \verbatim
*>          SIDE is CHARACTER*1
*>          = 'L': apply Q, Q**T, P or P**T from the Left;
*>          = 'R': apply Q, Q**T, P or P**T from the Right.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          = 'N':  No transpose, apply Q  or P;
*>          = 'T':  Transpose, apply Q**T or P**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
*>          If VECT = 'Q', the number of columns in the original
*>          matrix reduced by DGEBRD.
*>          If VECT = 'P', the number of rows in the original
*>          matrix reduced by DGEBRD.
*>          K >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension
*>                                (LDA,min(nq,K)) if VECT = 'Q'
*>                                (LDA,nq)        if VECT = 'P'
*>          The vectors which define the elementary reflectors H(i) and
*>          G(i), whose products determine the matrices Q and P, as
*>          returned by DGEBRD.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.
*>          If VECT = 'Q', LDA >= max(1,nq);
*>          if VECT = 'P', LDA >= max(1,min(nq,K)).
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is DOUBLE PRECISION array, dimension (min(nq,K))
*>          TAU(i) must contain the scalar factor of the elementary
*>          reflector H(i) or G(i) which determines Q or P, as returned
*>          by DGEBRD in the array argument TAUQ or TAUP.
*> \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
*>          or P*C or P**T*C or C*P or C*P**T.
*> \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 optimum performance LWORK >= N*NB if SIDE = 'L', and
*>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
*>          blocksize.
*>
*>          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 unmbr
*
*  =====================================================================
      SUBROUTINE dormbr( VECT, 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, VECT
      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            APPLYQ, LEFT, LQUERY, NOTRAN
      CHARACTER          TRANST
      INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           lsame, ilaenv
*     ..
*     .. External Subroutines ..
      EXTERNAL           dormlq, dormqr, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      applyq = lsame( vect, 'Q' )
      left = lsame( side, 'L' )
      notran = lsame( trans, 'N' )
      lquery = ( lwork.EQ.-1 )
*
*     NQ is the order of Q or P 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.applyq .AND. .NOT.lsame( vect, 'P' ) ) THEN
         info = -1
      ELSE IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
         info = -2
      ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
         info = -3
      ELSE IF( m.LT.0 ) THEN
         info = -4
      ELSE IF( n.LT.0 ) THEN
         info = -5
      ELSE IF( k.LT.0 ) THEN
         info = -6
      ELSE IF( ( applyq .AND. lda.LT.max( 1, nq ) ) .OR.
     $         ( .NOT.applyq .AND. lda.LT.max( 1, min( nq, k ) ) ) )
     $          THEN
         info = -8
      ELSE IF( ldc.LT.max( 1, m ) ) THEN
         info = -11
      ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
         info = -13
      END IF
*
      IF( info.EQ.0 ) THEN
         IF( applyq ) THEN
            IF( left ) THEN
               nb = ilaenv( 1, 'DORMQR', side // trans, m-1, n, m-1,
     $              -1 )
            ELSE
               nb = ilaenv( 1, 'DORMQR', side // trans, m, n-1, n-1,
     $              -1 )
            END IF
         ELSE
            IF( left ) THEN
               nb = ilaenv( 1, 'DORMLQ', side // trans, m-1, n, m-1,
     $              -1 )
            ELSE
               nb = ilaenv( 1, 'DORMLQ', side // trans, m, n-1, n-1,
     $              -1 )
            END IF
         END IF
         lwkopt = nw*nb
         work( 1 ) = lwkopt
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DORMBR', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      work( 1 ) = 1
      IF( m.EQ.0 .OR. n.EQ.0 )
     $   RETURN
*
      IF( applyq ) THEN
*
*        Apply Q
*
         IF( nq.GE.k ) THEN
*
*           Q was determined by a call to DGEBRD with nq >= k
*
            CALL dormqr( side, trans, m, n, k, a, lda, tau, c, ldc,
     $                   work, lwork, iinfo )
         ELSE IF( nq.GT.1 ) THEN
*
*           Q was determined by a call to DGEBRD with nq < k
*
            IF( left ) THEN
               mi = m - 1
               ni = n
               i1 = 2
               i2 = 1
            ELSE
               mi = m
               ni = n - 1
               i1 = 1
               i2 = 2
            END IF
            CALL dormqr( side, trans, mi, ni, nq-1, a( 2, 1 ), lda, tau,
     $                   c( i1, i2 ), ldc, work, lwork, iinfo )
         END IF
      ELSE
*
*        Apply P
*
         IF( notran ) THEN
            transt = 'T'
         ELSE
            transt = 'N'
         END IF
         IF( nq.GT.k ) THEN
*
*           P was determined by a call to DGEBRD with nq > k
*
            CALL dormlq( side, transt, m, n, k, a, lda, tau, c, ldc,
     $                   work, lwork, iinfo )
         ELSE IF( nq.GT.1 ) THEN
*
*           P was determined by a call to DGEBRD with nq <= k
*
            IF( left ) THEN
               mi = m - 1
               ni = n
               i1 = 2
               i2 = 1
            ELSE
               mi = m
               ni = n - 1
               i1 = 1
               i2 = 2
            END IF
            CALL dormlq( side, transt, mi, ni, nq-1, a( 1, 2 ), lda,
     $                   tau, c( i1, i2 ), ldc, work, lwork, iinfo )
         END IF
      END IF
      work( 1 ) = lwkopt
      RETURN
*
*     End of DORMBR
*
      END