d1/d9d/dormbr_8f_source.html

 *> \brief \b DORMBR
 *
 *  =========== DOCUMENTATION ===========
 *
 * Online html documentation available at
 *            http://www.netlib.org/lapack/explore-html/
 *
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 *> \endhtmlonly
 *
 *  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.
 *
 *> \date December 2016
 *
 *> \ingroup doubleOTHERcomputational
 *
 *  =====================================================================
       SUBROUTINE dormbr( VECT, 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, 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 = n
       ELSE
          nq = n
          nw = 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.max( 1, 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 = max( 1, 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
dormqr
subroutine dormqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMQR
Definition: dormqr.f:169

dormbr
subroutine dormbr(VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMBR
Definition: dormbr.f:197

xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62

dormlq
subroutine dormlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMLQ
Definition: dormlq.f:169