dorgbr.f

*> \brief \b DORGBR
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          VECT
*       INTEGER            INFO, K, LDA, LWORK, M, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DORGBR generates one of the real orthogonal matrices Q or P**T
*> 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) or G(i) respectively.
*>
*> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
*> is of order M:
*> if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n
*> columns of Q, where m >= n >= k;
*> if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an
*> M-by-M matrix.
*>
*> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
*> is of order N:
*> if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m
*> rows of P**T, where n >= m >= k;
*> if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as
*> an N-by-N matrix.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] VECT
*> \verbatim
*>          VECT is CHARACTER*1
*>          Specifies whether the matrix Q or the matrix P**T is
*>          required, as defined in the transformation applied by DGEBRD:
*>          = 'Q':  generate Q;
*>          = 'P':  generate P**T.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix Q or P**T to be returned.
*>          M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix Q or P**T to be returned.
*>          N >= 0.
*>          If VECT = 'Q', M >= N >= min(M,K);
*>          if VECT = 'P', N >= M >= min(N,K).
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*>          K is INTEGER
*>          If VECT = 'Q', the number of columns in the original M-by-K
*>          matrix reduced by DGEBRD.
*>          If VECT = 'P', the number of rows in the original K-by-N
*>          matrix reduced by DGEBRD.
*>          K >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          On entry, the vectors which define the elementary reflectors,
*>          as returned by DGEBRD.
*>          On exit, the M-by-N matrix Q or P**T.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is DOUBLE PRECISION array, dimension
*>                                (min(M,K)) if VECT = 'Q'
*>                                (min(N,K)) if VECT = 'P'
*>          TAU(i) must contain the scalar factor of the elementary
*>          reflector H(i) or G(i), which determines Q or P**T, as
*>          returned by DGEBRD in its array argument TAUQ or TAUP.
*> \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. LWORK >= max(1,min(M,N)).
*>          For optimum performance LWORK >= min(M,N)*NB, 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 doubleGBcomputational
*
*  =====================================================================
      SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, 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          VECT
      INTEGER            INFO, K, LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, WANTQ
      INTEGER            I, IINFO, J, LWKOPT, MN
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           DORGLQ, DORGQR, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      WANTQ = LSAME( VECT, 'Q' )
      MN = MIN( M, N )
      LQUERY = ( LWORK.EQ.-1 )
      IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
         INFO = -1
      ELSE IF( M.LT.0 ) THEN
         INFO = -2
      ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
     $         K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
     $         MIN( N, K ) ) ) ) THEN
         INFO = -3
      ELSE IF( K.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -6
      ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN
         INFO = -9
      END IF
*
      IF( INFO.EQ.0 ) THEN
         WORK( 1 ) = 1
         IF( WANTQ ) THEN
            IF( M.GE.K ) THEN
               CALL DORGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
            ELSE
               IF( M.GT.1 ) THEN
                  CALL DORGQR( M-1, M-1, M-1, A, LDA, TAU, WORK, -1,
     $                         IINFO )
               END IF
            END IF
         ELSE
            IF( K.LT.N ) THEN
               CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
            ELSE
               IF( N.GT.1 ) THEN
                  CALL DORGLQ( N-1, N-1, N-1, A, LDA, TAU, WORK, -1,
     $                         IINFO )
               END IF
            END IF
         END IF
         LWKOPT = INT( WORK( 1 ) )
         LWKOPT = MAX (LWKOPT, MN)
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DORGBR', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         WORK( 1 ) = LWKOPT
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( M.EQ.0 .OR. N.EQ.0 ) THEN
         WORK( 1 ) = 1
         RETURN
      END IF
*
      IF( WANTQ ) THEN
*
*        Form Q, determined by a call to DGEBRD to reduce an m-by-k
*        matrix
*
         IF( M.GE.K ) THEN
*
*           If m >= k, assume m >= n >= k
*
            CALL DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
*
         ELSE
*
*           If m < k, assume m = n
*
*           Shift the vectors which define the elementary reflectors one
*           column to the right, and set the first row and column of Q
*           to those of the unit matrix
*
            DO 20 J = M, 2, -1
               A( 1, J ) = ZERO
               DO 10 I = J + 1, M
                  A( I, J ) = A( I, J-1 )
   10          CONTINUE
   20       CONTINUE
            A( 1, 1 ) = ONE
            DO 30 I = 2, M
               A( I, 1 ) = ZERO
   30       CONTINUE
            IF( M.GT.1 ) THEN
*
*              Form Q(2:m,2:m)
*
               CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
     $                      LWORK, IINFO )
            END IF
         END IF
      ELSE
*
*        Form P**T, determined by a call to DGEBRD to reduce a k-by-n
*        matrix
*
         IF( K.LT.N ) THEN
*
*           If k < n, assume k <= m <= n
*
            CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
*
         ELSE
*
*           If k >= n, assume m = n
*
*           Shift the vectors which define the elementary reflectors one
*           row downward, and set the first row and column of P**T to
*           those of the unit matrix
*
            A( 1, 1 ) = ONE
            DO 40 I = 2, N
               A( I, 1 ) = ZERO
   40       CONTINUE
            DO 60 J = 2, N
               DO 50 I = J - 1, 2, -1
                  A( I, J ) = A( I-1, J )
   50          CONTINUE
               A( 1, J ) = ZERO
   60       CONTINUE
            IF( N.GT.1 ) THEN
*
*              Form P**T(2:n,2:n)
*
               CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
     $                      LWORK, IINFO )
            END IF
         END IF
      END IF
      WORK( 1 ) = LWKOPT
      RETURN
*
*     End of DORGBR
*
      END