dorgbr.f

          SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          VECT
          INTEGER            INFO, K, LDA, LWORK, M, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  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.
    *
    *  Arguments
    *  =========
    *
    *  VECT    (input) 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.
    *
    *  M       (input) INTEGER
    *          The number of rows of the matrix Q or P**T to be returned.
    *          M >= 0.
    *
    *  N       (input) 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).
    *
    *  K       (input) 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.
    *
    *  A       (input/output) 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.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A. LDA >= max(1,M).
    *
    *  TAU     (input) 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.
    *
    *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) 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.
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *
    *  =====================================================================
    *
    *     .. 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, NB
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          EXTERNAL           LSAME, ILAENV
    *     ..
    *     .. 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
             IF( WANTQ ) THEN
                NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 )
             ELSE
                NB = ILAENV( 1, 'DORGLQ', ' ', M, N, K, -1 )
             END IF
             LWKOPT = MAX( 1, MN )*NB
             WORK( 1 ) = LWKOPT
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DORGBR', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             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', 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' 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'(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