dorgbr()

subroutine dorgbr	(	character	vect,
		integer	m,
		integer	n,
		integer	k,
		double precision, dimension( lda, * )	a,
		integer	lda,
		double precision, dimension( * )	tau,
		double precision, dimension( * )	work,
		integer	lwork,
		integer	info
	)

DORGBR

Download DORGBR + dependencies [TGZ] [ZIP] [TXT]

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.

Parameters

[in]	VECT	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.
[in]	M	M is INTEGER The number of rows of the matrix Q or P**T to be returned. M >= 0.
[in]	N	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).
[in]	K	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.
[in,out]	A	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.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
[in]	TAU	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.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]	LWORK	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.
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 156 of file dorgbr.f.

*
*  -- 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
*

Here is the call graph for this function:

Here is the caller graph for this function: