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*> \brief \b DORGTR
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DORGTR + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgtr.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgtr.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgtr.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, LDA, LWORK, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DORGTR generates a real orthogonal matrix Q which is defined as the
*> product of n-1 elementary reflectors of order N, as returned by
*> DSYTRD:
*>
*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangle of A contains elementary reflectors
*> from DSYTRD;
*> = 'L': Lower triangle of A contains elementary reflectors
*> from DSYTRD.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix Q. N >= 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 DSYTRD.
*> On exit, the N-by-N orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is DOUBLE PRECISION array, dimension (N-1)
*> TAU(i) must contain the scalar factor of the elementary
*> reflector H(i), as returned by DSYTRD.
*> \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,N-1).
*> For optimum performance LWORK >= (N-1)*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 ungtr
*
* =====================================================================
SUBROUTINE DORGTR( UPLO, N, 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 UPLO
INTEGER INFO, LDA, LWORK, 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, UPPER
INTEGER I, IINFO, J, LWKOPT, NB
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL DORGQL, DORGQR, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
LQUERY = ( LWORK.EQ.-1 )
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -4
ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
INFO = -7
END IF
*
IF( INFO.EQ.0 ) THEN
IF( UPPER ) THEN
NB = ILAENV( 1, 'DORGQL', ' ', N-1, N-1, N-1, -1 )
ELSE
NB = ILAENV( 1, 'DORGQR', ' ', N-1, N-1, N-1, -1 )
END IF
LWKOPT = MAX( 1, N-1 )*NB
WORK( 1 ) = LWKOPT
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DORGTR', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 ) THEN
WORK( 1 ) = 1
RETURN
END IF
*
IF( UPPER ) THEN
*
* Q was determined by a call to DSYTRD with UPLO = 'U'
*
* Shift the vectors which define the elementary reflectors one
* column to the left, and set the last row and column of Q to
* those of the unit matrix
*
DO 20 J = 1, N - 1
DO 10 I = 1, J - 1
A( I, J ) = A( I, J+1 )
10 CONTINUE
A( N, J ) = ZERO
20 CONTINUE
DO 30 I = 1, N - 1
A( I, N ) = ZERO
30 CONTINUE
A( N, N ) = ONE
*
* Generate Q(1:n-1,1:n-1)
*
CALL DORGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK,
$ IINFO )
*
ELSE
*
* Q was determined by a call to DSYTRD with UPLO = 'L'.
*
* 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 50 J = N, 2, -1
A( 1, J ) = ZERO
DO 40 I = J + 1, N
A( I, J ) = A( I, J-1 )
40 CONTINUE
50 CONTINUE
A( 1, 1 ) = ONE
DO 60 I = 2, N
A( I, 1 ) = ZERO
60 CONTINUE
IF( N.GT.1 ) THEN
*
* Generate Q(2:n,2:n)
*
CALL DORGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
$ LWORK, IINFO )
END IF
END IF
WORK( 1 ) = LWKOPT
RETURN
*
* End of DORGTR
*
END
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