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*> \brief \b SOPGTR
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SOPGTR + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sopgtr.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sopgtr.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sopgtr.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, LDQ, N
* ..
* .. Array Arguments ..
* REAL AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SOPGTR generates a real orthogonal matrix Q which is defined as the
*> product of n-1 elementary reflectors H(i) of order n, as returned by
*> SSPTRD using packed storage:
*>
*> 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 triangular packed storage used in previous
*> call to SSPTRD;
*> = 'L': Lower triangular packed storage used in previous
*> call to SSPTRD.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix Q. N >= 0.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*> AP is REAL array, dimension (N*(N+1)/2)
*> The vectors which define the elementary reflectors, as
*> returned by SSPTRD.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is REAL array, dimension (N-1)
*> TAU(i) must contain the scalar factor of the elementary
*> reflector H(i), as returned by SSPTRD.
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*> Q is REAL array, dimension (LDQ,N)
*> The N-by-N orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*> LDQ is INTEGER
*> The leading dimension of the array Q. LDQ >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (N-1)
*> \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 realOTHERcomputational
*
* =====================================================================
SUBROUTINE SOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, 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 UPLO
INTEGER INFO, LDQ, N
* ..
* .. Array Arguments ..
REAL AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, IINFO, IJ, J
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL SORG2L, SORG2R, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
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( LDQ.LT.MAX( 1, N ) ) THEN
INFO = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SOPGTR', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Q was determined by a call to SSPTRD with UPLO = 'U'
*
* Unpack the vectors which define the elementary reflectors and
* set the last row and column of Q equal to those of the unit
* matrix
*
IJ = 2
DO 20 J = 1, N - 1
DO 10 I = 1, J - 1
Q( I, J ) = AP( IJ )
IJ = IJ + 1
10 CONTINUE
IJ = IJ + 2
Q( N, J ) = ZERO
20 CONTINUE
DO 30 I = 1, N - 1
Q( I, N ) = ZERO
30 CONTINUE
Q( N, N ) = ONE
*
* Generate Q(1:n-1,1:n-1)
*
CALL SORG2L( N-1, N-1, N-1, Q, LDQ, TAU, WORK, IINFO )
*
ELSE
*
* Q was determined by a call to SSPTRD with UPLO = 'L'.
*
* Unpack the vectors which define the elementary reflectors and
* set the first row and column of Q equal to those of the unit
* matrix
*
Q( 1, 1 ) = ONE
DO 40 I = 2, N
Q( I, 1 ) = ZERO
40 CONTINUE
IJ = 3
DO 60 J = 2, N
Q( 1, J ) = ZERO
DO 50 I = J + 1, N
Q( I, J ) = AP( IJ )
IJ = IJ + 1
50 CONTINUE
IJ = IJ + 2
60 CONTINUE
IF( N.GT.1 ) THEN
*
* Generate Q(2:n,2:n)
*
CALL SORG2R( N-1, N-1, N-1, Q( 2, 2 ), LDQ, TAU, WORK,
$ IINFO )
END IF
END IF
RETURN
*
* End of SOPGTR
*
END
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