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SUBROUTINE DOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
*
* -- LAPACK routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDQ, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DOPGTR 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
* DSPTRD 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).
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangular packed storage used in previous
* call to DSPTRD;
* = 'L': Lower triangular packed storage used in previous
* call to DSPTRD.
*
* N (input) INTEGER
* The order of the matrix Q. N >= 0.
*
* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
* The vectors which define the elementary reflectors, as
* returned by DSPTRD.
*
* TAU (input) DOUBLE PRECISION array, dimension (N-1)
* TAU(i) must contain the scalar factor of the elementary
* reflector H(i), as returned by DSPTRD.
*
* Q (output) DOUBLE PRECISION array, dimension (LDQ,N)
* The N-by-N orthogonal matrix Q.
*
* LDQ (input) INTEGER
* The leading dimension of the array Q. LDQ >= max(1,N).
*
* WORK (workspace) DOUBLE PRECISION array, dimension (N-1)
*
* 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 UPPER
INTEGER I, IINFO, IJ, J
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL DORG2L, DORG2R, 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( 'DOPGTR', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Q was determined by a call to DSPTRD 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 DORG2L( N-1, N-1, N-1, Q, LDQ, TAU, WORK, IINFO )
*
ELSE
*
* Q was determined by a call to DSPTRD 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 DORG2R( N-1, N-1, N-1, Q( 2, 2 ), LDQ, TAU, WORK,
$ IINFO )
END IF
END IF
RETURN
*
* End of DOPGTR
*
END
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