sorgtr()

subroutine sorgtr	(	character	uplo,
		integer	n,
		real, dimension( lda, * )	a,
		integer	lda,
		real, dimension( * )	tau,
		real, dimension( * )	work,
		integer	lwork,
		integer	info )

SORGTR

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Purpose:

!>
!> SORGTR generates a real orthogonal matrix Q which is defined as the
!> product of n-1 elementary reflectors of order N, as returned by
!> SSYTRD:
!>
!> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
!>
!> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
!> 

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A contains elementary reflectors !> from SSYTRD; !> = 'L': Lower triangle of A contains elementary reflectors !> from SSYTRD. !>
[in]	N	!> N is INTEGER !> The order of the matrix Q. N >= 0. !>
[in,out]	A	!> A is REAL array, dimension (LDA,N) !> On entry, the vectors which define the elementary reflectors, !> as returned by SSYTRD. !> On exit, the N-by-N orthogonal matrix Q. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[in]	TAU	!> TAU is REAL array, dimension (N-1) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by SSYTRD. !>
[out]	WORK	!> WORK is REAL 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,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. !>
[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 120 of file sorgtr.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          UPLO
      INTEGER            INFO, LDA, LWORK, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, UPPER
      INTEGER            I, IINFO, J, LWKOPT, NB
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      REAL               SROUNDUP_LWORK
      EXTERNAL           ilaenv, lsame, sroundup_lwork
*     ..
*     .. External Subroutines ..
      EXTERNAL           sorgql, sorgqr, 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, 'SORGQL', ' ', n-1, n-1, n-1, -1 )
         ELSE
           nb = ilaenv( 1, 'SORGQR', ' ', n-1, n-1, n-1, -1 )
         END IF
         lwkopt = max( 1, n-1 )*nb
         work( 1 ) = sroundup_lwork(lwkopt)
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'SORGTR', -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 SSYTRD 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 sorgql( n-1, n-1, n-1, a, lda, tau, work, lwork,
     $                iinfo )
*
      ELSE
*
*        Q was determined by a call to SSYTRD 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 sorgqr( n-1, n-1, n-1, a( 2, 2 ), lda, tau, work,
     $                   lwork, iinfo )
         END IF
      END IF
      work( 1 ) = sroundup_lwork(lwkopt)
      RETURN
*
*     End of SORGTR
*

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