sorgtr.f

          SUBROUTINE SORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, LDA, LWORK, N
    *     ..
    *     .. Array Arguments ..
          REAL               A( LDA, * ), TAU( * ), WORK( * )
    *     ..
    *
    *  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).
    *
    *  Arguments
    *  =========
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U': Upper triangle of A contains elementary reflectors
    *                 from SSYTRD;
    *          = 'L': Lower triangle of A contains elementary reflectors
    *                 from SSYTRD.
    *
    *  N       (input) INTEGER
    *          The order of the matrix Q. N >= 0.
    *
    *  A       (input/output) 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.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A. LDA >= max(1,N).
    *
    *  TAU     (input) REAL array, dimension (N-1)
    *          TAU(i) must contain the scalar factor of the elementary
    *          reflector H(i), as returned by SSYTRD.
    *
    *  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) 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.
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *
    *  =====================================================================
    *
    *     .. 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
          EXTERNAL           ILAENV, LSAME
    *     ..
    *     .. 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 ) = 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 ) = LWKOPT
          RETURN
    *
    *     End of SORGTR
    *
          END