dorghr.f

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      SUBROUTINE dorghr( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      INTEGER            IHI, ILO, INFO, LDA, LWORK, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  DORGHR generates a real orthogonal matrix Q which is defined as the
*  product of IHI-ILO elementary reflectors of order N, as returned by
*  DGEHRD:
*
*  Q = H(ilo) H(ilo+1) . . . H(ihi-1).
*
*  Arguments
*  =========
*
*  N       (input) INTEGER
*          The order of the matrix Q. N >= 0.
*
*  ILO     (input) INTEGER
*  IHI     (input) INTEGER
*          ILO and IHI must have the same values as in the previous call
*          of DGEHRD. Q is equal to the unit matrix except in the
*          submatrix Q(ilo+1:ihi,ilo+1:ihi).
*          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
*
*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
*          On entry, the vectors which define the elementary reflectors,
*          as returned by DGEHRD.
*          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) DOUBLE PRECISION array, dimension (N-1)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by DGEHRD.
*
*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= IHI-ILO.
*          For optimum performance LWORK >= (IHI-ILO)*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 ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            I, IINFO, J, LWKOPT, NB, NH
*     ..
*     .. External Subroutines ..
      EXTERNAL           dorgqr, xerbla
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      EXTERNAL           ilaenv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      nh = ihi - ilo
      lquery = ( lwork.EQ.-1 )
      IF( n.LT.0 ) THEN
         info = -1
      ELSE IF( ilo.LT.1 .OR. ilo.GT.max( 1, n ) ) THEN
         info = -2
      ELSE IF( ihi.LT.min( ilo, n ) .OR. ihi.GT.n ) THEN
         info = -3
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -5
      ELSE IF( lwork.LT.max( 1, nh ) .AND. .NOT.lquery ) THEN
         info = -8
      END IF
*
      IF( info.EQ.0 ) THEN
         nb = ilaenv( 1, 'DORGQR', ' ', nh, nh, nh, -1 )
         lwkopt = max( 1, nh )*nb
         work( 1 ) = lwkopt
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DORGHR', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 ) THEN
         work( 1 ) = 1
         RETURN
      END IF
*
*     Shift the vectors which define the elementary reflectors one
*     column to the right, and set the first ilo and the last n-ihi
*     rows and columns to those of the unit matrix
*
      DO 40 j = ihi, ilo + 1, -1
         DO 10 i = 1, j - 1
            a( i, j ) = zero
   10    CONTINUE
         DO 20 i = j + 1, ihi
            a( i, j ) = a( i, j-1 )
   20    CONTINUE
         DO 30 i = ihi + 1, n
            a( i, j ) = zero
   30    CONTINUE
   40 CONTINUE
      DO 60 j = 1, ilo
         DO 50 i = 1, n
            a( i, j ) = zero
   50    CONTINUE
         a( j, j ) = one
   60 CONTINUE
      DO 80 j = ihi + 1, n
         DO 70 i = 1, n
            a( i, j ) = zero
   70    CONTINUE
         a( j, j ) = one
   80 CONTINUE
*
      IF( nh.GT.0 ) THEN
*
*        Generate Q(ilo+1:ihi,ilo+1:ihi)
*
         CALL dorgqr( nh, nh, nh, a( ilo+1, ilo+1 ), lda, tau( ilo ),
     $                work, lwork, iinfo )
      END IF
      work( 1 ) = lwkopt
      RETURN
*
*     End of DORGHR
*
      END