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    1:       SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
    2: *
    3: *  -- LAPACK routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       INTEGER            IHI, ILO, INFO, LDA, LWORK, N
   10: *     ..
   11: *     .. Array Arguments ..
   12:       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
   13: *     ..
   14: *
   15: *  Purpose
   16: *  =======
   17: *
   18: *  DORGHR generates a real orthogonal matrix Q which is defined as the
   19: *  product of IHI-ILO elementary reflectors of order N, as returned by
   20: *  DGEHRD:
   21: *
   22: *  Q = H(ilo) H(ilo+1) . . . H(ihi-1).
   23: *
   24: *  Arguments
   25: *  =========
   26: *
   27: *  N       (input) INTEGER
   28: *          The order of the matrix Q. N >= 0.
   29: *
   30: *  ILO     (input) INTEGER
   31: *  IHI     (input) INTEGER
   32: *          ILO and IHI must have the same values as in the previous call
   33: *          of DGEHRD. Q is equal to the unit matrix except in the
   34: *          submatrix Q(ilo+1:ihi,ilo+1:ihi).
   35: *          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
   36: *
   37: *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
   38: *          On entry, the vectors which define the elementary reflectors,
   39: *          as returned by DGEHRD.
   40: *          On exit, the N-by-N orthogonal matrix Q.
   41: *
   42: *  LDA     (input) INTEGER
   43: *          The leading dimension of the array A. LDA >= max(1,N).
   44: *
   45: *  TAU     (input) DOUBLE PRECISION array, dimension (N-1)
   46: *          TAU(i) must contain the scalar factor of the elementary
   47: *          reflector H(i), as returned by DGEHRD.
   48: *
   49: *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
   50: *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   51: *
   52: *  LWORK   (input) INTEGER
   53: *          The dimension of the array WORK. LWORK >= IHI-ILO.
   54: *          For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
   55: *          the optimal blocksize.
   56: *
   57: *          If LWORK = -1, then a workspace query is assumed; the routine
   58: *          only calculates the optimal size of the WORK array, returns
   59: *          this value as the first entry of the WORK array, and no error
   60: *          message related to LWORK is issued by XERBLA.
   61: *
   62: *  INFO    (output) INTEGER
   63: *          = 0:  successful exit
   64: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   65: *
   66: *  =====================================================================
   67: *
   68: *     .. Parameters ..
   69:       DOUBLE PRECISION   ZERO, ONE
   70:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
   71: *     ..
   72: *     .. Local Scalars ..
   73:       LOGICAL            LQUERY
   74:       INTEGER            I, IINFO, J, LWKOPT, NB, NH
   75: *     ..
   76: *     .. External Subroutines ..
   77:       EXTERNAL           DORGQR, XERBLA
   78: *     ..
   79: *     .. External Functions ..
   80:       INTEGER            ILAENV
   81:       EXTERNAL           ILAENV
   82: *     ..
   83: *     .. Intrinsic Functions ..
   84:       INTRINSIC          MAX, MIN
   85: *     ..
   86: *     .. Executable Statements ..
   87: *
   88: *     Test the input arguments
   89: *
   90:       INFO = 0
   91:       NH = IHI - ILO
   92:       LQUERY = ( LWORK.EQ.-1 )
   93:       IF( N.LT.0 ) THEN
   94:          INFO = -1
   95:       ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
   96:          INFO = -2
   97:       ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
   98:          INFO = -3
   99:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  100:          INFO = -5
  101:       ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN
  102:          INFO = -8
  103:       END IF
  104: *
  105:       IF( INFO.EQ.0 ) THEN
  106:          NB = ILAENV( 1, 'DORGQR', ' ', NH, NH, NH, -1 )
  107:          LWKOPT = MAX( 1, NH )*NB
  108:          WORK( 1 ) = LWKOPT
  109:       END IF
  110: *
  111:       IF( INFO.NE.0 ) THEN
  112:          CALL XERBLA( 'DORGHR', -INFO )
  113:          RETURN
  114:       ELSE IF( LQUERY ) THEN
  115:          RETURN
  116:       END IF
  117: *
  118: *     Quick return if possible
  119: *
  120:       IF( N.EQ.0 ) THEN
  121:          WORK( 1 ) = 1
  122:          RETURN
  123:       END IF
  124: *
  125: *     Shift the vectors which define the elementary reflectors one
  126: *     column to the right, and set the first ilo and the last n-ihi
  127: *     rows and columns to those of the unit matrix
  128: *
  129:       DO 40 J = IHI, ILO + 1, -1
  130:          DO 10 I = 1, J - 1
  131:             A( I, J ) = ZERO
  132:    10    CONTINUE
  133:          DO 20 I = J + 1, IHI
  134:             A( I, J ) = A( I, J-1 )
  135:    20    CONTINUE
  136:          DO 30 I = IHI + 1, N
  137:             A( I, J ) = ZERO
  138:    30    CONTINUE
  139:    40 CONTINUE
  140:       DO 60 J = 1, ILO
  141:          DO 50 I = 1, N
  142:             A( I, J ) = ZERO
  143:    50    CONTINUE
  144:          A( J, J ) = ONE
  145:    60 CONTINUE
  146:       DO 80 J = IHI + 1, N
  147:          DO 70 I = 1, N
  148:             A( I, J ) = ZERO
  149:    70    CONTINUE
  150:          A( J, J ) = ONE
  151:    80 CONTINUE
  152: *
  153:       IF( NH.GT.0 ) THEN
  154: *
  155: *        Generate Q(ilo+1:ihi,ilo+1:ihi)
  156: *
  157:          CALL DORGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
  158:      $                WORK, LWORK, IINFO )
  159:       END IF
  160:       WORK( 1 ) = LWKOPT
  161:       RETURN
  162: *
  163: *     End of DORGHR
  164: *
  165:       END