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    1:       SUBROUTINE ZUNGHR( 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:       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
   13: *     ..
   14: *
   15: *  Purpose
   16: *  =======
   17: *
   18: *  ZUNGHR generates a complex unitary matrix Q which is defined as the
   19: *  product of IHI-ILO elementary reflectors of order N, as returned by
   20: *  ZGEHRD:
   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 ZGEHRD. 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) COMPLEX*16 array, dimension (LDA,N)
   38: *          On entry, the vectors which define the elementary reflectors,
   39: *          as returned by ZGEHRD.
   40: *          On exit, the N-by-N unitary matrix Q.
   41: *
   42: *  LDA     (input) INTEGER
   43: *          The leading dimension of the array A. LDA >= max(1,N).
   44: *
   45: *  TAU     (input) COMPLEX*16 array, dimension (N-1)
   46: *          TAU(i) must contain the scalar factor of the elementary
   47: *          reflector H(i), as returned by ZGEHRD.
   48: *
   49: *  WORK    (workspace/output) COMPLEX*16 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:       COMPLEX*16         ZERO, ONE
   70:       PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ),
   71:      $                   ONE = ( 1.0D+0, 0.0D+0 ) )
   72: *     ..
   73: *     .. Local Scalars ..
   74:       LOGICAL            LQUERY
   75:       INTEGER            I, IINFO, J, LWKOPT, NB, NH
   76: *     ..
   77: *     .. External Subroutines ..
   78:       EXTERNAL           XERBLA, ZUNGQR
   79: *     ..
   80: *     .. External Functions ..
   81:       INTEGER            ILAENV
   82:       EXTERNAL           ILAENV
   83: *     ..
   84: *     .. Intrinsic Functions ..
   85:       INTRINSIC          MAX, MIN
   86: *     ..
   87: *     .. Executable Statements ..
   88: *
   89: *     Test the input arguments
   90: *
   91:       INFO = 0
   92:       NH = IHI - ILO
   93:       LQUERY = ( LWORK.EQ.-1 )
   94:       IF( N.LT.0 ) THEN
   95:          INFO = -1
   96:       ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
   97:          INFO = -2
   98:       ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
   99:          INFO = -3
  100:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  101:          INFO = -5
  102:       ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN
  103:          INFO = -8
  104:       END IF
  105: *
  106:       IF( INFO.EQ.0 ) THEN
  107:          NB = ILAENV( 1, 'ZUNGQR', ' ', NH, NH, NH, -1 )
  108:          LWKOPT = MAX( 1, NH )*NB
  109:          WORK( 1 ) = LWKOPT
  110:       END IF
  111: *
  112:       IF( INFO.NE.0 ) THEN
  113:          CALL XERBLA( 'ZUNGHR', -INFO )
  114:          RETURN
  115:       ELSE IF( LQUERY ) THEN
  116:          RETURN
  117:       END IF
  118: *
  119: *     Quick return if possible
  120: *
  121:       IF( N.EQ.0 ) THEN
  122:          WORK( 1 ) = 1
  123:          RETURN
  124:       END IF
  125: *
  126: *     Shift the vectors which define the elementary reflectors one
  127: *     column to the right, and set the first ilo and the last n-ihi
  128: *     rows and columns to those of the unit matrix
  129: *
  130:       DO 40 J = IHI, ILO + 1, -1
  131:          DO 10 I = 1, J - 1
  132:             A( I, J ) = ZERO
  133:    10    CONTINUE
  134:          DO 20 I = J + 1, IHI
  135:             A( I, J ) = A( I, J-1 )
  136:    20    CONTINUE
  137:          DO 30 I = IHI + 1, N
  138:             A( I, J ) = ZERO
  139:    30    CONTINUE
  140:    40 CONTINUE
  141:       DO 60 J = 1, ILO
  142:          DO 50 I = 1, N
  143:             A( I, J ) = ZERO
  144:    50    CONTINUE
  145:          A( J, J ) = ONE
  146:    60 CONTINUE
  147:       DO 80 J = IHI + 1, N
  148:          DO 70 I = 1, N
  149:             A( I, J ) = ZERO
  150:    70    CONTINUE
  151:          A( J, J ) = ONE
  152:    80 CONTINUE
  153: *
  154:       IF( NH.GT.0 ) THEN
  155: *
  156: *        Generate Q(ilo+1:ihi,ilo+1:ihi)
  157: *
  158:          CALL ZUNGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
  159:      $                WORK, LWORK, IINFO )
  160:       END IF
  161:       WORK( 1 ) = LWKOPT
  162:       RETURN
  163: *
  164: *     End of ZUNGHR
  165: *
  166:       END