```      SUBROUTINE ZGEHRD( N, ILO, IHI, 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 ..
INTEGER            IHI, ILO, INFO, LDA, LWORK, N
*     ..
*     .. Array Arguments ..
COMPLEX*16        A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by
*  an unitary similarity transformation:  Q' * A * Q = H .
*
*  Arguments
*  =========
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  ILO     (input) INTEGER
*  IHI     (input) INTEGER
*          It is assumed that A is already upper triangular in rows
*          and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
*          set by a previous call to ZGEBAL; otherwise they should be
*          set to 1 and N respectively. See Further Details.
*          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
*
*  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
*          On entry, the N-by-N general matrix to be reduced.
*          On exit, the upper triangle and the first subdiagonal of A
*          are overwritten with the upper Hessenberg matrix H, and the
*          elements below the first subdiagonal, with the array TAU,
*          represent the unitary matrix Q as a product of elementary
*          reflectors. See Further Details.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  TAU     (output) COMPLEX*16 array, dimension (N-1)
*          The scalar factors of the elementary reflectors (see Further
*          Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
*          zero.
*
*  WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The length of the array WORK.  LWORK >= max(1,N).
*          For optimum performance LWORK >= N*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.
*
*  Further Details
*  ===============
*
*  The matrix Q is represented as a product of (ihi-ilo) elementary
*  reflectors
*
*     Q = H(ilo) H(ilo+1) . . . H(ihi-1).
*
*  Each H(i) has the form
*
*     H(i) = I - tau * v * v'
*
*  where tau is a complex scalar, and v is a complex vector with
*  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
*  exit in A(i+2:ihi,i), and tau in TAU(i).
*
*  The contents of A are illustrated by the following example, with
*  n = 7, ilo = 2 and ihi = 6:
*
*  on entry,                        on exit,
*
*  ( a   a   a   a   a   a   a )    (  a   a   h   h   h   h   a )
*  (     a   a   a   a   a   a )    (      a   h   h   h   h   a )
*  (     a   a   a   a   a   a )    (      h   h   h   h   h   h )
*  (     a   a   a   a   a   a )    (      v2  h   h   h   h   h )
*  (     a   a   a   a   a   a )    (      v2  v3  h   h   h   h )
*  (     a   a   a   a   a   a )    (      v2  v3  v4  h   h   h )
*  (                         a )    (                          a )
*
*  where a denotes an element of the original matrix A, h denotes a
*  modified element of the upper Hessenberg matrix H, and vi denotes an
*  element of the vector defining H(i).
*
*  This file is a slight modification of LAPACK-3.0's ZGEHRD
*  subroutine incorporating improvements proposed by Quintana-Orti and
*  Van de Geijn (2005).
*
*  =====================================================================
*
*     .. Parameters ..
INTEGER            NBMAX, LDT
PARAMETER          ( NBMAX = 64, LDT = NBMAX+1 )
COMPLEX*16        ZERO, ONE
PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ),
\$                     ONE = ( 1.0D+0, 0.0D+0 ) )
*     ..
*     .. Local Scalars ..
LOGICAL            LQUERY
INTEGER            I, IB, IINFO, IWS, J, LDWORK, LWKOPT, NB,
\$                   NBMIN, NH, NX
COMPLEX*16        EI
*     ..
*     .. Local Arrays ..
COMPLEX*16        T( LDT, NBMAX )
*     ..
*     .. External Subroutines ..
EXTERNAL           ZAXPY, ZGEHD2, ZGEMM, ZLAHR2, ZLARFB, ZTRMM,
\$                   XERBLA
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          MAX, MIN
*     ..
*     .. External Functions ..
INTEGER            ILAENV
EXTERNAL           ILAENV
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters
*
INFO = 0
NB = MIN( NBMAX, ILAENV( 1, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) )
LWKOPT = N*NB
WORK( 1 ) = LWKOPT
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, N ) .AND. .NOT.LQUERY ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZGEHRD', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
*     Set elements 1:ILO-1 and IHI:N-1 of TAU to zero
*
DO 10 I = 1, ILO - 1
TAU( I ) = ZERO
10 CONTINUE
DO 20 I = MAX( 1, IHI ), N - 1
TAU( I ) = ZERO
20 CONTINUE
*
*     Quick return if possible
*
NH = IHI - ILO + 1
IF( NH.LE.1 ) THEN
WORK( 1 ) = 1
RETURN
END IF
*
*     Determine the block size
*
NB = MIN( NBMAX, ILAENV( 1, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) )
NBMIN = 2
IWS = 1
IF( NB.GT.1 .AND. NB.LT.NH ) THEN
*
*        Determine when to cross over from blocked to unblocked code
*        (last block is always handled by unblocked code)
*
NX = MAX( NB, ILAENV( 3, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) )
IF( NX.LT.NH ) THEN
*
*           Determine if workspace is large enough for blocked code
*
IWS = N*NB
IF( LWORK.LT.IWS ) THEN
*
*              Not enough workspace to use optimal NB:  determine the
*              minimum value of NB, and reduce NB or force use of
*              unblocked code
*
NBMIN = MAX( 2, ILAENV( 2, 'ZGEHRD', ' ', N, ILO, IHI,
\$                 -1 ) )
IF( LWORK.GE.N*NBMIN ) THEN
NB = LWORK / N
ELSE
NB = 1
END IF
END IF
END IF
END IF
LDWORK = N
*
IF( NB.LT.NBMIN .OR. NB.GE.NH ) THEN
*
*        Use unblocked code below
*
I = ILO
*
ELSE
*
*        Use blocked code
*
DO 40 I = ILO, IHI - 1 - NX, NB
IB = MIN( NB, IHI-I )
*
*           Reduce columns i:i+ib-1 to Hessenberg form, returning the
*           matrices V and T of the block reflector H = I - V*T*V'
*           which performs the reduction, and also the matrix Y = A*V*T
*
CALL ZLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), T, LDT,
\$                   WORK, LDWORK )
*
*           Apply the block reflector H to A(1:ihi,i+ib:ihi) from the
*           right, computing  A := A - Y * V'. V(i+ib,ib-1) must be set
*           to 1
*
EI = A( I+IB, I+IB-1 )
A( I+IB, I+IB-1 ) = ONE
CALL ZGEMM( 'No transpose', 'Conjugate transpose',
\$                  IHI, IHI-I-IB+1,
\$                  IB, -ONE, WORK, LDWORK, A( I+IB, I ), LDA, ONE,
\$                  A( 1, I+IB ), LDA )
A( I+IB, I+IB-1 ) = EI
*
*           Apply the block reflector H to A(1:i,i+1:i+ib-1) from the
*           right
*
CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
\$                  'Unit', I, IB-1,
\$                  ONE, A( I+1, I ), LDA, WORK, LDWORK )
DO 30 J = 0, IB-2
CALL ZAXPY( I, -ONE, WORK( LDWORK*J+1 ), 1,
\$                     A( 1, I+J+1 ), 1 )
30       CONTINUE
*
*           Apply the block reflector H to A(i+1:ihi,i+ib:n) from the
*           left
*
CALL ZLARFB( 'Left', 'Conjugate transpose', 'Forward',
\$                   'Columnwise',
\$                   IHI-I, N-I-IB+1, IB, A( I+1, I ), LDA, T, LDT,
\$                   A( I+1, I+IB ), LDA, WORK, LDWORK )
40    CONTINUE
END IF
*
*     Use unblocked code to reduce the rest of the matrix
*
CALL ZGEHD2( N, I, IHI, A, LDA, TAU, WORK, IINFO )
WORK( 1 ) = IWS
*
RETURN
*
*     End of ZGEHRD
*
END

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