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      SUBROUTINE <a name="ZHSEIN.1"></a><a href="zhsein.f.html#ZHSEIN.1">ZHSEIN</a>( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL,
     $                   LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL,
     $                   IFAILR, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          EIGSRC, INITV, SIDE
      INTEGER            INFO, LDH, LDVL, LDVR, M, MM, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      LOGICAL            SELECT( * )
      INTEGER            IFAILL( * ), IFAILR( * )
      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         H( LDH, * ), VL( LDVL, * ), VR( LDVR, * ),
     $                   W( * ), WORK( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="ZHSEIN.24"></a><a href="zhsein.f.html#ZHSEIN.1">ZHSEIN</a> uses inverse iteration to find specified right and/or left
</span><span class="comment">*</span><span class="comment">  eigenvectors of a complex upper Hessenberg matrix H.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The right eigenvector x and the left eigenvector y of the matrix H
</span><span class="comment">*</span><span class="comment">  corresponding to an eigenvalue w are defined by:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">               H * x = w * x,     y**h * H = w * y**h
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where y**h denotes the conjugate transpose of the vector y.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SIDE    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'R': compute right eigenvectors only;
</span><span class="comment">*</span><span class="comment">          = 'L': compute left eigenvectors only;
</span><span class="comment">*</span><span class="comment">          = 'B': compute both right and left eigenvectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  EIGSRC  (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies the source of eigenvalues supplied in W:
</span><span class="comment">*</span><span class="comment">          = 'Q': the eigenvalues were found using <a name="ZHSEQR.44"></a><a href="zhseqr.f.html#ZHSEQR.1">ZHSEQR</a>; thus, if
</span><span class="comment">*</span><span class="comment">                 H has zero subdiagonal elements, and so is
</span><span class="comment">*</span><span class="comment">                 block-triangular, then the j-th eigenvalue can be
</span><span class="comment">*</span><span class="comment">                 assumed to be an eigenvalue of the block containing
</span><span class="comment">*</span><span class="comment">                 the j-th row/column.  This property allows <a name="ZHSEIN.48"></a><a href="zhsein.f.html#ZHSEIN.1">ZHSEIN</a> to
</span><span class="comment">*</span><span class="comment">                 perform inverse iteration on just one diagonal block.
</span><span class="comment">*</span><span class="comment">          = 'N': no assumptions are made on the correspondence
</span><span class="comment">*</span><span class="comment">                 between eigenvalues and diagonal blocks.  In this
</span><span class="comment">*</span><span class="comment">                 case, <a name="ZHSEIN.52"></a><a href="zhsein.f.html#ZHSEIN.1">ZHSEIN</a> must always perform inverse iteration
</span><span class="comment">*</span><span class="comment">                 using the whole matrix H.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INITV   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N': no initial vectors are supplied;
</span><span class="comment">*</span><span class="comment">          = 'U': user-supplied initial vectors are stored in the arrays
</span><span class="comment">*</span><span class="comment">                 VL and/or VR.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SELECT  (input) LOGICAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          Specifies the eigenvectors to be computed. To select the
</span><span class="comment">*</span><span class="comment">          eigenvector corresponding to the eigenvalue W(j),
</span><span class="comment">*</span><span class="comment">          SELECT(j) must be set to .TRUE..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix H.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  H       (input) COMPLEX*16 array, dimension (LDH,N)
</span><span class="comment">*</span><span class="comment">          The upper Hessenberg matrix H.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDH     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array H.  LDH &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  W       (input/output) COMPLEX*16 array, dimension (N)
</span><span class="comment">*</span><span class="comment">          On entry, the eigenvalues of H.
</span><span class="comment">*</span><span class="comment">          On exit, the real parts of W may have been altered since
</span><span class="comment">*</span><span class="comment">          close eigenvalues are perturbed slightly in searching for
</span><span class="comment">*</span><span class="comment">          independent eigenvectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VL      (input/output) COMPLEX*16 array, dimension (LDVL,MM)
</span><span class="comment">*</span><span class="comment">          On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must
</span><span class="comment">*</span><span class="comment">          contain starting vectors for the inverse iteration for the
</span><span class="comment">*</span><span class="comment">          left eigenvectors; the starting vector for each eigenvector
</span><span class="comment">*</span><span class="comment">          must be in the same column in which the eigenvector will be
</span><span class="comment">*</span><span class="comment">          stored.
</span><span class="comment">*</span><span class="comment">          On exit, if SIDE = 'L' or 'B', the left eigenvectors
</span><span class="comment">*</span><span class="comment">          specified by SELECT will be stored consecutively in the
</span><span class="comment">*</span><span class="comment">          columns of VL, in the same order as their eigenvalues.
</span><span class="comment">*</span><span class="comment">          If SIDE = 'R', VL is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDVL    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array VL.
</span><span class="comment">*</span><span class="comment">          LDVL &gt;= max(1,N) if SIDE = 'L' or 'B'; LDVL &gt;= 1 otherwise.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VR      (input/output) COMPLEX*16 array, dimension (LDVR,MM)
</span><span class="comment">*</span><span class="comment">          On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must
</span><span class="comment">*</span><span class="comment">          contain starting vectors for the inverse iteration for the
</span><span class="comment">*</span><span class="comment">          right eigenvectors; the starting vector for each eigenvector
</span><span class="comment">*</span><span class="comment">          must be in the same column in which the eigenvector will be
</span><span class="comment">*</span><span class="comment">          stored.
</span><span class="comment">*</span><span class="comment">          On exit, if SIDE = 'R' or 'B', the right eigenvectors
</span><span class="comment">*</span><span class="comment">          specified by SELECT will be stored consecutively in the
</span><span class="comment">*</span><span class="comment">          columns of VR, in the same order as their eigenvalues.
</span><span class="comment">*</span><span class="comment">          If SIDE = 'L', VR is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDVR    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array VR.
</span><span class="comment">*</span><span class="comment">          LDVR &gt;= max(1,N) if SIDE = 'R' or 'B'; LDVR &gt;= 1 otherwise.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  MM      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of columns in the arrays VL and/or VR. MM &gt;= M.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  M       (output) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of columns in the arrays VL and/or VR required to
</span><span class="comment">*</span><span class="comment">          store the eigenvectors (= the number of .TRUE. elements in
</span><span class="comment">*</span><span class="comment">          SELECT).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) COMPLEX*16 array, dimension (N*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IFAILL  (output) INTEGER array, dimension (MM)
</span><span class="comment">*</span><span class="comment">          If SIDE = 'L' or 'B', IFAILL(i) = j &gt; 0 if the left
</span><span class="comment">*</span><span class="comment">          eigenvector in the i-th column of VL (corresponding to the
</span><span class="comment">*</span><span class="comment">          eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the
</span><span class="comment">*</span><span class="comment">          eigenvector converged satisfactorily.
</span><span class="comment">*</span><span class="comment">          If SIDE = 'R', IFAILL is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IFAILR  (output) INTEGER array, dimension (MM)
</span><span class="comment">*</span><span class="comment">          If SIDE = 'R' or 'B', IFAILR(i) = j &gt; 0 if the right
</span><span class="comment">*</span><span class="comment">          eigenvector in the i-th column of VR (corresponding to the
</span><span class="comment">*</span><span class="comment">          eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the
</span><span class="comment">*</span><span class="comment">          eigenvector converged satisfactorily.
</span><span class="comment">*</span><span class="comment">          If SIDE = 'L', IFAILR is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">          &gt; 0:  if INFO = i, i is the number of eigenvectors which
</span><span class="comment">*</span><span class="comment">                failed to converge; see IFAILL and IFAILR for further
</span><span class="comment">*</span><span class="comment">                details.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Each eigenvector is normalized so that the element of largest
</span><span class="comment">*</span><span class="comment">  magnitude has magnitude 1; here the magnitude of a complex number
</span><span class="comment">*</span><span class="comment">  (x,y) is taken to be |x|+|y|.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      COMPLEX*16         ZERO
      PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
      DOUBLE PRECISION   RZERO
      PARAMETER          ( RZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            BOTHV, FROMQR, LEFTV, NOINIT, RIGHTV
      INTEGER            I, IINFO, K, KL, KLN, KR, KS, LDWORK
      DOUBLE PRECISION   EPS3, HNORM, SMLNUM, ULP, UNFL
      COMPLEX*16         CDUM, WK
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.165"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      DOUBLE PRECISION   <a name="DLAMCH.166"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="ZLANHS.166"></a><a href="zlanhs.f.html#ZLANHS.1">ZLANHS</a>
      EXTERNAL           <a name="LSAME.167"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="DLAMCH.167"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="ZLANHS.167"></a><a href="zlanhs.f.html#ZLANHS.1">ZLANHS</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
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