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      SUBROUTINE <a name="SGEEV.1"></a><a href="sgeev.f.html#SGEEV.1">SGEEV</a>( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR,
     $                  LDVR, WORK, LWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK driver 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          JOBVL, JOBVR
      INTEGER            INFO, LDA, LDVL, LDVR, LWORK, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
     $                   WI( * ), WORK( * ), WR( * )
<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="SGEEV.20"></a><a href="sgeev.f.html#SGEEV.1">SGEEV</a> computes for an N-by-N real nonsymmetric matrix A, the
</span><span class="comment">*</span><span class="comment">  eigenvalues and, optionally, the left and/or right eigenvectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The right eigenvector v(j) of A satisfies
</span><span class="comment">*</span><span class="comment">                   A * v(j) = lambda(j) * v(j)
</span><span class="comment">*</span><span class="comment">  where lambda(j) is its eigenvalue.
</span><span class="comment">*</span><span class="comment">  The left eigenvector u(j) of A satisfies
</span><span class="comment">*</span><span class="comment">                u(j)**H * A = lambda(j) * u(j)**H
</span><span class="comment">*</span><span class="comment">  where u(j)**H denotes the conjugate transpose of u(j).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The computed eigenvectors are normalized to have Euclidean norm
</span><span class="comment">*</span><span class="comment">  equal to 1 and largest component real.
</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">  JOBVL   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N': left eigenvectors of A are not computed;
</span><span class="comment">*</span><span class="comment">          = 'V': left eigenvectors of A are computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  JOBVR   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N': right eigenvectors of A are not computed;
</span><span class="comment">*</span><span class="comment">          = 'V': right eigenvectors of A are computed.
</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 A. N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) REAL array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          On entry, the N-by-N matrix A.
</span><span class="comment">*</span><span class="comment">          On exit, A has been overwritten.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.  LDA &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WR      (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">  WI      (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          WR and WI contain the real and imaginary parts,
</span><span class="comment">*</span><span class="comment">          respectively, of the computed eigenvalues.  Complex
</span><span class="comment">*</span><span class="comment">          conjugate pairs of eigenvalues appear consecutively
</span><span class="comment">*</span><span class="comment">          with the eigenvalue having the positive imaginary part
</span><span class="comment">*</span><span class="comment">          first.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VL      (output) REAL array, dimension (LDVL,N)
</span><span class="comment">*</span><span class="comment">          If JOBVL = 'V', the left eigenvectors u(j) are stored one
</span><span class="comment">*</span><span class="comment">          after another in the columns of VL, in the same order
</span><span class="comment">*</span><span class="comment">          as their eigenvalues.
</span><span class="comment">*</span><span class="comment">          If JOBVL = 'N', VL is not referenced.
</span><span class="comment">*</span><span class="comment">          If the j-th eigenvalue is real, then u(j) = VL(:,j),
</span><span class="comment">*</span><span class="comment">          the j-th column of VL.
</span><span class="comment">*</span><span class="comment">          If the j-th and (j+1)-st eigenvalues form a complex
</span><span class="comment">*</span><span class="comment">          conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and
</span><span class="comment">*</span><span class="comment">          u(j+1) = VL(:,j) - i*VL(:,j+1).
</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.  LDVL &gt;= 1; if
</span><span class="comment">*</span><span class="comment">          JOBVL = 'V', LDVL &gt;= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VR      (output) REAL array, dimension (LDVR,N)
</span><span class="comment">*</span><span class="comment">          If JOBVR = 'V', the right eigenvectors v(j) are stored one
</span><span class="comment">*</span><span class="comment">          after another in the columns of VR, in the same order
</span><span class="comment">*</span><span class="comment">          as their eigenvalues.
</span><span class="comment">*</span><span class="comment">          If JOBVR = 'N', VR is not referenced.
</span><span class="comment">*</span><span class="comment">          If the j-th eigenvalue is real, then v(j) = VR(:,j),
</span><span class="comment">*</span><span class="comment">          the j-th column of VR.
</span><span class="comment">*</span><span class="comment">          If the j-th and (j+1)-st eigenvalues form a complex
</span><span class="comment">*</span><span class="comment">          conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and
</span><span class="comment">*</span><span class="comment">          v(j+1) = VR(:,j) - i*VR(:,j+1).
</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.  LDVR &gt;= 1; if
</span><span class="comment">*</span><span class="comment">          JOBVR = 'V', LDVR &gt;= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LWORK   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The dimension of the array WORK.  LWORK &gt;= max(1,3*N), and
</span><span class="comment">*</span><span class="comment">          if JOBVL = 'V' or JOBVR = 'V', LWORK &gt;= 4*N.  For good
</span><span class="comment">*</span><span class="comment">          performance, LWORK must generally be larger.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment">          only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment">          this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment">          message related to LWORK is issued by <a name="XERBLA.103"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</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, the QR algorithm failed to compute all the
</span><span class="comment">*</span><span class="comment">                eigenvalues, and no eigenvectors have been computed;
</span><span class="comment">*</span><span class="comment">                elements i+1:N of WR and WI contain eigenvalues which
</span><span class="comment">*</span><span class="comment">                have converged.
</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>      REAL               ZERO, ONE
      PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LQUERY, SCALEA, WANTVL, WANTVR
      CHARACTER          SIDE
      INTEGER            HSWORK, I, IBAL, IERR, IHI, ILO, ITAU, IWRK, K,
     $                   MAXWRK, MINWRK, NOUT
      REAL               ANRM, BIGNUM, CS, CSCALE, EPS, R, SCL, SMLNUM,
     $                   SN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      LOGICAL            SELECT( 1 )
      REAL               DUM( 1 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..

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