cgeev.f.html

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      SUBROUTINE <a name="CGEEV.1"></a><a href="cgeev.f.html#CGEEV.1">CGEEV</a>( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
     $                  WORK, LWORK, RWORK, 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               RWORK( * )
      COMPLEX            A( LDA, * ), 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="CGEEV.21"></a><a href="cgeev.f.html#CGEEV.1">CGEEV</a> computes for an N-by-N complex 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 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) COMPLEX 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">  W       (output) COMPLEX array, dimension (N)
</span><span class="comment">*</span><span class="comment">          W contains the computed eigenvalues.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VL      (output) COMPLEX 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">          u(j) = VL(:,j), the j-th column of VL.
</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) COMPLEX 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">          v(j) = VR(:,j), the j-th column of VR.
</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) COMPLEX 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(1,2*N).
</span><span class="comment">*</span><span class="comment">          For good 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.90"></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">  RWORK   (workspace) REAL array, dimension (2*N)
</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 and i+1:N of W contain eigenvalues which have
</span><span class="comment">*</span><span class="comment">                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, IRWORK, ITAU,
     $                   IWRK, K, MAXWRK, MINWRK, NOUT
      REAL               ANRM, BIGNUM, CSCALE, EPS, SCL, SMLNUM
      COMPLEX            TMP
<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 ..
</span>      EXTERNAL           <a name="CGEBAK.121"></a><a href="cgebak.f.html#CGEBAK.1">CGEBAK</a>, <a name="CGEBAL.121"></a><a href="cgebal.f.html#CGEBAL.1">CGEBAL</a>, <a name="CGEHRD.121"></a><a href="cgehrd.f.html#CGEHRD.1">CGEHRD</a>, <a name="CHSEQR.121"></a><a href="chseqr.f.html#CHSEQR.1">CHSEQR</a>, <a name="CLACPY.121"></a><a href="clacpy.f.html#CLACPY.1">CLACPY</a>, <a name="CLASCL.121"></a><a href="clascl.f.html#CLASCL.1">CLASCL</a>,
     $                   CSCAL, CSSCAL, <a name="CTREVC.122"></a><a href="ctrevc.f.html#CTREVC.1">CTREVC</a>, <a name="CUNGHR.122"></a><a href="cunghr.f.html#CUNGHR.1">CUNGHR</a>, <a name="SLABAD.122"></a><a href="slabad.f.html#SLABAD.1">SLABAD</a>, <a name="XERBLA.122"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
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