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SUBROUTINE <a name="CGGBAK.1"></a><a href="cggbak.f.html#CGGBAK.1">CGGBAK</a>( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
$ LDV, 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 JOB, SIDE
INTEGER IHI, ILO, INFO, LDV, M, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL LSCALE( * ), RSCALE( * )
COMPLEX V( LDV, * )
<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="CGGBAK.20"></a><a href="cggbak.f.html#CGGBAK.1">CGGBAK</a> forms the right or left eigenvectors of a complex generalized
</span><span class="comment">*</span><span class="comment"> eigenvalue problem A*x = lambda*B*x, by backward transformation on
</span><span class="comment">*</span><span class="comment"> the computed eigenvectors of the balanced pair of matrices output by
</span><span class="comment">*</span><span class="comment"> <a name="CGGBAL.23"></a><a href="cggbal.f.html#CGGBAL.1">CGGBAL</a>.
</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"> JOB (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies the type of backward transformation required:
</span><span class="comment">*</span><span class="comment"> = 'N': do nothing, return immediately;
</span><span class="comment">*</span><span class="comment"> = 'P': do backward transformation for permutation only;
</span><span class="comment">*</span><span class="comment"> = 'S': do backward transformation for scaling only;
</span><span class="comment">*</span><span class="comment"> = 'B': do backward transformations for both permutation and
</span><span class="comment">*</span><span class="comment"> scaling.
</span><span class="comment">*</span><span class="comment"> JOB must be the same as the argument JOB supplied to <a name="CGGBAL.35"></a><a href="cggbal.f.html#CGGBAL.1">CGGBAL</a>.
</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': V contains right eigenvectors;
</span><span class="comment">*</span><span class="comment"> = 'L': V contains left eigenvectors.
</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 number of rows of the matrix V. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ILO (input) INTEGER
</span><span class="comment">*</span><span class="comment"> IHI (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The integers ILO and IHI determined by <a name="CGGBAL.46"></a><a href="cggbal.f.html#CGGBAL.1">CGGBAL</a>.
</span><span class="comment">*</span><span class="comment"> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LSCALE (input) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> Details of the permutations and/or scaling factors applied
</span><span class="comment">*</span><span class="comment"> to the left side of A and B, as returned by <a name="CGGBAL.51"></a><a href="cggbal.f.html#CGGBAL.1">CGGBAL</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RSCALE (input) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> Details of the permutations and/or scaling factors applied
</span><span class="comment">*</span><span class="comment"> to the right side of A and B, as returned by <a name="CGGBAL.55"></a><a href="cggbal.f.html#CGGBAL.1">CGGBAL</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> M (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of columns of the matrix V. M >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> V (input/output) COMPLEX array, dimension (LDV,M)
</span><span class="comment">*</span><span class="comment"> On entry, the matrix of right or left eigenvectors to be
</span><span class="comment">*</span><span class="comment"> transformed, as returned by <a name="CTGEVC.62"></a><a href="ctgevc.f.html#CTGEVC.1">CTGEVC</a>.
</span><span class="comment">*</span><span class="comment"> On exit, V is overwritten by the transformed eigenvectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDV (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the matrix V. LDV >= max(1,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"> < 0: if INFO = -i, the i-th argument had an illegal value.
</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"> See R.C. Ward, Balancing the generalized eigenvalue problem,
</span><span class="comment">*</span><span class="comment"> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
</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"> .. Local Scalars ..
</span> LOGICAL LEFTV, RIGHTV
INTEGER I, K
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.85"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.86"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL CSSCAL, CSWAP, <a name="XERBLA.89"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC MAX
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input parameters
</span><span class="comment">*</span><span class="comment">
</span> RIGHTV = <a name="LSAME.98"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'R'</span> )
LEFTV = <a name="LSAME.99"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'L'</span> )
<span class="comment">*</span><span class="comment">
</span> INFO = 0
IF( .NOT.<a name="LSAME.102"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'N'</span> ) .AND. .NOT.<a name="LSAME.102"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'P'</span> ) .AND.
$ .NOT.<a name="LSAME.103"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'S'</span> ) .AND. .NOT.<a name="LSAME.103"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'B'</span> ) ) THEN
INFO = -1
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