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SUBROUTINE <a name="CGEBAK.1"></a><a href="cgebak.f.html#CGEBAK.1">CGEBAK</a>( JOB, SIDE, N, ILO, IHI, SCALE, 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 SCALE( * )
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="CGEBAK.20"></a><a href="cgebak.f.html#CGEBAK.1">CGEBAK</a> forms the right or left eigenvectors of a complex general
</span><span class="comment">*</span><span class="comment"> matrix by backward transformation on the computed eigenvectors of the
</span><span class="comment">*</span><span class="comment"> balanced matrix output by <a name="CGEBAL.22"></a><a href="cgebal.f.html#CGEBAL.1">CGEBAL</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="CGEBAL.34"></a><a href="cgebal.f.html#CGEBAL.1">CGEBAL</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="CGEBAL.45"></a><a href="cgebal.f.html#CGEBAL.1">CGEBAL</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"> SCALE (input) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> Details of the permutation and scaling factors, as returned
</span><span class="comment">*</span><span class="comment"> by <a name="CGEBAL.50"></a><a href="cgebal.f.html#CGEBAL.1">CGEBAL</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="CHSEIN.57"></a><a href="chsein.f.html#CHSEIN.1">CHSEIN</a> or <a name="CTREVC.57"></a><a href="ctrevc.f.html#CTREVC.1">CTREVC</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 array 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"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> REAL ONE
PARAMETER ( ONE = 1.0E+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL LEFTV, RIGHTV
INTEGER I, II, K
REAL S
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.79"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.80"></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.83"></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, MIN
<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"> Decode and Test the input parameters
</span><span class="comment">*</span><span class="comment">
</span> RIGHTV = <a name="LSAME.92"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'R'</span> )
LEFTV = <a name="LSAME.93"></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.96"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'N'</span> ) .AND. .NOT.<a name="LSAME.96"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'P'</span> ) .AND.
$ .NOT.<a name="LSAME.97"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'S'</span> ) .AND. .NOT.<a name="LSAME.97"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'B'</span> ) ) THEN
INFO = -1
ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
INFO = -4
ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
INFO = -5
ELSE IF( M.LT.0 ) THEN
INFO = -7
ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
INFO = -9
END IF
IF( INFO.NE.0 ) THEN
CALL <a name="XERBLA.113"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CGEBAK.113"></a><a href="cgebak.f.html#CGEBAK.1">CGEBAK</a>'</span>, -INFO )
RETURN
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span> IF( N.EQ.0 )
$ RETURN
IF( M.EQ.0 )
$ RETURN
IF( <a name="LSAME.123"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'N'</span> ) )
$ RETURN
<span class="comment">*</span><span class="comment">
</span> IF( ILO.EQ.IHI )
$ GO TO 30
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Backward balance
</span><span class="comment">*</span><span class="comment">
</span> IF( <a name="LSAME.131"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'S'</span> ) .OR. <a name="LSAME.131"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'B'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span> IF( RIGHTV ) THEN
DO 10 I = ILO, IHI
S = SCALE( I )
CALL CSSCAL( M, S, V( I, 1 ), LDV )
10 CONTINUE
END IF
<span class="comment">*</span><span class="comment">
</span> IF( LEFTV ) THEN
DO 20 I = ILO, IHI
S = ONE / SCALE( I )
CALL CSSCAL( M, S, V( I, 1 ), LDV )
20 CONTINUE
END IF
<span class="comment">*</span><span class="comment">
</span> END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Backward permutation
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> For I = ILO-1 step -1 until 1,
</span><span class="comment">*</span><span class="comment"> IHI+1 step 1 until N do --
</span><span class="comment">*</span><span class="comment">
</span> 30 CONTINUE
IF( <a name="LSAME.155"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'P'</span> ) .OR. <a name="LSAME.155"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOB, <span class="string">'B'</span> ) ) THEN
IF( RIGHTV ) THEN
DO 40 II = 1, N
I = II
IF( I.GE.ILO .AND. I.LE.IHI )
$ GO TO 40
IF( I.LT.ILO )
$ I = ILO - II
K = SCALE( I )
IF( K.EQ.I )
$ GO TO 40
CALL CSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
40 CONTINUE
END IF
<span class="comment">*</span><span class="comment">
</span> IF( LEFTV ) THEN
DO 50 II = 1, N
I = II
IF( I.GE.ILO .AND. I.LE.IHI )
$ GO TO 50
IF( I.LT.ILO )
$ I = ILO - II
K = SCALE( I )
IF( K.EQ.I )
$ GO TO 50
CALL CSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
50 CONTINUE
END IF
END IF
<span class="comment">*</span><span class="comment">
</span> RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> End of <a name="CGEBAK.187"></a><a href="cgebak.f.html#CGEBAK.1">CGEBAK</a>
</span><span class="comment">*</span><span class="comment">
</span> END
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