190 lines
5.2 KiB
FortranFixed
190 lines
5.2 KiB
FortranFixed
SUBROUTINE ZGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
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$ INFO )
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*
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* -- LAPACK routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER JOB, SIDE
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INTEGER IHI, ILO, INFO, LDV, M, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION SCALE( * )
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COMPLEX*16 V( LDV, * )
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* ..
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*
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* Purpose
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* =======
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*
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* ZGEBAK forms the right or left eigenvectors of a complex general
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* matrix by backward transformation on the computed eigenvectors of the
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* balanced matrix output by ZGEBAL.
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*
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* Arguments
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* =========
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*
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* JOB (input) CHARACTER*1
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* Specifies the type of backward transformation required:
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* = 'N', do nothing, return immediately;
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* = 'P', do backward transformation for permutation only;
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* = 'S', do backward transformation for scaling only;
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* = 'B', do backward transformations for both permutation and
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* scaling.
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* JOB must be the same as the argument JOB supplied to ZGEBAL.
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*
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* SIDE (input) CHARACTER*1
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* = 'R': V contains right eigenvectors;
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* = 'L': V contains left eigenvectors.
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*
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* N (input) INTEGER
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* The number of rows of the matrix V. N >= 0.
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*
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* ILO (input) INTEGER
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* IHI (input) INTEGER
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* The integers ILO and IHI determined by ZGEBAL.
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* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
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*
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* SCALE (input) DOUBLE PRECISION array, dimension (N)
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* Details of the permutation and scaling factors, as returned
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* by ZGEBAL.
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*
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* M (input) INTEGER
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* The number of columns of the matrix V. M >= 0.
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*
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* V (input/output) COMPLEX*16 array, dimension (LDV,M)
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* On entry, the matrix of right or left eigenvectors to be
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* transformed, as returned by ZHSEIN or ZTREVC.
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* On exit, V is overwritten by the transformed eigenvectors.
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*
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* LDV (input) INTEGER
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* The leading dimension of the array V. LDV >= max(1,N).
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value.
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE
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PARAMETER ( ONE = 1.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL LEFTV, RIGHTV
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INTEGER I, II, K
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DOUBLE PRECISION S
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZDSCAL, ZSWAP
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Decode and Test the input parameters
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*
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RIGHTV = LSAME( SIDE, 'R' )
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LEFTV = LSAME( SIDE, 'L' )
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*
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INFO = 0
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IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND.
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$ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
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INFO = -4
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ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
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INFO = -5
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ELSE IF( M.LT.0 ) THEN
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INFO = -7
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ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
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INFO = -9
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZGEBAK', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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IF( M.EQ.0 )
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$ RETURN
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IF( LSAME( JOB, 'N' ) )
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$ RETURN
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*
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IF( ILO.EQ.IHI )
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$ GO TO 30
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*
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* Backward balance
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*
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IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN
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*
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IF( RIGHTV ) THEN
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DO 10 I = ILO, IHI
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S = SCALE( I )
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CALL ZDSCAL( M, S, V( I, 1 ), LDV )
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10 CONTINUE
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END IF
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*
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IF( LEFTV ) THEN
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DO 20 I = ILO, IHI
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S = ONE / SCALE( I )
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CALL ZDSCAL( M, S, V( I, 1 ), LDV )
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20 CONTINUE
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END IF
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*
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END IF
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*
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* Backward permutation
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*
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* For I = ILO-1 step -1 until 1,
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* IHI+1 step 1 until N do --
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*
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30 CONTINUE
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IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN
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IF( RIGHTV ) THEN
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DO 40 II = 1, N
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I = II
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IF( I.GE.ILO .AND. I.LE.IHI )
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$ GO TO 40
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IF( I.LT.ILO )
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$ I = ILO - II
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K = SCALE( I )
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IF( K.EQ.I )
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$ GO TO 40
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CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
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40 CONTINUE
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END IF
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*
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IF( LEFTV ) THEN
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DO 50 II = 1, N
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I = II
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IF( I.GE.ILO .AND. I.LE.IHI )
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$ GO TO 50
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IF( I.LT.ILO )
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$ I = ILO - II
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K = SCALE( I )
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IF( K.EQ.I )
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$ GO TO 50
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CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
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50 CONTINUE
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END IF
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END IF
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*
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RETURN
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*
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* End of ZGEBAK
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*
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END
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