version 1.9, 2011/11/21 22:19:45
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version 1.13, 2016/08/27 15:27:12
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*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
* |
*> \date November 2011 |
*> \date June 2016 |
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* |
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* @precisions fortran z -> c |
* |
* |
*> \ingroup complex16GEeigen |
*> \ingroup complex16GEeigen |
* |
* |
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SUBROUTINE ZGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL, |
SUBROUTINE ZGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL, |
$ LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, |
$ LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, |
$ RCONDV, WORK, LWORK, RWORK, INFO ) |
$ RCONDV, WORK, LWORK, RWORK, INFO ) |
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implicit none |
* |
* |
* -- LAPACK driver routine (version 3.4.0) -- |
* -- LAPACK driver routine (version 3.6.1) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2011 |
* June 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER BALANC, JOBVL, JOBVR, SENSE |
CHARACTER BALANC, JOBVL, JOBVR, SENSE |
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LOGICAL LQUERY, SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE, |
LOGICAL LQUERY, SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE, |
$ WNTSNN, WNTSNV |
$ WNTSNN, WNTSNV |
CHARACTER JOB, SIDE |
CHARACTER JOB, SIDE |
INTEGER HSWORK, I, ICOND, IERR, ITAU, IWRK, K, MAXWRK, |
INTEGER HSWORK, I, ICOND, IERR, ITAU, IWRK, K, |
$ MINWRK, NOUT |
$ LWORK_TREVC, MAXWRK, MINWRK, NOUT |
DOUBLE PRECISION ANRM, BIGNUM, CSCALE, EPS, SCL, SMLNUM |
DOUBLE PRECISION ANRM, BIGNUM, CSCALE, EPS, SCL, SMLNUM |
COMPLEX*16 TMP |
COMPLEX*16 TMP |
* .. |
* .. |
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* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL DLABAD, DLASCL, XERBLA, ZDSCAL, ZGEBAK, ZGEBAL, |
EXTERNAL DLABAD, DLASCL, XERBLA, ZDSCAL, ZGEBAK, ZGEBAL, |
$ ZGEHRD, ZHSEQR, ZLACPY, ZLASCL, ZSCAL, ZTREVC, |
$ ZGEHRD, ZHSEQR, ZLACPY, ZLASCL, ZSCAL, ZTREVC3, |
$ ZTRSNA, ZUNGHR |
$ ZTRSNA, ZUNGHR |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
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EXTERNAL LSAME, IDAMAX, ILAENV, DLAMCH, DZNRM2, ZLANGE |
EXTERNAL LSAME, IDAMAX, ILAENV, DLAMCH, DZNRM2, ZLANGE |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC DBLE, DCMPLX, DCONJG, DIMAG, MAX, SQRT |
INTRINSIC DBLE, DCMPLX, CONJG, AIMAG, MAX, SQRT |
* .. |
* .. |
* .. Executable Statements .. |
* .. Executable Statements .. |
* |
* |
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MAXWRK = N + N*ILAENV( 1, 'ZGEHRD', ' ', N, 1, N, 0 ) |
MAXWRK = N + N*ILAENV( 1, 'ZGEHRD', ' ', N, 1, N, 0 ) |
* |
* |
IF( WANTVL ) THEN |
IF( WANTVL ) THEN |
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CALL ZTREVC3( 'L', 'B', SELECT, N, A, LDA, |
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$ VL, LDVL, VR, LDVR, |
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$ N, NOUT, WORK, -1, RWORK, -1, IERR ) |
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LWORK_TREVC = INT( WORK(1) ) |
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MAXWRK = MAX( MAXWRK, LWORK_TREVC ) |
CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VL, LDVL, |
CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VL, LDVL, |
$ WORK, -1, INFO ) |
$ WORK, -1, INFO ) |
ELSE IF( WANTVR ) THEN |
ELSE IF( WANTVR ) THEN |
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CALL ZTREVC3( 'R', 'B', SELECT, N, A, LDA, |
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$ VL, LDVL, VR, LDVR, |
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$ N, NOUT, WORK, -1, RWORK, -1, IERR ) |
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LWORK_TREVC = INT( WORK(1) ) |
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MAXWRK = MAX( MAXWRK, LWORK_TREVC ) |
CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VR, LDVR, |
CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VR, LDVR, |
$ WORK, -1, INFO ) |
$ WORK, -1, INFO ) |
ELSE |
ELSE |
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$ WORK, -1, INFO ) |
$ WORK, -1, INFO ) |
END IF |
END IF |
END IF |
END IF |
HSWORK = WORK( 1 ) |
HSWORK = INT( WORK(1) ) |
* |
* |
IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN |
IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN |
MINWRK = 2*N |
MINWRK = 2*N |
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$ WORK( IWRK ), LWORK-IWRK+1, INFO ) |
$ WORK( IWRK ), LWORK-IWRK+1, INFO ) |
END IF |
END IF |
* |
* |
* If INFO > 0 from ZHSEQR, then quit |
* If INFO .NE. 0 from ZHSEQR, then quit |
* |
* |
IF( INFO.GT.0 ) |
IF( INFO.NE.0 ) |
$ GO TO 50 |
$ GO TO 50 |
* |
* |
IF( WANTVL .OR. WANTVR ) THEN |
IF( WANTVL .OR. WANTVR ) THEN |
* |
* |
* Compute left and/or right eigenvectors |
* Compute left and/or right eigenvectors |
* (CWorkspace: need 2*N) |
* (CWorkspace: need 2*N, prefer N + 2*N*NB) |
* (RWorkspace: need N) |
* (RWorkspace: need N) |
* |
* |
CALL ZTREVC( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR, |
CALL ZTREVC3( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR, |
$ N, NOUT, WORK( IWRK ), RWORK, IERR ) |
$ N, NOUT, WORK( IWRK ), LWORK-IWRK+1, |
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$ RWORK, N, IERR ) |
END IF |
END IF |
* |
* |
* Compute condition numbers if desired |
* Compute condition numbers if desired |
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CALL ZDSCAL( N, SCL, VL( 1, I ), 1 ) |
CALL ZDSCAL( N, SCL, VL( 1, I ), 1 ) |
DO 10 K = 1, N |
DO 10 K = 1, N |
RWORK( K ) = DBLE( VL( K, I ) )**2 + |
RWORK( K ) = DBLE( VL( K, I ) )**2 + |
$ DIMAG( VL( K, I ) )**2 |
$ AIMAG( VL( K, I ) )**2 |
10 CONTINUE |
10 CONTINUE |
K = IDAMAX( N, RWORK, 1 ) |
K = IDAMAX( N, RWORK, 1 ) |
TMP = DCONJG( VL( K, I ) ) / SQRT( RWORK( K ) ) |
TMP = CONJG( VL( K, I ) ) / SQRT( RWORK( K ) ) |
CALL ZSCAL( N, TMP, VL( 1, I ), 1 ) |
CALL ZSCAL( N, TMP, VL( 1, I ), 1 ) |
VL( K, I ) = DCMPLX( DBLE( VL( K, I ) ), ZERO ) |
VL( K, I ) = DCMPLX( DBLE( VL( K, I ) ), ZERO ) |
20 CONTINUE |
20 CONTINUE |
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CALL ZDSCAL( N, SCL, VR( 1, I ), 1 ) |
CALL ZDSCAL( N, SCL, VR( 1, I ), 1 ) |
DO 30 K = 1, N |
DO 30 K = 1, N |
RWORK( K ) = DBLE( VR( K, I ) )**2 + |
RWORK( K ) = DBLE( VR( K, I ) )**2 + |
$ DIMAG( VR( K, I ) )**2 |
$ AIMAG( VR( K, I ) )**2 |
30 CONTINUE |
30 CONTINUE |
K = IDAMAX( N, RWORK, 1 ) |
K = IDAMAX( N, RWORK, 1 ) |
TMP = DCONJG( VR( K, I ) ) / SQRT( RWORK( K ) ) |
TMP = CONJG( VR( K, I ) ) / SQRT( RWORK( K ) ) |
CALL ZSCAL( N, TMP, VR( 1, I ), 1 ) |
CALL ZSCAL( N, TMP, VR( 1, I ), 1 ) |
VR( K, I ) = DCMPLX( DBLE( VR( K, I ) ), ZERO ) |
VR( K, I ) = DCMPLX( DBLE( VR( K, I ) ), ZERO ) |
40 CONTINUE |
40 CONTINUE |