version 1.11, 2012/08/22 09:48:12
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version 1.15, 2016/08/27 15:27:08
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*> A * v(j) = lambda(j) * v(j) |
*> A * v(j) = lambda(j) * v(j) |
*> where lambda(j) is its eigenvalue. |
*> where lambda(j) is its eigenvalue. |
*> The left eigenvector u(j) of A satisfies |
*> The left eigenvector u(j) of A satisfies |
*> u(j)**T * A = lambda(j) * u(j)**T |
*> u(j)**H * A = lambda(j) * u(j)**H |
*> where u(j)**T denotes the transpose of u(j). |
*> where u(j)**H denotes the conjugate-transpose of u(j). |
*> |
*> |
*> The computed eigenvectors are normalized to have Euclidean norm |
*> The computed eigenvectors are normalized to have Euclidean norm |
*> equal to 1 and largest component real. |
*> equal to 1 and largest component real. |
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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 d -> s |
* |
* |
*> \ingroup doubleGEeigen |
*> \ingroup doubleGEeigen |
* |
* |
* ===================================================================== |
* ===================================================================== |
SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR, |
SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR, |
$ LDVR, WORK, LWORK, INFO ) |
$ LDVR, WORK, LWORK, 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 JOBVL, JOBVR |
CHARACTER JOBVL, JOBVR |
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LOGICAL LQUERY, SCALEA, WANTVL, WANTVR |
LOGICAL LQUERY, SCALEA, WANTVL, WANTVR |
CHARACTER SIDE |
CHARACTER SIDE |
INTEGER HSWORK, I, IBAL, IERR, IHI, ILO, ITAU, IWRK, K, |
INTEGER HSWORK, I, IBAL, IERR, IHI, ILO, ITAU, IWRK, K, |
$ MAXWRK, MINWRK, NOUT |
$ LWORK_TREVC, MAXWRK, MINWRK, NOUT |
DOUBLE PRECISION ANRM, BIGNUM, CS, CSCALE, EPS, R, SCL, SMLNUM, |
DOUBLE PRECISION ANRM, BIGNUM, CS, CSCALE, EPS, R, SCL, SMLNUM, |
$ SN |
$ SN |
* .. |
* .. |
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* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL DGEBAK, DGEBAL, DGEHRD, DHSEQR, DLABAD, DLACPY, |
EXTERNAL DGEBAK, DGEBAL, DGEHRD, DHSEQR, DLABAD, DLACPY, |
$ DLARTG, DLASCL, DORGHR, DROT, DSCAL, DTREVC, |
$ DLARTG, DLASCL, DORGHR, DROT, DSCAL, DTREVC3, |
$ XERBLA |
$ XERBLA |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
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MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*ILAENV( 1, |
MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*ILAENV( 1, |
$ 'DORGHR', ' ', N, 1, N, -1 ) ) |
$ 'DORGHR', ' ', N, 1, N, -1 ) ) |
CALL DHSEQR( 'S', 'V', N, 1, N, A, LDA, WR, WI, VL, LDVL, |
CALL DHSEQR( 'S', 'V', N, 1, N, A, LDA, WR, WI, VL, LDVL, |
$ WORK, -1, INFO ) |
$ WORK, -1, INFO ) |
HSWORK = WORK( 1 ) |
HSWORK = INT( WORK(1) ) |
MAXWRK = MAX( MAXWRK, N + 1, N + HSWORK ) |
MAXWRK = MAX( MAXWRK, N + 1, N + HSWORK ) |
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CALL DTREVC3( 'L', 'B', SELECT, N, A, LDA, |
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$ VL, LDVL, VR, LDVR, N, NOUT, |
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$ WORK, -1, IERR ) |
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LWORK_TREVC = INT( WORK(1) ) |
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MAXWRK = MAX( MAXWRK, N + LWORK_TREVC ) |
MAXWRK = MAX( MAXWRK, 4*N ) |
MAXWRK = MAX( MAXWRK, 4*N ) |
ELSE IF( WANTVR ) THEN |
ELSE IF( WANTVR ) THEN |
MINWRK = 4*N |
MINWRK = 4*N |
MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*ILAENV( 1, |
MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*ILAENV( 1, |
$ 'DORGHR', ' ', N, 1, N, -1 ) ) |
$ 'DORGHR', ' ', N, 1, N, -1 ) ) |
CALL DHSEQR( 'S', 'V', N, 1, N, A, LDA, WR, WI, VR, LDVR, |
CALL DHSEQR( 'S', 'V', N, 1, N, A, LDA, WR, WI, VR, LDVR, |
$ WORK, -1, INFO ) |
$ WORK, -1, INFO ) |
HSWORK = WORK( 1 ) |
HSWORK = INT( WORK(1) ) |
MAXWRK = MAX( MAXWRK, N + 1, N + HSWORK ) |
MAXWRK = MAX( MAXWRK, N + 1, N + HSWORK ) |
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CALL DTREVC3( 'R', 'B', SELECT, N, A, LDA, |
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$ VL, LDVL, VR, LDVR, N, NOUT, |
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$ WORK, -1, IERR ) |
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LWORK_TREVC = INT( WORK(1) ) |
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MAXWRK = MAX( MAXWRK, N + LWORK_TREVC ) |
MAXWRK = MAX( MAXWRK, 4*N ) |
MAXWRK = MAX( MAXWRK, 4*N ) |
ELSE |
ELSE |
MINWRK = 3*N |
MINWRK = 3*N |
CALL DHSEQR( 'E', 'N', N, 1, N, A, LDA, WR, WI, VR, LDVR, |
CALL DHSEQR( 'E', 'N', N, 1, N, A, LDA, WR, WI, VR, LDVR, |
$ WORK, -1, INFO ) |
$ WORK, -1, INFO ) |
HSWORK = WORK( 1 ) |
HSWORK = INT( WORK(1) ) |
MAXWRK = MAX( MAXWRK, N + 1, N + HSWORK ) |
MAXWRK = MAX( MAXWRK, N + 1, N + HSWORK ) |
END IF |
END IF |
MAXWRK = MAX( MAXWRK, MINWRK ) |
MAXWRK = MAX( MAXWRK, MINWRK ) |
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$ WORK( IWRK ), LWORK-IWRK+1, INFO ) |
$ WORK( IWRK ), LWORK-IWRK+1, INFO ) |
END IF |
END IF |
* |
* |
* If INFO > 0 from DHSEQR, then quit |
* If INFO .NE. 0 from DHSEQR, 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 |
* (Workspace: need 4*N) |
* (Workspace: need 4*N, prefer N + N + 2*N*NB) |
* |
* |
CALL DTREVC( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR, |
CALL DTREVC3( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR, |
$ N, NOUT, WORK( IWRK ), IERR ) |
$ N, NOUT, WORK( IWRK ), LWORK-IWRK+1, IERR ) |
END IF |
END IF |
* |
* |
IF( WANTVL ) THEN |
IF( WANTVL ) THEN |