dtrevc()

subroutine dtrevc	(	character	side,
		character	howmny,
		logical, dimension( * )	select,
		integer	n,
		double precision, dimension( ldt, * )	t,
		integer	ldt,
		double precision, dimension( ldvl, * )	vl,
		integer	ldvl,
		double precision, dimension( ldvr, * )	vr,
		integer	ldvr,
		integer	mm,
		integer	m,
		double precision, dimension( * )	work,
		integer	info )

DTREVC

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Purpose:

!>
!> DTREVC computes some or all of the right and/or left eigenvectors of
!> a real upper quasi-triangular matrix T.
!> Matrices of this type are produced by the Schur factorization of
!> a real general matrix:  A = Q*T*Q**T, as computed by DHSEQR.
!>
!> The right eigenvector x and the left eigenvector y of T corresponding
!> to an eigenvalue w are defined by:
!>
!>    T*x = w*x,     (y**H)*T = w*(y**H)
!>
!> where y**H denotes the conjugate transpose of y.
!> The eigenvalues are not input to this routine, but are read directly
!> from the diagonal blocks of T.
!>
!> This routine returns the matrices X and/or Y of right and left
!> eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
!> input matrix.  If Q is the orthogonal factor that reduces a matrix
!> A to Schur form T, then Q*X and Q*Y are the matrices of right and
!> left eigenvectors of A.
!> 

Parameters

[in]	SIDE	!> SIDE is CHARACTER*1 !> = 'R': compute right eigenvectors only; !> = 'L': compute left eigenvectors only; !> = 'B': compute both right and left eigenvectors. !>
[in]	HOWMNY	!> HOWMNY is CHARACTER*1 !> = 'A': compute all right and/or left eigenvectors; !> = 'B': compute all right and/or left eigenvectors, !> backtransformed by the matrices in VR and/or VL; !> = 'S': compute selected right and/or left eigenvectors, !> as indicated by the logical array SELECT. !>
[in,out]	SELECT	!> SELECT is LOGICAL array, dimension (N) !> If HOWMNY = 'S', SELECT specifies the eigenvectors to be !> computed. !> If w(j) is a real eigenvalue, the corresponding real !> eigenvector is computed if SELECT(j) is .TRUE.. !> If w(j) and w(j+1) are the real and imaginary parts of a !> complex eigenvalue, the corresponding complex eigenvector is !> computed if either SELECT(j) or SELECT(j+1) is .TRUE., and !> on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to !> .FALSE.. !> Not referenced if HOWMNY = 'A' or 'B'. !>
[in]	N	!> N is INTEGER !> The order of the matrix T. N >= 0. !>
[in]	T	!> T is DOUBLE PRECISION array, dimension (LDT,N) !> The upper quasi-triangular matrix T in Schur canonical form. !>
[in]	LDT	!> LDT is INTEGER !> The leading dimension of the array T. LDT >= max(1,N). !>
[in,out]	VL	!> VL is DOUBLE PRECISION array, dimension (LDVL,MM) !> On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must !> contain an N-by-N matrix Q (usually the orthogonal matrix Q !> of Schur vectors returned by DHSEQR). !> On exit, if SIDE = 'L' or 'B', VL contains: !> if HOWMNY = 'A', the matrix Y of left eigenvectors of T; !> if HOWMNY = 'B', the matrix Q*Y; !> if HOWMNY = 'S', the left eigenvectors of T specified by !> SELECT, stored consecutively in the columns !> of VL, in the same order as their !> eigenvalues. !> A complex eigenvector corresponding to a complex eigenvalue !> is stored in two consecutive columns, the first holding the !> real part, and the second the imaginary part. !> Not referenced if SIDE = 'R'. !>
[in]	LDVL	!> LDVL is INTEGER !> The leading dimension of the array VL. LDVL >= 1, and if !> SIDE = 'L' or 'B', LDVL >= N. !>
[in,out]	VR	!> VR is DOUBLE PRECISION array, dimension (LDVR,MM) !> On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must !> contain an N-by-N matrix Q (usually the orthogonal matrix Q !> of Schur vectors returned by DHSEQR). !> On exit, if SIDE = 'R' or 'B', VR contains: !> if HOWMNY = 'A', the matrix X of right eigenvectors of T; !> if HOWMNY = 'B', the matrix Q*X; !> if HOWMNY = 'S', the right eigenvectors of T specified by !> SELECT, stored consecutively in the columns !> of VR, in the same order as their !> eigenvalues. !> A complex eigenvector corresponding to a complex eigenvalue !> is stored in two consecutive columns, the first holding the !> real part and the second the imaginary part. !> Not referenced if SIDE = 'L'. !>
[in]	LDVR	!> LDVR is INTEGER !> The leading dimension of the array VR. LDVR >= 1, and if !> SIDE = 'R' or 'B', LDVR >= N. !>
[in]	MM	!> MM is INTEGER !> The number of columns in the arrays VL and/or VR. MM >= M. !>
[out]	M	!> M is INTEGER !> The number of columns in the arrays VL and/or VR actually !> used to store the eigenvectors. !> If HOWMNY = 'A' or 'B', M is set to N. !> Each selected real eigenvector occupies one column and each !> selected complex eigenvector occupies two columns. !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension (3*N) !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  The algorithm used in this program is basically backward (forward)
!>  substitution, with scaling to make the the code robust against
!>  possible overflow.
!>
!>  Each eigenvector is normalized so that the element of largest
!>  magnitude has magnitude 1; here the magnitude of a complex number
!>  (x,y) is taken to be |x| + |y|.
!>