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DSTEVX(3F)							    DSTEVX(3F)


NAME    [Toc]    [Back]

     DSTEVX - compute selected eigenvalues and,	optionally, eigenvectors of a
     real symmetric tridiagonal	matrix A

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DSTEVX(	JOBZ, RANGE, N,	D, E, VL, VU, IL, IU, ABSTOL, M, W, Z,
			LDZ, WORK, IWORK, IFAIL, INFO )

	 CHARACTER	JOBZ, RANGE

	 INTEGER	IL, INFO, IU, LDZ, M, N

	 DOUBLE		PRECISION ABSTOL, VL, VU

	 INTEGER	IFAIL( * ), IWORK( * )

	 DOUBLE		PRECISION D( * ), E( * ), W( * ), WORK(	* ), Z(	LDZ, *
			)

PURPOSE    [Toc]    [Back]

     DSTEVX computes selected eigenvalues and, optionally, eigenvectors	of a
     real symmetric tridiagonal	matrix A.  Eigenvalues and eigenvectors	can be
     selected by specifying either a range of values or	a range	of indices for
     the desired eigenvalues.

ARGUMENTS    [Toc]    [Back]

     JOBZ    (input) CHARACTER*1
	     = 'N':  Compute eigenvalues only;
	     = 'V':  Compute eigenvalues and eigenvectors.

     RANGE   (input) CHARACTER*1
	     = 'A': all	eigenvalues will be found.
	     = 'V': all	eigenvalues in the half-open interval (VL,VU] will be
	     found.  = 'I': the	IL-th through IU-th eigenvalues	will be	found.

     N	     (input) INTEGER
	     The order of the matrix.  N >= 0.

     D	     (input/output) DOUBLE PRECISION array, dimension (N)
	     On	entry, the n diagonal elements of the tridiagonal matrix A.
	     On	exit, D	may be multiplied by a constant	factor chosen to avoid
	     over/underflow in computing the eigenvalues.

     E	     (input/output) DOUBLE PRECISION array, dimension (N)
	     On	entry, the (n-1) subdiagonal elements of the tridiagonal
	     matrix A in elements 1 to N-1 of E; E(N) need not be set.	On
	     exit, E may be multiplied by a constant factor chosen to avoid
	     over/underflow in computing the eigenvalues.






									Page 1






DSTEVX(3F)							    DSTEVX(3F)



     VL	     (input) DOUBLE PRECISION
	     VU	     (input) DOUBLE PRECISION If RANGE='V', the	lower and
	     upper bounds of the interval to be	searched for eigenvalues. VL <
	     VU.  Not referenced if RANGE = 'A'	or 'I'.

     IL	     (input) INTEGER
	     IU	     (input) INTEGER If	RANGE='I', the indices (in ascending
	     order) of the smallest and	largest	eigenvalues to be returned.  1
	     <=	IL <= IU <= N, if N > 0; IL = 1	and IU = 0 if N	= 0.  Not
	     referenced	if RANGE = 'A' or 'V'.

     ABSTOL  (input) DOUBLE PRECISION
	     The absolute error	tolerance for the eigenvalues.	An approximate
	     eigenvalue	is accepted as converged when it is determined to lie
	     in	an interval [a,b] of width less	than or	equal to

	     ABSTOL + EPS *   max( |a|,|b| ) ,

	     where EPS is the machine precision.  If ABSTOL is less than or
	     equal to zero, then  EPS*|T|  will	be used	in its place, where
	     |T| is the	1-norm of the tridiagonal matrix.

	     Eigenvalues will be computed most accurately when ABSTOL is set
	     to	twice the underflow threshold 2*DLAMCH('S'), not zero.	If
	     this routine returns with INFO>0, indicating that some
	     eigenvectors did not converge, try	setting	ABSTOL to
	     2*DLAMCH('S').

	     See "Computing Small Singular Values of Bidiagonal	Matrices with
	     Guaranteed	High Relative Accuracy," by Demmel and Kahan, LAPACK
	     Working Note #3.

     M	     (output) INTEGER
	     The total number of eigenvalues found.  0 <= M <= N.  If RANGE =
	     'A', M = N, and if	RANGE =	'I', M = IU-IL+1.

     W	     (output) DOUBLE PRECISION array, dimension	(N)
	     The first M elements contain the selected eigenvalues in
	     ascending order.

     Z	     (output) DOUBLE PRECISION array, dimension	(LDZ, max(1,M) )
	     If	JOBZ = 'V', then if INFO = 0, the first	M columns of Z contain
	     the orthonormal eigenvectors of the matrix	A corresponding	to the
	     selected eigenvalues, with	the i-th column	of Z holding the
	     eigenvector associated with W(i).	If an eigenvector fails	to
	     converge (INFO > 0), then that column of Z	contains the latest
	     approximation to the eigenvector, and the index of	the
	     eigenvector is returned in	IFAIL.	If JOBZ	= 'N', then Z is not
	     referenced.  Note:	the user must ensure that at least max(1,M)
	     columns are supplied in the array Z; if RANGE = 'V', the exact
	     value of M	is not known in	advance	and an upper bound must	be
	     used.



									Page 2






DSTEVX(3F)							    DSTEVX(3F)



     LDZ     (input) INTEGER
	     The leading dimension of the array	Z.  LDZ	>= 1, and if JOBZ =
	     'V', LDZ >= max(1,N).

     WORK    (workspace) DOUBLE	PRECISION array, dimension (5*N)

     IWORK   (workspace) INTEGER array,	dimension (5*N)

     IFAIL   (output) INTEGER array, dimension (N)
	     If	JOBZ = 'V', then if INFO = 0, the first	M elements of IFAIL
	     are zero.	If INFO	> 0, then IFAIL	contains the indices of	the
	     eigenvectors that failed to converge.  If JOBZ = 'N', then	IFAIL
	     is	not referenced.

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value
	     > 0:  if INFO = i,	then i eigenvectors failed to converge.	 Their
	     indices are stored	in array IFAIL.
DSTEVX(3F)							    DSTEVX(3F)


NAME    [Toc]    [Back]

     DSTEVX - compute selected eigenvalues and,	optionally, eigenvectors of a
     real symmetric tridiagonal	matrix A

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DSTEVX(	JOBZ, RANGE, N,	D, E, VL, VU, IL, IU, ABSTOL, M, W, Z,
			LDZ, WORK, IWORK, IFAIL, INFO )

	 CHARACTER	JOBZ, RANGE

	 INTEGER	IL, INFO, IU, LDZ, M, N

	 DOUBLE		PRECISION ABSTOL, VL, VU

	 INTEGER	IFAIL( * ), IWORK( * )

	 DOUBLE		PRECISION D( * ), E( * ), W( * ), WORK(	* ), Z(	LDZ, *
			)

PURPOSE    [Toc]    [Back]

     DSTEVX computes selected eigenvalues and, optionally, eigenvectors	of a
     real symmetric tridiagonal	matrix A.  Eigenvalues and eigenvectors	can be
     selected by specifying either a range of values or	a range	of indices for
     the desired eigenvalues.

ARGUMENTS    [Toc]    [Back]

     JOBZ    (input) CHARACTER*1
	     = 'N':  Compute eigenvalues only;
	     = 'V':  Compute eigenvalues and eigenvectors.

     RANGE   (input) CHARACTER*1
	     = 'A': all	eigenvalues will be found.
	     = 'V': all	eigenvalues in the half-open interval (VL,VU] will be
	     found.  = 'I': the	IL-th through IU-th eigenvalues	will be	found.

     N	     (input) INTEGER
	     The order of the matrix.  N >= 0.

     D	     (input/output) DOUBLE PRECISION array, dimension (N)
	     On	entry, the n diagonal elements of the tridiagonal matrix A.
	     On	exit, D	may be multiplied by a constant	factor chosen to avoid
	     over/underflow in computing the eigenvalues.

     E	     (input/output) DOUBLE PRECISION array, dimension (N)
	     On	entry, the (n-1) subdiagonal elements of the tridiagonal
	     matrix A in elements 1 to N-1 of E; E(N) need not be set.	On
	     exit, E may be multiplied by a constant factor chosen to avoid
	     over/underflow in computing the eigenvalues.






									Page 1






DSTEVX(3F)							    DSTEVX(3F)



     VL	     (input) DOUBLE PRECISION
	     VU	     (input) DOUBLE PRECISION If RANGE='V', the	lower and
	     upper bounds of the interval to be	searched for eigenvalues. VL <
	     VU.  Not referenced if RANGE = 'A'	or 'I'.

     IL	     (input) INTEGER
	     IU	     (input) INTEGER If	RANGE='I', the indices (in ascending
	     order) of the smallest and	largest	eigenvalues to be returned.  1
	     <=	IL <= IU <= N, if N > 0; IL = 1	and IU = 0 if N	= 0.  Not
	     referenced	if RANGE = 'A' or 'V'.

     ABSTOL  (input) DOUBLE PRECISION
	     The absolute error	tolerance for the eigenvalues.	An approximate
	     eigenvalue	is accepted as converged when it is determined to lie
	     in	an interval [a,b] of width less	than or	equal to

	     ABSTOL + EPS *   max( |a|,|b| ) ,

	     where EPS is the machine precision.  If ABSTOL is less than or
	     equal to zero, then  EPS*|T|  will	be used	in its place, where
	     |T| is the	1-norm of the tridiagonal matrix.

	     Eigenvalues will be computed most accurately when ABSTOL is set
	     to	twice the underflow threshold 2*DLAMCH('S'), not zero.	If
	     this routine returns with INFO>0, indicating that some
	     eigenvectors did not converge, try	setting	ABSTOL to
	     2*DLAMCH('S').

	     See "Computing Small Singular Values of Bidiagonal	Matrices with
	     Guaranteed	High Relative Accuracy," by Demmel and Kahan, LAPACK
	     Working Note #3.

     M	     (output) INTEGER
	     The total number of eigenvalues found.  0 <= M <= N.  If RANGE =
	     'A', M = N, and if	RANGE =	'I', M = IU-IL+1.

     W	     (output) DOUBLE PRECISION array, dimension	(N)
	     The first M elements contain the selected eigenvalues in
	     ascending order.

     Z	     (output) DOUBLE PRECISION array, dimension	(LDZ, max(1,M) )
	     If	JOBZ = 'V', then if INFO = 0, the first	M columns of Z contain
	     the orthonormal eigenvectors of the matrix	A corresponding	to the
	     selected eigenvalues, with	the i-th column	of Z holding the
	     eigenvector associated with W(i).	If an eigenvector fails	to
	     converge (INFO > 0), then that column of Z	contains the latest
	     approximation to the eigenvector, and the index of	the
	     eigenvector is returned in	IFAIL.	If JOBZ	= 'N', then Z is not
	     referenced.  Note:	the user must ensure that at least max(1,M)
	     columns are supplied in the array Z; if RANGE = 'V', the exact
	     value of M	is not known in	advance	and an upper bound must	be
	     used.



									Page 2






DSTEVX(3F)							    DSTEVX(3F)



     LDZ     (input) INTEGER
	     The leading dimension of the array	Z.  LDZ	>= 1, and if JOBZ =
	     'V', LDZ >= max(1,N).

     WORK    (workspace) DOUBLE	PRECISION array, dimension (5*N)

     IWORK   (workspace) INTEGER array,	dimension (5*N)

     IFAIL   (output) INTEGER array, dimension (N)
	     If	JOBZ = 'V', then if INFO = 0, the first	M elements of IFAIL
	     are zero.	If INFO	> 0, then IFAIL	contains the indices of	the
	     eigenvectors that failed to converge.  If JOBZ = 'N', then	IFAIL
	     is	not referenced.

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value
	     > 0:  if INFO = i,	then i eigenvectors failed to converge.	 Their
	     indices are stored	in array IFAIL.


									PPPPaaaaggggeeee 3333
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