
DSTEVX(l) ) DSTEVX(l)
NAME
DSTEVX  compute selected eigenvalues and, optionally, eigenvectors of a real symmetric
tridiagonal matrix A
SYNOPSIS
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
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
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 halfopen interval (VL,VU] will be found. = 'I':
the ILth through IUth 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 (n1) subdiagonal elements of the tridiagonal matrix A in elements 1
to N1 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.
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 1norm 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 = IUIL+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
ith 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 approxima
tion 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.
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 ith argument had an illegal value
> 0: if INFO = i, then i eigenvectors failed to converge. Their indices are
stored in array IFAIL.
LAPACK version 3.0 15 June 2000 DSTEVX(l) 
