DSTEVX(l) ) DSTEVX(l)
DSTEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric
tridiagonal matrix A
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, * )
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.
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
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.
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'
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
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
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 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 >=
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.
LAPACK version 3.0 15 June 2000 DSTEVX(l)