DSTEVX(3) LAPACK routine of NEC Numeric Library Collection DSTEVX(3)
NAME
DSTEVX
SYNOPSIS
SUBROUTINE DSTEVX (JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W,
Z, LDZ, WORK, IWORK, IFAIL, INFO)
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)
JOBZ is CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
RANGE (input)
RANGE is 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)
N is INTEGER
The order of the matrix. N >= 0.
D (input/output)
D is 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)
E is DOUBLE PRECISION array, dimension (max(1,N-1))
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A in elements 1 to N-1 of E.
On exit, E may be multiplied by a constant factor chosen
to avoid over/underflow in computing the eigenvalues.
VL (input)
VL is DOUBLE PRECISION
VU (input)
VU is 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)
IL is INTEGER
IU (input)
IU is 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)
ABSTOL is 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)
M is 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)
W is DOUBLE PRECISION array, dimension (N)
The first M elements contain the selected eigenvalues in
ascending order.
Z (output)
Z is 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.
LDZ (input)
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N).
WORK (output)
WORK is DOUBLE PRECISION array, dimension (5*N)
IWORK (output)
IWORK is INTEGER array, dimension (5*N)
IFAIL (output)
IFAIL is 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)
INFO is 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 routine 31 October 2017 DSTEVX(3)