dstevx (l) - Linux Manuals
dstevx: computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
Command to display dstevx manual in Linux: $ man l dstevx
NAME
DSTEVX - computes 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
-
= aqNaq: Compute eigenvalues only;
= aqVaq: Compute eigenvalues and eigenvectors.
- RANGE (input) CHARACTER*1
-
= aqAaq: all eigenvalues will be found.
= aqVaq: all eigenvalues in the half-open interval (VL,VU]
will be found.
= aqIaq: 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 (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) DOUBLE PRECISION
-
VU (input) DOUBLE PRECISION
If RANGE=aqVaq, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = aqAaq or aqIaq.
- IL (input) INTEGER
-
IU (input) INTEGER
If RANGE=aqIaq, 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 = aqAaq or aqVaq.
- 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(aqSaq), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*DLAMCH(aqSaq).
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 = aqAaq, M = N, and if RANGE = aqIaq, 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 = aqVaq, 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 = aqNaq, 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 = aqVaq, 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 = aqVaq, 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 = aqVaq, 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 = aqNaq, 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.