chbevx (l) - Linux Manuals
chbevx: computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
Command to display chbevx manual in Linux: $ man l chbevx
NAME
CHBEVX - computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
SYNOPSIS
- SUBROUTINE CHBEVX(
-
JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL,
VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
IWORK, IFAIL, INFO )
-
CHARACTER
JOBZ, RANGE, UPLO
-
INTEGER
IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N
-
REAL
ABSTOL, VL, VU
-
INTEGER
IFAIL( * ), IWORK( * )
-
REAL
RWORK( * ), W( * )
-
COMPLEX
AB( LDAB, * ), Q( LDQ, * ), WORK( * ),
Z( LDZ, * )
PURPOSE
CHBEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian band 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.
- UPLO (input) CHARACTER*1
-
= aqUaq: Upper triangle of A is stored;
= aqLaq: Lower triangle of A is stored.
- N (input) INTEGER
-
The order of the matrix A. N >= 0.
- KD (input) INTEGER
-
The number of superdiagonals of the matrix A if UPLO = aqUaq,
or the number of subdiagonals if UPLO = aqLaq. KD >= 0.
- AB (input/output) COMPLEX array, dimension (LDAB, N)
-
On entry, the upper or lower triangle of the Hermitian band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = aqUaq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = aqLaq, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
On exit, AB is overwritten by values generated during the
reduction to tridiagonal form.
- LDAB (input) INTEGER
-
The leading dimension of the array AB. LDAB >= KD + 1.
- Q (output) COMPLEX array, dimension (LDQ, N)
-
If JOBZ = aqVaq, the N-by-N unitary matrix used in the
reduction to tridiagonal form.
If JOBZ = aqNaq, the array Q is not referenced.
- LDQ (input) INTEGER
-
The leading dimension of the array Q. If JOBZ = aqVaq, then
LDQ >= max(1,N).
- VL (input) REAL
-
VU (input) REAL
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) REAL
-
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 obtained
by reducing AB to tridiagonal form.
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*SLAMCH(aqSaq), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*SLAMCH(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) REAL array, dimension (N)
-
The first M elements contain the selected eigenvalues in
ascending order.
- Z (output) COMPLEX 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, 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) COMPLEX array, dimension (N)
-
- RWORK (workspace) REAL array, dimension (7*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.