CHBEVD(1) LAPACK driver routine (version 3.2) CHBEVD(1)NAME
CHBEVD - computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A
SYNOPSIS
SUBROUTINE CHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK,
RWORK, LRWORK, IWORK, LIWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, KD, LDAB, LDZ, LIWORK, LRWORK, LWORK, N
INTEGER IWORK( * )
REAL RWORK( * ), W( * )
COMPLEX AB( LDAB, * ), WORK( * ), Z( LDZ, * )
PURPOSE
CHBEVD computes all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian band matrix A. If eigenvectors are desired, it uses
a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard digit
in add/subtract, or on those binary machines without guard digits which
subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
conceivably fail on hexadecimal or decimal machines without guard dig‐
its, but we know of none.
ARGUMENTS
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': 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 = 'U', or
the number of subdiagonals if UPLO = 'L'. 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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
j<=i<=min(n,j+kd). On exit, AB is overwritten by values gener‐
ated during the reduction to tridiagonal form. If UPLO = 'U',
the first superdiagonal and the diagonal of the tridiagonal
matrix T are returned in rows KD and KD+1 of AB, and if UPLO =
'L', the diagonal and first subdiagonal of T are returned in
the first two rows of AB.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD + 1.
W (output) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) COMPLEX array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z holding
the eigenvector associated with W(i). If JOBZ = 'N', then Z is
not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
'V', LDZ >= max(1,N).
WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. If N <= 1,
LWORK must be at least 1. If JOBZ = 'N' and N > 1, LWORK must
be at least N. If JOBZ = 'V' and N > 1, LWORK must be at least
2*N**2. If LWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message related
to LWORK or LRWORK or LIWORK is issued by XERBLA.
RWORK (workspace/output) REAL array,
dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the
optimal LRWORK.
LRWORK (input) INTEGER
The dimension of array RWORK. If N <= 1, LRWORK
must be at least 1. If JOBZ = 'N' and N > 1, LRWORK must be at
least N. If JOBZ = 'V' and N > 1, LRWORK must be at least 1 +
5*N + 2*N**2. If LRWORK = -1, then a workspace query is
assumed; the routine only calculates the optimal sizes of the
WORK, RWORK and IWORK arrays, returns these values as the first
entries of the WORK, RWORK and IWORK arrays, and no error mes‐
sage related to LWORK or LRWORK or LIWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of array IWORK. If JOBZ = 'N' or N <= 1, LIWORK
must be at least 1. If JOBZ = 'V' and N > 1, LIWORK must be at
least 3 + 5*N . If LIWORK = -1, then a workspace query is
assumed; the routine only calculates the optimal sizes of the
WORK, RWORK and IWORK arrays, returns these values as the first
entries of the WORK, RWORK and IWORK arrays, and no error mes‐
sage related to LWORK or LRWORK or LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, the algorithm failed to converge; i off-
diagonal elements of an intermediate tridiagonal form did not
converge to zero.
LAPACK driver routine (version 3November 2008 CHBEVD(1)
