CHBEVD - compute 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 assump
tions 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 with
out guard digits, 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
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 generated
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 associ
ated with W(i). If JOBZ = 'N', then Z is not ref
erenced.
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
(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 size of
the WORK array, returns this value as the first
entry of the WORK array, and no error message
related to LWORK is issued by XERBLA.
RWORK (workspace/output) REAL array,
dimension (LRWORK) On exit, if INFO = 0, RWORK(1)
returns the optimal LRWORK.
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 size of
the RWORK array, returns this value as the first
entry of the RWORK array, and no error message
related to LRWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension
(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 size of
the IWORK array, returns this value as the first
entry of the IWORK array, and no error message
related to LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille
gal value.
> 0: if INFO = i, the algorithm failed to con
verge; i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero.
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