CHEEVD - compute all eigenvalues and, optionally, eigen
vectors of a complex Hermitian matrix A
SYNOPSIS
SUBROUTINE CHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
RWORK, LRWORK, IWORK, LIWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N
INTEGER IWORK( * )
REAL RWORK( * ), W( * )
COMPLEX A( LDA, * ), WORK( * )
PURPOSE
CHEEVD computes all eigenvalues and, optionally, eigenvec
tors of a complex Hermitian 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.
A (input/output) COMPLEX array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U',
the leading N-by-N upper triangular part of A con
tains the upper triangular part of the matrix A.
If UPLO = 'L', the leading N-by-N lower triangular
part of A contains the lower triangular part of
the matrix A. On exit, if JOBZ = 'V', then if
INFO = 0, A contains the orthonormal eigenvectors
of the matrix A. If JOBZ = 'N', then on exit the
lower triangle (if UPLO='L') or the upper triangle
destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >=
max(1,N).
W (output) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) COMPLEX array, dimension
(LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.
LWORK (input) INTEGER
The length 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 + 1. If JOBZ = 'V'
and N > 1, LWORK must be at least 2*N + 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.
LRWORK (input) INTEGER
The dimension of the 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 the array IWORK. If N <= 1,
LIWORK must be at least 1. If JOBZ = 'N' and N >
1, LIWORK must be at least 1. If JOBZ = 'V' and
N > 1, LIWORK must be at least 3 + 5*N.
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.
FURTHER DETAILS
Based on contributions by
Jeff Rutter, Computer Science Division, University of
California
at Berkeley, USA
Man(1) output converted with
man2html