CHEEVD(1) LAPACK driver routine (version 3.2) CHEEVD(1)NAME
CHEEVD - computes all eigenvalues and, optionally, eigenvectors 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, eigenvectors of a com‐
plex Hermitian 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.
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 contains 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 tri‐
angle (if UPLO='U') of A, including the diagonal, is 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 (MAX(1,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 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.
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 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.
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 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. 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 and JOBZ = 'N', then the algorithm failed to
converge; i off-diagonal elements of an intermediate tridiago‐
nal form did not converge to zero; if INFO = i and JOBZ = 'V',
then the algorithm failed to compute an eigenvalue while work‐
ing on the submatrix lying in rows and columns INFO/(N+1)
through mod(INFO,N+1).
FURTHER DETAILS
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
LAPACK driver routine (version 3November 2008 CHEEVD(1)
