CHPEVD(l) ) CHPEVD(l)NAME
CHPEVD - compute all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A in packed storage
SYNOPSIS
SUBROUTINE CHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
LRWORK, IWORK, LIWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
INTEGER IWORK( * )
REAL RWORK( * ), W( * )
COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
PURPOSE
CHPEVD computes all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A in packed storage. 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.
AP (input/output) COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows: if UPLO = 'U', AP(i +
(j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
(j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the diagonal and
first superdiagonal of the tridiagonal matrix T overwrite the
corresponding elements of A, and if UPLO = 'L', the diagonal
and first subdiagonal of T overwrite the corresponding elements
of A.
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 (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of 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.
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 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 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 version 3.0 15 June 2000 CHPEVD(l)
