Contents
cheevd - compute all eigenvalues and, optionally, eigenvec-
tors of a complex Hermitian matrix A
SUBROUTINE CHEEVD(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
COMPLEX A(LDA,*), WORK(*)
INTEGER N, LDA, LWORK, LRWORK, LIWORK, INFO
INTEGER IWORK(*)
REAL W(*), RWORK(*)
SUBROUTINE CHEEVD_64(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
COMPLEX A(LDA,*), WORK(*)
INTEGER*8 N, LDA, LWORK, LRWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
REAL W(*), RWORK(*)
F95 INTERFACE
SUBROUTINE HEEVD(JOBZ, UPLO, [N], A, [LDA], W, [WORK], [LWORK],
[RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: N, LDA, LWORK, LRWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, RWORK
SUBROUTINE HEEVD_64(JOBZ, UPLO, [N], A, [LDA], W, [WORK], [LWORK],
[RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A
INTEGER(8) :: N, LDA, LWORK, LRWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, RWORK
C INTERFACE
#include <sunperf.h>
void cheevd(char jobz, char uplo, int n, complex *a, int
lda, float *w, int *info);
void cheevd_64(char jobz, char uplo, long n, complex *a,
long lda, float *w, long *info);
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 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
digits, but we know of none.
JOBZ (input)
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
A (input/output)
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
(if UPLO='U') of A, including the diagonal, is
destroyed.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,N).
W (output)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.
LWORK (input)
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)
dimension (LRWORK) On exit, if INFO = 0, RWORK(1)
returns the optimal LRWORK.
LRWORK (input)
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)
On exit, if INFO = 0, IWORK(1) returns the optimal
LIWORK.
LIWORK (input)
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 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)
= 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.
Based on contributions by
Jeff Rutter, Computer Science Division, University of
California
at Berkeley, USA