zheevd - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
SUBROUTINE ZHEEVD(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO DOUBLE COMPLEX A(LDA,*), WORK(*) INTEGER N, LDA, LWORK, LRWORK, LIWORK, INFO INTEGER IWORK(*) DOUBLE PRECISION W(*), RWORK(*) SUBROUTINE ZHEEVD_64(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO DOUBLE COMPLEX A(LDA,*), WORK(*) INTEGER*8 N, LDA, LWORK, LRWORK, LIWORK, INFO INTEGER*8 IWORK(*) DOUBLE PRECISION 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(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A INTEGER :: N, LDA, LWORK, LRWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: IWORK REAL(8), 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(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A INTEGER(8) :: N, LDA, LWORK, LRWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL(8), DIMENSION(:) :: W, RWORK C INTERFACE #include <sunperf.h> void zheevd(char jobz, char uplo, int n, doublecomplex *a, int lda, double *w, int *info); void zheevd_64(char jobz, char uplo, long n, doublecomplex *a, long lda, double *w, long *info);
Oracle Solaris Studio Performance Library zheevd(3P)
NAME
zheevd - compute all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A
SYNOPSIS
SUBROUTINE ZHEEVD(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
LRWORK, IWORK, LIWORK, INFO)
CHARACTER*1 JOBZ, UPLO
DOUBLE COMPLEX A(LDA,*), WORK(*)
INTEGER N, LDA, LWORK, LRWORK, LIWORK, INFO
INTEGER IWORK(*)
DOUBLE PRECISION W(*), RWORK(*)
SUBROUTINE ZHEEVD_64(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
LRWORK, IWORK, LIWORK, INFO)
CHARACTER*1 JOBZ, UPLO
DOUBLE COMPLEX A(LDA,*), WORK(*)
INTEGER*8 N, LDA, LWORK, LRWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
DOUBLE PRECISION 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(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: N, LDA, LWORK, LRWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL(8), 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(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: N, LDA, LWORK, LRWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: W, RWORK
C INTERFACE
#include <sunperf.h>
void zheevd(char jobz, char uplo, int n, doublecomplex *a, int lda,
double *w, int *info);
void zheevd_64(char jobz, char uplo, long n, doublecomplex *a, long
lda, double *w, long *info);
PURPOSE
zheevd 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)
= '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 contains the upper triangu-
lar 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 diago-
nal, 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 rou-
tine 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 rou-
tine 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 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.
FURTHER DETAILS
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
7 Nov 2015 zheevd(3P)