chpevd(3P) Sun Performance Library chpevd(3P)NAMEchpevd - 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 * 1 JOBZ, UPLO
COMPLEX AP(*), Z(LDZ,*), WORK(*)
INTEGER N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER IWORK(*)
REAL W(*), RWORK(*)
SUBROUTINE CHPEVD_64(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
RWORK, LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
COMPLEX AP(*), Z(LDZ,*), WORK(*)
INTEGER*8 N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
REAL W(*), RWORK(*)
F95 INTERFACE
SUBROUTINE HPEVD(JOBZ, UPLO, [N], AP, W, Z, [LDZ], [WORK], [LWORK],
[RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: AP, WORK
COMPLEX, DIMENSION(:,:) :: Z
INTEGER :: N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, RWORK
SUBROUTINE HPEVD_64(JOBZ, UPLO, [N], AP, W, Z, [LDZ], [WORK], [LWORK],
[RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: AP, WORK
COMPLEX, DIMENSION(:,:) :: Z
INTEGER(8) :: N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, RWORK
C INTERFACE
#include <sunperf.h>
void chpevd(char jobz, char uplo, int n, complex *ap, float *w, complex
*z, int ldz, int *info);
void chpevd_64(char jobz, char uplo, long n, complex *ap, float *w,
complex *z, long ldz, long *info);
PURPOSEchpevd 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)
= '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.
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 diag‐
onal 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 hold‐
ing the eigenvector associated with W(i). If JOBZ = 'N',
then Z is not referenced.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ
= 'V', LDZ >= max(1,N).
WORK (workspace) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
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)
REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1)
returns the optimal LRWORK.
LRWORK (input)
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 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) INTEGER array, dimension (LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input)
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 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.
6 Mar 2009 chpevd(3P)
