Contents
zhpevd - compute all the eigenvalues and, optionally, eigen-
vectors of a complex Hermitian matrix A in packed storage
SUBROUTINE ZHPEVD(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
DOUBLE COMPLEX AP(*), Z(LDZ,*), WORK(*)
INTEGER N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER IWORK(*)
DOUBLE PRECISION W(*), RWORK(*)
SUBROUTINE ZHPEVD_64(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
RWORK, LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
DOUBLE COMPLEX AP(*), Z(LDZ,*), WORK(*)
INTEGER*8 N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
DOUBLE PRECISION 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(8), DIMENSION(:) :: AP, WORK
COMPLEX(8), DIMENSION(:,:) :: Z
INTEGER :: N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL(8), 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(8), DIMENSION(:) :: AP, WORK
COMPLEX(8), DIMENSION(:,:) :: Z
INTEGER(8) :: N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: W, RWORK
C INTERFACE
#include <sunperf.h>
void zhpevd(char jobz, char uplo, int n, doublecomplex *ap,
double *w, doublecomplex *z, int ldz, int *info);
void zhpevd_64(char jobz, char uplo, long n, doublecomplex
*ap, double *w, doublecomplex *z, long ldz, long
*info);
zhpevd computes all the eigenvalues and, optionally, eigen-
vectors 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
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.
AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Her-
mitian 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) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (input) COMPLEX*16 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 associ-
ated 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*16 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)
DOUBLE PRECISION 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 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)
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)
= 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.