zhbevd(3P) Sun Performance Library zhbevd(3P)NAMEzhbevd - compute all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian band matrix A
SYNOPSIS
SUBROUTINE ZHBEVD(JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
DOUBLE COMPLEX AB(LDAB,*), Z(LDZ,*), WORK(*)
INTEGER N, KD, LDAB, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER IWORK(*)
DOUBLE PRECISION W(*), RWORK(*)
SUBROUTINE ZHBEVD_64(JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
DOUBLE COMPLEX AB(LDAB,*), Z(LDZ,*), WORK(*)
INTEGER*8 N, KD, LDAB, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
DOUBLE PRECISION W(*), RWORK(*)
F95 INTERFACE
SUBROUTINE HBEVD(JOBZ, UPLO, [N], KD, AB, [LDAB], W, Z, [LDZ], [WORK],
[LWORK], [RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: AB, Z
INTEGER :: N, KD, LDAB, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: W, RWORK
SUBROUTINE HBEVD_64(JOBZ, UPLO, [N], KD, AB, [LDAB], W, Z, [LDZ],
[WORK], [LWORK], [RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: AB, Z
INTEGER(8) :: N, KD, LDAB, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: W, RWORK
C INTERFACE
#include <sunperf.h>
void zhbevd(char jobz, char uplo, int n, int kd, doublecomplex *ab, int
ldab, double *w, doublecomplex *z, int ldz, int *info);
void zhbevd_64(char jobz, char uplo, long n, long kd, doublecomplex
*ab, long ldab, double *w, doublecomplex *z, long ldz, long
*info);
PURPOSEzhbevd computes all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian band 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.
KD (input)
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0.
AB (input/output)
On entry, the upper or lower triangle of the Hermitian band
matrix A, stored in the first KD+1 rows of the array. The j-
th column of A is stored in the j-th column of the array AB
as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for
max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
j<=i<=min(n,j+kd).
On exit, AB is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
the diagonal and first subdiagonal of T are returned in the
first two rows of AB.
LDAB (input)
The leading dimension of the array AB. LDAB >= KD + 1.
W (output)
If INFO = 0, the eigenvalues in ascending order.
Z (output)
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)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The dimension 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. If JOBZ = 'V' and N > 1, LWORK must be
at least 2*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 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 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 zhbevd(3P)
