zhbevx(3P) Sun Performance Library zhbevx(3P)NAMEzhbevx - compute selected eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A
SYNOPSIS
SUBROUTINE ZHBEVX(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL,
VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL,
INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
DOUBLE COMPLEX A(LDA,*), Q(LDQ,*), Z(LDZ,*), WORK(*)
INTEGER N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER IWORK3(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION W(*), WORK2(*)
SUBROUTINE ZHBEVX_64(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL,
VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL,
INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
DOUBLE COMPLEX A(LDA,*), Q(LDQ,*), Z(LDZ,*), WORK(*)
INTEGER*8 N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER*8 IWORK3(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION W(*), WORK2(*)
F95 INTERFACE
SUBROUTINE HBEVX(JOBZ, RANGE, UPLO, [N], KD, A, [LDA], Q, [LDQ],
VL, VU, IL, IU, ABTOL, [NFOUND], W, Z, [LDZ], [WORK], [WORK2],
[IWORK3], IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, Q, Z
INTEGER :: N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER, DIMENSION(:) :: IWORK3, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: W, WORK2
SUBROUTINE HBEVX_64(JOBZ, RANGE, UPLO, [N], KD, A, [LDA], Q, [LDQ],
VL, VU, IL, IU, ABTOL, [NFOUND], W, Z, [LDZ], [WORK], [WORK2],
[IWORK3], IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, Q, Z
INTEGER(8) :: N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER(8), DIMENSION(:) :: IWORK3, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: W, WORK2
C INTERFACE
#include <sunperf.h>
void zhbevx(char jobz, char range, char uplo, int n, int kd, doublecom‐
plex *a, int lda, doublecomplex *q, int ldq, double vl, dou‐
ble vu, int il, int iu, double abtol, int *nfound, double *w,
doublecomplex *z, int ldz, int *ifail, int *info);
void zhbevx_64(char jobz, char range, char uplo, long n, long kd, dou‐
blecomplex *a, long lda, doublecomplex *q, long ldq, double
vl, double vu, long il, long iu, double abtol, long *nfound,
double *w, doublecomplex *z, long ldz, long *ifail, long
*info);
PURPOSEzhbevx computes selected eigenvalues and, optionally, eigenvectors of a
complex Hermitian band matrix A. Eigenvalues and eigenvectors can be
selected by specifying either a range of values or a range of indices
for the desired eigenvalues.
ARGUMENTS
JOBZ (input)
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
RANGE (input)
= 'A': all eigenvalues will be found;
= 'V': all eigenvalues in the half-open interval (VL,VU] will
be found; = 'I': the IL-th through IU-th eigenvalues will be
found.
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.
A (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 A as
follows: if UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j-
kd)<=i<=j; if UPLO = 'L', A(1+i-j,j) = A(i,j) for
j<=i<=min(n,j+kd).
On exit, A is overwritten by values generated during the
reduction to tridiagonal form.
LDA (input)
The leading dimension of the array A. LDA >= KD + 1.
Q (output)
If JOBZ = 'V', the N-by-N unitary matrix used in the reduc‐
tion to tridiagonal form. If JOBZ = 'N', the array Q is not
referenced.
LDQ (input)
The leading dimension of the array Q. If JOBZ = 'V', then
LDQ >= max(1,N).
VL (input)
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU. Not referenced if
RANGE = 'A' or 'I'.
VU (input)
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU. Not referenced if
RANGE = 'A' or 'I'.
IL (input)
If RANGE='I', the indices (in ascending order) of the small‐
est and largest eigenvalues to be returned. 1 <= IL <= IU <=
N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if
RANGE = 'A' or 'V'.
IU (input)
If RANGE='I', the indices (in ascending order) of the small‐
est and largest eigenvalues to be returned. 1 <= IL <= IU <=
N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if
RANGE = 'A' or 'V'.
ABTOL (input)
The absolute error tolerance for the eigenvalues. An approx‐
imate eigenvalue is accepted as converged when it is deter‐
mined to lie in an interval [a,b] of width less than or equal
to
ABTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABTOL is less than or
equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained by
reducing A to tridiagonal form.
Eigenvalues will be computed most accurately when ABTOL is
set to twice the underflow threshold 2*DLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABTOL to
2*DLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy," by Demmel and Kahan,
LAPACK Working Note #3.
NFOUND (output)
The total number of eigenvalues found. 0 <= NFOUND <= N. If
RANGE = 'A', NFOUND = N, and if RANGE = 'I', NFOUND = IU-
IL+1.
W (output)
The first NFOUND elements contain the selected eigenvalues in
ascending order.
Z (output)
If JOBZ = 'V', then if INFO = 0, the first NFOUND columns of
Z contain the orthonormal eigenvectors of the matrix A corre‐
sponding to the selected eigenvalues, with the i-th column of
Z holding the eigenvector associated with W(i). If an eigen‐
vector fails to converge, then that column of Z contains the
latest approximation to the eigenvector, and the index of the
eigenvector is returned in IFAIL. If JOBZ = 'N', then Z is
not referenced. Note: the user must ensure that at least
max(1,NFOUND) columns are supplied in the array Z; if RANGE =
'V', the exact value of NFOUND is not known in advance and an
upper bound must be used.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ
= 'V', LDZ >= max(1,N).
WORK (workspace)
dimension(N)
WORK2 (workspace)
dimension(7*N)
IWORK3 (workspace)
dimension(5*N)
IFAIL (output)
If JOBZ = 'V', then if INFO = 0, the first NFOUND elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the indices
of the eigenvectors that failed to converge. If JOBZ = 'N',
then IFAIL is not referenced.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.
6 Mar 2009 zhbevx(3P)
