Contents
zheevx - compute selected eigenvalues and, optionally,
eigenvectors of a complex Hermitian matrix A
SUBROUTINE ZHEEVX(JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
ABTOL, NFOUND, W, Z, LDZ, WORK, LDWORK, WORK2, IWORK3, IFAIL,
INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
DOUBLE COMPLEX A(LDA,*), Z(LDZ,*), WORK(*)
INTEGER N, LDA, IL, IU, NFOUND, LDZ, LDWORK, INFO
INTEGER IWORK3(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION W(*), WORK2(*)
SUBROUTINE ZHEEVX_64(JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
ABTOL, NFOUND, W, Z, LDZ, WORK, LDWORK, WORK2, IWORK3, IFAIL,
INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
DOUBLE COMPLEX A(LDA,*), Z(LDZ,*), WORK(*)
INTEGER*8 N, LDA, IL, IU, NFOUND, LDZ, LDWORK, INFO
INTEGER*8 IWORK3(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION W(*), WORK2(*)
F95 INTERFACE
SUBROUTINE HEEVX(JOBZ, RANGE, UPLO, [N], A, [LDA], VL, VU, IL, IU,
ABTOL, [NFOUND], W, Z, [LDZ], [WORK], [LDWORK], [WORK2], [IWORK3],
IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, Z
INTEGER :: N, LDA, IL, IU, NFOUND, LDZ, LDWORK, INFO
INTEGER, DIMENSION(:) :: IWORK3, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: W, WORK2
SUBROUTINE HEEVX_64(JOBZ, RANGE, UPLO, [N], A, [LDA], VL, VU, IL, IU,
ABTOL, [NFOUND], W, Z, [LDZ], [WORK], [LDWORK], [WORK2], [IWORK3],
IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, Z
INTEGER(8) :: N, LDA, IL, IU, NFOUND, LDZ, LDWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK3, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: W, WORK2
C INTERFACE
#include <sunperf.h>
void zheevx(char jobz, char range, char uplo, int n, doub-
lecomplex *a, int lda, double vl, double vu, int
il, int iu, double abtol, int *nfound, double *w,
doublecomplex *z, int ldz, int *ifail, int *info);
void zheevx_64(char jobz, char range, char uplo, long n,
doublecomplex *a, long lda, double vl, double vu,
long il, long iu, double abtol, long *nfound, dou-
ble *w, doublecomplex *z, long ldz, long *ifail,
long *info);
zheevx computes selected eigenvalues and, optionally, eigen-
vectors of a complex Hermitian matrix A. Eigenvalues and
eigenvectors can be selected by specifying either a range of
values or a range of indices for the desired eigenvalues.
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.
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 triangular part of the matrix
A. If UPLO = 'L', the leading N-by-N lower tri-
angular part of A contains the lower triangular
part of the matrix A. On exit, the lower triangle
(if UPLO='L') or the upper triangle (if UPLO='U')
of A, including the diagonal, is destroyed.
LDA (input)
The leading dimension of the array A. LDA >=
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 smallest 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 smallest 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 approximate eigenvalue is accepted as converged
when it is determined 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 tri-
diagonal form.
Eigenvalues will be computed most accurately when
ABTOL is set to twice the underflow threshold
2*SLAMCH('S'), not zero. If this routine returns
with INFO>0, indicating that some eigenvectors did
not converge, try setting ABTOL to 2*SLAMCH('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)
On normal exit, the first NFOUND elements contain
the selected eigenvalues in ascending order.
Z (input) If JOBZ = 'V', then if INFO = 0, the first NFOUND
columns of Z contain the orthonormal eigenvectors
of the matrix A corresponding to the selected
eigenvalues, with the i-th column of Z holding the
eigenvector associated with W(i). If an eigenvec-
tor fails to converge, then that column of Z con-
tains 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)
On exit, if INFO = 0, WORK(1) returns the optimal
LDWORK.
LDWORK (input)
The length of the array WORK. LDWORK >=
max(1,2*N). For optimal efficiency, LDWORK >=
(NB+1)*N, where NB is the max of the blocksize for
CHETRD and for CUNMTR as returned by ILAENV.
If LDWORK = -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 LDWORK is issued by XERBLA.
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 ille-
gal value
> 0: if INFO = i, then i eigenvectors failed to
converge. Their indices are stored in array
IFAIL.