cheevx(3P) Sun Performance Library cheevx(3P)NAMEcheevx - compute selected eigenvalues and, optionally, eigenvectors of
a complex Hermitian matrix A
SYNOPSIS
SUBROUTINE CHEEVX(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
COMPLEX A(LDA,*), Z(LDZ,*), WORK(*)
INTEGER N, LDA, IL, IU, NFOUND, LDZ, LDWORK, INFO
INTEGER IWORK3(*), IFAIL(*)
REAL VL, VU, ABTOL
REAL W(*), WORK2(*)
SUBROUTINE CHEEVX_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
COMPLEX A(LDA,*), Z(LDZ,*), WORK(*)
INTEGER*8 N, LDA, IL, IU, NFOUND, LDZ, LDWORK, INFO
INTEGER*8 IWORK3(*), IFAIL(*)
REAL VL, VU, ABTOL
REAL 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, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, Z
INTEGER :: N, LDA, IL, IU, NFOUND, LDZ, LDWORK, INFO
INTEGER, DIMENSION(:) :: IWORK3, IFAIL
REAL :: VL, VU, ABTOL
REAL, 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, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, Z
INTEGER(8) :: N, LDA, IL, IU, NFOUND, LDZ, LDWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK3, IFAIL
REAL :: VL, VU, ABTOL
REAL, DIMENSION(:) :: W, WORK2
C INTERFACE
#include <sunperf.h>
void cheevx(char jobz, char range, char uplo, int n, complex *a, int
lda, float vl, float vu, int il, int iu, float abtol, int
*nfound, float *w, complex *z, int ldz, int *ifail, int
*info);
void cheevx_64(char jobz, char range, char uplo, long n, complex *a,
long lda, float vl, float vu, long il, long iu, float abtol,
long *nfound, float *w, complex *z, long ldz, long *ifail,
long *info);
PURPOSEcheevx computes selected eigenvalues and, optionally, eigenvectors 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.
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.
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 triangu‐
lar part of the matrix A. If UPLO = 'L', the leading N-by-N
lower triangular 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 diag‐
onal, 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 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*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 (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)
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 rou‐
tine 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 illegal value
> 0: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.
6 Mar 2009 cheevx(3P)
