dsbevx(3P) Sun Performance Library dsbevx(3P)NAMEdsbevx - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A
SYNOPSIS
SUBROUTINE DSBEVX(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL,
VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER IWORK2(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION A(LDA,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE DSBEVX_64(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL,
VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER*8 N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER*8 IWORK2(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION A(LDA,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE SBEVX(JOBZ, RANGE, UPLO, [N], KD, A, [LDA], Q, [LDQ],
VL, VU, IL, IU, ABTOL, NFOUND, W, Z, [LDZ], [WORK], [IWORK2],
IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER :: N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER, DIMENSION(:) :: IWORK2, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: A, Q, Z
SUBROUTINE SBEVX_64(JOBZ, RANGE, UPLO, [N], KD, A, [LDA], Q, [LDQ],
VL, VU, IL, IU, ABTOL, NFOUND, W, Z, [LDZ], [WORK], [IWORK2],
IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER(8) :: N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER(8), DIMENSION(:) :: IWORK2, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: A, Q, Z
C INTERFACE
#include <sunperf.h>
void dsbevx(char jobz, char range, char uplo, int n, int kd, double *a,
int lda, double *q, int ldq, double vl, double vu, int il,
int iu, double abtol, int *nfound, double *w, double *z, int
ldz, int *ifail, int *info);
void dsbevx_64(char jobz, char range, char uplo, long n, long kd, dou‐
ble *a, long lda, double *q, long ldq, double vl, double vu,
long il, long iu, double abtol, long *nfound, double *w, dou‐
ble *z, long ldz, long *ifail, long *info);
PURPOSEdsbevx computes selected eigenvalues and, optionally, eigenvectors of a
real symmetric 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) DOUBLE PRECISION array, dimension (LDA, N)
On entry, the upper or lower triangle of the symmetric 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. If UPLO = 'U', the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of A, and if UPLO = 'L', the
diagonal and first subdiagonal of T are returned in the first
two rows of A.
LDA (input)
The leading dimension of the array A. LDA >= KD + 1.
Q (output) DOUBLE PRECISION array, dimension (LDQ, N)
If JOBZ = 'V', the N-by-N orthogonal matrix used in the
reduction 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)
See the description of VL.
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)
See the description of IL.
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) DOUBLE PRECISION array, dimension (N)
The first NFOUND elements contain the selected eigenvalues in
ascending order.
Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))
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) DOUBLE PRECISION array, dimension (7*N)
IWORK2 (workspace) INTEGER array, dimension (5*N)
IFAIL (output) INTEGER array, dimension (N)
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 dsbevx(3P)
