dspevx(3P) Sun Performance Library dspevx(3P)NAMEdspevx - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric matrix A in packed storage
SYNOPSIS
SUBROUTINE DSPEVX(JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABTOL,
NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER N, IL, IU, NFOUND, LDZ, INFO
INTEGER IWORK2(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION AP(*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE DSPEVX_64(JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABTOL,
NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER*8 N, IL, IU, NFOUND, LDZ, INFO
INTEGER*8 IWORK2(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION AP(*), W(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE SPEVX(JOBZ, RANGE, UPLO, [N], AP, VL, VU, IL, IU, ABTOL,
NFOUND, W, Z, [LDZ], [WORK], [IWORK2], IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER :: N, IL, IU, NFOUND, LDZ, INFO
INTEGER, DIMENSION(:) :: IWORK2, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: AP, W, WORK
REAL(8), DIMENSION(:,:) :: Z
SUBROUTINE SPEVX_64(JOBZ, RANGE, UPLO, [N], AP, VL, VU, IL, IU, ABTOL,
NFOUND, W, Z, [LDZ], [WORK], [IWORK2], IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER(8) :: N, IL, IU, NFOUND, LDZ, INFO
INTEGER(8), DIMENSION(:) :: IWORK2, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: AP, W, WORK
REAL(8), DIMENSION(:,:) :: Z
C INTERFACE
#include <sunperf.h>
void dspevx(char jobz, char range, char uplo, int n, double *ap, double
vl, double vu, int il, int iu, double abtol, int *nfound,
double *w, double *z, int ldz, int *ifail, int *info);
void dspevx_64(char jobz, char range, char uplo, long n, double *ap,
double vl, double vu, long il, long iu, double abtol, long
*nfound, double *w, double *z, long ldz, long *ifail, long
*info);
PURPOSEdspevx computes selected eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage. Eigenvalues/vectors 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.
AP (input/output)
Double precision array, dimension (N*(N+1)/2) On entry, the
upper or lower triangle of the symmetric matrix A, packed
columnwise in a linear array. The j-th column of A is stored
in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2)
= A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2)
= A(i,j) for j<=i<=n.
On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = 'L', the diag‐
onal and first subdiagonal of T overwrite the corresponding
elements of A.
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 AP 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) If INFO = 0, 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 corresponding to
the selected eigenvalues, with the i-th column of Z holding
the eigenvector associated with W(i). If an eigenvector
fails to converge, then that column of Z contains the latest
approximation to the eigenvector, and the index of the eigen‐
vector 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(8*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 refer‐
enced.
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 dspevx(3P)
