sspevx(3P) Sun Performance Library sspevx(3P)NAMEsspevx - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric matrix A in packed storage
SYNOPSIS
SUBROUTINE SSPEVX(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(*)
REAL VL, VU, ABTOL
REAL AP(*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SSPEVX_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(*)
REAL VL, VU, ABTOL
REAL 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 :: VL, VU, ABTOL
REAL, DIMENSION(:) :: AP, W, WORK
REAL, 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 :: VL, VU, ABTOL
REAL, DIMENSION(:) :: AP, W, WORK
REAL, DIMENSION(:,:) :: Z
C INTERFACE
#include <sunperf.h>
void sspevx(char jobz, char range, char uplo, int n, float *ap, float
vl, float vu, int il, int iu, float abtol, int *nfound, float
*w, float *z, int ldz, int *ifail, int *info);
void sspevx_64(char jobz, char range, char uplo, long n, float *ap,
float vl, float vu, long il, long iu, float abtol, long
*nfound, float *w, float *z, long ldz, long *ifail, long
*info);
PURPOSEsspevx 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)
Real 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*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)
Real array, dimension (N) If INFO = 0, the selected eigenval‐
ues in ascending order.
Z (output)
Real array, dimension (LDZ, max(1,M)) If JOBZ = 'V', then if
INFO = 0, the first NFOUND columns of Z contain the orthonor‐
mal 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 approxi‐
mation to the eigenvector, and the index of the eigenvector
is returned in IFAIL. If JOBZ = 'N', then Z is not refer‐
enced. 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)
Real 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 sspevx(3P)
