Contents
sspevx - compute selected eigenvalues and, optionally,
eigenvectors of a real symmetric matrix A in packed storage
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);
sspevx computes selected eigenvalues and, optionally, eigen-
vectors 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 eigen-
values.
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 diagonal 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 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)
See the description of IL.
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 AP 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)
Real array, dimension (N) If INFO = 0, the
selected eigenvalues 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 orthonormal eigenvectors of the
matrix A corresponding to the selected eigen-
values, 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)
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 con-
verge. 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.