dspevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
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);
Oracle Solaris Studio Performance Library dspevx(3P)
NAME
dspevx - 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);
PURPOSE
dspevx 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.
7 Nov 2015 dspevx(3P)