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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine sstevx | ( | character | jobz, |
| character | range, | ||
| integer | n, | ||
| real, dimension( * ) | d, | ||
| real, dimension( * ) | e, | ||
| real | vl, | ||
| real | vu, | ||
| integer | il, | ||
| integer | iu, | ||
| real | abstol, | ||
| integer | m, | ||
| real, dimension( * ) | w, | ||
| real, dimension( ldz, * ) | z, | ||
| integer | ldz, | ||
| real, dimension( * ) | work, | ||
| integer, dimension( * ) | iwork, | ||
| integer, dimension( * ) | ifail, | ||
| integer | info | ||
| ) |
SSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Download SSTEVX + dependencies [TGZ] [ZIP] [TXT]
SSTEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
| [in] | JOBZ | JOBZ is CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors. |
| [in] | RANGE | RANGE is CHARACTER*1
= '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. |
| [in] | N | N is INTEGER
The order of the matrix. N >= 0. |
| [in,out] | D | D is REAL array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix
A.
On exit, D may be multiplied by a constant factor chosen
to avoid over/underflow in computing the eigenvalues. |
| [in,out] | E | E is REAL array, dimension (max(1,N-1))
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A in elements 1 to N-1 of E.
On exit, E may be multiplied by a constant factor chosen
to avoid over/underflow in computing the eigenvalues. |
| [in] | VL | VL is REAL
If RANGE='V', the lower bound of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'. |
| [in] | VU | VU is REAL
If RANGE='V', the upper bound of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'. |
| [in] | IL | IL is INTEGER
If RANGE='I', the index of the
smallest eigenvalue 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'. |
| [in] | IU | IU is INTEGER
If RANGE='I', the index of the
largest eigenvalue 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'. |
| [in] | ABSTOL | ABSTOL is REAL
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
ABSTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABSTOL 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.
Eigenvalues will be computed most accurately when ABSTOL 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 ABSTOL 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. |
| [out] | M | M is INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. |
| [out] | W | W is REAL array, dimension (N)
The first M elements contain the selected eigenvalues in
ascending order. |
| [out] | Z | Z is REAL array, dimension (LDZ, max(1,M) )
If JOBZ = 'V', then if INFO = 0, the first M 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 (INFO > 0), 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,M) columns are
supplied in the array Z; if RANGE = 'V', the exact value of M
is not known in advance and an upper bound must be used. |
| [in] | LDZ | LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N). |
| [out] | WORK | WORK is REAL array, dimension (5*N) |
| [out] | IWORK | IWORK is INTEGER array, dimension (5*N) |
| [out] | IFAIL | IFAIL is INTEGER array, dimension (N)
If JOBZ = 'V', then if INFO = 0, the first M 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. |
| [out] | INFO | INFO is INTEGER
= 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. |
Definition at line 225 of file sstevx.f.
1.9.7