-
template<typename T>
void stevx(char *jobz, char *range, integer *n, T *d, T *e, T *vl, T *vu, integer *il, integer *iu, T *abstol, integer *m, T *w, T *z, integer *ldz, float *work, integer *iwork, integer *ifail, integer *info)# STEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices.
Purpose:
STEVX 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.
- Parameters:
JOBZ – [in]
JOBZ is CHARACTER*1
= ‘N’: Compute eigenvalues only;
= ‘V’: Compute eigenvalues and eigenvectors.RANGE – [in]
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.
N – [in]
N is INTEGER
The order of the matrix. N >= 0.
D – [inout]
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.E – [inout]
E is REAL array, dimension (fla_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.VL – [in]
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’.VU – [in]
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’.IL – [in]
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’.
IU – [in]
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’.
ABSTOL – [in]
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 * fla_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.
M – [out]
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.
W – [out]
W is REAL array, dimension (N)
The first M elements contain the selected eigenvalues in ascending order.
Z – [out]
Z is REAL array, dimension (LDZ, fla_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 fla_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.LDZ – [in]
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ = ‘V’, LDZ >= fla_max(1,N).
WORK – [out] WORK is REAL array, dimension (5*N)
IWORK – [out] IWORK is INTEGER array, dimension (5*N)
IFAIL – [out]
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.INFO – [out]
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.