Visible to Intel only — GUID: GUID-0262B467-B5BB-48DF-96AA-3D03B2A48577
Visible to Intel only — GUID: GUID-0262B467-B5BB-48DF-96AA-3D03B2A48577
?stein
Computes the eigenvectors corresponding to specified eigenvalues of a real symmetric tridiagonal matrix.
Syntax
call sstein(n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifailv, info)
call dstein(n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifailv, info)
call cstein(n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifailv, info)
call zstein(n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifailv, info)
call stein(d, e, w, iblock, isplit, z [,ifailv] [,info])
Include Files
- mkl.fi, lapack.f90
Description
The routine computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, by inverse iteration. It is designed to be used in particular after the specified eigenvalues have been computed by ?stebz with order = 'B', but may also be used when the eigenvalues have been computed by other routines.
If you use this routine after ?stebz, it can take advantage of the block structure by performing inverse iteration on each block Ti separately, which is more efficient than using the whole matrix T.
If T has been formed by reduction of a full symmetric or Hermitian matrix A to tridiagonal form, you can transform eigenvectors of T to eigenvectors of A by calling ?ormtr or ?opmtr (for real flavors) or by calling ?unmtr or ?upmtr (for complex flavors).
Input Parameters
- n
-
INTEGER. The order of the matrix T (n≥ 0).
- m
-
INTEGER. The number of eigenvectors to be returned.
- d, e, w
-
REAL for single-precision flavors
DOUBLE PRECISION for double-precision flavors.
Arrays:
d(*) contains the diagonal elements of T.
The size of d must be at least max(1, n).
e(*) contains the sub-diagonal elements of T stored in elements 1 to n-1
The size of e must be at least max(1, n-1).
w(*) contains the eigenvalues of T, stored in w(1) to w(m) (as returned by stebz). Eigenvalues of T1 must be supplied first, in non-decreasing order; then those of T2, again in non-decreasing order, and so on. Constraint:
if iblock(i) = iblock(i+1), w(i) ≤w(i+1).
The size of w must be at least max(1, n).
- iblock, isplit
-
INTEGER.
Arrays, size at least max(1, n). The arrays iblock and isplit, as returned by ?stebz with order = 'B'.
If you did not call ?stebz with order = 'B', set all elements of iblock to 1, and isplit(1) to n.)
- ldz
-
INTEGER. The leading dimension of the output array z; ldz≥ max(1, n).
- work
-
REAL for single-precision flavors
DOUBLE PRECISION for double-precision flavors.
Workspace array, size at least max(1, 5n).
- iwork
-
INTEGER.
Workspace array, size at least max(1, n).
Output Parameters
- z
-
REAL for sstein
DOUBLE PRECISION for dstein
COMPLEX for cstein
DOUBLE COMPLEX for zstein.
Array, size (ldz, *).
If info = 0, z contains an n-by-n matrix the columns of which are orthonormal eigenvectors. (The i-th column corresponds to the ith eigenvalue.)
- ifailv
-
INTEGER.
Array, size at least max(1, m).
If info = i > 0, the first i elements of ifailv contain the indices of any eigenvectors that failed to converge.
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = i, then i eigenvectors (as indicated by the parameter ifailv) each failed to converge in 5 iterations. The current iterates are stored in the corresponding columns of the array z.
If info = -i, the i-th parameter had an illegal value.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine stein interface are the following:
- d
-
Holds the vector of length n.
- e
-
Holds the vector of length n.
- w
-
Holds the vector of length n.
- iblock
-
Holds the vector of length n.
- isplit
-
Holds the vector of length n.
- z
-
Holds the matrix Z of size (n,m).
- ifailv
-
Holds the vector of length (m).
Application Notes
Each computed eigenvector zi is an exact eigenvector of a matrix T+Ei, where ||Ei||2 = O(ε)*||T||2. However, a set of eigenvectors computed by this routine may not be orthogonal to so high a degree of accuracy as those computed by ?steqr.