Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
?stein2
Computes the eigenvectors corresponding to specified eigenvalues of a real symmetric tridiagonal matrix, using inverse iteration.
Syntax
call sstein2(n, d, e, m, w, iblock, isplit, orfac, z, ldz, work, iwork, ifail, info)
call dstein2(n, d, e, m, w, iblock, isplit, orfac, z, ldz, work, iwork, ifail, info)Include Files
mkl_scalapack.h
Description
sstein2 dstein2 The ?stein2 routine function is a modified LAPACK routine function ?stein (Computes the eigenvectors corresponding to specified eigenvalues of a real symmetric tridiagonal matrix.) . It computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration.
The maximum number of iterations allowed for each eigenvector is specified by an internal parameter maxits (currently set to 5).
Input Parameters
n
INTEGER . The order of the matrix T(n ≥ 0) .
m
INTEGER . The number of eigenvectors to be found (0 ≤ m ≤ n) .
- d , e , w
-
REAL for single-precision flavors DOUBLE PRECISION for double-precision flavors. Arrays:
d (*) , of size n . The n diagonal elements of the tridiagonal matrix T .
e (*) , of size n .
The (n-1) subdiagonal elements of the tridiagonal matrix T , in elements 1 to n-1 . e ( n ) need not be set.
w (*) , of size n .
The first m elements of w contain the eigenvalues for which eigenvectors are to be computed. The eigenvalues should be grouped by split-off block and ordered from smallest to largest within the block. (The output array w from ?stebz (Computes selected eigenvalues of a real symmetric tridiagonal matrix by bisection.) with ORDER = 'B' is expected here). The size of w must be at least max(1, n) .
iblock
INTEGER .
Array of size n . The submatrix indices associated with the corresponding eigenvalues in w ;
iblock ( i ) = 1, if eigenvalue w ( i ) belongs to the first submatrix from the top,
iblock ( i ) = 2, if eigenvalue w ( i ) belongs to the second submatrix, etc. (The output array iblock from ?stebz is expected here).
isplit
INTEGER .
Array of size n .
The splitting points, at which T breaks up into submatrices. The first submatrix consists of rows/columns 1 to isplit (1) , the second submatrix consists of rows/columns isplit (1) +1 through isplit (2) , etc. (The output array isplit from ?stebz is expected here).
- orfac
-
REAL for single-precision flavors DOUBLE PRECISION for double-precision flavors. orfac specifies which eigenvectors should be orthogonalized. Eigenvectors that correspond to eigenvalues which are within orfac*||T|| of each other are to be orthogonalized.
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 of size 5 n .
iwork
INTEGER . Workspace array of size n .
Output Parameters
- z
-
REAL for sstein2 DOUBLE PRECISION for dstein2
Array of size ldz by m .
The computed eigenvectors. The eigenvector associated with the eigenvalue w ( i ) is stored in the i -th column of z . Any vector that fails to converge is set to its current iterate after maxits iterations.
ifail
INTEGER .
Array of size m . On normal exit, all elements of ifail are zero. If one or more eigenvectors fail to converge after maxits iterations, then their indices are stored in the array ifail .
info
INTEGER .
info = 0 , the exit is successful. info < 0 : if info = -i , the i -th had an illegal value. info > 0 : if info = i , then i eigenvectors failed to converge in maxits iterations. Their indices are stored in the array ifail .