CSTEIN - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration

SUBROUTINE CSTEIN(

N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO )

INTEGER INFO, LDZ, M, N

INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), IWORK( * )

REAL D( * ), E( * ), W( * ), WORK( * )

COMPLEX Z( LDZ, * )

CSTEIN 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).

Although the eigenvectors are real, they are stored in a complex array, which may be passed to CUNMTR or CUPMTR for back

transformation to the eigenvectors of a complex Hermitian matrix which was reduced to tridiagonal form.

N (input) INTEGER

The order of the matrix. N >= 0.

D (input) REAL array, dimension (N)

The n diagonal elements of the tridiagonal matrix T.

E (input) REAL array, dimension (N)

The (n-1) subdiagonal elements of the tridiagonal matrix T, stored in elements 1 to N-1; E(N) need not be set.

M (input) INTEGER

The number of eigenvectors to be found. 0 <= M <= N.

W (input) REAL array, dimension (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 SSTEBZ with ORDER = 'B' is expected here. )

IBLOCK (input) INTEGER array, dimension (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, =2 if W(i) belongs to the second submatrix, etc. ( The output array IBLOCK from SSTEBZ is expected here. )

ISPLIT (input) INTEGER array, dimension (N)

The splitting points, at which T breaks up into submatrices. The first submatrix consists of rows/columns 1 to ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 through ISPLIT( 2 ), etc. ( The output array ISPLIT from SSTEBZ is expected here. )

Z (output) COMPLEX array, dimension (LDZ, M)

The computed eigenvectors. The eigenvector associated with the eigenvalue W(i) is stored in the i-th column of Z. Any vector which fails to converge is set to its current iterate after MAXITS iterations. The imaginary parts of the eigenvectors are set to zero.

LDZ (input) INTEGER

The leading dimension of the array Z. LDZ >= max(1,N).

WORK (workspace) REAL array, dimension (5*N)

IWORK (workspace) INTEGER array, dimension (N)

IFAIL (output) INTEGER array, dimension (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 array IFAIL.

INFO (output) 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 in MAXITS iterations. Their indices are stored in array IFAIL.

MAXITS INTEGER, default = 5

The maximum number of iterations performed.

EXTRA INTEGER, default = 2

The number of iterations performed after norm growth criterion is satisfied, should be at least 1.