sstein.f âˆ’

**Functions/Subroutines**

subroutine **sstein** (N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO)

SSTEIN

**subroutine sstein (integerN, real, dimension( * )D, real, dimension( * )E, integerM, real, dimension( * )W, integer, dimension( * )IBLOCK, integer, dimension( * )ISPLIT, real, dimension( ldz, * )Z, integerLDZ, real, dimension( * )WORK, integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)
SSTEIN**

**Purpose:**

SSTEIN 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).

**Parameters:**

*N*

N is INTEGER

The order of the matrix. N >= 0.

*D*

D is REAL array, dimension (N)

The n diagonal elements of the tridiagonal matrix T.

*E*

E is REAL array, dimension (N-1)

The (n-1) subdiagonal elements of the tridiagonal matrix

T, in elements 1 to N-1.

*M*

M is INTEGER

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

*W*

W is 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 = â€™Bâ€™ is expected here. )

*IBLOCK*

IBLOCK is 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*

ISPLIT is 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*

Z is REAL 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.

*LDZ*

LDZ is INTEGER

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

*WORK*

WORK is REAL array, dimension (5*N)

*IWORK*

IWORK is INTEGER array, dimension (N)

*IFAIL*

IFAIL is 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*

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

in MAXITS iterations. Their indices are stored in

array IFAIL.

**Internal Parameters:**

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.

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 174 of file sstein.f.

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