# stein - Man Page

stein: eig, inverse iteration

## Synopsis

### Functions

subroutine cstein (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)
CSTEIN
subroutine dstein (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)
DSTEIN
subroutine sstein (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)
SSTEIN
subroutine zstein (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)
ZSTEIN

## Function Documentation

### subroutine cstein (integer n, real, dimension( * ) d, real, dimension( * ) e, integer m, real, dimension( * ) w, integer, dimension( * ) iblock, integer, dimension( * ) isplit, complex, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)

CSTEIN

Purpose:

``` 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.```
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, stored 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 = 'B' 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 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

```          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

NAG Ltd.

Definition at line 180 of file cstein.f.

### subroutine dstein (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, integer m, double precision, dimension( * ) w, integer, dimension( * ) iblock, integer, dimension( * ) isplit, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)

DSTEIN

Purpose:

``` DSTEIN 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 DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix T.```

E

```          E is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DSTEBZ with ORDER = 'B' 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 DSTEBZ 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 DSTEBZ is expected here. )```

Z

```          Z is DOUBLE PRECISION 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 DOUBLE PRECISION 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

NAG Ltd.

Definition at line 172 of file dstein.f.

### subroutine sstein (integer n, real, dimension( * ) d, real, dimension( * ) e, integer m, real, dimension( * ) w, integer, dimension( * ) iblock, integer, dimension( * ) isplit, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)

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 = 'B' 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

NAG Ltd.

Definition at line 172 of file sstein.f.

### subroutine zstein (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, integer m, double precision, dimension( * ) w, integer, dimension( * ) iblock, integer, dimension( * ) isplit, complex*16, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)

ZSTEIN

Purpose:

``` ZSTEIN 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 ZUNMTR or ZUPMTR for back
transformation to the eigenvectors of a complex Hermitian matrix
which was reduced to tridiagonal form.```
Parameters

N

```          N is INTEGER
The order of the matrix.  N >= 0.```

D

```          D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix T.```

E

```          E is DOUBLE PRECISION array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix
T, stored in elements 1 to N-1.```

M

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

W

```          W is DOUBLE PRECISION 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 DSTEBZ with ORDER = 'B' 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 DSTEBZ 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 DSTEBZ is expected here. )```

Z

```          Z is COMPLEX*16 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

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

WORK

`          WORK is DOUBLE PRECISION 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