# dsteqr.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index

dsteqr.f

## SYNOPSIS

### Functions/Subroutines

subroutine dsteqr (COMPZ, N, D, E, Z, LDZ, WORK, INFO)
DSTEQR

## Function/Subroutine Documentation

### subroutine dsteqr (character COMPZ, integer N, double precision, dimension( * ) D, double precision, dimension( * ) E, double precision, dimension( ldz, * ) Z, integer LDZ, double precision, dimension( * ) WORK, integer INFO)

DSTEQR

Purpose:

``` DSTEQR computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the implicit QL or QR method.
The eigenvectors of a full or band symmetric matrix can also be found
if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to
tridiagonal form.
```

Parameters:

COMPZ

```          COMPZ is CHARACTER*1
= 'N':  Compute eigenvalues only.
= 'V':  Compute eigenvalues and eigenvectors of the original
symmetric matrix.  On entry, Z must contain the
orthogonal matrix used to reduce the original matrix
to tridiagonal form.
= 'I':  Compute eigenvalues and eigenvectors of the
tridiagonal matrix.  Z is initialized to the identity
matrix.
```

N

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

D

```          D is DOUBLE PRECISION array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix.
On exit, if INFO = 0, the eigenvalues in ascending order.
```

E

```          E is DOUBLE PRECISION array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix.
On exit, E has been destroyed.
```

Z

```          Z is DOUBLE PRECISION array, dimension (LDZ, N)
On entry, if  COMPZ = 'V', then Z contains the orthogonal
matrix used in the reduction to tridiagonal form.
On exit, if INFO = 0, then if  COMPZ = 'V', Z contains the
orthonormal eigenvectors of the original symmetric matrix,
and if COMPZ = 'I', Z contains the orthonormal eigenvectors
of the symmetric tridiagonal matrix.
If COMPZ = 'N', then Z is not referenced.
```

LDZ

```          LDZ is INTEGER
The leading dimension of the array Z.  LDZ >= 1, and if
eigenvectors are desired, then  LDZ >= max(1,N).
```

WORK

```          WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2))
If COMPZ = 'N', then WORK is not referenced.
```

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  the algorithm has failed to find all the eigenvalues in
a total of 30*N iterations; if INFO = i, then i
elements of E have not converged to zero; on exit, D
and E contain the elements of a symmetric tridiagonal
matrix which is orthogonally similar to the original
matrix.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley