# zsteqr.f man page

zsteqr.f —

## Synopsis

### Functions/Subroutines

subroutinezsteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)ZSTEQR

## Function/Subroutine Documentation

### subroutine zsteqr (characterCOMPZ, integerN, double precision, dimension( * )D, double precision, dimension( * )E, complex*16, dimension( ldz, * )Z, integerLDZ, double precision, dimension( * )WORK, integerINFO)

**ZSTEQR**

**Purpose:**

```
ZSTEQR 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 complex Hermitian matrix can also
be found if ZHETRD or ZHPTRD or ZHBTRD 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
Hermitian matrix. On entry, Z must contain the
unitary 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 COMPLEX*16 array, dimension (LDZ, N)
On entry, if COMPZ = 'V', then Z contains the unitary
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 Hermitian 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 unitarily similar to the original
matrix.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 133 of file zsteqr.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zsteqr(3) is an alias of zsteqr.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK