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# zsteqr

```
NAME
ZSTEQR - compute all eigenvalues and, optionally, eigenvec-
tors of a symmetric tridiagonal matrix using the implicit QL
or QR method

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

CHARACTER      COMPZ

INTEGER        INFO, LDZ, N

DOUBLE         PRECISION D( * ), E( * ), WORK( * )

COMPLEX*16     Z( LDZ, * )

PURPOSE
ZSTEQR computes all eigenvalues and, optionally, eigenvec-
tors 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 ZSYTRD or ZSPTRD or
ZSBTRD has been used to reduce this matrix to tridiagonal
form.

ARGUMENTS
COMPZ   (input) 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 eigen-
values and eigenvectors of the tridiagonal matrix.
Z is initialized to the identity matrix.

N       (input) INTEGER
The order of the matrix.  N >= 0.

D       (input/output) 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       (input/output) DOUBLE PRECISION array, dimension (N-
1)
On entry, the (n-1) subdiagonal elements of the tri-
diagonal matrix.  On exit, E has been destroyed.

Z       (input/output) COMPLEX*16 array, dimension (LDZ, N)
On entry, if  COMPZ = 'V', then Z contains the uni-
tary matrix used in the reduction to tridiagonal
form.  On exit, if  COMPZ = 'V', Z contains the

orthonormal eigenvectors of the original Hermitian
matrix, and if COMPZ = 'I', Z contains the orthonor-
mal eigenvectors of the symmetric tridiagonal
matrix.  If an error exit is made, Z contains the
eigenvectors associated with the stored eigenvalues.
If COMPZ = 'N', then Z is not referenced.

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

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

INFO    (output) 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.
```