Homepage > Man Pages > Category > Subroutines
Homepage > Man Pages > Name > L

# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: the divide and conquer method, ZLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal

```NAME
LAPACK-3   -  the  divide  and  conquer  method,  ZLAED0  computes  all
eigenvalues of a symmetric tridiagonal matrix  which  is  one  diagonal
block  of  those  from  reducing  a  dense or band Hermitian matrix and
corresponding eigenvectors of the dense or band matrix

SYNOPSIS
SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,  RWORK,  IWORK,
INFO )

INTEGER        INFO, LDQ, LDQS, N, QSIZ

INTEGER        IWORK( * )

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

COMPLEX*16     Q( LDQ, * ), QSTORE( LDQS, * )

PURPOSE
Using the divide and conquer method, ZLAED0 computes all eigenvalues of
a symmetric tridiagonal matrix which is one  diagonal  block  of  those
from  reducing  a  dense  or  band  Hermitian  matrix and corresponding
eigenvectors of the dense or band matrix.

ARGUMENTS
QSIZ   (input) INTEGER
The dimension of the unitary matrix used to reduce
the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

N      (input) INTEGER
The dimension of the symmetric tridiagonal matrix.  N >= 0.

D      (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix.
On exit, the eigenvalues in ascending order.

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

Q      (input/output) COMPLEX*16 array, dimension (LDQ,N)
On entry, Q must contain an QSIZ x N matrix whose columns
unitarily orthonormal. It is a part of the unitary matrix
that reduces the full dense Hermitian matrix to a
(reducible) symmetric tridiagonal matrix.

LDQ    (input) INTEGER
The leading dimension of the array Q.  LDQ >= max(1,N).

IWORK  (workspace) INTEGER array,
the dimension of IWORK must be at least
6 + 6*N + 5*N*lg N
( lg( N ) = smallest integer k
such that 2^k >= N )

RWORK  (workspace) DOUBLE PRECISION array,
dimension (1 + 3*N + 2*N*lg N + 3*N**2)
( lg( N ) = smallest integer k
such that 2^k >= N )
QSTORE (workspace) COMPLEX*16 array, dimension (LDQS, N)
Used to store parts of
the eigenvector matrix when the updating matrix multiplies
take place.

LDQS   (input) INTEGER
The leading dimension of the array QSTORE.
LDQS >= max(1,N).

INFO   (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  The algorithm failed to compute an eigenvalue while
working on the submatrix lying in rows and columns
INFO/(N+1) through mod(INFO,N+1).

LAPACK routine (version 3.2)     March 2011                       LAPACK-3(3)
```