Provided by: liblapack-doc_3.3.1-1_all 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)               April 2011                            ZLAED0(3lapack)