 ZLAED0(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).