zlaed0(3)

NAME

ZLAED0 - 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 diago

nal 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 tridiag

onal 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 ille

gal value.
> 0: The algorithm failed to compute an eigenvalue

while working on the submatrix lying in rows and columns IN

FO/(N+1) through mod(INFO,N+1).

LAPACK version 3.0 15 June 2000

ZLAED0(3)