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 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).