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)