---
name: "zlaed0"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/zlaed0/3lapack"
---

# zlaed0(3lapack)

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

## 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).