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 Her
mitian 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 Hermi
tian matrix to a (reducible) symmetric tridiagonal
matrix.
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 INFO/(N+1) through mod(INFO,N+1).
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