ZLAED0(3F) ZLAED0(3F)
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
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, * )
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.
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).
Page 1
ZLAED0(3F) ZLAED0(3F)
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).
ZLAED0(3F) ZLAED0(3F)
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
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, * )
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.
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).
Page 1
ZLAED0(3F) ZLAED0(3F)
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).
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