F08FCF (DSYEVD) computes all the eigenvalues and, optionally, all the eigenvectors of a real symmetric matrix.
If the eigenvectors are requested, then it uses a divide-and-conquer algorithm to compute eigenvalues and eigenvectors. However, if only eigenvalues are required, then it uses the Pal–Walker–Kahan variant of the or algorithm.
SUBROUTINE F08FCF ( |
JOB, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK, INFO) |
INTEGER |
N, LDA, LWORK, IWORK(max(1,LIWORK)), LIWORK, INFO |
REAL (KIND=nag_wp) |
A(LDA,*), W(*), WORK(max(1,LWORK)) |
CHARACTER(1) |
JOB, UPLO |
|
F08FCF (DSYEVD) computes all the eigenvalues and, optionally, all the eigenvectors of a real symmetric matrix
.
In other words, it can compute the spectral factorization of
as
where
is a diagonal matrix whose diagonal elements are the eigenvalues
, and
is the orthogonal matrix whose columns are the eigenvectors
. Thus
Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J J, Du Croz J J, Greenbaum A, Hammarling S, McKenney A and Sorensen D (1999)
LAPACK Users' Guide (3rd Edition) SIAM, Philadelphia
http://www.netlib.org/lapack/lug
The computed eigenvalues and eigenvectors are exact for a nearby matrix
, where
and
is the
machine precision. See Section 4.7 of
Anderson et al. (1999) for further details.
The complex analogue of this routine is
F08FQF (ZHEEVD).
This example computes all the eigenvalues and eigenvectors of the symmetric matrix
, where