f08tec reduces a real symmetric-definite generalized eigenproblem
,
or
to the standard form
, where
is a real symmetric matrix and
has been factorized by
f07gdc, using packed storage.
To reduce the real symmetric-definite generalized eigenproblem
,
or
to the standard form
using packed storage,
f08tec must be preceded by a call to
f07gdc which computes the Cholesky factorization of
;
must be positive definite.
The different problem types are specified by the argument
comp_type, as indicated in the table below. The table shows how
is computed by the function, and also how the eigenvectors
of the original problem can be recovered from the eigenvectors of the standard form.
Background information to multithreading can be found in the
Multithreading documentation.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The complex analogue of this function is
f08tsc.
This example computes all the eigenvalues of
, where
using packed storage. Here
is symmetric positive definite and must first be factorized by
f07gdc. The program calls
f08tec to reduce the problem to the standard form
; then
f08gec to reduce
to tridiagonal form, and
f08jfc to compute the eigenvalues.