nag_dspgst (f08tec) reduces a real symmetric-definite generalized eigenproblem
,
or
to the standard form
, where
is a real symmetric matrix and
has been factorized by
nag_dpptrf (f07gdc), using packed storage.
To reduce the real symmetric-definite generalized eigenproblem
,
or
to the standard form
using packed storage,
nag_dspgst (f08tec) must be preceded by a call to
nag_dpptrf (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.
comp_type |
Problem |
uplo |
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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
nag_zhpgst (f08tsc).
This example computes all the eigenvalues of
, where
using packed storage. Here
is symmetric positive definite and must first be factorized by
nag_dpptrf (f07gdc). The program calls
nag_dspgst (f08tec) to reduce the problem to the standard form
; then
nag_dsptrd (f08gec) to reduce
to tridiagonal form, and
nag_dsterf (f08jfc) to compute the eigenvalues.