g02anf finds a correlation matrix,
, starting from an approximate correlation matrix,
, with positive definite leading principal submatrix of order
. The returned correlation matrix,
, has the following structure:
where
is the
leading principal submatrix of the input matrix
and positive definite, and
.
Higham N J, Strabić N and Šego V (2014) Restoring definiteness via shrinking, with an application to correlation matrices with a fixed block MIMS EPrint 2014.54 Manchester Institute for Mathematical Sciences, The University of Manchester, UK
If on entry
or
, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
The algorithm uses a bisection method. It is terminated when the computed
is within
errtol of the minimum value. The positive definiteness of
is such that it can be successfully factorized with a call to
f07fdf.
The number of iterations taken for the bisection will be:
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 routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
This example finds the smallest uniform perturbation
to
, such that the output is a correlation matrix and the
leading principal submatrix of the input is preserved,