[Gretl-devel] Re: fractional power of pos-def matrix
Am 26.02.2021 um 14:07 schrieb Allin Cottrell:
On Fri, 26 Feb 2021, Riccardo (Jack) Lucchetti wrote:
> On Fri, 26 Feb 2021, Sven Schreiber wrote:
>> I just stumbled over old hansl code by Jack that implements the
>> fractional power of a pd matrix (see at the end). The comment hints at
>> the plan to integrate this somewhere, but it never happened. Should it
>> go into the 'extra' addon?
>
> It's now in git, under the name "psdpwr" (because in fact it applies
> to positive SEMI-definite matrices). If you're ok with it I'll write
> the documentation as soon as I get the chance to.
One thought on this: we already have built-in support for raising a
matrix to a power (fractional or integer) as a whole, as opposed to
".^" for the element-wise case. See matrix_frac_pow() in gretl_matrix.c
So wouldn't it make sense just to inflect that code to handle the PSD
case specially, rather than adding a special function?
Actually, I just checked section 17.6 of the guide, where it says that
the matrix must be PSD if the power is fractional. (And must be
invertible --and thus PD-- if the power is negative.)
So maybe the whole issue is moot because it is already fixed and done?
Three follow-up questions on this:
- The power operation should be added to table 17.2 of the guide, not
only mentioned in the text of section 17.6.
- Since which gretl version has this been available? I'm asking because
of package requirements.
- How does the psdroot() function relate to all this?
thanks
sven