[Gretl-devel] implicit inversion with pos-def matrices

Hi all, this is a question about the "matrix division" operators / and \. As explained in the guide section 17.5, they can replace the pre- or post-multiplication with an inverse (and more). So A * inv(B) will be equal to A / B up to numerical error. Typically this implicit way is recommended over explicit inversion for numerical stability and also speed, I think. But what about the special case with positive-definite matrices and invpd() ? I was going to use / and \ there as well, but the following simple test showed that it's slower. <hansl> M = mnormal(50,10) MM = M'M pre = mnormal(20,10) iter = 1000 set stopwatch loop iter     m1 = pre * invpd(MM) endloop print $stopwatch loop iter     m2 = pre / MM endloop print $stopwatch print m1 m2 </hansl> The second version takes about 2-3 times longer here. (But I know that such stuff can heavily depend on the matrix sizes.) Basically the question is: do we need specialized variants of / and \ for pos-def. arguments? Or is there nothing to be gained over the explicit inversion with invpd? thanks sven