Weighted `pca` returns erroneous Hotelling's T-squared statistics

[pr0m1th3as]

When using weighted observations, pca returns different Hotelling'sT-squared statistics compared to MATLAB.
In Octave we get

x=[1,2,3;2,1,3]';
>> [COEFF, SCORE, latent, tsquare] = pca (x, "Economy", false, "weights", [1 2 1], "variableweights", "variance")
COEFF =

   0.6325  -0.6325
   0.7416   0.7416

SCORE =

  -0.622019   0.959119
  -0.505650  -0.505650
   1.633319   0.052180

latent =

   1.7830
   0.7170

tsquare =

   1.3333
   0.6667
   1.3333

In MATLAB

tsquare =

   1.5000
   0.5000
   1.5000