Output to prove that QML kernels are positive definite.

output.txt

andersx@beauty:~/projects/definite$ ./test_fchl_acsf_forces.py ethanol 4
['./test_fchl_acsf_forces.py', 'ethanol', '4']
Max atoms: 9
Elements: [1, 6, 8]
FCHL19 representations: 4it [00:00, 513.03it/s]
KRR Kernel
[3.73448002e-02 5.42538018e-02 1.44732447e-01 1.46094006e+02]
GDML Kernel
[9.99942283e-11 9.99946682e-11 9.99962908e-11 9.99965466e-11
 9.99970303e-11 9.99970583e-11 9.99977671e-11 9.99980227e-11
 9.99983880e-11 9.99986889e-11 9.99994103e-11 1.00000056e-10
 1.00000080e-10 1.00000608e-10 1.00001045e-10 1.00001582e-10
 1.00001719e-10 1.00001815e-10 1.00002715e-10 1.00003051e-10
 1.00003246e-10 1.00004091e-10 1.00004301e-10 1.00005353e-10
 1.35920528e-04 1.74003206e-04 4.62698796e-04 5.33503873e-04
 5.45889621e-04 6.45169714e-04 7.80114797e-04 8.21980440e-04
 9.15007168e-04 1.19496178e-03 1.23820233e-03 1.50488450e-03
 1.57060768e-03 1.69292848e-03 1.85180917e-03 2.11657866e-03
 2.26474413e-03 2.45209850e-03 2.89949315e-03 3.10884230e-03
 3.50318082e-03 3.70716975e-03 3.95854576e-03 4.39657800e-03
 4.60987676e-03 5.57837962e-03 6.41884007e-03 7.03429952e-03
 7.33513014e-03 8.36429882e-03 8.97147852e-03 9.50057604e-03
 1.02743222e-02 1.10228039e-02 1.13760536e-02 1.25476214e-02
 1.41771090e-02 1.59599181e-02 1.75101233e-02 1.87007323e-02
 2.00487011e-02 2.05211013e-02 2.35874315e-02 2.52458306e-02
 2.79129260e-02 3.36234390e-02 3.64956341e-02 3.74660833e-02
 4.45383672e-02 4.63079139e-02 5.29063892e-02 5.92219744e-02
 6.65249773e-02 6.81891337e-02 7.63337457e-02 8.87191311e-02
 9.52664758e-02 1.06689372e-01 1.17654584e-01 1.38187786e-01
 1.40342177e-01 1.61744412e-01 1.71401922e-01 1.91002019e-01
 2.19261165e-01 2.43957772e-01 3.00800604e-01 3.42757558e-01
 3.64288601e-01 4.66737137e-01 5.42079879e-01 7.89442693e-01
 9.80938097e-01 1.15413322e+00 1.27701660e+00 2.00553124e+00
 3.89720175e+00 5.17223814e+00 8.81558495e+00 1.11819039e+01
 1.47764659e+01 2.83180670e+01 8.80814676e+01 1.46440379e+02]
GPR Kernel
[9.99950810e-11 9.99958511e-11 9.99963712e-11 9.99971499e-11
 9.99971869e-11 9.99977356e-11 9.99982085e-11 9.99982941e-11
 9.99983328e-11 9.99991487e-11 9.99991593e-11 9.99998568e-11
 1.00000071e-10 1.00000215e-10 1.00000843e-10 1.00001092e-10
 1.00001352e-10 1.00001400e-10 1.00001691e-10 1.00002516e-10
 1.00003430e-10 1.00003956e-10 1.00004765e-10 1.00005690e-10
 4.21272342e-05 5.01488182e-05 1.01276518e-04 1.65656295e-04
 1.90197402e-04 4.98941893e-04 5.44937082e-04 6.03768427e-04
 6.28751889e-04 7.82354966e-04 8.50736661e-04 9.53449486e-04
 1.19628287e-03 1.24718021e-03 1.54641495e-03 1.57112499e-03
 1.71694244e-03 1.84902403e-03 2.10985647e-03 2.27037818e-03
 2.52200844e-03 2.93081740e-03 3.16162321e-03 3.54619273e-03
 3.73225113e-03 3.95229142e-03 4.47230605e-03 4.59842075e-03
 5.63246940e-03 6.42203175e-03 7.01599155e-03 7.35554997e-03
 8.37016092e-03 8.85339199e-03 9.66109559e-03 1.03026054e-02
 1.09465970e-02 1.14869969e-02 1.22917525e-02 1.42847642e-02
 1.62824114e-02 1.75503040e-02 1.85351982e-02 2.00970736e-02
 2.06322352e-02 2.35779049e-02 2.52825640e-02 2.77520749e-02
 3.29604648e-02 3.67826337e-02 3.73596592e-02 4.46362608e-02
 4.65187791e-02 5.30231426e-02 5.96303444e-02 6.73881191e-02
 6.82514466e-02 7.61899106e-02 8.45964989e-02 9.54192108e-02
 1.06654363e-01 1.17539949e-01 1.36925644e-01 1.41460215e-01
 1.63740152e-01 1.71488105e-01 1.90243971e-01 2.20595481e-01
 2.41803525e-01 2.99147340e-01 3.30131595e-01 3.64895727e-01
 4.52969080e-01 5.42692654e-01 7.92043457e-01 9.81372538e-01
 1.12419313e+00 1.29427106e+00 1.98291548e+00 3.86243364e+00
 4.88620392e+00 8.69944419e+00 1.11979170e+01 1.46254412e+01
 2.83006042e+01 8.25194198e+01 1.37857144e+02 1.61125762e+02]