Test to verify that kernel matrices for FCHL19 are positive-definite.

test_definite.py

#!/usr/bin/env python3
#
# Data must be downloaded from from http://quantum-machine.org/gdml/#datasets
#

import sys

import numpy as np

import qml
from qml.math import cho_solve
from qml.representations import generate_fchl_acsf
from qml.kernels import get_local_symmetric_kernel
from qml.kernels import get_symmetric_gdml_kernel
from qml.kernels import get_symmetric_gp_kernel

from tqdm import tqdm


def get_reps_fchl(indexes, coords, charges):
    
    max_atoms = len(charges)
    
    elements = sorted(list(set(charges)))

    print("Max atoms:", max_atoms)
    print("Elements:", elements)
    
    X   = []
    dX  = []
    Q   = []

    for i, idx in tqdm(enumerate(indexes), desc="FCHL19 representations"):

        # print(i, idx, coords[idx])
        (x, dx) = generate_fchl_acsf(charges, coords[idx], elements=elements, gradients=True)

        dX.append(dx)
        X.append(x)
        Q.append(charges)

    X = np.array(X)
    dX = np.array(dX)

    return X, dX, Q


def test_definite():

    
    print(sys.argv)

    name = sys.argv[1]
    n = int(sys.argv[2])

    Q_data = np.load("%s_dft_charges.npy" % name)
    R_data = np.load("%s_dft_coords.npy" % name)

    indexes = list(range(n))
    X,  dX,  Q  = get_reps_fchl(indexes, R_data, Q_data)

    sigma = 2.0
    llambda = 1e-10
    
    print("KRR Kernel")
    K = get_local_symmetric_kernel(X, Q, sigma)
    K[np.diag_indices_from(K)] += llambda
    eigen_vals, eigen_vectors = np.linalg.eigh(K)
    print(eigen_vals)
    
    print("GDML Kernel")
    K = get_symmetric_gdml_kernel(X, dX, Q, sigma)
    K[np.diag_indices_from(K)] += llambda
    eigen_vals, eigen_vectors = np.linalg.eigh(K)
    print(eigen_vals)
    
    print("GPR Kernel")
    K = get_symmetric_gp_kernel(X, dX, Q, sigma)
    K[np.diag_indices_from(K)] += llambda
    eigen_vals, eigen_vectors = np.linalg.eigh(K)
    print(eigen_vals)


if __name__ == "__main__":
    
    test_definite()