def linear_discriminant_func(self, x, k):
"""
linear discriminant function.
Define by (4.10)
:return: delta_k(x)
"""
mu_k = self.Mu[k]
pi_k = self.Pi[k]
sigma_inv = self.math.pinv(self.Sigma_hat)
result = mu_k @ sigma_inv @ x.T - (mu_k @ sigma_inv @ mu_k.T)/2 + log(pi_k)
return result
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