def compute_cavity(self, n, alpha=1.0):
"""Summary
Args:
n (TYPE): Description
alpha (float, optional): Description
Returns:
TYPE: Description
"""
# compute the leave one out moments
t1n = self.t1[n, :, :]
t2n = self.t2[n, :, :, :]
Suinvhat = self.Suinv - alpha * t2n
SuinvMuhat = self.SuinvMu - alpha * t1n
Suhat = np.linalg.inv(Suinvhat)
muhat = np.einsum('ndab,ndb->nda', Suhat, SuinvMuhat)
return muhat, Suhat, SuinvMuhat, Suinvhat
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