def alat(self, A): if A.shape[-1] == 1: assert self.dim == 1 A_ = A[..., :, 0] Q = A_ / np.sqrt((A_**2).sum(-1))[..., nax] d = (A_**2).sum(-1) * self._s return FixedEigMatrix(d[..., nax], Q[..., nax], 0.) return FullMatrix(dot(A, transp(A)) * self._s[..., nax, nax])
def alat(self, A): return FullMatrix(dot(A, dot(self._S, transp(A))))
def sqrt_dot(self, x): result = dot(self._Q, np.sqrt(self._d) * dot(transp(self._Q), x)) x_perp = x - dot(self._Q, dot(transp(self._Q), x)) result += x_perp * np.sqrt(self._s_perp[..., nax]) return result
def qform(self, x): result = (self._d * dot(transp(self._Q), x)**2).sum(-1) x_perp = x - dot(self._Q, dot(transp(self._Q), x)) result += (x_perp**2).sum(-1) * self._s_perp return result
def dot(self, x): result = dot(self._Q, self._d * dot(transp(self._Q), x)) x_perp = x - dot(self._Q, dot(transp(self._Q), x)) result += x_perp * self._s_perp[..., nax] return result
def full(self): S = dot(self._Q, self._d[..., nax] * transp(self._Q)) S += (np.eye(self.dim) - dot(self._Q, transp(self._Q))) * self._s_perp[..., nax, nax] return FullMatrix(S)
def random(shape, dim, rank=None): if rank is None: rank = dim A = np.random.normal(size=shape + (dim, rank)) S = dot(A, transp(A)) return FullMatrix(S)
def transform(self, A): J = dot(transp(A), self._J) Lambda = self._Lambda.alat(transp(A)) return Potential(J, Lambda, self._Z)