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):
## 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 transform(self, A):
J = dot(transp(A), self._J)
Lambda = self._Lambda.alat(transp(A))
return Potential(J, Lambda, self._Z)
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 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 alat(self, A):
return FullMatrix(dot(A, dot(self._S, transp(A))))
def transform(self, A):
J = dot(transp(A), self._J)
Lambda = self._Lambda.alat(transp(A))
return Potential(J, Lambda, self._Z)
