def inner(self, X, G, H):
GR, GI = frac(G)
HR, HI = frac(H)
# (AR + iAI)(BR + iBI) = ARBR - AIBI + i(ARBI + AIBR)
# we return only real part of sum(hadamard(G, H))
# old # return T.real(T.sum((GR + 1j * GI) *(HR + 1j * HI)))
return tensor.sum(GR * HR - GI * HI)
def retr(self, X, U, mode="default"):
if mode == "exp":
return self.exp(X, U)
elif mode == "qr":
YR, YI = frac(X + U)
Q, R = tensor.nlinalg.qr(YR + 1j * YI)
Y = tensor.stack([Q.real, Q.imag])
return Y
elif mode == "svd":
YR, YI = frac(X + U)
U, S, V = tensor.nlinalg.svd(YR + 1j * YI, full_matrices=False)
Y = U.dot(tensor.eye(S.size)).dot(V)
Y = tensor.stack([Y.real, Y.imag])
return Y
elif mode == "cayley":
A = complex_dot(hconj(U), X) + complex_dot(hconj(X), U)
return complex_dot(
complex_matrix_inverse(identity(self._n) + 0.5 * A),
(identity(self._n) - 0.5 * A))
elif mode == "default":
return self.retr(X, U, mode=self.retr_mode)
else:
raise ValueError(
'mode must equal to "svd", "qr", "exp" or "default", but "{}" is given'
.format(mode))
def inner(self, X, G, H):
GR, GI = frac(G)
HR, HI = frac(H)
# (AR + iAI)(BR + iBI) = ARBR - AIBI + i(ARBI + AIBR)
# we return only real part of sum(hadamard(G, H))
# old # return T.real(T.sum((GR + 1j * GI) *(HR + 1j * HI)))
return tensor.sum(GR * HR - GI * HI)
def get_output_for(self, input, **kwargs):
UR, UI = frac(self.U)
if input.ndim > 2:
# if the input has more than two dimensions, flatten it into a
# batch of feature vectors.
input = input.flatten(2)
unitary_input = T.reshape(input, (input.shape[0], 2, self.num_inputs))
IR, II = unitary_input[:, 0, :], unitary_input[:, 1, :]
output = T.stack([IR.dot(UR) - II.dot(UI), IR.dot(UR) + II.dot(UR)], axis=1)
output = output.reshape((input.shape[0], -1))
return output
def retr(self, X, U, mode="default"):
if mode == "exp":
return self.exp(X, U)
elif mode == "qr":
YR, YI = frac(X + U)
Q, R = tensor.nlinalg.qr(YR + 1j * YI)
Y = tensor.stack([Q.real, Q.imag])
return Y
elif mode == "svd":
YR, YI = frac(X + U)
U, S, V = tensor.nlinalg.svd(YR + 1j * YI, full_matrices=False)
Y = U.dot(tensor.eye(S.size)).dot(V)
Y = tensor.stack([Y.real, Y.imag])
return Y
elif mode == "default":
return self.retr(X, U, mode=self.retr_mode)
else:
raise ValueError(
'mode must equal to "svd", "qr", "exp" or "default", but "{}" is given'
.format(mode))
def retr(self, X, U, mode="default"):
if mode == "exp":
return self.exp(X, U)
elif mode == "qr":
YR, YI = frac(X + U)
Q, R = tensor.nlinalg.qr(YR + 1j * YI)
Y = tensor.stack([Q.real, Q.imag])
return Y
elif mode == "svd":
YR, YI = frac(X + U)
U, S, V = tensor.nlinalg.svd(YR + 1j * YI, full_matrices=False)
Y = U.dot(tensor.eye(S.size)).dot(V)
Y = tensor.stack([Y.real, Y.imag])
return Y
elif mode == "cayley":
A = complex_dot(hconj(U), X) + complex_dot(hconj(X), U)
return complex_dot(complex_matrix_inverse(identity(self._n) + 0.5 * A),
(identity(self._n) - 0.5 * A))
elif mode == "default":
return self.retr(X, U, mode=self.retr_mode)
else:
raise ValueError('mode must equal to "svd", "qr", "exp" or "default", but "{}" is given'.format(mode))
def norm(self, X, G):
GR, GI = frac(G)
return (GR + 1j * GI).norm()
def norm(self, X, G):
GR, GI = frac(G)
return (GR + 1j * GI).norm()