def position(self,
site: int,
normalize: Optional[bool] = True) -> np.number:
"""
Shift FiniteMPS.center_position to `site`.
Args:
site: The site to which FiniteMPS.center_position should be shifted
normalize: If `True`, normalize matrices when shifting.
Returns:
Tensor: The norm of the tensor at FiniteMPS.center_position
"""
#`site` has to be between 0 and len(mps) - 1
if site >= len(self.nodes) or site < 0:
raise ValueError('site = {} not between values'
' 0 < site < N = {}'.format(site, len(self)))
#nothing to do
if site == self.center_position:
return self.backend.norm(self.nodes[self.center_position].tensor)
#shift center_position to the right using QR decomposition
if site > self.center_position:
n = self.center_position
for n in range(self.center_position, site):
Q, R = split_node_qr(
self.nodes[n],
left_edges=[self.nodes[n][0], self.nodes[n][1]],
right_edges=[self.nodes[n][2]],
left_name=self.nodes[n].name)
self.nodes[n] = Q #Q is a left-isometric tensor of rank 3
self.nodes[n + 1] = contract(R[1], name=self.nodes[n + 1].name)
Z = norm(self.nodes[n + 1])
# for an mps with > O(10) sites one needs to normalize to avoid
# over or underflow errors; this takes care of the normalization
if normalize:
self.nodes[n + 1].tensor /= Z
self.center_position = site
#shift center_position to the left using RQ decomposition
elif site < self.center_position:
for n in reversed(range(site + 1, self.center_position + 1)):
R, Q = split_node_rq(
self.nodes[n],
left_edges=[self.nodes[n][0]],
right_edges=[self.nodes[n][1], self.nodes[n][2]],
right_name=self.nodes[n].name)
# for an mps with > O(10) sites one needs to normalize to avoid
# over or underflow errors; this takes care of the normalization
self.nodes[n] = Q #Q is a right-isometric tensor of rank 3
self.nodes[n - 1] = contract(R[0], name=self.nodes[n - 1].name)
Z = norm(self.nodes[n - 1])
if normalize:
self.nodes[n - 1].tensor /= Z
self.center_position = site
#return the norm of the last R tensor (useful for checks)
return Z
def contract(self,
edge: network_components.Edge,
name: Optional[Text] = None) -> network_components.BaseNode:
"""Contract an edge connecting two nodes in the TensorNetwork.
Args:
edge: The edge contract next.
name: Name of the new node created.
Returns:
The new node created after the contraction.
Raises:
ValueError: When edge is a dangling edge or if it already has been
contracted.
"""
#contract disables contracted edges; if we have to access them, we need
#to do it beforehand.
trace_edge = edge.node1 is edge.node2
node1 = edge.node1
node2 = edge.node2
new_node = self.add_node(
network_components.contract(edge, name, axis_names=None))
# disable nodes
if trace_edge:
self.nodes_set.remove(node1)
node1.disable()
else:
self.nodes_set.remove(node1)
self.nodes_set.remove(node2)
node1.disable()
node2.disable()
return new_node