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 split_node_qr(
self,
node: network_components.BaseNode,
left_edges: List[network_components.Edge],
right_edges: List[network_components.Edge],
left_name: Optional[Text] = None,
right_name: Optional[Text] = None,
edge_name: Optional[Text] = None,
) -> Tuple[network_components.BaseNode, network_components.BaseNode]:
"""Split a `Node` using QR decomposition
Let M be the matrix created by flattening left_edges and right_edges into
2 axes. Let :math:`QR = M` be the QR Decomposition of
:math:`M`. This will split the network into 2 nodes. The left node's
tensor will be :math:`Q` (an orthonormal matrix) and the right node's tensor will be
:math:`R` (an upper triangular matrix)
Args:
node: The node you want to split.
left_edges: The edges you want connected to the new left node.
right_edges: The edges you want connected to the new right node.
left_name: The name of the new left node. If `None`, a name will be generated
automatically.
right_name: The name of the new right node. If `None`, a name will be generated
automatically.
edge_name: The name of the new `Edge` connecting the new left and right node.
If `None`, a name will be generated automatically.
Returns:
A tuple containing:
left_node:
A new node created that connects to all of the `left_edges`.
Its underlying tensor is :math:`Q`
right_node:
A new node created that connects to all of the `right_edges`.
Its underlying tensor is :math:`R`
"""
q, r = network_operations.split_node_qr(node, left_edges, right_edges,
left_name, right_name,
edge_name)
left_node = self.add_node(q)
right_node = self.add_node(r)
self.nodes_set.remove(node)
node.disable()
return left_node, right_node