Operations#

Edge Operations#

connect#

tensorkrowch.connect(edge1, edge2)[source]#

Connects two dangling edges. It is necessary that both edges have the same size so that contractions along that edge can be computed.

Note that this connectes edges from leaf (or data, virtual) nodes, but never from resultant nodes. If one tries to connect one of the inherited edges of a resultant node, the new connected edge will be attached to the original leaf nodes from which the resultant node inherited its edges. Hence, the resultant node will not “see” the connection until the TensorNetwork is reset().

If the nodes that are being connected come from different networks, the node2 (and its connected component) will be movec to node1’s network. See also move_to_network().

This operation is the same as Edge.connect().

Parameters

  • edge1 (Edge) – The first edge that will be connected. Its node will become the node1 of the resultant edge.

  • edge2 (Edge) – The second edge that will be connected. Its node will become the node2 of the resultant edge.

Return type

Edge

Examples

>>> nodeA = tk.Node(shape=(2, 3),
...                 name='nodeA',
...                 axes_names=('left', 'right'))
>>> nodeB = tk.Node(shape=(3, 4),
...                 name='nodeB',
...                 axes_names=('left', 'right'))
>>> new_edge = tk.connect(nodeA['right'], nodeB['left'])
>>> print(new_edge.name)
nodeA[right] <-> nodeB[left]

connect_stack#

tensorkrowch.connect_stack(edge1, edge2)[source]#

Same as connect() but it is first verified that all stacked edges corresponding to both StackEdges are the same. That is, this is a redundant operation to re-connect a list of edges that should be already connected. However, this is mandatory, since when stacking two sequences of nodes independently it cannot be inferred that the resultant StackNodes had to be connected.

This operation is the same as StackEdge.connect().

Parameters

  • edge1 (StackEdge) – The first edge that will be connected. Its node will become the node1 of the resultant edge.

  • edge2 (StackEdge) – The second edge that will be connected. Its node will become the node2 of the resultant edge.

disconnect#

tensorkrowch.disconnect(edge)[source]#

Disconnects connected edge, that is, the connected edge is split into two dangling edges, one for each node.

This operation is the same as Edge.disconnect().

Parameters

edge (Edge or StackEdge) – Edge that is going to be disconnected (split in two).

Return type

tuple[Edge, Edge] or tuple[StackEdge, StackEdge]

svd#

tensorkrowch.svd(edge, side='left', rank=None, cum_percentage=None, cutoff=None)[source]#

Contracts an edge via contract() and splits it via split() using mode = "svd". See split() for a more complete explanation.

This only works if the nodes connected through the edge are leaf nodes. Otherwise, this will perform the contraction between the leaf nodes that were connected through this edge.

This operation is the same as svd().

Parameters

  • edge (Edge) – Edge whose nodes are to be contracted and split.

  • side (str, optional) – Indicates the side to which the diagonal matrix \(S\) should be contracted. If “left”, the first resultant node’s tensor will be \(US\), and the other node’s tensor will be \(V^{\dagger}\). If “right”, their tensors will be \(U\) and \(SV^{\dagger}\), respectively.

  • rank (int, optional) – Number of singular values to keep.

  • cum_percentage (float, optional) –

    Proportion that should be satisfied between the sum of all singular values kept and the total sum of all singular values.

    \[\frac{\sum_{i \in \{kept\}}{s_i}}{\sum_{i \in \{all\}}{s_i}} \ge cum\_percentage\]

  • cutoff (float, optional) – Quantity that lower bounds singular values in order to be kept.

Return type

tuple[Node, Node]

Examples

>>> nodeA = tk.randn(shape=(10, 15, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(15, 20, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeB')
...
>>> new_edge = nodeA['right'] ^ nodeB['left']
>>> new_nodeA, new_nodeB = tk.svd(new_edge, rank=7)
...
>>> new_nodeA.shape
torch.Size([10, 7, 100])

>>> new_nodeB.shape
torch.Size([7, 20, 100])

>>> print(new_nodeA.axes_names)
['left', 'right', 'batch']

>>> print(new_nodeB.axes_names)
['left', 'right', 'batch']

Original nodes still exist in the network

>>> assert nodeA.network == new_nodeA.network
>>> assert nodeB.network == new_nodeB.network

svd_#

tensorkrowch.svd_(edge, side='left', rank=None, cum_percentage=None, cutoff=None)[source]#

In-place version of svd().

Contracts an edge in-place via contract_() and splits it in-place via split_() using mode = "svd". See split() for a more complete explanation.

Following the PyTorch convention, names of functions ended with an underscore indicate in-place operations.

Nodes resultant from this operation use the same names as the original nodes connected by edge.

This operation is the same as svd_().

Parameters

  • edge (Edge) – Edge whose nodes are to be contracted and split.

  • side (str, optional) – Indicates the side to which the diagonal matrix \(S\) should be contracted. If “left”, the first resultant node’s tensor will be \(US\), and the other node’s tensor will be \(V^{\dagger}\). If “right”, their tensors will be \(U\) and \(SV^{\dagger}\), respectively.

  • rank (int, optional) – Number of singular values to keep.

  • cum_percentage (float, optional) –

    Proportion that should be satisfied between the sum of all singular values kept and the total sum of all singular values.

    \[\frac{\sum_{i \in \{kept\}}{s_i}}{\sum_{i \in \{all\}}{s_i}} \ge cum\_percentage\]

  • cutoff (float, optional) – Quantity that lower bounds singular values in order to be kept.

Return type

tuple[Node, Node]

Examples

>>> nodeA = tk.randn(shape=(10, 15, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(15, 20, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeB')
...
>>> new_edge = nodeA['right'] ^ nodeB['left']
>>> nodeA, nodeB = tk.svd_(new_edge, rank=7)
...
>>> nodeA.shape
torch.Size([10, 7, 100])

>>> nodeB.shape
torch.Size([7, 20, 100])

>>> print(nodeA.axes_names)
['left', 'right', 'batch']

>>> print(nodeB.axes_names)
['left', 'right', 'batch']

svdr#

tensorkrowch.svdr(edge, side='left', rank=None, cum_percentage=None, cutoff=None)[source]#

Contracts an edge via contract() and splits it via split() using mode = "svdr". See split() for a more complete explanation.

This only works if the nodes connected through the edge are leaf nodes. Otherwise, this will perform the contraction between the leaf nodes that were connected through this edge.

This operation is the same as svdr().

Parameters

  • edge (Edge) – Edge whose nodes are to be contracted and split.

  • side (str, optional) – Indicates the side to which the diagonal matrix \(S\) should be contracted. If “left”, the first resultant node’s tensor will be \(US\), and the other node’s tensor will be \(V^{\dagger}\). If “right”, their tensors will be \(U\) and \(SV^{\dagger}\), respectively.

  • rank (int, optional) – Number of singular values to keep.

  • cum_percentage (float, optional) –

    Proportion that should be satisfied between the sum of all singular values kept and the total sum of all singular values.

    \[\frac{\sum_{i \in \{kept\}}{s_i}}{\sum_{i \in \{all\}}{s_i}} \ge cum\_percentage\]

  • cutoff (float, optional) – Quantity that lower bounds singular values in order to be kept.

Return type

tuple[Node, Node]

Examples

>>> nodeA = tk.randn(shape=(10, 15, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(15, 20, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeB')
...
>>> new_edge = nodeA['right'] ^ nodeB['left']
>>> new_nodeA, new_nodeB = tk.svdr(new_edge, rank=7)
...
>>> new_nodeA.shape
torch.Size([10, 7, 100])

>>> new_nodeB.shape
torch.Size([7, 20, 100])

>>> print(new_nodeA.axes_names)
['left', 'right', 'batch']

>>> print(new_nodeB.axes_names)
['left', 'right', 'batch']

Original nodes still exist in the network

>>> assert nodeA.network == new_nodeA.network
>>> assert nodeB.network == new_nodeB.network

svdr_#

tensorkrowch.svdr_(edge, side='left', rank=None, cum_percentage=None, cutoff=None)[source]#

In-place version of svdr().

Contracts an edge in-place via contract_() and splits it in-place via split_() using mode = "svdr". See split() for a more complete explanation.

Following the PyTorch convention, names of functions ended with an underscore indicate in-place operations.

Nodes resultant from this operation use the same names as the original nodes connected by edge.

This operation is the same as svdr_().

Parameters

  • edge (Edge) – Edge whose nodes are to be contracted and split.

  • side (str, optional) – Indicates the side to which the diagonal matrix \(S\) should be contracted. If “left”, the first resultant node’s tensor will be \(US\), and the other node’s tensor will be \(V^{\dagger}\). If “right”, their tensors will be \(U\) and \(SV^{\dagger}\), respectively.

  • rank (int, optional) – Number of singular values to keep.

  • cum_percentage (float, optional) –

    Proportion that should be satisfied between the sum of all singular values kept and the total sum of all singular values.

    \[\frac{\sum_{i \in \{kept\}}{s_i}}{\sum_{i \in \{all\}}{s_i}} \ge cum\_percentage\]

  • cutoff (float, optional) – Quantity that lower bounds singular values in order to be kept.

Return type

tuple[Node, Node]

Examples

>>> nodeA = tk.randn(shape=(10, 15, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(15, 20, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeB')
...
>>> new_edge = nodeA['right'] ^ nodeB['left']
>>> nodeA, nodeB = tk.svdr_(new_edge, rank=7)
...
>>> nodeA.shape
torch.Size([10, 7, 100])

>>> nodeB.shape
torch.Size([7, 20, 100])

>>> print(nodeA.axes_names)
['left', 'right', 'batch']

>>> print(nodeB.axes_names)
['left', 'right', 'batch']

qr#

tensorkrowch.qr(edge)[source]#

Contracts an edge via contract() and splits it via split() using mode = "qr". See split() for a more complete explanation.

This only works if the nodes connected through the edge are leaf nodes. Otherwise, this will perform the contraction between the leaf nodes that were connected through this edge.

This operation is the same as qr().

Parameters

edge (Edge) – Edge whose nodes are to be contracted and split.

Return type

tuple[Node, Node]

Examples

>>> nodeA = tk.randn(shape=(10, 15, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(15, 20, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeB')
...
>>> new_edge = nodeA['right'] ^ nodeB['left']
>>> new_nodeA, new_nodeB = tk.qr(new_edge)
...
>>> new_nodeA.shape
torch.Size([10, 10, 100])

>>> new_nodeB.shape
torch.Size([10, 20, 100])

>>> print(new_nodeA.axes_names)
['left', 'right', 'batch']

>>> print(new_nodeB.axes_names)
['left', 'right', 'batch']

Original nodes still exist in the network

>>> assert nodeA.network == new_nodeA.network
>>> assert nodeB.network == new_nodeB.network

qr_#

tensorkrowch.qr_(edge)[source]#

In-place version of qr().

Contracts an edge in-place via contract_() and splits it in-place via split_() using mode = "qr". See split() for a more complete explanation.

Following the PyTorch convention, names of functions ended with an underscore indicate in-place operations.

Nodes resultant from this operation use the same names as the original nodes connected by edge.

This operation is the same as qr_().

Parameters

edge (Edge) – Edge whose nodes are to be contracted and split.

Return type

tuple[Node, Node]

Examples

>>> nodeA = tk.randn(shape=(10, 15, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(15, 20, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeB')
...
>>> new_edge = nodeA['right'] ^ nodeB['left']
>>> nodeA, nodeB = tk.qr_(new_edge)
...
>>> nodeA.shape
torch.Size([10, 10, 100])

>>> nodeB.shape
torch.Size([10, 20, 100])

>>> print(nodeA.axes_names)
['left', 'right', 'batch']

>>> print(nodeB.axes_names)
['left', 'right', 'batch']

rq#

tensorkrowch.rq(edge)[source]#

Contracts an edge via contract() and splits it via split() using mode = "rq". See split() for a more complete explanation.

This only works if the nodes connected through the edge are leaf nodes. Otherwise, this will perform the contraction between the leaf nodes that were connected through this edge.

This operation is the same as rq().

Parameters

edge (Edge) – Edge whose nodes are to be contracted and split.

Return type

tuple[Node, Node]

Examples

>>> nodeA = tk.randn(shape=(10, 15, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(15, 20, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeB')
...
>>> new_edge = nodeA['right'] ^ nodeB['left']
>>> new_nodeA, new_nodeB = tk.rq(new_edge)
...
>>> new_nodeA.shape
torch.Size([10, 10, 100])

>>> new_nodeB.shape
torch.Size([10, 20, 100])

>>> print(new_nodeA.axes_names)
['left', 'right', 'batch']

>>> print(new_nodeB.axes_names)
['left', 'right', 'batch']

Original nodes still exist in the network

>>> assert nodeA.network == new_nodeA.network
>>> assert nodeB.network == new_nodeB.network

rq_#

tensorkrowch.rq_(edge)[source]#

In-place version of rq().

Contracts an edge in-place via contract_() and splits it in-place via split_() using mode = "rq". See split() for a more complete explanation.

Following the PyTorch convention, names of functions ended with an underscore indicate in-place operations.

Nodes resultant from this operation use the same names as the original nodes connected by edge.

This operation is the same as rq_().

Parameters

edge (Edge) – Edge whose nodes are to be contracted and split.

Return type

tuple[Node, Node]

Examples

>>> nodeA = tk.randn(shape=(10, 15, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(15, 20, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeB')
...
>>> new_edge = nodeA['right'] ^ nodeB['left']
>>> nodeA, nodeB = tk.rq_(new_edge)
...
>>> nodeA.shape
torch.Size([10, 10, 100])

>>> nodeB.shape
torch.Size([10, 20, 100])

>>> print(nodeA.axes_names)
['left', 'right', 'batch']

>>> print(nodeB.axes_names)
['left', 'right', 'batch']

contract#

tensorkrowch.contract(edge)[source]#

Contracts the nodes that are connected through the edge.

This only works if the nodes connected through the edge are leaf nodes. Otherwise, this will perform the contraction between the leaf nodes that were connected through this edge.

Nodes resultant from this operation are called "contract_edges". The node that keeps information about the Successor is edge.node1.

This operation is the same as contract().

Parameters

edge (Edge) – Edge that is to be contracted. Batch contraction is automatically performed when both nodes have batch edges with the same names.

Return type

Node

Examples

>>> nodeA = tk.randn(shape=(10, 15, 20),
...                  axes_names=('one', 'two', 'three'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(10, 15, 20),
...                  axes_names=('one', 'two', 'three'),
...                  name='nodeB')
...
>>> _ = nodeA['one'] ^ nodeB['one']
>>> _ = nodeA['two'] ^ nodeB['two']
>>> _ = nodeA['three'] ^ nodeB['three']
>>> result = tk.contract(nodeA['one'])
>>> result.shape
torch.Size([15, 20, 15, 20])

contract_#

tensorkrowch.contract_(edge)[source]#

In-place version of contract().

Following the PyTorch convention, names of functions ended with an underscore indicate in-place operations.

Nodes resultant from this operation are called "contract_edges_ip".

This operation is the same as contract_().

Parameters

edge (Edge) – Edges that is to be contracted. Batch contraction is automatically performed when both nodes have batch edges with the same names.

Return type

Node

Examples

>>> nodeA = tk.randn(shape=(10, 15, 20),
...                  axes_names=('one', 'two', 'three'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(10, 15, 20),
...                  axes_names=('one', 'two', 'three'),
...                  name='nodeB')
...
>>> _ = nodeA['one'] ^ nodeB['one']
>>> _ = nodeA['two'] ^ nodeB['two']
>>> _ = nodeA['three'] ^ nodeB['three']
>>> result = tk.contract_(nodeA['one'])
>>> result.shape
torch.Size([15, 20, 15, 20])

nodeA and nodeB have been removed from the network.

>>> nodeA.network is None
True

>>> nodeB.network is None
True

>>> del nodeA
>>> del nodeB

Operation Class#

class tensorkrowch.Operation(name, check_first, fn_first, fn_next)[source]#

Class for node operations.

A node operation is made up of two functions, the one that is executed the first time the operation is called and the one that is executed in every other call (with the same arguments). Both functions are usually similar, though the former computes extra things regarding the creation of the resultant nodes and some auxiliary operations whose result will be the same in every call (e.g. when contracting two nodes, maybe a permutation of the tensors should be first performed; how this permutation is carried out is always the same, though the tensors themselves are different).

Parameters

  • name (str) – Name of the operation. It cannot coincide with another operation’s name. Operation names can be checked via net.operations.

  • check_first (callable) – Function that checks if the operation has been called at least one time.

  • fn_first (callable) – Function that is called the first time the operation is performed.

  • fn_next (callable) – Function that is called the next times the operation is performed.

Tensor-like Operations#

permute#

tensorkrowch.permute(node, axes)[source]#

Permutes the nodes’ tensor, as well as its axes and edges to match the new shape.

See permute in the PyTorch documentation.

Nodes resultant from this operation are called "permute". The node that keeps information about the Successor is node.

This operation is the same as permute().

Parameters

  • node (Node or ParamNode) – Node whose tensor is to be permuted.

  • axes (list[int, str or Axis]) – List of axes in the permuted order.

Return type

Node

Examples

>>> node = tk.randn((2, 5, 7))
>>> result = tk.permute(node, (2, 0, 1))
>>> result.shape
torch.Size([7, 2, 5])

permute_#

tensorkrowch.permute_(node, axes)[source]#

Permutes the nodes’ tensor, as well as its axes and edges to match the new shape (in-place).

Following the PyTorch convention, names of functions ended with an underscore indicate in-place operations.

See permute.

Nodes resultant from this operation use the same name as node.

This operation is the same as permute_().

Parameters

  • node (Node or ParamNode) – Node whose tensor is to be permuted.

  • axes (list[int, str or Axis]) – List of axes in the permuted order.

Return type

Node

Examples

>>> node = tk.randn((2, 5, 7))
>>> node = tk.permute_(node, (2, 0, 1))
>>> node.shape
torch.Size([7, 2, 5])

tprod#

tensorkrowch.tprod(node1, node2)[source]#

Tensor product between two nodes. It can also be performed using the operator %.

Nodes resultant from this operation are called "tprod". The node that keeps information about the Successor is node1.

Parameters

  • node1 (Node or ParamNode) – First node to be multiplied. Its edges will appear first in the resultant node.

  • node2 (Node or ParamNode) – Second node to be multiplied. Its edges will appear second in the resultant node.

Return type

Node

Examples

>>> net = tk.TensorNetwork()
>>> nodeA = tk.randn((2, 3), network=net)
>>> nodeB = tk.randn((4, 5), network=net)
>>> result = nodeA % nodeB
>>> result.shape
torch.Size([2, 3, 4, 5])

mul#

tensorkrowch.mul(node1, node2)[source]#

Element-wise product between two nodes. It can also be performed using the operator *.

It also admits to take as node2 a number or tensor, that will be multiplied by the node1 tensor as node1.tensor * node2. If this is used like this in the contract() method of a TensorNetwork, this will have to be called explicitly to contract the network, rather than relying on its internal call via the forward().

Nodes resultant from this operation are called "mul". The node that keeps information about the Successor is node1.

Parameters

  • node1 (Node or ParamNode) – First node to be multiplied. Its edges will appear in the resultant node.

  • node2 (Node, ParamNode, torch.Tensor or number) – Second node to be multiplied. It can also be a number or tensor with appropiate shape.

Return type

Node

Examples

>>> net = tk.TensorNetwork()
>>> nodeA = tk.randn((2, 3), network=net)
>>> nodeB = tk.randn((2, 3), network=net)
>>> result = nodeA * nodeB
>>> result.shape
torch.Size([2, 3])

>>> net = tk.TensorNetwork()
>>> nodeA = tk.randn((2, 3), network=net)
>>> tensorB = torch.randn(2, 3)
>>> result = nodeA * tensorB
>>> result.shape
torch.Size([2, 3])

div#

tensorkrowch.div(node1, node2)[source]#

Element-wise division between two nodes. It can also be performed using the operator /.

It also admits to take as node2 a number or tensor, that will divide the node1 tensor as node1.tensor / node2. If this is used like this in the contract() method of a TensorNetwork, this will have to be called explicitly to contract the network, rather than relying on its internal call via the forward().

Nodes resultant from this operation are called "div". The node that keeps information about the Successor is node1.

Parameters

  • node1 (Node or ParamNode) – First node to be divided. Its edges will appear in the resultant node.

  • node2 (Node, ParamNode, torch.Tensor or number) – Second node, the divisor. It can also be a number or tensor with appropiate shape.

Return type

Node

Examples

>>> net = tk.TensorNetwork()
>>> nodeA = tk.randn((2, 3), network=net)
>>> nodeB = tk.randn((2, 3), network=net)
>>> result = nodeA / nodeB
>>> result.shape
torch.Size([2, 3])

>>> net = tk.TensorNetwork()
>>> nodeA = tk.randn((2, 3), network=net)
>>> tensorB = torch.randn(2, 3)
>>> result = nodeA / tensorB
>>> result.shape
torch.Size([2, 3])

add#

tensorkrowch.add(node1, node2)[source]#

Element-wise addition between two nodes. It can also be performed using the operator +.

It also admits to take as node2 a number or tensor, that will be added to the node1 tensor as node1.tensor + node2. If this is used like this in the contract() method of a TensorNetwork, this will have to be called explicitly to contract the network, rather than relying on its internal call via the forward().

Nodes resultant from this operation are called "add". The node that keeps information about the Successor is node1.

Parameters

  • node1 (Node or ParamNode) – First node to be added. Its edges will appear in the resultant node.

  • node2 (Node, ParamNode, torch.Tensor or numeric) – Second node to be added. It can also be a number or tensor with appropiate shape.

Return type

Node

Examples

>>> net = tk.TensorNetwork()
>>> nodeA = tk.randn((2, 3), network=net)
>>> nodeB = tk.randn((2, 3), network=net)
>>> result = nodeA + nodeB
>>> result.shape
torch.Size([2, 3])

>>> net = tk.TensorNetwork()
>>> nodeA = tk.randn((2, 3), network=net)
>>> tensorB = torch.randn(2, 3)
>>> result = nodeA + tensorB
>>> result.shape
torch.Size([2, 3])

sub#

tensorkrowch.sub(node1, node2)[source]#

Element-wise subtraction between two nodes. It can also be performed using the operator -.

It also admits to take as node2 a number or tensor, that will be subtracted from the node1 tensor as node1.tensor - node2. If this is used like this in the contract() method of a TensorNetwork, this will have to be called explicitly to contract the network, rather than relying on its internal call via the forward().

Nodes resultant from this operation are called "sub". The node that keeps information about the Successor is node1.

Parameters

  • node1 (Node or ParamNode) – First node, minuend . Its edges will appear in the resultant node.

  • node2 (Node, ParamNode, torch.Tensor or number) – Second node, subtrahend. It can also be a number or tensor with appropiate shape.

Return type

Node

Examples

>>> net = tk.TensorNetwork()
>>> nodeA = tk.randn((2, 3), network=net)
>>> nodeB = tk.randn((2, 3), network=net)
>>> result = nodeA - nodeB
>>> result.shape
torch.Size([2, 3])

>>> net = tk.TensorNetwork()
>>> nodeA = tk.randn((2, 3), network=net)
>>> tensorB = torch.randn(2, 3)
>>> result = nodeA - tensorB
>>> result.shape
torch.Size([2, 3])

renormalize#

tensorkrowch.renormalize(node, p=2, axis=None)[source]#

Normalizes the node with the specified norm. That is, the tensor of node is divided by its norm.

Different norms can be taken, specifying the argument p, and accross different dimensions, or node axes, specifying the argument axis.

See also torch.norm().

Parameters

  • node (Node or ParamNode) – Node that is to be renormalized.

  • p (int, float) – The order of the norm.

  • axis (int, str, Axis or list[int, str or Axis], optional) – Axis or sequence of axes over which to reduce.

Return type

Node

Examples

>>> nodeA = tk.randn((3, 3))
>>> renormA = tk.renormalize(nodeA)
>>> renormA.norm()
tensor(1.)

conj#

tensorkrowch.conj(node)[source]#

Returns a view of the node’s tensor with a flipped conjugate bit. If the node has a non-complex dtype, this function returns a new node with the same tensor.

See conj in the PyTorch documentation.

Parameters

node (Node or ParamNode) – Node that is to be conjugated.

Return type

Node

Examples

>>> nodeA = tk.randn((3, 3), dtype=torch.complex64)
>>> conjA = tk.conj(nodeA)
>>> conjA.is_conj()
True

Node-like Operations#

split#

tensorkrowch.split(node, node1_axes, node2_axes, mode='svd', side='left', rank=None, cum_percentage=None, cutoff=None)[source]#

Splits one node in two via the decomposition specified in mode. To perform this operation the set of edges has to be split in two sets, corresponding to the edges of the first and second resultant nodes. Batch edges that don’t appear in any of the lists will be repeated in both nodes, and will appear as the first edges of the resultant nodes, in the order they appeared in node.

Having specified the two sets of edges, the node’s tensor is reshaped as a batch matrix, with batch dimensions first, a single input dimension (adding up all edges in the first set) and a single output dimension (adding up all edges in the second set). With this shape, each matrix in the batch is decomposed according to mode.

  • “svd”: Singular Value Decomposition

    \[M = USV^{\dagger}\]

    where \(U\) and \(V\) are unitary, and \(S\) is diagonal.

  • “svdr”: Singular Value Decomposition adding Random phases (square diagonal matrices with random 1’s and -1’s)

    \[M = UR_1SR_2V^{\dagger}\]

    where \(U\) and \(V\) are unitary, \(S\) is diagonal, and \(R_1\) and \(R_2\) are square diagonal matrices with random 1’s and -1’s.

  • “qr”: QR decomposition

    \[M = QR\]

    where Q is unitary and R is an upper triangular matrix.

  • “rq”: RQ decomposition

    \[M = RQ\]

    where R is a lower triangular matrix and Q is unitary.

If mode is “svd” or “svdr”, side must be provided. Besides, at least one of rank, cum_percentage and cutoff is required. If more than one is specified, the resulting rank will be the one that satisfies all conditions.

Since the node is split in two, a new edge appears connecting both nodes. The axis that corresponds to this edge has the name "split".

Nodes resultant from this operation are called "split". The node that keeps information about the Successor is node.

This operation is the same as split().

Parameters

  • node (AbstractNode) – Node that is to be split.

  • node1_axes (list[int, str or Axis]) – First set of edges, will appear as the edges of the first (left) resultant node.

  • node2_axes (list[int, str or Axis]) – Second set of edges, will appear as the edges of the second (right) resultant node.

  • mode ({"svd", "svdr", "qr", "rq"}) – Decomposition to be used.

  • side (str, optional) – If mode is “svd” or “svdr”, indicates the side to which the diagonal matrix \(S\) should be contracted. If “left”, the first resultant node’s tensor will be \(US\), and the other node’s tensor will be \(V^{\dagger}\). If “right”, their tensors will be \(U\) and \(SV^{\dagger}\), respectively.

  • rank (int, optional) – Number of singular values to keep.

  • cum_percentage (float, optional) –

    Proportion that should be satisfied between the sum of all singular values kept and the total sum of all singular values.

    \[\frac{\sum_{i \in \{kept\}}{s_i}}{\sum_{i \in \{all\}}{s_i}} \ge cum\_percentage\]

  • cutoff (float, optional) – Quantity that lower bounds singular values in order to be kept.

Return type

tuple[Node, Node]

Examples

>>> node = tk.randn(shape=(10, 15, 100),
...                 axes_names=('left', 'right', 'batch'))
>>> node_left, node_right = tk.split(node,
...                                  ['left'], ['right'],
...                                  mode='svd',
...                                  rank=5)
>>> node_left.shape
torch.Size([100, 10, 5])

>>> node_right.shape
torch.Size([100, 5, 15])

>>> node_left['split']
Edge( split_0[split] <-> split_1[split] )

split_#

tensorkrowch.split_(node, node1_axes, node2_axes, mode='svd', side='left', rank=None, cum_percentage=None, cutoff=None)[source]#

In-place version of split().

Following the PyTorch convention, names of functions ended with an underscore indicate in-place operations.

Since the node is split in two, a new edge appears connecting both nodes. The axis that corresponds to this edge has the name "split".

Nodes resultant from this operation are called "split_ip".

This operation is the same as split_().

Parameters

  • node (AbstractNode) – Node that is to be split.

  • node1_axes (list[int, str or Axis]) – First set of edges, will appear as the edges of the first (left) resultant node.

  • node2_axes (list[int, str or Axis]) – Second set of edges, will appear as the edges of the second (right) resultant node.

  • mode ({"svd", "svdr", "qr", "rq"}) – Decomposition to be used.

  • side (str, optional) – If mode is “svd” or “svdr”, indicates the side to which the diagonal matrix \(S\) should be contracted. If “left”, the first resultant node’s tensor will be \(US\), and the other node’s tensor will be \(V^{\dagger}\). If “right”, their tensors will be \(U\) and \(SV^{\dagger}\), respectively.

  • rank (int, optional) – Number of singular values to keep.

  • cum_percentage (float, optional) –

    Proportion that should be satisfied between the sum of all singular values kept and the total sum of all singular values.

    \[\frac{\sum_{i \in \{kept\}}{s_i}}{\sum_{i \in \{all\}}{s_i}} \ge cum\_percentage\]

  • cutoff (float, optional) – Quantity that lower bounds singular values in order to be kept.

Return type

tuple[Node, Node]

Examples

>>> node = tk.randn(shape=(10, 15, 100),
...                 axes_names=('left', 'right', 'batch'))
>>> node_left, node_right = tk.split_(node,
...                                   ['left'], ['right'],
...                                   mode='svd',
...                                   rank=5)
>>> node_left.shape
torch.Size([100, 10, 5])

>>> node_right.shape
torch.Size([100, 5, 15])

>>> node_left['split']
Edge( split_ip_0[split] <-> split_ip_1[split] )

node has been deleted (removed from the network), but it still exists until is deleted.

>>> node.network is None
True

>>> del node

contract_edges#

tensorkrowch.contract_edges(edges, node1, node2)[source]#

Contracts all selected edges between two nodes.

Nodes resultant from this operation are called "contract_edges". The node that keeps information about the Successor is node1.

Parameters

  • edges (list[Edge]) – List of edges that are to be contracted. They must be edges shared between node1 and node2. Batch contraction is automatically performed when both nodes have batch edges with the same names.

  • node1 (AbstractNode) – First node of the contraction. Its non-contracted edges will appear first in the list of inherited edges of the resultant node.

  • node2 (AbstractNode) – Second node of the contraction. Its non-contracted edges will appear last in the list of inherited edges of the resultant node.

Return type

Node

Examples

>>> nodeA = tk.randn(shape=(10, 15, 20),
...                  axes_names=('one', 'two', 'three'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(10, 15, 20),
...                  axes_names=('one', 'two', 'three'),
...                  name='nodeB')
...
>>> _ = nodeA['one'] ^ nodeB['one']
>>> _ = nodeA['two'] ^ nodeB['two']
>>> _ = nodeA['three'] ^ nodeB['three']
>>> result = tk.contract_edges([nodeA['one'], nodeA['three']],
...                            nodeA, nodeB)
>>> result.shape
torch.Size([15, 15])

If node1 and node2 are the same node, the contraction is a trace.

>>> result2 = tk.contract_edges([result['two_0']], result, result)
>>> result2.shape
torch.Size([])

contract_between#

tensorkrowch.contract_between(node1, node2)[source]#

Contracts all edges shared between two nodes. Batch contraction is automatically performed when both nodes have batch edges with the same names. It can also be performed using the operator @.

Nodes resultant from this operation are called "contract_edges". The node that keeps information about the Successor is node1.

This operation is the same as contract_between().

Parameters

  • node1 (AbstractNode) – First node of the contraction. Its non-contracted edges will appear first in the list of inherited edges of the resultant node.

  • node2 (AbstractNode) – Second node of the contraction. Its non-contracted edges will appear last in the list of inherited edges of the resultant node.

Return type

Node

Examples

>>> nodeA = tk.randn(shape=(10, 15, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(15, 7, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeB')
...
>>> _ = nodeA['right'] ^ nodeB['left']
>>> result = tk.contract_between(nodeA, nodeB)
>>> result.shape
torch.Size([100, 10, 7])

contract_between_#

tensorkrowch.contract_between_(node1, node2)[source]#

In-place version of contract_between().

Following the PyTorch convention, names of functions ended with an underscore indicate in-place operations.

Nodes resultant from this operation are called "contract_edges_ip".

This operation is the same as contract_between_().

Parameters

  • node1 (AbstractNode) – First node of the contraction. Its non-contracted edges will appear first in the list of inherited edges of the resultant node.

  • node2 (AbstractNode) – Second node of the contraction. Its non-contracted edges will appear last in the list of inherited edges of the resultant node.

Return type

Node

Examples

>>> nodeA = tk.randn(shape=(10, 15, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(15, 7, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeB')
...
>>> _ = nodeA['right'] ^ nodeB['left']
>>> result = tk.contract_between_(nodeA, nodeB)
>>> result.shape
torch.Size([100, 10, 7])

nodeA and nodeB have been removed from the network.

>>> nodeA.network is None
True

>>> nodeB.network is None
True

>>> del nodeA
>>> del nodeB

stack#

tensorkrowch.stack(nodes)[source]#

Creates a StackNode or ParamStackNode by stacking a collection of Nodes or ParamNodes, respectively. Restrictions that are applied to the nodes in order to be stackable are the same as in StackNode.

The stack dimension will be the first one in the resultant node.

See ParamStackNode and TensorNetwork to learn how the auto_stack() mode affects the computation of stack().

If this operation is used several times with the same input nodes, but their dimensions can change from one call to another, this will lead to undesired behaviour. The network should be reset(). This situation should be avoided in the contract() method. Otherwise it will fail in subsequent calls to contract or forward()

Nodes resultant from this operation are called "stack". If this operation returns a virtual ParamStackNode, it will be called "virtual_result_stack". See :class:AbstractNode` to learn about this reserved name. The node that keeps information about the Successor is nodes[0], the first stacked node.

Parameters

nodes (list[AbstractNode] or tuple[AbstractNode]) – Sequence of nodes that are to be stacked. They must be of the same type, have the same rank and axes names, be in the same tensor network, and have edges with the same types.

Examples

>>> net = tk.TensorNetwork()
>>> nodes = [tk.randn(shape=(2, 4, 2),
...                   axes_names=('left', 'input', 'right'),
...                   network=net)
...          for _ in range(10)]
>>> stack_node = tk.stack(nodes)
>>> stack_node.shape
torch.Size([10, 2, 4, 2])

unbind#

tensorkrowch.unbind(node)[source]#

Unbinds a StackNode or ParamStackNode, where the first dimension is assumed to be the stack dimension.

If auto_unbind() is set to False, each resultant node will store its own tensor. Otherwise, they will have only a reference to the corresponding slice of the (Param)StackNode.

See TensorNetwork to learn how the auto_unbind mode affects the computation of unbind().

Nodes resultant from this operation are called "unbind". The node that keeps information about the Successor is node.

Parameters

node (StackNode or ParamStackNode) – Node that is to be unbound.

Return type

list[Node]

Examples

>>> net = tk.TensorNetwork()
>>> nodes = [tk.randn(shape=(2, 4, 2),
...                   axes_names=('left', 'input', 'right'),
...                   network=net)
...          for _ in range(10)]
>>> data = [tk.randn(shape=(4,),
...                  axes_names=('feature',),
...                  network=net)
...         for _ in range(10)]
...
>>> for i in range(10):
...     _ = nodes[i]['input'] ^ data[i]['feature']
...
>>> stack_nodes = tk.stack(nodes)
>>> stack_data = tk.stack(data)
...
>>> # It is necessary to re-connect stacks
>>> _ = stack_nodes['input'] ^ stack_data['feature']
>>> result = tk.unbind(stack_nodes @ stack_data)
>>> print(result[0].name)
unbind_0

>>> result[0].axes
[Axis( left (0) ), Axis( right (1) )]

>>> result[0].shape
torch.Size([2, 2])

einsum#

tensorkrowch.einsum(string, *nodes)[source]#

Performs einsum contraction based on opt_einsum. This operation facilitates contracting several nodes at once, specifying directly the order of appearance of the resultant edges. Without this operation, several contractions and permutations would be needed.

Since it adapts a tensor operation for nodes, certain nodes’ properties are first checked. Thus, it verifies that all edges are correctly connected and all nodes are in the same network. It also performs batch contraction whenever corresponding edges are batch edges.

Nodes resultant from this operation are called "einsum". The node that keeps information about the Successor is nodes[0], the first node involved in the operation.

Parameters

  • string (str) –

    Einsum-like string indicating how the contraction should be performed. It consists of a comma-separated list of inputs and an output separated by an arrow. For instance, the contraction

    \[T_{j,l} = \sum_{i,k,m}{A_{i,j,k}B_{k,l,m}C_{i,m}}\]

    can be expressed as:

    string = 'ijk,klm,im->jl'

  • nodes (AbstractNode...) – Nodes that are involved in the contraction. Should appear in the same order as it is specified in the string. They should either be all (Param)StackNode’s or none of them be a (Param)StackNode.

Return type

Node

Examples

>>> nodeA = tk.randn(shape=(10, 15, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeA')
>>> nodeB = tk.randn(shape=(15, 7, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeB')
>>> nodeC = tk.randn(shape=(7, 10, 100),
...                  axes_names=('left', 'right', 'batch'),
...                  name='nodeC')
...
>>> _ = nodeA['right'] ^ nodeB['left']
>>> _ = nodeB['right'] ^ nodeC['left']
>>> _ = nodeC['right'] ^ nodeA['left']
...
>>> result = tk.einsum('ijb,jkb,kib->b', nodeA, nodeB, nodeC)
>>> result.shape
torch.Size([100])

stacked_einsum#

tensorkrowch.stacked_einsum(string, *nodes_lists)[source]#

Applies the same einsum() operation (same string) to a sequence of groups of nodes (all groups having the same amount of nodes, with the same properties, etc.). That is, it stacks these groups of nodes into a single collection of StackNodes that is then contracted via einsum() (using the stack dimensions as batch), and unbound afterwards.

Parameters

  • string (str) –

    Einsum-like string indicating how the contraction should be performed. It consists of a comma-separated list of inputs and an output separated by an arrow. For instance, the contraction

    \[T_{j,l} = \sum_{i,k,m}{A_{i,j,k}B_{k,l,m}C_{i,m}}\]

    can be expressed as:

    string = 'ijk,klm,im->jl'

  • nodes_lists (List[Node or ParamNode]...) – Lists of nodes that are involved in the contraction. Should appear in the same order as it is specified in the string.

Return type

list[Node]

Examples

>>> net = tk.TensorNetwork()
>>> nodesA = [tk.randn(shape=(10, 15, 100),
...                    axes_names=('left', 'right', 'batch'),
...                    name='nodeA',
...                    network=net)
...           for _ in range(10)]
>>> nodesB = [tk.randn(shape=(15, 7, 100),
...                    axes_names=('left', 'right', 'batch'),
...                    name='nodeB',
...                    network=net)
...           for _ in range(10)]
>>> nodesC = [tk.randn(shape=(7, 10, 100),
...                    axes_names=('left', 'right', 'batch'),
...                    name='nodeC',
...                    network=net)
...           for _ in range(10)]
...
>>> for i in range(10):
...     _ = nodesA[i]['right'] ^ nodesB[i]['left']
...     _ = nodesB[i]['right'] ^ nodesC[i]['left']
...     _ = nodesC[i]['right'] ^ nodesA[i]['left']
...
>>> result = tk.stacked_einsum('ijb,jkb,kib->b', nodesA, nodesB, nodesC)
>>> len(result)
10

>>> result[0].shape
torch.Size([100])