quimb.tensor.optimize

Support for optimizing tensor networks using automatic differentiation to automatically derive gradients for input to scipy optimizers.

Attributes

Classes

TensorNetwork

A collection of (as yet uncontracted) Tensors.

ArrayInfo

Simple container for recording size and dtype information about arrays.

Vectorizer

Object for mapping back and forth between any pytree of mixed

AutoGradHandler

JaxHandler

TensorFlowHandler

TorchHandler

MultiLossHandler

SGD

Stateful scipy.optimize.minimize compatible implementation of

RMSPROP

Stateful scipy.optimize.minimize compatible implementation of

ADAM

Stateful scipy.optimize.minimize compatible implementation of

NADAM

Stateful scipy.optimize.minimize compatible implementation of

ADABELIEF

Stateful scipy.optimize.minimize compatible implementation of

MakeArrayFn

Class wrapper so picklable.

TNOptimizer

Globally optimize tensors within a tensor network with respect to any

Functions

prod(iterable)

default_to_neutral_style(fn)

Wrap a function or method to use the neutral style by default.

ensure_dict(x)

Make sure x is a dict, creating an empty one if x is None.

tree_flatten(tree[, get_ref, is_leaf])

Flatten tree into a list of leaves.

tree_map(f, tree[, is_leaf])

Map f over all leaves in tree, returning a new pytree.

tree_unflatten(objs, tree[, is_leaf])

Unflatten objs into a pytree of the same structure as tree.

contract_backend(backend[, set_globally])

A context manager to temporarily set the default backend used for tensor

get_jax()

tags_to_oset(tags)

Parse a tags argument into an ordered set.

_parse_opt_in(tn, tags, shared_tags, to_constant)

Parse a tensor network where tensors are assumed to be constant unless

_parse_opt_out(tn, constant_tags, to_constant)

Parse a tensor network where tensors are assumed to be variables unless

_parse_pytree_to_backend(x, to_constant)

Parse a arbitrary pytree, collecting variables. There is not opting in

parse_network_to_backend(tn, to_constant[, tags, ...])

Parse tensor network to:

_inject_variables_pytree(arrays, tree)

inject_variables(arrays, tn)

Given the list of optimized variables arrays and the target tensor

convert_raw_arrays(x, f)

Given a TensorNetwork, Tensor, or other possibly structured raw

convert_variables_to_numpy(x)

get_autograd()

get_tensorflow()

get_torch()

identity_fn(x)

Module Contents

quimb.tensor.optimize.prod(iterable)
quimb.tensor.optimize.default_to_neutral_style(fn)[source]

Wrap a function or method to use the neutral style by default.

quimb.tensor.optimize.ensure_dict(x)[source]

Make sure x is a dict, creating an empty one if x is None.

quimb.tensor.optimize.tree_flatten(tree, get_ref=False, is_leaf=is_not_container)[source]

Flatten tree into a list of leaves.

Parameters:
  • tree (pytree) – A nested sequence of tuples, lists, dicts and other objects.

  • is_leaf (callable) – A function to determine if an object is a leaf, only objects for which is_leaf(x) returns True are returned in the flattened list.

Returns:

  • objs (list) – The flattened list of leaf objects.

  • (ref_tree) (pytree) – If get_ref is True, a reference tree, with leaves of type Leaf, is returned which can be used to reconstruct the original tree.

quimb.tensor.optimize.tree_map(f, tree, is_leaf=is_not_container)[source]

Map f over all leaves in tree, returning a new pytree.

Parameters:
  • f (callable) – A function to apply to all leaves in tree.

  • tree (pytree) – A nested sequence of tuples, lists, dicts and other objects.

  • is_leaf (callable) – A function to determine if an object is a leaf, f is only applied to objects for which is_leaf(x) returns True.

Return type:

pytree

quimb.tensor.optimize.tree_unflatten(objs, tree, is_leaf=is_leaf_object)[source]

Unflatten objs into a pytree of the same structure as tree.

Parameters:
  • objs (sequence) – A sequence of objects to be unflattened into a pytree.

  • tree (pytree) – A nested sequence of tuples, lists, dicts and other objects, the objs will be inserted into a new pytree of the same structure.

  • is_leaf (callable) – A function to determine if an object is a leaf, only objects for which is_leaf(x) returns True will have the next item from objs inserted. By default checks for the Leaf object inserted by tree_flatten(..., get_ref=True).

Return type:

pytree

quimb.tensor.optimize.contract_backend(backend, set_globally=False)[source]

A context manager to temporarily set the default backend used for tensor contractions, via ‘cotengra’. By default, this only sets the contract backend for the current thread.

Parameters:

set_globally (bool, optimize) – Whether to set the backend just for this thread, or for all threads. If you are entering the context, then using multithreading, you might want True.

quimb.tensor.optimize.get_jax()[source]
class quimb.tensor.optimize.TensorNetwork(ts=(), *, virtual=False, check_collisions=True)[source]

Bases: object

A collection of (as yet uncontracted) Tensors.

Parameters:
  • ts (sequence of Tensor or TensorNetwork) – The objects to combine. The new network will copy these (but not the underlying data) by default. For a view set virtual=True.

  • virtual (bool, optional) – Whether the TensorNetwork should be a view onto the tensors it is given, or a copy of them. E.g. if a virtual TN is constructed, any changes to a Tensor’s indices or tags will propagate to all TNs viewing that Tensor.

  • check_collisions (bool, optional) – If True, the default, then TensorNetwork instances with double indices which match another TensorNetwork instances double indices will have those indices’ names mangled. Can be explicitly turned off when it is known that no collisions will take place – i.e. when not adding any new tensors.

tensor_map

Mapping of unique ids to tensors, like``{tensor_id: tensor, …}``. I.e. this is where the tensors are ‘stored’ by the network.

Type:

dict

tag_map

Mapping of tags to a set of tensor ids which have those tags. I.e. {tag: {tensor_id_1, tensor_id_2, ...}}. Thus to select those tensors could do: map(tensor_map.__getitem__, tag_map[tag]).

Type:

dict

ind_map

Like tag_map but for indices. So ind_map[ind]] returns the tensor ids of those tensors with ind.

Type:

dict

exponent

A scalar prefactor for the tensor network, stored in base 10 like 10**exponent. This is mostly for conditioning purposes and will be 0.0 unless you use use equalize_norms(value) or tn.strip_exponent(tid_or_tensor).

Type:

float

_EXTRA_PROPS = ()
_CONTRACT_STRUCTURED = False
combine(other, *, virtual=False, check_collisions=True)[source]

Combine this tensor network with another, returning a new tensor network. This can be overriden by subclasses to check for a compatible structured type.

Parameters:
  • other (TensorNetwork) – The other tensor network to combine with.

  • virtual (bool, optional) – Whether the new tensor network should copy all the incoming tensors (False, the default), or view them as virtual (True).

  • check_collisions (bool, optional) – Whether to check for index collisions between the two tensor networks before combining them. If True (the default), any inner indices that clash will be mangled.

Return type:

TensorNetwork

__and__(other)[source]

Combine this tensor network with more tensors, without contracting. Copies the tensors.

__or__(other)[source]

Combine this tensor network with more tensors, without contracting. Views the constituent tensors.

_update_properties(cls, like=None, current=None, **kwargs)[source]
classmethod new(like=None, **kwargs)[source]

Create a new tensor network, without any tensors, of type cls, with all the requisite properties specified by kwargs or inherited from like.

classmethod from_TN(tn, like=None, inplace=False, **kwargs)[source]

Construct a specific tensor network subclass (i.e. one with some promise about structure/geometry and tags/inds such as an MPS) from a generic tensor network which should have that structure already.

Parameters:
  • cls (class) – The TensorNetwork subclass to convert tn to.

  • tn (TensorNetwork) – The TensorNetwork to convert.

  • like (TensorNetwork, optional) – If specified, try and retrieve the neccesary attribute values from this tensor network.

  • inplace (bool, optional) – Whether to perform the conversion inplace or not.

  • kwargs – Extra properties of the TN subclass that should be specified.

view_as(cls, inplace=False, **kwargs)[source]

View this tensor network as subclass cls.

view_as_[source]
view_like(like, inplace=False, **kwargs)[source]

View this tensor network as the same subclass cls as like inheriting its extra properties as well.

view_like_[source]
copy(virtual=False, deep=False)[source]

Copy this TensorNetwork. If deep=False, (the default), then everything but the actual numeric data will be copied.

__copy__[source]
get_params()[source]

Get a pytree of the ‘parameters’, i.e. all underlying data arrays.

set_params(params)[source]

Take a pytree of the ‘parameters’, i.e. all underlying data arrays, as returned by get_params and set them.

Link tid to each of tags.

“Unlink tid from each of tags.

Link tid to each of inds.

“Unlink tid from each of inds.

_reset_inner_outer(inds)[source]
_next_tid()[source]
add_tensor(tensor, tid=None, virtual=False)[source]

Add a single tensor to this network - mangle its tid if neccessary.

add_tensor_network(tn, virtual=False, check_collisions=True)[source]
add(t, virtual=False, check_collisions=True)[source]

Add Tensor, TensorNetwork or sequence thereof to self.

make_tids_consecutive(tid0=0)[source]

Reset the tids - node identifies - to be consecutive integers.

__iand__(tensor)[source]

Inplace, but non-virtual, addition of a Tensor or TensorNetwork to this network. It should not have any conflicting indices.

__ior__(tensor)[source]

Inplace, virtual, addition of a Tensor or TensorNetwork to this network. It should not have any conflicting indices.

_modify_tensor_tags(old, new, tid)[source]
_modify_tensor_inds(old, new, tid)[source]
property num_tensors
The total number of tensors in the tensor network.
property num_indices
The total number of indices in the tensor network.
pop_tensor(tid)[source]

Remove tensor with tid from this network, and return it.

remove_all_tensors()[source]

Remove all tensors from this network.

_pop_tensor[source]
delete(tags, which='all')[source]

Delete any tensors which match all or any of tags.

Parameters:
  • tags (str or sequence of str) – The tags to match.

  • which ({'all', 'any'}, optional) – Whether to match all or any of the tags.

check()[source]

Check some basic diagnostics of the tensor network.

add_tag(tag, where=None, which='all')[source]

Add tag to every tensor in this network, or if where is specified, the tensors matching those tags – i.e. adds the tag to all tensors in self.select_tensors(where, which=which).

drop_tags(tags=None)[source]

Remove a tag or tags from this tensor network, defaulting to all. This is an inplace operation.

Parameters:

tags (str or sequence of str or None, optional) – The tag or tags to drop. If None, drop all tags.

retag(tag_map, inplace=False)[source]

Rename tags for all tensors in this network, optionally in-place.

Parameters:
  • tag_map (dict-like) – Mapping of pairs {old_tag: new_tag, ...}.

  • inplace (bool, optional) – Perform operation inplace or return copy (default).

retag_[source]
reindex(index_map, inplace=False)[source]

Rename indices for all tensors in this network, optionally in-place.

Parameters:

index_map (dict-like) – Mapping of pairs {old_ind: new_ind, ...}.

reindex_[source]
mangle_inner_(append=None, which=None)[source]

Generate new index names for internal bonds, meaning that when this tensor network is combined with another, there should be no collisions.

Parameters:
  • append (None or str, optional) – Whether and what to append to the indices to perform the mangling. If None a whole new random UUID will be generated.

  • which (sequence of str, optional) – Which indices to rename, if None (the default), all inner indices.

conj(mangle_inner=False, inplace=False)[source]

Conjugate all the tensors in this network (leaves all indices).

conj_[source]
property H
Conjugate all the tensors in this network (leaves all indices).
item()[source]

Return the scalar value of this tensor network, if it is a scalar.

largest_element()[source]

Return the ‘largest element’, in terms of absolute magnitude, of this tensor network. This is defined as the product of the largest elements of each tensor in the network, which would be the largest single term occuring if the TN was summed explicitly.

norm(**contract_opts)[source]

Frobenius norm of this tensor network. Computed by exactly contracting the TN with its conjugate:

\[\|T\|_F = \sqrt{\mathrm{Tr} \left(T^{\dagger} T\right)}\]

where the trace is taken over all indices. Equivalent to the square root of the sum of squared singular values across any partition.

make_norm(mangle_append='*', layer_tags=('KET', 'BRA'), return_all=False)[source]

Make the norm tensor network of this tensor network tn.H & tn.

Parameters:
  • mangle_append ({str, False or None}, optional) – How to mangle the inner indices of the bra.

  • layer_tags ((str, str), optional) – The tags to identify the top and bottom.

  • return_all (bool, optional) – Return the norm, the ket and the bra.

multiply(x, inplace=False, spread_over=8)[source]

Scalar multiplication of this tensor network with x.

Parameters:
  • x (scalar) – The number to multiply this tensor network by.

  • inplace (bool, optional) – Whether to perform the multiplication inplace.

  • spread_over (int, optional) – How many tensors to try and spread the multiplication over, in order that the effect of multiplying by a very large or small scalar is not concentrated.

multiply_[source]
multiply_each(x, inplace=False)[source]

Scalar multiplication of each tensor in this tensor network with x. If trying to spread a multiplicative factor fac uniformly over all tensors in the network and the number of tensors is large, then calling multiply(fac) can be inaccurate due to precision loss. If one has a routine that can precisely compute the x to be applied to each tensor, then this function avoids the potential inaccuracies in multiply().

Parameters:
  • x (scalar) – The number that multiplies each tensor in the network

  • inplace (bool, optional) – Whether to perform the multiplication inplace.

multiply_each_[source]
negate(inplace=False)[source]

Negate this tensor network.

negate_[source]
__mul__(other)[source]

Scalar multiplication.

__rmul__(other)[source]

Right side scalar multiplication.

__imul__(other)[source]

Inplace scalar multiplication.

__truediv__(other)[source]

Scalar division.

__itruediv__(other)[source]

Inplace scalar division.

__neg__()[source]

Negate this tensor network.

__iter__()[source]
property tensors
Get the tuple of tensors in this tensor network.
property arrays
Get the tuple of raw arrays containing all the tensor network data.
get_symbol_map()[source]

Get the mapping of the current indices to einsum style single unicode characters. The symbols are generated in the order they appear on the tensors.

get_equation(output_inds=None)[source]

Get the ‘equation’ describing this tensor network, in einsum style with a single unicode letter per index. The symbols are generated in the order they appear on the tensors.

Parameters:

output_inds (None or sequence of str, optional) – Manually specify which are the output indices.

Returns:

eq

Return type:

str

Examples

>>> tn = qtn.TN_rand_reg(10, 3, 2)
>>> tn.get_equation()
'abc,dec,fgb,hia,jke,lfk,mnj,ing,omd,ohl->'
get_inputs_output_size_dict(output_inds=None)[source]

Get a tuple of inputs, output and size_dict suitable for e.g. passing to path optimizers. The symbols are generated in the order they appear on the tensors.

Parameters:

output_inds (None or sequence of str, optional) – Manually specify which are the output indices.

Returns:

  • inputs (tuple[str])

  • output (str)

  • size_dict (dict[str, ix])

geometry_hash(output_inds=None, strict_index_order=False)[source]

A hash of this tensor network’s shapes & geometry. A useful check for determinism. Moreover, if this matches for two tensor networks then they can be contracted using the same tree for the same cost. Order of tensors matters for this - two isomorphic tensor networks with shuffled tensor order will not have the same hash value. Permuting the indices of individual of tensors or the output does not matter unless you set strict_index_order=True.

Parameters:
  • output_inds (None or sequence of str, optional) – Manually specify which indices are output indices and their order, otherwise assumed to be all indices that appear once.

  • strict_index_order (bool, optional) – If False, then the permutation of the indices of each tensor and the output does not matter.

Return type:

str

Examples

If we transpose some indices, then only the strict hash changes:

>>> tn = qtn.TN_rand_reg(100, 3, 2, seed=0)
>>> tn.geometry_hash()
'18c702b2d026dccb1a69d640b79d22f3e706b6ad'
>>> tn.geometry_hash(strict_index_order=True)
'c109fdb43c5c788c0aef7b8df7bb83853cf67ca1'
>>> t = tn['I0']
>>> t.transpose_(t.inds[2], t.inds[1], t.inds[0])
>>> tn.geometry_hash()
'18c702b2d026dccb1a69d640b79d22f3e706b6ad'
>>> tn.geometry_hash(strict_index_order=True)
'52c32c1d4f349373f02d512f536b1651dfe25893'
tensors_sorted()[source]

Return a tuple of tensors sorted by their respective tags, such that the tensors of two networks with the same tag structure can be iterated over pairwise.

apply_to_arrays(fn)[source]

Modify every tensor’s array inplace by applying fn to it. This is meant for changing how the raw arrays are backed (e.g. converting between dtypes or libraries) but not their ‘numerical meaning’.

_get_tids_from(xmap, xs, which)[source]
_get_tids_from_tags(tags, which='all')[source]

Return the set of tensor ids that match tags.

Parameters:
  • tags (seq or str, str, None, ..., int, slice) – Tag specifier(s).

  • which ({'all', 'any', '!all', '!any'}) –

    How to select based on the tags, if:

    • ’all’: get ids of tensors matching all tags

    • ’any’: get ids of tensors matching any tags

    • ’!all’: get ids of tensors not matching all tags

    • ’!any’: get ids of tensors not matching any tags

Return type:

set[str]

_get_tids_from_inds(inds, which='all')[source]

Like _get_tids_from_tags but specify inds instead.

_tids_get(*tids)[source]

Convenience function that generates unique tensors from tids.

_inds_get(*inds)[source]

Convenience function that generates unique tensors from inds.

_tags_get(*tags)[source]

Convenience function that generates unique tensors from tags.

select_tensors(tags, which='all')[source]

Return the sequence of tensors that match tags. If which='all', each tensor must contain every tag. If which='any', each tensor can contain any of the tags.

Parameters:
  • tags (str or sequence of str) – The tag or tag sequence.

  • which ({'all', 'any'}) – Whether to require matching all or any of the tags.

Returns:

tagged_tensors – The tagged tensors.

Return type:

tuple of Tensor

_select_tids(tids, virtual=True)[source]

Get a copy or a virtual copy (doesn’t copy the tensors) of this TensorNetwork, only with the tensors corresponding to tids.

_select_without_tids(tids, virtual=True)[source]

Get a copy or a virtual copy (doesn’t copy the tensors) of this TensorNetwork, without the tensors corresponding to tids.

select(tags, which='all', virtual=True)[source]

Get a TensorNetwork comprising tensors that match all or any of tags, inherit the network properties/structure from self. This returns a view of the tensors not a copy.

Parameters:
  • tags (str or sequence of str) – The tag or tag sequence.

  • which ({'all', 'any'}) – Whether to require matching all or any of the tags.

  • virtual (bool, optional) – Whether the returned tensor network views the same tensors (the default) or takes copies (virtual=False) from self.

Returns:

tagged_tn – A tensor network containing the tagged tensors.

Return type:

TensorNetwork

select_any[source]
select_all[source]
select_neighbors(tags, which='any')[source]

Select any neighbouring tensors to those specified by tags.self

Parameters:
  • tags (sequence of str, int) – Tags specifying tensors.

  • which ({'any', 'all'}, optional) – How to select tensors based on tags.

Returns:

The neighbouring tensors.

Return type:

tuple[Tensor]

_select_local_tids(tids, max_distance=1, fillin=False, reduce_outer=None, inwards=False, virtual=True, include=None, exclude=None)[source]
select_local(tags, which='all', max_distance=1, fillin=False, reduce_outer=None, virtual=True, include=None, exclude=None)[source]

Select a local region of tensors, based on graph distance max_distance to any tagged tensors.

Parameters:
  • tags (str or sequence of str) – The tag or tag sequence defining the initial region.

  • which ({'all', 'any', '!all', '!any'}, optional) – Whether to require matching all or any of the tags.

  • max_distance (int, optional) – The maximum distance to the initial tagged region.

  • fillin (bool or int, optional) –

    Once the local region has been selected based on graph distance, whether and how many times to ‘fill-in’ corners by adding tensors connected multiple times. For example, if R is an initially tagged tensor and x are locally selected tensors:

      fillin=0       fillin=1       fillin=2
    
     | | | | |      | | | | |      | | | | |
    -o-o-x-o-o-    -o-x-x-x-o-    -x-x-x-x-x-
     | | | | |      | | | | |      | | | | |
    -o-x-x-x-o-    -x-x-x-x-x-    -x-x-x-x-x-
     | | | | |      | | | | |      | | | | |
    -x-x-R-x-x-    -x-x-R-x-x-    -x-x-R-x-x-
    

  • reduce_outer ({'sum', 'svd', 'svd-sum', 'reflect'}, optional) – Whether and how to reduce any outer indices of the selected region.

  • virtual (bool, optional) – Whether the returned tensor network should be a view of the tensors or a copy (virtual=False).

  • include (sequence of int, optional) – Only include tensor with these tids.

  • exclude (sequence of int, optional) – Only include tensor without these tids.

Return type:

TensorNetwork

__getitem__(tags)[source]

Get the tensor(s) associated with tags.

Parameters:

tags (str or sequence of str) – The tags used to select the tensor(s).

Return type:

Tensor or sequence of Tensors

__setitem__(tags, tensor)[source]

Set the single tensor uniquely associated with tags.

__delitem__(tags)[source]

Delete any tensors which have all of tags.

partition_tensors(tags, inplace=False, which='any')[source]

Split this TN into a list of tensors containing any or all of tags and a TensorNetwork of the the rest.

Parameters:
  • tags (sequence of str) – The list of tags to filter the tensors by. Use ... (Ellipsis) to filter all.

  • inplace (bool, optional) – If true, remove tagged tensors from self, else create a new network with the tensors removed.

  • which ({'all', 'any'}) – Whether to require matching all or any of the tags.

Returns:

(u_tn, t_ts) – The untagged tensor network, and the sequence of tagged Tensors.

Return type:

(TensorNetwork, tuple of Tensors)

partition(tags, which='any', inplace=False)[source]

Split this TN into two, based on which tensors have any or all of tags. Unlike partition_tensors, both results are TNs which inherit the structure of the initial TN.

Parameters:
  • tags (sequence of str) – The tags to split the network with.

  • which ({'any', 'all'}) – Whether to split based on matching any or all of the tags.

  • inplace (bool) – If True, actually remove the tagged tensors from self.

Returns:

untagged_tn, tagged_tn – The untagged and tagged tensor networs.

Return type:

(TensorNetwork, TensorNetwork)

_split_tensor_tid(tid, left_inds, **split_opts)[source]
split_tensor(tags, left_inds, **split_opts)[source]

Split the single tensor uniquely identified by tags, adding the resulting tensors from the decomposition back into the network. Inplace operation.

replace_with_identity(where, which='any', inplace=False)[source]

Replace all tensors marked by where with an identity. E.g. if X denote where tensors:

---1  X--X--2---         ---1---2---
   |  |  |  |      ==>          |
   X--X--X  |                   |
Parameters:
  • where (tag or seq of tags) – Tags specifying the tensors to replace.

  • which ({'any', 'all'}) – Whether to replace tensors matching any or all the tags where.

  • inplace (bool) – Perform operation in place.

Returns:

The TN, with section replaced with identity.

Return type:

TensorNetwork

See also

replace_with_svd

replace_with_svd(where, left_inds, eps, *, which='any', right_inds=None, method='isvd', max_bond=None, absorb='both', cutoff_mode='rel', renorm=None, ltags=None, rtags=None, keep_tags=True, start=None, stop=None, inplace=False)[source]

Replace all tensors marked by where with an iteratively constructed SVD. E.g. if X denote where tensors:

                        :__       ___:
---X  X--X  X---        :  \     /   :
   |  |  |  |      ==>  :   U~s~VH---:
---X--X--X--X---        :__/     \   :
      |     +---        :         \__:
      X              left_inds       :
                                 right_inds
Parameters:
  • where (tag or seq of tags) – Tags specifying the tensors to replace.

  • left_inds (ind or sequence of inds) – The indices defining the left hand side of the SVD.

  • eps (float) – The tolerance to perform the SVD with, affects the number of singular values kept. See quimb.linalg.rand_linalg.estimate_rank().

  • which ({'any', 'all', '!any', '!all'}, optional) – Whether to replace tensors matching any or all the tags where, prefix with ‘!’ to invert the selection.

  • right_inds (ind or sequence of inds, optional) – The indices defining the right hand side of the SVD, these can be automatically worked out, but for hermitian decompositions the order is important and thus can be given here explicitly.

  • method (str, optional) – How to perform the decomposition, if not an iterative method the subnetwork dense tensor will be formed first, see tensor_split() for options.

  • max_bond (int, optional) – The maximum bond to keep, defaults to no maximum (-1).

  • ltags (sequence of str, optional) – Tags to add to the left tensor.

  • rtags (sequence of str, optional) – Tags to add to the right tensor.

  • keep_tags (bool, optional) – Whether to propagate tags found in the subnetwork to both new tensors or drop them, defaults to True.

  • start (int, optional) – If given, assume can use TNLinearOperator1D.

  • stop (int, optional) – If given, assume can use TNLinearOperator1D.

  • inplace (bool, optional) – Perform operation in place.

Return type:

TensorNetwork

replace_with_svd_[source]
replace_section_with_svd(start, stop, eps, **replace_with_svd_opts)[source]

Take a 1D tensor network, and replace a section with a SVD. See replace_with_svd().

Parameters:
  • start (int) – Section start index.

  • stop (int) – Section stop index, not included itself.

  • eps (float) – Precision of SVD.

  • replace_with_svd_opts – Supplied to replace_with_svd().

Return type:

TensorNetwork

convert_to_zero()[source]

Inplace conversion of this network to an all zero tensor network.

_contract_between_tids(tid1, tid2, equalize_norms=False, gauges=None, output_inds=None, **contract_opts)[source]
contract_between(tags1, tags2, **contract_opts)[source]

Contract the two tensors specified by tags1 and tags2 respectively. This is an inplace operation. No-op if the tensor specified by tags1 and tags2 is the same tensor.

Parameters:
  • tags1 – Tags uniquely identifying the first tensor.

  • tags2 (str or sequence of str) – Tags uniquely identifying the second tensor.

  • contract_opts – Supplied to tensor_contract().

contract_ind(ind, output_inds=None, **contract_opts)[source]

Contract tensors connected by ind.

gate_inds[source]
gate_inds_[source]
gate_inds_with_tn(inds, gate, gate_inds_inner, gate_inds_outer, inplace=False)[source]

Gate some indices of this tensor network with another tensor network. That is, rewire and then combine them such that the new tensor network has the same outer indices as before, but now includes gate:

gate_inds_outer
 :
 :         gate_inds_inner
 :         :
 :         :   inds               inds
 :  ┌────┐ :   : ┌────┬───        : ┌───────┬───
 ───┤    ├──  a──┤    │          a──┤       │
    │    │       │    ├───          │       ├───
 ───┤gate├──  b──┤self│     -->  b──┤  new  │
    │    │       │    ├───          │       ├───
 ───┤    ├──  c──┤    │          c──┤       │
    └────┘       └────┴───          └───────┴───

Where there can be arbitrary structure of tensors within both self and gate.

The case where some of target inds are not present is handled as so (here ‘c’ is missing so ‘x’ and ‘y’ are kept):

gate_inds_outer
 :
 :         gate_inds_inner
 :         :
 :         :   inds               inds
 :  ┌────┐ :   : ┌────┬───        : ┌───────┬───
 ───┤    ├──  a──┤    │          a──┤       │
    │    │       │    ├───          │       ├───
 ───┤gate├──  b──┤self│     -->  b──┤  new  │
    │    │       │    ├───          │       ├───
x───┤    ├──y    └────┘          x──┤    ┌──┘
    └────┘                          └────┴───y

Which enables convinient construction of various tensor networks, for example propagators, from scratch.

Parameters:
  • inds (str or sequence of str) – The current indices to gate. If an index is not present on the target tensor network, it is ignored and instead the resulting tensor network will have both the corresponding inner and outer index of the gate tensor network.

  • gate (Tensor or TensorNetwork) – The tensor network to gate with.

  • gate_inds_inner (sequence of str) – The indices of gate to join to the old inds, must be the same length as inds.

  • gate_inds_outer (sequence of str) – The indices of gate to make the new outer inds, must be the same length as inds.

Returns:

tn_gated

Return type:

TensorNetwork

gate_inds_with_tn_[source]
_compute_tree_gauges(tree, outputs)[source]

Given a tree of connected tensors, absorb the gauges from outside inwards, finally outputing the gauges associated with the outputs.

Parameters:
  • tree (sequence of (tid_outer, tid_inner, distance)) – The tree of connected tensors, see get_tree_span().

  • outputs (sequence of (tid, ind)) – Each output is specified by a tensor id and an index, such that having absorbed all gauges in the tree, the effective reduced factor of the tensor with respect to the index is returned.

Returns:

Gouts – The effective reduced factors of the tensor index pairs specified in outputs, each a matrix.

Return type:

sequence of array

_compress_between_virtual_tree_tids(tidl, tidr, max_bond, cutoff, r, absorb='both', include=None, exclude=None, span_opts=None, **compress_opts)[source]
_compute_bond_env(tid1, tid2, select_local_distance=None, select_local_opts=None, max_bond=None, cutoff=None, method='contract_around', contract_around_opts=None, contract_compressed_opts=None, optimize='auto-hq', include=None, exclude=None)[source]

Compute the local tensor environment of the bond(s), if cut, between two tensors.

_compress_between_full_bond_tids(tid1, tid2, max_bond, cutoff=0.0, absorb='both', renorm=False, method='eigh', select_local_distance=None, select_local_opts=None, env_max_bond='max_bond', env_cutoff='cutoff', env_method='contract_around', contract_around_opts=None, contract_compressed_opts=None, env_optimize='auto-hq', include=None, exclude=None)[source]
_compress_between_local_fit(tid1, tid2, max_bond, cutoff=0.0, absorb='both', method='als', select_local_distance=1, select_local_opts=None, include=None, exclude=None, **fit_opts)[source]
_compress_between_tids(tid1, tid2, max_bond=None, cutoff=1e-10, absorb='both', canonize_distance=None, canonize_opts=None, canonize_after_distance=None, canonize_after_opts=None, mode='basic', equalize_norms=False, gauges=None, gauge_smudge=1e-06, callback=None, **compress_opts)[source]
compress_between(tags1, tags2, max_bond=None, cutoff=1e-10, absorb='both', canonize_distance=0, canonize_opts=None, equalize_norms=False, **compress_opts)[source]

Compress the bond between the two single tensors in this network specified by tags1 and tags2 using tensor_compress_bond():

  |    |    |    |           |    |    |    |
==●====●====●====●==       ==●====●====●====●==
 /|   /|   /|   /|          /|   /|   /|   /|
  |    |    |    |           |    |    |    |
==●====1====2====●==  ==>  ==●====L----R====●==
 /|   /|   /|   /|          /|   /|   /|   /|
  |    |    |    |           |    |    |    |
==●====●====●====●==       ==●====●====●====●==
 /|   /|   /|   /|          /|   /|   /|   /|

This is an inplace operation. The compression is unlikely to be optimal with respect to the frobenius norm, unless the TN is already canonicalized at the two tensors. The absorb kwarg can be specified to yield an isometry on either the left or right resulting tensors.

Parameters:
  • tags1 – Tags uniquely identifying the first (‘left’) tensor.

  • tags2 (str or sequence of str) – Tags uniquely identifying the second (‘right’) tensor.

  • max_bond (int or None, optional) – The maxmimum bond dimension.

  • cutoff (float, optional) – The singular value cutoff to use.

  • canonize_distance (int, optional) – How far to locally canonize around the target tensors first.

  • canonize_opts (None or dict, optional) – Other options for the local canonization.

  • equalize_norms (bool or float, optional) – If set, rescale the norms of all tensors modified to this value, stripping the rescaling factor into the exponent attribute.

  • compress_opts – Supplied to tensor_compress_bond().

See also

canonize_between

compress_all(max_bond=None, cutoff=1e-10, canonize=True, tree_gauge_distance=None, canonize_distance=None, canonize_after_distance=None, mode='auto', inplace=False, **compress_opts)[source]

Compress all bonds one by one in this network.

Parameters:
  • max_bond (int or None, optional) – The maxmimum bond dimension to compress to.

  • cutoff (float, optional) – The singular value cutoff to use.

  • tree_gauge_distance (int, optional) – How far to include local tree gauge information when compressing. If the local geometry is a tree, then each compression will be locally optimal up to this distance.

  • canonize_distance (int, optional) – How far to locally canonize around the target tensors first, this is set automatically by tree_gauge_distance if not specified.

  • canonize_after_distance (int, optional) – How far to locally canonize around the target tensors after, this is set automatically by tree_gauge_distance, depending on mode if not specified.

  • mode ({'auto', 'basic', 'virtual-tree'}, optional) – The mode to use for compressing the bonds. If ‘auto’, will use ‘basic’ if tree_gauge_distance == 0 else ‘virtual-tree’.

  • inplace (bool, optional) – Whether to perform the compression inplace.

  • compress_opts – Supplied to compress_between().

Return type:

TensorNetwork

See also

compress_between, canonize_all

compress_all_[source]
compress_all_tree(inplace=False, **compress_opts)[source]

Canonically compress this tensor network, assuming it to be a tree. This generates a tree spanning out from the most central tensor, then compresses all bonds inwards in a depth-first manner, using an infinite canonize_distance to shift the orthogonality center.

compress_all_tree_[source]
compress_all_1d(max_bond=None, cutoff=1e-10, canonize=True, inplace=False, **compress_opts)[source]

Compress a tensor network that you know has a 1D topology, this proceeds by generating a spanning ‘tree’ from around the least central tensor, then optionally canonicalizing all bonds outwards and compressing inwards.

Parameters:
  • max_bond (int, optional) – The maximum bond dimension to compress to.

  • cutoff (float, optional) – The singular value cutoff to use.

  • canonize (bool, optional) – Whether to canonize all bonds outwards first.

  • inplace (bool, optional) – Whether to perform the compression inplace.

  • compress_opts – Supplied to tensor_compress_bond().

Return type:

TensorNetwork

compress_all_1d_[source]
compress_all_simple(max_bond=None, cutoff=1e-10, gauges=None, max_iterations=5, tol=0.0, smudge=1e-12, power=1.0, inplace=False, **gauge_simple_opts)[source]
compress_all_simple_[source]
_canonize_between_tids(tid1, tid2, absorb='right', gauges=None, gauge_smudge=1e-06, equalize_norms=False, **canonize_opts)[source]
canonize_between(tags1, tags2, absorb='right', **canonize_opts)[source]

‘Canonize’ the bond between the two single tensors in this network specified by tags1 and tags2 using tensor_canonize_bond:

  |    |    |    |           |    |    |    |
--●----●----●----●--       --●----●----●----●--
 /|   /|   /|   /|          /|   /|   /|   /|
  |    |    |    |           |    |    |    |
--●----1----2----●--  ==>  --●---->~~~~R----●--
 /|   /|   /|   /|          /|   /|   /|   /|
  |    |    |    |           |    |    |    |
--●----●----●----●--       --●----●----●----●--
 /|   /|   /|   /|          /|   /|   /|   /|

This is an inplace operation. This can only be used to put a TN into truly canonical form if the geometry is a tree, such as an MPS.

Parameters:
  • tags1 – Tags uniquely identifying the first (‘left’) tensor, which will become an isometry.

  • tags2 (str or sequence of str) – Tags uniquely identifying the second (‘right’) tensor.

  • absorb ({'left', 'both', 'right'}, optional) – Which side of the bond to absorb the non-isometric operator.

  • canonize_opts – Supplied to tensor_canonize_bond().

See also

compress_between

reduce_inds_onto_bond(inda, indb, tags=None, drop_tags=False, combine=True, ndim_cutoff=3)[source]

Use QR factorization to ‘pull’ the indices inda and indb off of their respective tensors and onto the bond between them. This is an inplace operation.

_get_neighbor_tids(tids, exclude_inds=())[source]

Get the tids of tensors connected to the tensor(s) at tids.

Parameters:
  • tids (int or sequence of int) – The tensor identifier(s) to get the neighbors of.

  • exclude_inds (sequence of str, optional) – Exclude these indices from being considered as connections.

Return type:

oset[int]

_get_neighbor_inds(inds)[source]

Get the indices connected to the index(es) at inds.

Parameters:

inds (str or sequence of str) – The index(es) to get the neighbors of.

Return type:

oset[str]

_get_subgraph_tids(tids)[source]

Get the tids of tensors connected, by any distance, to the tensor or region of tensors tids.

_ind_to_subgraph_tids(ind)[source]

Get the tids of tensors connected, by any distance, to the index ind.

istree()[source]

Check if this tensor network has a tree structure, (treating multibonds as a single edge).

Examples

>>> MPS_rand_state(10, 7).istree()
True
>>> MPS_rand_state(10, 7, cyclic=True).istree()
False
isconnected()[source]

Check whether this tensor network is connected, i.e. whether there is a path between any two tensors, (including size 1 indices).

subgraphs(virtual=False)[source]

Split this tensor network into disconneceted subgraphs.

Parameters:

virtual (bool, optional) – Whether the tensor networks should view the original tensors or not - by default take copies.

Return type:

list[TensorNetwork]

get_tree_span(tids, min_distance=0, max_distance=None, include=None, exclude=None, ndim_sort='max', distance_sort='min', sorter=None, weight_bonds=True, inwards=True)[source]

Generate a tree on the tensor network graph, fanning out from the tensors identified by tids, up to a maximum of max_distance away. The tree can be visualized with draw_tree_span().

Parameters:
  • tids (sequence of str) – The nodes that define the region to span out of.

  • min_distance (int, optional) – Don’t add edges to the tree until this far from the region. For example, 1 will not include the last merges from neighboring tensors in the region defined by tids.

  • max_distance (None or int, optional) – Terminate branches once they reach this far away. If None there is no limit,

  • include (sequence of str, optional) – If specified, only tids specified here can be part of the tree.

  • exclude (sequence of str, optional) – If specified, tids specified here cannot be part of the tree.

  • ndim_sort ({'min', 'max', 'none'}, optional) – When expanding the tree, how to choose what nodes to expand to next, once connectivity to the current surface has been taken into account.

  • distance_sort ({'min', 'max', 'none'}, optional) – When expanding the tree, how to choose what nodes to expand to next, once connectivity to the current surface has been taken into account.

  • weight_bonds (bool, optional) – Whether to weight the ‘connection’ of a candidate tensor to expand out to using bond size as well as number of bonds.

Returns:

The ordered list of merges, each given as tuple (tid1, tid2, d) indicating merge tid1 -> tid2 at distance d.

Return type:

list[(str, str, int)]

See also

draw_tree_span

_draw_tree_span_tids(tids, span=None, min_distance=0, max_distance=None, include=None, exclude=None, ndim_sort='max', distance_sort='min', sorter=None, weight_bonds=True, color='order', colormap='Spectral', **draw_opts)[source]
draw_tree_span(tags, which='all', min_distance=0, max_distance=None, include=None, exclude=None, ndim_sort='max', distance_sort='min', weight_bonds=True, color='order', colormap='Spectral', **draw_opts)[source]

Visualize a generated tree span out of the tensors tagged by tags.

Parameters:
  • tags (str or sequence of str) – Tags specifiying a region of tensors to span out of.

  • which ({'all', 'any': '!all', '!any'}, optional) – How to select tensors based on the tags.

  • min_distance (int, optional) – See get_tree_span().

  • max_distance (None or int, optional) – See get_tree_span().

  • include (sequence of str, optional) – See get_tree_span().

  • exclude (sequence of str, optional) – See get_tree_span().

  • distance_sort ({'min', 'max'}, optional) – See get_tree_span().

  • color ({'order', 'distance'}, optional) – Whether to color nodes based on the order of the contraction or the graph distance from the specified region.

  • colormap (str) – The name of a matplotlib colormap to use.

See also

get_tree_span

graph_tree_span[source]
_canonize_around_tids(tids, min_distance=0, max_distance=None, include=None, exclude=None, span_opts=None, absorb='right', gauge_links=False, link_absorb='both', inwards=True, gauges=None, gauge_smudge=1e-06, **canonize_opts)[source]
canonize_around(tags, which='all', min_distance=0, max_distance=None, include=None, exclude=None, span_opts=None, absorb='right', gauge_links=False, link_absorb='both', equalize_norms=False, inplace=False, **canonize_opts)[source]

Expand a locally canonical region around tags:

          --●---●--
        |   |   |   |
      --●---v---v---●--
    |   |   |   |   |   |
  --●--->---v---v---<---●--
|   |   |   |   |   |   |   |
●--->--->---O---O---<---<---●
|   |   |   |   |   |   |   |
  --●--->---^---^---^---●--
    |   |   |   |   |   |
      --●---^---^---●--
        |   |   |   |
          --●---●--

                 <=====>
                 max_distance = 2 e.g.

Shown on a grid here but applicable to arbitrary geometry. This is a way of gauging a tensor network that results in a canonical form if the geometry is described by a tree (e.g. an MPS or TTN). The canonizations proceed inwards via QR decompositions.

The sequence generated by round-robin expanding the boundary of the originally specified tensors - it will only be unique for trees.

Parameters:
  • tags (str, or sequence or str) – Tags defining which set of tensors to locally canonize around.

  • which ({'all', 'any', '!all', '!any'}, optional) – How select the tensors based on tags.

  • min_distance (int, optional) – How close, in terms of graph distance, to canonize tensors away. See get_tree_span().

  • max_distance (None or int, optional) – How far, in terms of graph distance, to canonize tensors away. See get_tree_span().

  • include (sequence of str, optional) – How to build the spanning tree to canonize along. See get_tree_span().

  • exclude (sequence of str, optional) – How to build the spanning tree to canonize along. See get_tree_span().

  • {'min' (distance_sort) – How to build the spanning tree to canonize along. See get_tree_span().

  • 'max'} – How to build the spanning tree to canonize along. See get_tree_span().

  • optional – How to build the spanning tree to canonize along. See get_tree_span().

  • absorb ({'right', 'left', 'both'}, optional) – As we canonize inwards from tensor A to tensor B which to absorb the singular values into.

  • gauge_links (bool, optional) – Whether to gauge the links between branches of the spanning tree generated (in a Simple Update like fashion).

  • link_absorb ({'both', 'right', 'left'}, optional) – If performing the link gauging, how to absorb the singular values.

  • equalize_norms (bool or float, optional) – Scale the norms of tensors acted on to this value, accumulating the log10 scaled factors in self.exponent.

  • inplace (bool, optional) – Whether to perform the canonization inplace.

Return type:

TensorNetwork

See also

get_tree_span

canonize_around_[source]
gauge_all_canonize(max_iterations=5, absorb='both', gauges=None, gauge_smudge=1e-06, equalize_norms=False, inplace=False, **canonize_opts)[source]

Iterative gauge all the bonds in this tensor network with a basic ‘canonization’ strategy.

gauge_all_canonize_[source]
gauge_all_simple(max_iterations=5, tol=0.0, smudge=1e-12, power=1.0, gauges=None, equalize_norms=False, progbar=False, inplace=False)[source]

Iterative gauge all the bonds in this tensor network with a ‘simple update’ like strategy.

gauge_all_simple_[source]
gauge_all_random(max_iterations=1, unitary=True, seed=None, inplace=False)[source]

Gauge all the bonds in this network randomly. This is largely for testing purposes.

gauge_all_random_[source]
gauge_all(method='canonize', **gauge_opts)[source]

Gauge all bonds in this network using one of several strategies.

Parameters:
  • method (str, optional) – The method to use for gauging. One of “canonize”, “simple”, or “random”. Default is “canonize”.

  • gauge_opts (dict, optional) – Additional keyword arguments to pass to the chosen method.

gauge_all_[source]
_gauge_local_tids(tids, max_distance=1, max_iterations='max_distance', method='canonize', inwards=False, include=None, exclude=None, **gauge_local_opts)[source]

Iteratively gauge all bonds in the local tensor network defined by tids according to one of several strategies.

gauge_local(tags, which='all', max_distance=1, max_iterations='max_distance', method='canonize', inplace=False, **gauge_local_opts)[source]

Iteratively gauge all bonds in the tagged sub tensor network according to one of several strategies.

gauge_local_[source]
gauge_simple_insert(gauges, remove=False, smudge=0.0, power=1.0)[source]

Insert the simple update style bond gauges found in gauges if they are present in this tensor network. The gauges inserted are also returned so that they can be removed later.

Parameters:
  • gauges (dict[str, array_like]) – The store of bond gauges, the keys being indices and the values being the vectors. Only bonds present in this dictionary will be gauged.

  • remove (bool, optional) – Whether to remove the gauges from the store after inserting them.

  • smudge (float, optional) – A small value to add to the gauge vectors to avoid singularities.

Returns:

  • outer (list[(Tensor, str, array_like)]) – The sequence of gauges applied to outer indices, each a tuple of the tensor, the index and the gauge vector.

  • inner (list[((Tensor, Tensor), str, array_like)]) – The sequence of gauges applied to inner indices, each a tuple of the two inner tensors, the inner bond and the gauge vector applied.

static gauge_simple_remove(outer=None, inner=None)[source]

Remove the simple update style bond gauges inserted by gauge_simple_insert.

gauge_simple_temp(gauges, smudge=1e-12, ungauge_outer=True, ungauge_inner=True)[source]

Context manager that temporarily inserts simple update style bond gauges into this tensor network, before optionally ungauging them.

Parameters:
  • self (TensorNetwork) – The TensorNetwork to be gauge-bonded.

  • gauges (dict[str, array_like]) – The store of gauge bonds, the keys being indices and the values being the vectors. Only bonds present in this dictionary will be gauged.

  • ungauge_outer (bool, optional) – Whether to ungauge the outer bonds.

  • ungauge_inner (bool, optional) – Whether to ungauge the inner bonds.

Yields:
  • outer (list[(Tensor, int, array_like)]) – The tensors, indices and gauges that were performed on outer indices.

  • inner (list[((Tensor, Tensor), int, array_like)]) – The tensors, indices and gauges that were performed on inner bonds.

Examples

>>> tn = TN_rand_reg(10, 4, 3)
>>> tn ^ all
-51371.66630218866
>>> gauges = {}
>>> tn.gauge_all_simple_(gauges=gauges)
>>> len(gauges)
20
>>> tn ^ all
28702551.673767876
>>> with gauged_bonds(tn, gauges):
...     # temporarily insert gauges
...     print(tn ^ all)
-51371.66630218887
>>> tn ^ all
28702551.67376789
_contract_compressed_tid_sequence(seq, max_bond=None, cutoff=1e-10, output_inds=None, tree_gauge_distance=1, canonize_distance=None, canonize_opts=None, canonize_after_distance=None, canonize_after_opts=None, gauge_boundary_only=True, compress_opts=None, compress_late=True, compress_mode='auto', compress_min_size=None, compress_span=False, compress_matrices=True, compress_exclude=None, equalize_norms=False, gauges=None, gauge_smudge=1e-06, callback_pre_contract=None, callback_post_contract=None, callback_pre_compress=None, callback_post_compress=None, callback=None, preserve_tensor=False, progbar=False, inplace=False)[source]
_contract_around_tids(tids, seq=None, min_distance=0, max_distance=None, span_opts=None, max_bond=None, cutoff=1e-10, canonize_opts=None, **kwargs)[source]

Contract around tids, by following a greedily generated spanning tree, and compressing whenever two tensors in the outer ‘boundary’ share more than one index.

compute_centralities()[source]
most_central_tid()[source]
least_central_tid()[source]
contract_around_center(**opts)[source]
contract_around_corner(**opts)[source]
contract_around(tags, which='all', min_distance=0, max_distance=None, span_opts=None, max_bond=None, cutoff=1e-10, tree_gauge_distance=1, canonize_distance=None, canonize_opts=None, canonize_after_distance=None, canonize_after_opts=None, gauge_boundary_only=True, compress_late=True, compress_min_size=None, compress_opts=None, compress_span=False, compress_matrices=True, equalize_norms=False, gauges=None, gauge_smudge=1e-06, callback_pre_contract=None, callback_post_contract=None, callback_pre_compress=None, callback_post_compress=None, callback=None, inplace=False, **kwargs)[source]

Perform a compressed contraction inwards towards the tensors identified by tags.

contract_around_[source]
contract_compressed(optimize, output_inds=None, max_bond=None, cutoff=1e-10, tree_gauge_distance=1, canonize_distance=None, canonize_opts=None, canonize_after_distance=None, canonize_after_opts=None, gauge_boundary_only=True, compress_late=True, compress_min_size=None, compress_opts=None, compress_span=True, compress_matrices=True, compress_exclude=None, equalize_norms=False, gauges=None, gauge_smudge=1e-06, callback_pre_contract=None, callback_post_contract=None, callback_pre_compress=None, callback_post_compress=None, callback=None, progbar=False, **kwargs)[source]
contract_compressed_[source]
new_bond(tags1, tags2, **opts)[source]

Inplace addition of a dummmy (size 1) bond between the single tensors specified by by tags1 and tags2.

Parameters:
  • tags1 (sequence of str) – Tags identifying the first tensor.

  • tags2 (sequence of str) – Tags identifying the second tensor.

  • opts – Supplied to new_bond().

See also

new_bond

_cut_between_tids(tid1, tid2, left_ind, right_ind)[source]
cut_between(left_tags, right_tags, left_ind, right_ind)[source]

Cut the bond between the tensors specified by left_tags and right_tags, giving them the new inds left_ind and right_ind respectively.

cut_bond(bond, new_left_ind=None, new_right_ind=None)[source]

Cut the bond index specified by bond between the tensors it connects. Use cut_between for control over which tensor gets which new index new_left_ind or new_right_ind. The index must connect exactly two tensors.

Parameters:
  • bond (str) – The index to cut.

  • new_left_ind (str, optional) – The new index to give to the left tensor (lowest tid value).

  • new_right_ind (str, optional) – The new index to give to the right tensor (highest tid value).

drape_bond_between(tagsa, tagsb, tags_target, left_ind=None, right_ind=None, inplace=False)[source]

Take the bond(s) connecting the tensors tagged at tagsa and tagsb, and ‘drape’ it through the tensor tagged at tags_target, effectively adding an identity tensor between the two and contracting it with the third:

 ┌─┐    ┌─┐      ┌─┐     ┌─┐
─┤A├─Id─┤B├─    ─┤A├─┐ ┌─┤B├─
 └─┘    └─┘      └─┘ │ │ └─┘
             left_ind│ │right_ind
     ┌─┐     -->     ├─┤
    ─┤C├─           ─┤D├─
     └┬┘             └┬┘     where D = C ⊗ Id
      │               │

This increases the size of the target tensor by d**2, and disconnects the tensors at tagsa and tagsb.

Parameters:
  • tagsa (str or sequence of str) – The tag(s) identifying the first tensor.

  • tagsb (str or sequence of str) – The tag(s) identifying the second tensor.

  • tags_target (str or sequence of str) – The tag(s) identifying the target tensor.

  • left_ind (str, optional) – The new index to give to the left tensor.

  • right_ind (str, optional) – The new index to give to the right tensor.

  • inplace (bool, optional) – Whether to perform the draping inplace.

Return type:

TensorNetwork

drape_bond_between_[source]
isel(selectors, inplace=False)[source]

Select specific values for some dimensions/indices of this tensor network, thereby removing them.

Parameters:
  • selectors (dict[str, int]) – Mapping of index(es) to which value to take.

  • inplace (bool, optional) – Whether to select inplace or not.

Return type:

TensorNetwork

See also

Tensor.isel

isel_[source]
sum_reduce(ind, inplace=False)[source]

Sum over the index ind of this tensor network, removing it. This is like contracting a vector of ones in, or marginalizing a classical probability distribution.

Parameters:
  • ind (str) – The index to sum over.

  • inplace (bool, optional) – Whether to perform the reduction inplace.

sum_reduce_[source]
vector_reduce(ind, v, inplace=False)[source]

Contract the vector v with the index ind of this tensor network, removing it.

Parameters:
  • ind (str) – The index to contract.

  • v (array_like) – The vector to contract with.

  • inplace (bool, optional) – Whether to perform the reduction inplace.

Return type:

TensorNetwork

vector_reduce_[source]
cut_iter(*inds)[source]

Cut and iterate over one or more indices in this tensor network. Each network yielded will have that index removed, and the sum of all networks will equal the original network. This works by iterating over the product of all combinations of each bond supplied to isel. As such, the number of networks produced is exponential in the number of bonds cut.

Parameters:

inds (sequence of str) – The bonds to cut.

Yields:

TensorNetwork

Examples

Here we’ll cut the two extra bonds of a cyclic MPS and sum the contraction of the resulting 49 OBC MPS norms:

>>> psi = MPS_rand_state(10, bond_dim=7, cyclic=True)
>>> norm = psi.H & psi
>>> bnds = bonds(norm[0], norm[-1])
>>> sum(tn ^ all for tn in norm.cut_iter(*bnds))
1.0
insert_operator(A, where1, where2, tags=None, inplace=False)[source]

Insert an operator on the bond between the specified tensors, e.g.:

  |   |              |   |
--1---2--    ->    --1-A-2--
  |                  |
Parameters:
  • A (array) – The operator to insert.

  • where1 (str, sequence of str, or int) – The tags defining the ‘left’ tensor.

  • where2 (str, sequence of str, or int) – The tags defining the ‘right’ tensor.

  • tags (str or sequence of str) – Tags to add to the new operator’s tensor.

  • inplace (bool, optional) – Whether to perform the insertion inplace.

insert_operator_[source]
_insert_gauge_tids(U, tid1, tid2, Uinv=None, tol=1e-10, bond=None)[source]
insert_gauge(U, where1, where2, Uinv=None, tol=1e-10)[source]

Insert the gauge transformation U^-1 @ U into the bond between the tensors, T1 and T2, defined by where1 and where2. The resulting tensors at those locations will be T1 @ U^-1 and U @ T2.

Parameters:
  • U (array) – The gauge to insert.

  • where1 (str, sequence of str, or int) – Tags defining the location of the ‘left’ tensor.

  • where2 (str, sequence of str, or int) – Tags defining the location of the ‘right’ tensor.

  • Uinv (array) – The inverse gauge, U @ Uinv == Uinv @ U == eye, to insert. If not given will be calculated using numpy.linalg.inv().

contract_tags(tags, which='any', output_inds=None, optimize=None, get=None, backend=None, preserve_tensor=False, inplace=False, **contract_opts)[source]

Contract the tensors that match any or all of tags.

Parameters:
  • tags (sequence of str) – The list of tags to filter the tensors by. Use all or ... (Ellipsis) to contract all tensors.

  • which ({'all', 'any'}) – Whether to require matching all or any of the tags.

  • output_inds (sequence of str, optional) – The indices to specify as outputs of the contraction. If not given, and the tensor network has no hyper-indices, these are computed automatically as every index appearing once.

  • optimize ({None, str, path_like, PathOptimizer}, optional) –

    The contraction path optimization strategy to use.

    • None: use the default strategy,

    • str: use the preset strategy with the given name,

    • path_like: use this exact path,

    • cotengra.HyperOptimizer: find the contraction using this optimizer, supports slicing,

    • cotengra.ContractionTree: use this exact tree, supports

    slicing, - opt_einsum.PathOptimizer: find the path using this

    optimizer.

    Contraction with cotengra might be a bit more efficient but the main reason would be to handle sliced contraction automatically.

  • get (str, optional) –

    What to return. If:

    • None (the default) - return the resulting scalar or Tensor.

    • 'expression' - return a callbable expression that performs the contraction and operates on the raw arrays.

    • 'tree' - return the cotengra.ContractionTree describing the contraction.

    • 'path' - return the raw ‘path’ as a list of tuples.

    • 'symbol-map' - return the dict mapping indices to ‘symbols’ (single unicode letters) used internally by cotengra

    • 'path-info' - return the opt_einsum.PathInfo path object with detailed information such as flop cost. The symbol-map is also added to the quimb_symbol_map attribute.

  • backend ({'auto', 'numpy', 'jax', 'cupy', 'tensorflow', ...}, optional) – Which backend to use to perform the contraction. Supplied to cotengra.

  • preserve_tensor (bool, optional) – Whether to return a tensor regardless of whether the output object is a scalar (has no indices) or not.

  • inplace (bool, optional) – Whether to perform the contraction inplace.

  • contract_opts – Passed to tensor_contract().

Returns:

The result of the contraction, still a TensorNetwork if the contraction was only partial.

Return type:

TensorNetwork, Tensor or scalar

contract_tags_[source]
contract(tags=..., output_inds=None, optimize=None, get=None, backend=None, preserve_tensor=False, max_bond=None, inplace=False, **opts)[source]

Contract some, or all, of the tensors in this network. This method dispatches to contract_tags, contract_structured, or contract_compressed based on the various arguments.

Parameters:
  • tags (sequence of str, all, or Ellipsis, optional) – Any tensors with any of these tags with be contracted. Use all or ... (Ellipsis) to contract all tensors. ... will try and use a ‘structured’ contract method if possible.

  • output_inds (sequence of str, optional) – The indices to specify as outputs of the contraction. If not given, and the tensor network has no hyper-indices, these are computed automatically as every index appearing once.

  • optimize ({None, str, path_like, PathOptimizer}, optional) –

    The contraction path optimization strategy to use.

    • None: use the default strategy,

    • str: use the preset strategy with the given name,

    • path_like: use this exact path,

    • cotengra.HyperOptimizer: find the contraction using this optimizer, supports slicing,

    • cotengra.ContractionTree: use this exact tree, supports slicing,

    • opt_einsum.PathOptimizer: find the path using this optimizer.

    Contraction with cotengra might be a bit more efficient but the main reason would be to handle sliced contraction automatically.

  • get (str, optional) –

    What to return. If:

    • None (the default) - return the resulting scalar or Tensor.

    • 'expression' - return a callbable expression that performs the contraction and operates on the raw arrays.

    • 'tree' - return the cotengra.ContractionTree describing the contraction.

    • 'path' - return the raw ‘path’ as a list of tuples.

    • 'symbol-map' - return the dict mapping indices to ‘symbols’ (single unicode letters) used internally by cotengra

    • 'path-info' - return the opt_einsum.PathInfo path object with detailed information such as flop cost. The symbol-map is also added to the quimb_symbol_map attribute.

  • backend ({'auto', 'numpy', 'jax', 'cupy', 'tensorflow', ...}, optional) – Which backend to use to perform the contraction. Supplied to cotengra.

  • preserve_tensor (bool, optional) – Whether to return a tensor regardless of whether the output object is a scalar (has no indices) or not.

  • inplace (bool, optional) – Whether to perform the contraction inplace. This is only valid if not all tensors are contracted (which doesn’t produce a TN).

  • opts – Passed to tensor_contract(), contract_compressed() .

Returns:

The result of the contraction, still a TensorNetwork if the contraction was only partial.

Return type:

TensorNetwork, Tensor or scalar

contract_[source]
contract_cumulative(tags_seq, output_inds=None, preserve_tensor=False, equalize_norms=False, inplace=False, **opts)[source]

Cumulative contraction of tensor network. Contract the first set of tags, then that set with the next set, then both of those with the next and so forth. Could also be described as an manually ordered contraction of all tags in tags_seq.

Parameters:
  • tags_seq (sequence of sequence of str) – The list of tag-groups to cumulatively contract.

  • output_inds (sequence of str, optional) – The indices to specify as outputs of the contraction. If not given, and the tensor network has no hyper-indices, these are computed automatically as every index appearing once.

  • preserve_tensor (bool, optional) – Whether to return a tensor regardless of whether the output object is a scalar (has no indices) or not.

  • inplace (bool, optional) – Whether to perform the contraction inplace.

  • opts – Passed to tensor_contract().

Returns:

The result of the contraction, still a TensorNetwork if the contraction was only partial.

Return type:

TensorNetwork, Tensor or scalar

contraction_path(optimize=None, **contract_opts)[source]

Compute the contraction path, a sequence of (int, int), for the contraction of this entire tensor network using path optimizer optimize.

contraction_info(optimize=None, **contract_opts)[source]

Compute the opt_einsum.PathInfo object decsribing the contraction of this entire tensor network using path optimizer optimize.

contraction_tree(optimize=None, output_inds=None, **kwargs)[source]

Return the cotengra.ContractionTree corresponding to contracting this entire tensor network with path finder optimize.

contraction_width(optimize=None, **contract_opts)[source]

Compute the ‘contraction width’ of this tensor network. This is defined as log2 of the maximum tensor size produced during the contraction sequence. If every index in the network has dimension 2 this corresponds to the maximum rank tensor produced.

contraction_cost(optimize=None, **contract_opts)[source]

Compute the ‘contraction cost’ of this tensor network. This is defined as log10 of the total number of scalar operations during the contraction sequence.

__rshift__(tags_seq)[source]

Overload of ‘>>’ for TensorNetwork.contract_cumulative.

__irshift__(tags_seq)[source]

Overload of ‘>>=’ for inplace TensorNetwork.contract_cumulative.

__xor__(tags)[source]

Overload of ‘^’ for TensorNetwork.contract.

__ixor__(tags)[source]

Overload of ‘^=’ for inplace TensorNetwork.contract.

__matmul__(other)[source]

Overload “@” to mean full contraction with another network.

as_network(virtual=True)[source]

Matching method (for ensuring object is a tensor network) to as_network(), which simply returns self if virtual=True.

aslinearoperator(left_inds, right_inds, ldims=None, rdims=None, backend=None, optimize=None)[source]

View this TensorNetwork as a TNLinearOperator.

split(left_inds, right_inds=None, **split_opts)[source]

Decompose this tensor network across a bipartition of outer indices.

This method matches Tensor.split by converting to a TNLinearOperator first. Note unless an iterative method is passed to method, the full dense tensor will be contracted.

trace(left_inds, right_inds, **contract_opts)[source]

Trace over left_inds joined with right_inds

to_dense(*inds_seq, to_qarray=False, **contract_opts)[source]

Convert this network into an dense array, with a single dimension for each of inds in inds_seqs. E.g. to convert several sites into a density matrix: TN.to_dense(('k0', 'k1'), ('b0', 'b1')).

to_qarray[source]
compute_reduced_factor(side, left_inds, right_inds, optimize='auto-hq', **contract_opts)[source]

Compute either the left or right ‘reduced factor’ of this tensor network. I.e., view as an operator, X, mapping left_inds to right_inds and compute L or R such that X = U_R @ R or X = L @ U_L, with U_R and U_L unitary operators that are not computed. Only dag(X) @ X or X @ dag(X) is contracted, which is generally cheaper than contracting X itself.

Parameters:
  • self (TensorNetwork) – The tensor network to compute the reduced factor of.

  • side ({'left', 'right'}) – Whether to compute the left or right reduced factor. If ‘right’ then dag(X) @ X is contracted, otherwise X @ dag(X).

  • left_inds (sequence of str) – The indices forming the left side of the operator.

  • right_inds (sequence of str) – The indices forming the right side of the operator.

  • contract_opts (dict, optional) – Options to pass to to_dense().

Return type:

array_like

insert_compressor_between_regions(ltags, rtags, max_bond=None, cutoff=1e-10, select_which='any', insert_into=None, new_tags=None, new_ltags=None, new_rtags=None, bond_ind=None, optimize='auto-hq', inplace=False, **compress_opts)[source]

Compute and insert a pair of ‘oblique’ projection tensors (see for example https://arxiv.org/abs/1905.02351) that effectively compresses between two regions of the tensor network. Useful for various approximate contraction methods such as HOTRG and CTMRG.

Parameters:
  • ltags (sequence of str) – The tags of the tensors in the left region.

  • rtags (sequence of str) – The tags of the tensors in the right region.

  • max_bond (int or None, optional) – The maximum bond dimension to use for the compression (i.e. shared by the two projection tensors). If None then the maximum is controlled by cutoff.

  • cutoff (float, optional) – The cutoff to use for the compression.

  • select_which ({'any', 'all', 'none'}, optional) – How to select the regions based on the tags, see select().

  • insert_into (TensorNetwork, optional) – If given, insert the new tensors into this tensor network, assumed to have the same relevant indices as self.

  • new_tags (str or sequence of str, optional) – The tag(s) to add to both the new tensors.

  • new_ltags (str or sequence of str, optional) – The tag(s) to add to the new left projection tensor.

  • new_rtags (str or sequence of str, optional) – The tag(s) to add to the new right projection tensor.

  • optimize (str or PathOptimizer, optional) – How to optimize the contraction of the projection tensors.

  • inplace (bool, optional) – Whether perform the insertion in-place. If insert_into is supplied then this doesn’t matter, and that tensor network will be modified and returned.

Return type:

TensorNetwork

insert_compressor_between_regions_[source]
distance(*args, **kwargs)[source]
distance_normalized[source]
fit(tn_target, method='als', tol=1e-09, inplace=False, progbar=False, **fitting_opts)[source]

Optimize the entries of this tensor network with respect to a least squares fit of tn_target which should have the same outer indices. Depending on method this calls tensor_network_fit_als() or tensor_network_fit_autodiff(). The quantity minimized is:

\[D(A, B) = | A - B |_{\mathrm{fro}} = \mathrm{Tr} [(A - B)^{\dagger}(A - B)]^{1/2} = ( \langle A | A \rangle - 2 \mathrm{Re} \langle A | B \rangle| + \langle B | B \rangle ) ^{1/2}\]
Parameters:
  • tn_target (TensorNetwork) – The target tensor network to try and fit the current one to.

  • method ({'als', 'autodiff'}, optional) – Whether to use alternating least squares (ALS) or automatic differentiation to perform the optimization. Generally ALS is better for simple geometries, autodiff better for complex ones.

  • tol (float, optional) – The target norm distance.

  • inplace (bool, optional) – Update the current tensor network in place.

  • progbar (bool, optional) – Show a live progress bar of the fitting process.

  • fitting_opts – Supplied to either tensor_network_fit_als() or tensor_network_fit_autodiff().

Returns:

tn_opt – The optimized tensor network.

Return type:

TensorNetwork

See also

tensor_network_fit_als, tensor_network_fit_autodiff, tensor_network_distance

fit_[source]
property tags
all_inds()[source]

Return a tuple of all indices in this network.

ind_size(ind)[source]

Find the size of ind.

inds_size(inds)[source]

Return the total size of dimensions corresponding to inds.

ind_sizes()[source]

Get dict of each index mapped to its size.

inner_inds()[source]

Tuple of interior indices, assumed to be any indices that appear twice or more (this only holds generally for non-hyper tensor networks).

outer_inds()[source]

Tuple of exterior indices, assumed to be any lone indices (this only holds generally for non-hyper tensor networks).

outer_dims_inds()[source]

Get the ‘outer’ pairs of dimension and indices, i.e. as if this tensor network was fully contracted.

outer_size()[source]

Get the total size of the ‘outer’ indices, i.e. as if this tensor network was fully contracted.

get_multibonds(include=None, exclude=None)[source]

Get a dict of ‘multibonds’ in this tensor network, i.e. groups of two or more indices that appear on exactly the same tensors and thus could be fused, for example.

Parameters:
  • include (sequence of str, optional) – Only consider these indices, by default all indices.

  • exclude (sequence of str, optional) – Ignore these indices, by default the outer indices of this TN.

Returns:

A dict mapping the tuple of indices that could be fused to the tuple of tensor ids they appear on.

Return type:

dict[tuple[str], tuple[int]]

get_hyperinds(output_inds=None)[source]

Get a tuple of all ‘hyperinds’, defined as those indices which don’t appear exactly twice on either the tensors or in the ‘outer’ (i.e. output) indices.

Note the default set of ‘outer’ indices is calculated as only those indices that appear once on the tensors, so these likely need to be manually specified, otherwise, for example, an index that appears on two tensors and the output will incorrectly be identified as non-hyper.

Parameters:

output_inds (None, str or sequence of str, optional) – The outer or output index or indices. If not specified then taken as every index that appears only once on the tensors (and thus non-hyper).

Returns:

The tensor network hyperinds.

Return type:

tuple[str]

compute_contracted_inds(*tids, output_inds=None)[source]

Get the indices describing the tensor contraction of tensors corresponding to tids.

squeeze(fuse=False, include=None, exclude=None, inplace=False)[source]

Drop singlet bonds and dimensions from this tensor network. If fuse=True also fuse all multibonds between tensors.

Parameters:
  • fuse (bool, optional) – Whether to fuse multibonds between tensors as well as squeezing.

  • include (sequence of str, optional) – Only squeeze these indices, by default all indices.

  • exclude (sequence of str, optional) – Ignore these indices, by default the outer indices of this TN.

  • inplace (bool, optional) – Whether to perform the squeeze and optional fuse inplace.

Return type:

TensorNetwork

squeeze_[source]
isometrize(method='qr', allow_no_left_inds=False, inplace=False)[source]

Project every tensor in this network into an isometric form, assuming they have left_inds marked.

Parameters:
  • method (str, optional) –

    The method used to generate the isometry. The options are:

    • ”qr”: use the Q factor of the QR decomposition of x with the constraint that the diagonal of R is positive.

    • ”svd”: uses U @ VH of the SVD decomposition of x. This is useful for finding the ‘closest’ isometric matrix to x, such as when it has been expanded with noise etc. But is less stable for differentiation / optimization.

    • ”exp”: use the matrix exponential of x - dag(x), first completing x with zeros if it is rectangular. This is a good parametrization for optimization, but more expensive for non-square x.

    • ”cayley”: use the Cayley transform of x - dag(x), first completing x with zeros if it is rectangular. This is a good parametrization for optimization (one the few compatible with HIPS/autograd e.g.), but more expensive for non-square x.

    • ”householder”: use the Householder reflection method directly. This requires that the backend implements “linalg.householder_product”.

    • ”torch_householder”: use the Householder reflection method directly, using the torch_householder package. This requires that the package is installed and that the backend is "torch". This is generally the best parametrizing method for “torch” if available.

    • ”mgs”: use a python implementation of the modified Gram Schmidt method directly. This is slow if not compiled but a useful reference.

    Not all backends support all methods or differentiating through all methods.

  • allow_no_left_inds (bool, optional) – If True then allow tensors with no left_inds to be left alone, rather than raising an error.

  • inplace (bool, optional) – If True then perform the operation in-place.

Return type:

TensorNetwork

isometrize_[source]
unitize[source]
unitize_
randomize(dtype=None, seed=None, inplace=False, **randn_opts)[source]

Randomize every tensor in this TN - see quimb.tensor.tensor_core.Tensor.randomize().

Parameters:
  • dtype ({None, str}, optional) – The data type of the random entries. If left as the default None, then the data type of the current array will be used.

  • seed (None or int, optional) – Seed for the random number generator.

  • inplace (bool, optional) – Whether to perform the randomization inplace, by default False.

  • randn_opts – Supplied to randn().

Return type:

TensorNetwork

randomize_[source]
strip_exponent(tid_or_tensor, value=None)[source]

Scale the elements of tensor corresponding to tid so that the norm of the array is some value, which defaults to 1. The log of the scaling factor, base 10, is then accumulated in the exponent attribute.

Parameters:
  • tid (str or Tensor) – The tensor identifier or actual tensor.

  • value (None or float, optional) – The value to scale the norm of the tensor to.

distribute_exponent()[source]

Distribute the exponent p of this tensor network (i.e. corresponding to tn * 10**p) equally among all tensors.

equalize_norms(value=None, inplace=False)[source]

Make the Frobenius norm of every tensor in this TN equal without changing the overall value if value=None, or set the norm of every tensor to value by scalar multiplication only.

Parameters:
  • value (None or float, optional) – Set the norm of each tensor to this value specifically. If supplied the change in overall scaling will be accumulated in tn.exponent in the form of a base 10 power.

  • inplace (bool, optional) – Whether to perform the norm equalization inplace or not.

Return type:

TensorNetwork

equalize_norms_[source]
balance_bonds(inplace=False)[source]

Apply tensor_balance_bond() to all bonds in this tensor network.

Parameters:

inplace (bool, optional) – Whether to perform the bond balancing inplace or not.

Return type:

TensorNetwork

balance_bonds_[source]
fuse_multibonds(gauges=None, include=None, exclude=None, inplace=False)[source]

Fuse any multi-bonds (more than one index shared by the same pair of tensors) into a single bond.

Parameters:
  • gauges (None or dict[str, array_like], optional) – If supplied, also fuse the gauges contained in this dict.

  • include (sequence of str, optional) – Only consider these indices, by default all indices.

  • exclude (sequence of str, optional) – Ignore these indices, by default the outer indices of this TN.

fuse_multibonds_[source]
expand_bond_dimension(new_bond_dim, mode=None, rand_strength=None, rand_dist='normal', inds_to_expand=None, inplace=False)[source]

Increase the dimension of all or some of the bonds in this tensor network to at least new_bond_dim, optinally adding some random noise to the new entries.

Parameters:
  • new_bond_dim (int) – The minimum bond dimension to expand to, if the bond dimension is already larger than this it will be left unchanged.

  • rand_strength (float, optional) – The strength of random noise to add to the new array entries, if any. The noise is drawn from a normal distribution with standard deviation rand_strength.

  • inds_to_expand (sequence of str, optional) – The indices to expand, if not all.

  • inplace (bool, optional) – Whether to expand this tensor network in place, or return a new one.

Return type:

TensorNetwork

expand_bond_dimension_[source]
flip(inds, inplace=False)[source]

Flip the dimension corresponding to indices inds on all tensors that share it.

flip_[source]
rank_simplify(output_inds=None, equalize_norms=False, cache=None, max_combinations=500, inplace=False)[source]

Simplify this tensor network by performing contractions that don’t increase the rank of any tensors.

Parameters:
  • output_inds (sequence of str, optional) – Explicitly set which indices of the tensor network are output indices and thus should not be modified.

  • equalize_norms (bool or float) – Actively renormalize the tensors during the simplification process. Useful for very large TNs. The scaling factor will be stored as an exponent in tn.exponent.

  • cache (None or set) – Persistent cache used to mark already checked tensors.

  • inplace (bool, optional) – Whether to perform the rand reduction inplace.

Return type:

TensorNetwork

rank_simplify_[source]
diagonal_reduce(output_inds=None, atol=1e-12, cache=None, inplace=False)[source]

Find tensors with diagonal structure and collapse those axes. This will create a tensor ‘hyper’ network with indices repeated 2+ times, as such, output indices should be explicitly supplied when contracting, as they can no longer be automatically inferred. For example:

>>> tn_diag = tn.diagonal_reduce()
>>> tn_diag.contract(all, output_inds=[])
Parameters:
  • output_inds (sequence of str, optional) – Which indices to explicitly consider as outer legs of the tensor network and thus not replace. If not given, these will be taken as all the indices that appear once.

  • atol (float, optional) – When identifying diagonal tensors, the absolute tolerance with which to compare to zero with.

  • cache (None or set) – Persistent cache used to mark already checked tensors.

  • inplace – Whether to perform the diagonal reduction inplace.

  • bool – Whether to perform the diagonal reduction inplace.

  • optional – Whether to perform the diagonal reduction inplace.

Return type:

TensorNetwork

diagonal_reduce_[source]
antidiag_gauge(output_inds=None, atol=1e-12, cache=None, inplace=False)[source]

Flip the order of any bonds connected to antidiagonal tensors. Whilst this is just a gauge fixing (with the gauge being the flipped identity) it then allows diagonal_reduce to then simplify those indices.

Parameters:
  • output_inds (sequence of str, optional) – Which indices to explicitly consider as outer legs of the tensor network and thus not flip. If not given, these will be taken as all the indices that appear once.

  • atol (float, optional) – When identifying antidiagonal tensors, the absolute tolerance with which to compare to zero with.

  • cache (None or set) – Persistent cache used to mark already checked tensors.

  • inplace – Whether to perform the antidiagonal gauging inplace.

  • bool – Whether to perform the antidiagonal gauging inplace.

  • optional – Whether to perform the antidiagonal gauging inplace.

Return type:

TensorNetwork

antidiag_gauge_[source]
column_reduce(output_inds=None, atol=1e-12, cache=None, inplace=False)[source]

Find bonds on this tensor network which have tensors where all but one column (of the respective index) is non-zero, allowing the ‘cutting’ of that bond.

Parameters:
  • output_inds (sequence of str, optional) – Which indices to explicitly consider as outer legs of the tensor network and thus not slice. If not given, these will be taken as all the indices that appear once.

  • atol (float, optional) – When identifying singlet column tensors, the absolute tolerance with which to compare to zero with.

  • cache (None or set) – Persistent cache used to mark already checked tensors.

  • inplace – Whether to perform the column reductions inplace.

  • bool – Whether to perform the column reductions inplace.

  • optional – Whether to perform the column reductions inplace.

Return type:

TensorNetwork

column_reduce_[source]
split_simplify(atol=1e-12, equalize_norms=False, cache=None, inplace=False, **split_opts)[source]

Find tensors which have low rank SVD decompositions across any combination of bonds and perform them.

Parameters:
  • atol (float, optional) – Cutoff used when attempting low rank decompositions.

  • equalize_norms (bool or float) – Actively renormalize the tensors during the simplification process. Useful for very large TNs. The scaling factor will be stored as an exponent in tn.exponent.

  • cache (None or set) – Persistent cache used to mark already checked tensors.

  • inplace – Whether to perform the split simplification inplace.

  • bool – Whether to perform the split simplification inplace.

  • optional – Whether to perform the split simplification inplace.

split_simplify_[source]
gen_loops(max_loop_length=None)[source]

Generate sequences of tids that represent loops in the TN.

Parameters:

max_loop_length (None or int) – Set the maximum number of tensors that can appear in a loop. If None, wait until any loop is found and set that as the maximum length.

Yields:

tuple[int]

See also

gen_inds_loops

gen_inds_loops(max_loop_length=None)[source]

Generate all sequences of indices, up to a specified length, that represent loops in this tensor network. Unlike gen_loops this function will return the indices of the tensors in the loop rather than the tensor ids, allowing one to differentiate between e.g. a double loop and a ‘figure of eight’ loop.

Parameters:

max_loop_length (None or int) – Set the maximum number of indices that can appear in a loop. If None, wait until any loop is found and set that as the maximum length.

Yields:

tuple[str]

gen_inds_connected(max_length)[source]

Generate all index ‘patches’ of size up to max_length.

Parameters:

max_length (int) – The maximum number of indices in the patch.

Yields:

tuple[str]

See also

gen_inds_loops

_get_string_between_tids(tida, tidb)[source]
tids_are_connected(tids)[source]

Check whether nodes tids are connected.

Parameters:

tids (sequence of int) – Nodes to check.

Return type:

bool

compute_shortest_distances(tids=None, exclude_inds=())[source]

Compute the minimum graph distances between all or some nodes tids.

compute_hierarchical_linkage(tids=None, method='weighted', optimal_ordering=True, exclude_inds=())[source]
compute_hierarchical_ssa_path(tids=None, method='weighted', optimal_ordering=True, exclude_inds=(), are_sorted=False, linkage=None)[source]

Compute a hierarchical grouping of tids, as a ssa_path.

compute_hierarchical_ordering(tids=None, method='weighted', optimal_ordering=True, exclude_inds=(), linkage=None)[source]
compute_hierarchical_grouping(max_group_size, tids=None, method='weighted', optimal_ordering=True, exclude_inds=(), linkage=None)[source]

Group tids (by default, all tensors) into groups of size max_group_size or less, using a hierarchical clustering.

pair_simplify(cutoff=1e-12, output_inds=None, max_inds=10, cache=None, equalize_norms=False, max_combinations=500, inplace=False, **split_opts)[source]
pair_simplify_[source]
loop_simplify(output_inds=None, max_loop_length=None, max_inds=10, cutoff=1e-12, loops=None, cache=None, equalize_norms=False, inplace=False, **split_opts)[source]

Try and simplify this tensor network by identifying loops and checking for low-rank decompositions across groupings of the loops outer indices.

Parameters:
  • max_loop_length (None or int, optional) – Largest length of loop to search for, if not set, the size will be set to the length of the first (and shortest) loop found.

  • cutoff (float, optional) – Cutoff to use for the operator decomposition.

  • loops (None, sequence or callable) – Loops to check, or a function that generates them.

  • cache (set, optional) – For performance reasons can supply a cache for already checked loops.

  • inplace (bool, optional) – Whether to replace the loops inplace.

  • split_opts – Supplied to tensor_split().

Return type:

TensorNetwork

loop_simplify_[source]
full_simplify(seq='ADCR', output_inds=None, atol=1e-12, equalize_norms=False, cache=None, inplace=False, progbar=False, rank_simplify_opts=None, loop_simplify_opts=None, split_simplify_opts=None, custom_methods=(), split_method='svd')[source]

Perform a series of tensor network ‘simplifications’ in a loop until there is no more reduction in the number of tensors or indices. Note that apart from rank-reduction, the simplification methods make use of the non-zero structure of the tensors, and thus changes to this will potentially produce different simplifications.

Parameters:
  • seq (str, optional) –

    Which simplifications and which order to perform them in.

    • 'A' : stands for antidiag_gauge

    • 'D' : stands for diagonal_reduce

    • 'C' : stands for column_reduce

    • 'R' : stands for rank_simplify

    • 'S' : stands for split_simplify

    • 'L' : stands for loop_simplify

    If you want to keep the tensor network ‘simple’, i.e. with no hyperedges, then don’t use 'D' (moreover 'A' is redundant).

  • output_inds (sequence of str, optional) – Explicitly set which indices of the tensor network are output indices and thus should not be modified. If not specified the tensor network is assumed to be a ‘standard’ one where indices that only appear once are the output indices.

  • atol (float, optional) – The absolute tolerance when indentifying zero entries of tensors and performing low-rank decompositions.

  • equalize_norms (bool or float) – Actively renormalize the tensors during the simplification process. Useful for very large TNs. If True, the norms, in the formed of stripped exponents, will be redistributed at the end. If an actual number, the final tensors will all have this norm, and the scaling factor will be stored as a base-10 exponent in tn.exponent.

  • cache (None or set) – A persistent cache for each simplification process to mark already processed tensors.

  • progbar (bool, optional) – Show a live progress bar of the simplification process.

  • inplace (bool, optional) – Whether to perform the simplification inplace.

Return type:

TensorNetwork

full_simplify_[source]
hyperinds_resolve(mode='dense', sorter=None, output_inds=None, inplace=False)[source]

Convert this into a regular tensor network, where all indices appear at most twice, by inserting COPY tensor or tensor networks for each hyper index.

Parameters:
  • mode ({'dense', 'mps', 'tree'}, optional) – What type of COPY tensor(s) to insert.

  • sorter (None or callable, optional) – If given, a function to sort the indices that a single hyperindex will be turned into. Th function is called like tids.sort(key=sorter).

  • inplace (bool, optional) – Whether to insert the COPY tensors inplace.

Return type:

TensorNetwork

hyperinds_resolve_[source]
compress_simplify(output_inds=None, atol=1e-06, simplify_sequence_a='ADCRS', simplify_sequence_b='RPL', hyperind_resolve_mode='tree', hyperind_resolve_sort='clustering', final_resolve=False, split_method='svd', max_simplification_iterations=100, converged_tol=0.01, equalize_norms=True, progbar=False, inplace=False, **full_simplify_opts)[source]
compress_simplify_[source]
max_bond()[source]

Return the size of the largest bond in this network.

property shape
Actual, i.e. exterior, shape of this TensorNetwork.
property dtype
The dtype of this TensorNetwork, this is the minimal common type
of all the tensors data.
iscomplex()[source]
astype(dtype, inplace=False)[source]

Convert the type of all tensors in this network to dtype.

astype_[source]
__getstate__()[source]

Helper for pickle.

__setstate__(state)[source]
_repr_info()[source]

General info to show in various reprs. Sublasses can add more relevant info to this dict.

_repr_info_str()[source]

Render the general info as a string.

_repr_html_()[source]

Render this TensorNetwork as HTML, for Jupyter notebooks.

__str__()[source]

Return str(self).

__repr__()[source]

Return repr(self).

draw[source]
draw_3d[source]
draw_interactive[source]
draw_3d_interactive[source]
graph[source]
visualize_tensors[source]
quimb.tensor.optimize.tags_to_oset(tags)[source]

Parse a tags argument into an ordered set.

quimb.tensor.optimize._DEFAULT_BACKEND = 'jax'
quimb.tensor.optimize._REAL_CONVERSION
quimb.tensor.optimize._COMPLEX_CONVERSION
class quimb.tensor.optimize.ArrayInfo(array)[source]

Simple container for recording size and dtype information about arrays.

__slots__ = ('shape', 'size', 'dtype', 'iscomplex', 'real_size', 'equivalent_real_type', 'equivalent_complex_type')
__repr__()[source]

Return repr(self).

class quimb.tensor.optimize.Vectorizer(tree)[source]

Object for mapping back and forth between any pytree of mixed real/complex n-dimensional arrays to a single, real, double precision numpy vector, as required by scipy.optimize routines.

Parameters:
  • tree (pytree of array) – Any nested container of arrays, which will be flattened and packed into a single float64 vector.

  • is_leaf (callable, optional) – A function which takes a single argument and returns True if it is a leaf node in the tree and should be extracted, False otherwise. Defaults to everything that is not a tuple, list or dict.

pack(tree, name='vector')[source]

Take arrays and pack their values into attribute .{name}, by default .vector.

unpack(vector=None)[source]

Turn the single, flat vector into a sequence of arrays.

quimb.tensor.optimize._VARIABLE_TAG = '__VARIABLE{}__'
quimb.tensor.optimize.variable_finder
quimb.tensor.optimize._parse_opt_in(tn, tags, shared_tags, to_constant)[source]

Parse a tensor network where tensors are assumed to be constant unless tagged.

quimb.tensor.optimize._parse_opt_out(tn, constant_tags, to_constant)[source]

Parse a tensor network where tensors are assumed to be variables unless tagged.

quimb.tensor.optimize._parse_pytree_to_backend(x, to_constant)[source]

Parse a arbitrary pytree, collecting variables. There is not opting in or out, all networks, tensors and raw arrays are considered variables.

quimb.tensor.optimize.parse_network_to_backend(tn, to_constant, tags=None, shared_tags=None, constant_tags=None)[source]

Parse tensor network to:

  • identify the dimension of the optimisation space and the initial point of the optimisation from the current values in the tensor network,

  • add variable tags to individual tensors so that optimisation vector values can be efficiently reinserted into the tensor network.

There are two different modes:

  • ‘opt in’ : tags (and optionally shared_tags) are specified and only these tensor tags will be optimised over. In this case constant_tags is ignored if it is passed,

  • ‘opt out’ : tags is not specified. In this case all tensors will be optimised over, unless they have one of constant_tags tags.

Parameters:
  • tn (TensorNetwork) – The initial tensor network to parse.

  • to_constant (Callable) – Function that fixes a tensor as constant.

  • tags (str, or sequence of str, optional) – Set of opt-in tags to optimise.

  • shared_tags (str, or sequence of str, optional) – Subset of opt-in tags to joint optimise i.e. all tensors with tag s in shared_tags will correspond to the same optimisation variables.

  • constant_tags (str, or sequence of str, optional) – Set of opt-out tags if tags not passed.

Returns:

  • tn_ag (TensorNetwork) – Tensor network tagged for reinsertion of optimisation variable values.

  • variables (list) – List of variables extracted from tn.

quimb.tensor.optimize._inject_variables_pytree(arrays, tree)[source]
quimb.tensor.optimize.inject_variables(arrays, tn)[source]

Given the list of optimized variables arrays and the target tensor network or pytree tn, inject the variables back in.

quimb.tensor.optimize.convert_raw_arrays(x, f)[source]

Given a TensorNetwork, Tensor, or other possibly structured raw array, return a copy where the underyling data has had f applied to it. Structured raw arrays should implement the tree = get_params() and set_params(tree) methods which get or set their underlying data using an arbitrary pytree.

quimb.tensor.optimize.convert_variables_to_numpy(x)[source]
quimb.tensor.optimize.get_autograd()[source]
class quimb.tensor.optimize.AutoGradHandler(device='cpu')[source]
to_variable(x)[source]
to_constant(x)[source]
setup_fn(fn)[source]
value(arrays)[source]
value_and_grad(arrays)[source]
class quimb.tensor.optimize.JaxHandler(jit_fn=True, device=None)[source]
to_variable(x)[source]
to_constant(x)[source]
setup_fn(fn)[source]
_setup_hessp(fn)[source]
value(arrays)[source]
value_and_grad(arrays)[source]
hessp(primals, tangents)[source]
quimb.tensor.optimize.get_tensorflow()[source]
class quimb.tensor.optimize.TensorFlowHandler(jit_fn=False, autograph=False, experimental_compile=False, device=None)[source]
to_variable(x)[source]
to_constant(x)[source]
setup_fn(fn)[source]
value(arrays)[source]
value_and_grad(arrays)[source]
quimb.tensor.optimize.get_torch()[source]
class quimb.tensor.optimize.TorchHandler(jit_fn=False, device=None)[source]
to_variable(x)[source]
to_constant(x)[source]
setup_fn(fn)[source]
_setup_backend_fn(arrays)[source]
value(arrays)[source]
value_and_grad(arrays)[source]
quimb.tensor.optimize._BACKEND_HANDLERS
class quimb.tensor.optimize.MultiLossHandler(autodiff_backend, executor=None, **backend_opts)[source]
setup_fn(funcs)[source]
_value_seq(arrays)[source]
_value_par_seq(arrays)[source]
value(arrays)[source]
_value_and_grad_seq(arrays)[source]
_value_and_grad_par(arrays)[source]
value_and_grad(arrays)[source]
class quimb.tensor.optimize.SGD[source]

Stateful scipy.optimize.minimize compatible implementation of stochastic gradient descent with momentum.

Adapted from autograd/misc/optimizers.py.

get_velocity(x)[source]
__call__(fun, x0, jac, args=(), learning_rate=0.1, mass=0.9, maxiter=1000, callback=None, bounds=None, **kwargs)[source]
class quimb.tensor.optimize.RMSPROP[source]

Stateful scipy.optimize.minimize compatible implementation of root mean squared prop: See Adagrad paper for details.

Adapted from autograd/misc/optimizers.py.

get_avg_sq_grad(x)[source]
__call__(fun, x0, jac, args=(), learning_rate=0.1, gamma=0.9, eps=1e-08, maxiter=1000, callback=None, bounds=None, **kwargs)[source]
class quimb.tensor.optimize.ADAM[source]

Stateful scipy.optimize.minimize compatible implementation of ADAM - http://arxiv.org/pdf/1412.6980.pdf.

Adapted from autograd/misc/optimizers.py.

get_m(x)[source]
get_v(x)[source]
__call__(fun, x0, jac, args=(), learning_rate=0.001, beta1=0.9, beta2=0.999, eps=1e-08, maxiter=1000, callback=None, bounds=None, **kwargs)[source]
class quimb.tensor.optimize.NADAM[source]

Stateful scipy.optimize.minimize compatible implementation of NADAM - [Dozat - http://cs229.stanford.edu/proj2015/054_report.pdf].

Adapted from autograd/misc/optimizers.py.

get_m(x)[source]
get_v(x)[source]
get_mus(beta1)[source]
__call__(fun, x0, jac, args=(), learning_rate=0.001, beta1=0.9, beta2=0.999, eps=1e-08, maxiter=1000, callback=None, bounds=None, **kwargs)[source]
class quimb.tensor.optimize.ADABELIEF[source]

Stateful scipy.optimize.minimize compatible implementation of ADABELIEF - https://arxiv.org/abs/2010.07468.

Adapted from autograd/misc/optimizers.py.

get_m(x)[source]
get_s(x)[source]
__call__(fun, x0, jac, args=(), learning_rate=0.001, beta1=0.9, beta2=0.999, eps=1e-08, maxiter=1000, callback=None, bounds=None, **kwargs)[source]
quimb.tensor.optimize._STOC_GRAD_METHODS
class quimb.tensor.optimize.MakeArrayFn(tn_opt, loss_fn, norm_fn, autodiff_backend)[source]

Class wrapper so picklable.

__name__ = 'MakeArrayFn'
__call__(arrays)[source]
quimb.tensor.optimize.identity_fn(x)[source]
class quimb.tensor.optimize.TNOptimizer(tn, loss_fn, norm_fn=None, loss_constants=None, loss_kwargs=None, tags=None, shared_tags=None, constant_tags=None, loss_target=None, optimizer='L-BFGS-B', progbar=True, bounds=None, autodiff_backend='AUTO', executor=None, callback=None, **backend_opts)[source]

Globally optimize tensors within a tensor network with respect to any loss function via automatic differentiation. If parametrized tensors are used, optimize the parameters rather than the raw arrays.

Parameters:
  • tn (TensorNetwork) – The core tensor network structure within which to optimize tensors.

  • loss_fn (callable or sequence of callable) – The function that takes tn (as well as loss_constants and loss_kwargs) and returns a single real ‘loss’ to be minimized. For Hamiltonians which can be represented as a sum over terms, an iterable collection of terms (e.g. list) can be given instead. In that case each term is evaluated independently and the sum taken as loss_fn. This can reduce the total memory requirements or allow for parallelization (see executor).

  • norm_fn (callable, optional) – A function to call before loss_fn that prepares or ‘normalizes’ the raw tensor network in some way.

  • loss_constants (dict, optional) – Extra tensor networks, tensors, dicts/list/tuples of arrays, or arrays which will be supplied to loss_fn but also converted to the correct backend array type.

  • loss_kwargs (dict, optional) – Extra options to supply to loss_fn (unlike loss_constants these are assumed to be simple options that don’t need conversion).

  • tags (str, or sequence of str, optional) – If supplied, only optimize tensors with any of these tags.

  • shared_tags (str, or sequence of str, optional) – If supplied, each tag in shared_tags corresponds to a group of tensors to be optimized together.

  • constant_tags (str, or sequence of str, optional) – If supplied, skip optimizing tensors with any of these tags. This ‘opt-out’ mode is overridden if either tags or shared_tags is supplied.

  • loss_target (float, optional) – Stop optimizing once this loss value is reached.

  • optimizer (str, optional) – Which scipy.optimize.minimize optimizer to use (the 'method' kwarg of that function). In addition, quimb implements a few custom optimizers compatible with this interface that you can reference by name - {'adam', 'nadam', 'rmsprop', 'sgd'}.

  • executor (None or Executor, optional) – To be used with term-by-term Hamiltonians. If supplied, this executor is used to parallelize the evaluation. Otherwise each term is evaluated in sequence. It should implement the basic concurrent.futures (PEP 3148) interface.

  • progbar (bool, optional) – Whether to show live progress.

  • bounds (None or (float, float), optional) – Constrain the optimized tensor entries within this range (if the scipy optimizer supports it).

  • autodiff_backend ({'jax', 'autograd', 'tensorflow', 'torch'}, optional) – Which backend library to use to perform the automatic differentation (and computation).

  • callback (callable, optional) –

    A function to call after each optimization step. It should take the current TNOptimizer instance as its only argument. Information such as the current loss and number of evaluations can then be accessed:

    def callback(tnopt):
        print(tnopt.nevals, tnopt.loss)
    

  • backend_opts – Supplied to the backend function compiler and array handler. For example jit_fn=True or device='cpu' .

_set_tn(tn)[source]
_reset_tracking_info(loss_target=None)[source]
reset(tn=None, clear_info=True, loss_target=None)[source]

Reset this optimizer without losing the compiled loss and gradient functions.

Parameters:
  • tn (TensorNetwork, optional) – Set this tensor network as the current state of the optimizer, it must exactly match the original tensor network.

  • clear_info (bool, optional) – Clear the tracked losses and iterations.

_maybe_init_pbar(n)[source]
_maybe_update_pbar()[source]
_maybe_close_pbar()[source]
_check_loss_target()[source]
_maybe_call_callback()[source]
vectorized_value(x)[source]

The value of the loss function at vector x.

vectorized_value_and_grad(x)[source]

The value and gradient of the loss function at vector x.

vectorized_hessp(x, p)[source]

The action of the hessian at point x on vector p.

__repr__()[source]

Return repr(self).

property d
property nevals
The number of gradient evaluations.
property optimizer
The underlying optimizer that works with the vectorized functions.
property bounds
get_tn_opt()[source]

Extract the optimized tensor network, this is a three part process:

  1. inject the current optimized vector into the target tensor network,

  2. run it through norm_fn,

  3. drop any tags used to identify variables.

Returns:

tn_opt

Return type:

TensorNetwork

optimize(n, tol=None, jac=True, hessp=False, optlib='scipy', **options)[source]

Run the optimizer for n function evaluations, using by default scipy.optimize.minimize() as the driver for the vectorized computation. Supplying the gradient and hessian vector product is controlled by the jac and hessp options respectively.

Parameters:
  • n (int) – Notionally the maximum number of iterations for the optimizer, note that depending on the optimizer being used, this may correspond to number of function evaluations rather than just iterations.

  • tol (None or float, optional) – Tolerance for convergence, note that various more specific tolerances can usually be supplied to options, depending on the optimizer being used.

  • jac (bool, optional) – Whether to supply the jacobian, i.e. gradient, of the loss function.

  • hessp (bool, optional) – Whether to supply the hessian vector product of the loss function.

  • optlib ({'scipy', 'nlopt'}, optional) – Which optimization library to use.

  • options – Supplied to scipy.optimize.minimize() or whichever optimizer is being used.

Returns:

tn_opt

Return type:

TensorNetwork

optimize_scipy(n, tol=None, jac=True, hessp=False, **options)[source]

Scipy based optimization, see optimize() for details.

optimize_basinhopping(n, nhop, temperature=1.0, jac=True, hessp=False, **options)[source]

Run the optimizer for using scipy.optimize.basinhopping() as the driver for the vectorized computation. This performs nhop local optimization each with n iterations.

Parameters:
  • n (int) – Number of iterations per local optimization.

  • nhop (int) – Number of local optimizations to hop between.

  • temperature (float, optional) – H

  • options – Supplied to the inner scipy.optimize.minimize() call.

Returns:

tn_opt

Return type:

TensorNetwork

optimize_nlopt(n, tol=None, jac=True, hessp=False, ftol_rel=None, ftol_abs=None, xtol_rel=None, xtol_abs=None)[source]

Run the optimizer for n function evaluations, using nlopt as the backend library to run the optimization. Whether the gradient is computed depends on which optimizer is selected, see valid options at https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/.

The following scipy optimizer options are automatically translated to the corresponding nlopt algorithms: {“l-bfgs-b”, “slsqp”, “tnc”, “cobyla”}.

Parameters:
  • n (int) – The maximum number of iterations for the optimizer.

  • tol (None or float, optional) – Tolerance for convergence, here this is taken to be the relative tolerance for the loss (ftol_rel below overrides this).

  • jac (bool, optional) – Whether to supply the jacobian, i.e. gradient, of the loss function.

  • hessp (bool, optional) – Whether to supply the hessian vector product of the loss function.

  • ftol_rel (float, optional) – Set relative tolerance on function value.

  • ftol_abs (float, optional) – Set absolute tolerance on function value.

  • xtol_rel (float, optional) – Set relative tolerance on optimization parameters.

  • xtol_abs (float, optional) – Set absolute tolerances on optimization parameters.

Returns:

tn_opt

Return type:

TensorNetwork

optimize_ipopt(n, tol=None, **options)[source]

Run the optimizer for n function evaluations, using ipopt as the backend library to run the optimization via the python package cyipopt.

Parameters:

n (int) – The maximum number of iterations for the optimizer.

Returns:

tn_opt

Return type:

TensorNetwork

optimize_nevergrad(n)[source]

Run the optimizer for n function evaluations, using nevergrad as the backend library to run the optimization. As the name suggests, the gradient is not required for this method.

Parameters:

n (int) – The maximum number of iterations for the optimizer.

Returns:

tn_opt

Return type:

TensorNetwork

plot(xscale='symlog', xscale_linthresh=20, zoom='auto', hlines=())[source]

Plot the loss function as a function of the number of iterations.

Parameters:
  • xscale (str, optional) – The scale of the x-axis. Default is "symlog", i.e. linear for the first part of the plot, and logarithmic for the rest, changing at xscale_linthresh.

  • xscale_linthresh (int, optional) – The threshold for the change from linear to logarithmic scale, if xscale is "symlog". Default is 20.

  • zoom (None or int, optional) – If not None, show an inset plot of the last zoom iterations.

  • hlines (dict, optional) – A dictionary of horizontal lines to plot. The keys are the labels of the lines, and the values are the y-values of the lines.

Returns:

  • fig (matplotlib.figure.Figure) – The figure object.

  • ax (matplotlib.axes.Axes) – The axes object.