quimb.tensor.optimize¶
Support for optimizing tensor networks using automatic differentiation to automatically derive gradients for input to scipy optimizers.
Attributes¶
Classes¶
A collection of (as yet uncontracted) Tensors. 

Simple container for recording size and dtype information about arrays. 

Object for mapping back and forth between any pytree of mixed 

Stateful 

Stateful 

Stateful 

Stateful 

Stateful 

Class wrapper so picklable. 

Globally optimize tensors within a tensor network with respect to any 
Functions¶


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


Make sure 

Flatten 

Map 

Unflatten 

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



Parse a 

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

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

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

Parse tensor network to: 



Given the list of optimized variables 

Given a 

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 adict
, creating an empty one ifx 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)
returnsTrue
are returned in the flattened list.
 Returns:
objs (list) – The flattened list of leaf objects.
(ref_tree) (pytree) – If
get_ref
isTrue
, a reference tree, with leaves of typeLeaf
, 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 intree
, 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 whichis_leaf(x)
returnsTrue
.
 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 astree
. 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)
returnsTrue
will have the next item fromobjs
inserted. By default checks for theLeaf
object inserted bytree_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
.
 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 anotherTensorNetwork
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:
 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:
 ind_map¶
Like
tag_map
but for indices. Soind_map[ind]]
returns the tensor ids of those tensors withind
. Type:
 exponent¶
A scalar prefactor for the tensor network, stored in base 10 like
10**exponent
. This is mostly for conditioning purposes and will be0.0
unless you use useequalize_norms(value)
ortn.strip_exponent(tid_or_tensor)
. Type:
 _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:
 __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.
 classmethod new(like=None, **kwargs)[source]¶
Create a new tensor network, without any tensors, of type
cls
, with all the requisite properties specified bykwargs
or inherited fromlike
.
 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_like(like, inplace=False, **kwargs)[source]¶
View this tensor network as the same subclass
cls
aslike
inheriting its extra properties as well.
 copy(virtual=False, deep=False)[source]¶
Copy this
TensorNetwork
. Ifdeep=False
, (the default), then everything but the actual numeric data will be copied.
 set_params(params)[source]¶
Take a pytree of the ‘parameters’, i.e. all underlying data arrays, as returned by
get_params
and set them.
 add_tensor(tensor, tid=None, virtual=False)[source]¶
Add a single tensor to this network  mangle its tid if neccessary.
 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 nonvirtual, 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.
 property num_tensors¶
 The total number of tensors in the tensor network.
 property num_indices¶
 The total number of indices in 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 inself.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.
 retag(tag_map, inplace=False)[source]¶
Rename tags for all tensors in this network, optionally inplace.
 Parameters:
tag_map (dictlike) – Mapping of pairs
{old_tag: new_tag, ...}
.inplace (bool, optional) – Perform operation inplace or return copy (default).
 reindex(index_map, inplace=False)[source]¶
Rename indices for all tensors in this network, optionally inplace.
 Parameters:
index_map (dictlike) – Mapping of pairs
{old_ind: new_ind, ...}
.
 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.
 conj(mangle_inner=False, inplace=False)[source]¶
Conjugate all the tensors in this network (leaves all indices).
 property H¶
 Conjugate all the tensors in this network (leaves all indices).
 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
.
 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_each(x, inplace=False)[source]¶
Scalar multiplication of each tensor in this tensor network with
x
. If trying to spread a multiplicative factorfac
uniformly over all tensors in the network and the number of tensors is large, then callingmultiply(fac)
can be inaccurate due to precision loss. If one has a routine that can precisely compute thex
to be applied to each tensor, then this function avoids the potential inaccuracies inmultiply()
. Parameters:
x (scalar) – The number that multiplies each tensor in the network
inplace (bool, optional) – Whether to perform the multiplication inplace.
 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.See also
 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:
Examples
>>> tn = qtn.TN_rand_reg(10, 3, 2) >>> tn.get_equation() 'abc,dec,fgb,hia,jke,lfk,mnj,ing,omd,ohl>'
See also
 get_inputs_output_size_dict(output_inds=None)[source]¶
Get a tuple of
inputs
,output
andsize_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])
See also
 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:
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_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:
 select_tensors(tags, which='all')[source]¶
Return the sequence of tensors that match
tags
. Ifwhich='all'
, each tensor must contain every tag. Ifwhich='any'
, each tensor can contain any of the tags. Parameters:
 Returns:
tagged_tensors – The tagged tensors.
 Return type:
See also
 _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 totids
.
 _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 totids
.
 select(tags, which='all', virtual=True)[source]¶
Get a TensorNetwork comprising tensors that match all or any of
tags
, inherit the network properties/structure fromself
. This returns a view of the tensors not a copy. Parameters:
 Returns:
tagged_tn – A tensor network containing the tagged tensors.
 Return type:
See also
select_tensors
,select_neighbors
,partition
,partition_tensors
 select_neighbors(tags, which='any')[source]¶
Select any neighbouring tensors to those specified by
tags
.self Parameters:
 Returns:
The neighbouring tensors.
 Return type:
See also
 _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 ‘fillin’ corners by adding tensors connected multiple times. For example, if
R
is an initially tagged tensor andx
are locally selected tensors:fillin=0 fillin=1 fillin=2                ooxoo oxxxo xxxxx                oxxxo xxxxx xxxxx                xxRxx xxRxx xxRxx
reduce_outer ({'sum', 'svd', 'svdsum', '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:
 partition_tensors(tags, inplace=False, which='any')[source]¶
Split this TN into a list of tensors containing any or all of
tags
and aTensorNetwork
of the the rest. Parameters:
 Returns:
(u_tn, t_ts) – The untagged tensor network, and the sequence of tagged Tensors.
 Return type:
(TensorNetwork, tuple of Tensors)
See also
 partition(tags, which='any', inplace=False)[source]¶
Split this TN into two, based on which tensors have any or all of
tags
. Unlikepartition_tensors
, both results are TNs which inherit the structure of the initial TN. Parameters:
 Returns:
untagged_tn, tagged_tn – The untagged and tagged tensor networs.
 Return type:
See also
 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. ifX
denotewhere
tensors:1 XX2 12     ==>  XXX  
 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:
See also
 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. ifX
denotewhere
tensors::__ ___: X XX X : \ / :     ==> : U~s~VH: XXXX :__/ \ :  + : \__: 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:
See also
 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:
 _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
andtags2
respectively. This is an inplace operation. Noop if the tensor specified bytags1
andtags2
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()
.
 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
andgate
.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 oldinds
, must be the same length asinds
.gate_inds_outer (sequence of str) – The indices of
gate
to make the new outerinds
, must be the same length asinds
.
 Returns:
tn_gated
 Return type:
See also
 _compute_tree_gauges(tree, outputs)[source]¶
Given a
tree
of connected tensors, absorb the gauges from outside inwards, finally outputing the gauges associated with theoutputs
. 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='autohq', 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='autohq', 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=1e10, 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=1e06, callback=None, **compress_opts)[source]¶
 compress_between(tags1, tags2, max_bond=None, cutoff=1e10, 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
andtags2
usingtensor_compress_bond()
:        ==●====●====●====●== ==●====●====●====●== / / / / / / / /         ==●====1====2====●== ==> ==●====LR====●== / / / / / / / /         ==●====●====●====●== ==●====●====●====●== / / / / / / / /
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
 compress_all(max_bond=None, cutoff=1e10, 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 onmode
if not specified.mode ({'auto', 'basic', 'virtualtree'}, optional) – The mode to use for compressing the bonds. If ‘auto’, will use ‘basic’ if
tree_gauge_distance == 0
else ‘virtualtree’.inplace (bool, optional) – Whether to perform the compression inplace.
compress_opts – Supplied to
compress_between()
.
 Return type:
See also
compress_between
,canonize_all
 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 depthfirst manner, using an infinite
canonize_distance
to shift the orthogonality center.
 compress_all_1d(max_bond=None, cutoff=1e10, 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:
 compress_all_simple(max_bond=None, cutoff=1e10, gauges=None, max_iterations=5, tol=0.0, smudge=1e12, power=1.0, inplace=False, **gauge_simple_opts)[source]¶
 _canonize_between_tids(tid1, tid2, absorb='right', gauges=None, gauge_smudge=1e06, 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
andtags2
usingtensor_canonize_bond
:        ●●●● ●●●● / / / / / / / /         ●12● ==> ●>~~~~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 nonisometric operator.
canonize_opts – Supplied to
tensor_canonize_bond()
.
See also
 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
andindb
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
.
 _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:
 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 ofmax_distance
away. The tree can be visualized withdraw_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 bytids
.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 mergetid1 > tid2
at distanced
. Return type:
See also
 _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
 _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=1e06, **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
:●●     ●vv●       ●>vv<●         ●>>OO<<●         ●>^^^●       ●^^●     ●● <=====> 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 roundrobin 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:
See also
 gauge_all_canonize(max_iterations=5, absorb='both', gauges=None, gauge_smudge=1e06, equalize_norms=False, inplace=False, **canonize_opts)[source]¶
Iterative gauge all the bonds in this tensor network with a basic ‘canonization’ strategy.
 gauge_all_simple(max_iterations=5, tol=0.0, smudge=1e12, 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_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(method='canonize', **gauge_opts)[source]¶
Gauge all bonds in this network using one of several strategies.
 Parameters:
See also
 _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_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=1e12, 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 gaugebonded.
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=1e10, 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=1e06, 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=1e10, 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.
 contract_around(tags, which='all', min_distance=0, max_distance=None, span_opts=None, max_bond=None, cutoff=1e10, 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=1e06, 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_compressed(optimize, output_inds=None, max_bond=None, cutoff=1e10, 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=1e06, callback_pre_contract=None, callback_post_contract=None, callback_pre_compress=None, callback_post_compress=None, callback=None, progbar=False, **kwargs)[source]¶
 new_bond(tags1, tags2, **opts)[source]¶
Inplace addition of a dummmy (size 1) bond between the single tensors specified by by
tags1
andtags2
. 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
 cut_between(left_tags, right_tags, left_ind, right_ind)[source]¶
Cut the bond between the tensors specified by
left_tags
andright_tags
, giving them the new indsleft_ind
andright_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. Usecut_between
for control over which tensor gets which new indexnew_left_ind
ornew_right_ind
. The index must connect exactly two tensors.
 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
andtagsb
, and ‘drape’ it through the tensor tagged attags_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 attagsa
andtagsb
. 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:
 isel(selectors, inplace=False)[source]¶
Select specific values for some dimensions/indices of this tensor network, thereby removing them.
 Parameters:
 Return type:
See also
Tensor.isel
 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.
 vector_reduce(ind, v, inplace=False)[source]¶
Contract the vector
v
with the indexind
of this tensor network, removing it. Parameters:
 Return type:
 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
See also
 insert_operator(A, where1, where2, tags=None, inplace=False)[source]¶
Insert an operator on the bond between the specified tensors, e.g.:
    12 > 1A2  
 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_gauge(U, where1, where2, Uinv=None, tol=1e10)[source]¶
Insert the gauge transformation
U^1 @ U
into the bond between the tensors,T1
andT2
, defined bywhere1
andwhere2
. The resulting tensors at those locations will beT1 @ U^1
andU @ 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 usingnumpy.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 hyperindices, 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 thisoptimizer.
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 thecotengra.ContractionTree
describing the contraction.'path'
 return the raw ‘path’ as a list of tuples.'symbolmap'
 return the dict mapping indices to ‘symbols’ (single unicode letters) used internally bycotengra
'pathinfo'
 return theopt_einsum.PathInfo
path object with detailed information such as flop cost. The symbolmap is also added to thequimb_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
See also
 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
, orcontract_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 hyperindices, 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 thecotengra.ContractionTree
describing the contraction.'path'
 return the raw ‘path’ as a list of tuples.'symbolmap'
 return the dict mapping indices to ‘symbols’ (single unicode letters) used internally bycotengra
'pathinfo'
 return theopt_einsum.PathInfo
path object with detailed information such as flop cost. The symbolmap is also added to thequimb_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
See also
 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 taggroups 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 hyperindices, 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
See also
 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 optimizeroptimize
.
 contraction_tree(optimize=None, output_inds=None, **kwargs)[source]¶
Return the
cotengra.ContractionTree
corresponding to contracting this entire tensor network with path finderoptimize
.
 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.
 as_network(virtual=True)[source]¶
Matching method (for ensuring object is a tensor network) to
as_network()
, which simply returnsself
ifvirtual=True
.
 aslinearoperator(left_inds, right_inds, ldims=None, rdims=None, backend=None, optimize=None)[source]¶
View this
TensorNetwork
as aTNLinearOperator
.
 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 aTNLinearOperator
first. Note unless an iterative method is passed tomethod
, the full dense tensor will be contracted.
 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'))
.
 compute_reduced_factor(side, left_inds, right_inds, optimize='autohq', **contract_opts)[source]¶
Compute either the left or right ‘reduced factor’ of this tensor network. I.e., view as an operator,
X
, mappingleft_inds
toright_inds
and computeL
orR
such thatX = U_R @ R
orX = L @ U_L
, withU_R
andU_L
unitary operators that are not computed. Onlydag(X) @ X
orX @ dag(X)
is contracted, which is generally cheaper than contractingX
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, otherwiseX @ 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=1e10, select_which='any', insert_into=None, new_tags=None, new_ltags=None, new_rtags=None, bond_ind=None, optimize='autohq', 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 bycutoff
.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 inplace. If
insert_into
is supplied then this doesn’t matter, and that tensor network will be modified and returned.
 Return type:
See also
 fit(tn_target, method='als', tol=1e09, 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 onmethod
this callstensor_network_fit_als()
ortensor_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()
ortensor_network_fit_autodiff()
.
 Returns:
tn_opt – The optimized tensor network.
 Return type:
See also
tensor_network_fit_als
,tensor_network_fit_autodiff
,tensor_network_distance
 property tags¶
 inner_inds()[source]¶
Tuple of interior indices, assumed to be any indices that appear twice or more (this only holds generally for nonhyper tensor networks).
 outer_inds()[source]¶
Tuple of exterior indices, assumed to be any lone indices (this only holds generally for nonhyper 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:
 Returns:
A dict mapping the tuple of indices that could be fused to the tuple of tensor ids they appear on.
 Return type:
 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 nonhyper.
 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:
 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 ofR
is positive.”svd”: uses
U @ VH
of the SVD decomposition ofx
. This is useful for finding the ‘closest’ isometric matrix tox
, 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 completingx
with zeros if it is rectangular. This is a good parametrization for optimization, but more expensive for nonsquarex
.”cayley”: use the Cayley transform of
x  dag(x)
, first completingx
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 nonsquarex
.”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 noleft_inds
to be left alone, rather than raising an error.inplace (bool, optional) – If
True
then perform the operation inplace.
 Return type:
 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:
 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 to1
. The log of the scaling factor, base 10, is then accumulated in theexponent
attribute.
 distribute_exponent()[source]¶
Distribute the exponent
p
of this tensor network (i.e. corresponding totn * 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 tovalue
by scalar multiplication only. Parameters:
 Return type:
 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:
 fuse_multibonds(gauges=None, include=None, exclude=None, inplace=False)[source]¶
Fuse any multibonds (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.
 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:
 flip(inds, inplace=False)[source]¶
Flip the dimension corresponding to indices
inds
on all tensors that share it.
 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:
See also
 diagonal_reduce(output_inds=None, atol=1e12, 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:
See also
 antidiag_gauge(output_inds=None, atol=1e12, 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:
See also
full_simplify
,rank_simplify
,diagonal_reduce
,column_reduce
 column_reduce(output_inds=None, atol=1e12, cache=None, inplace=False)[source]¶
Find bonds on this tensor network which have tensors where all but one column (of the respective index) is nonzero, 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:
See also
full_simplify
,rank_simplify
,diagonal_reduce
,antidiag_gauge
 split_simplify(atol=1e12, 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.
 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(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]
See also
 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
 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 assa_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 sizemax_group_size
or less, using a hierarchical clustering.
 pair_simplify(cutoff=1e12, output_inds=None, max_inds=10, cache=None, equalize_norms=False, max_combinations=500, inplace=False, **split_opts)[source]¶
 loop_simplify(output_inds=None, max_loop_length=None, max_inds=10, cutoff=1e12, loops=None, cache=None, equalize_norms=False, inplace=False, **split_opts)[source]¶
Try and simplify this tensor network by identifying loops and checking for lowrank 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:
 full_simplify(seq='ADCR', output_inds=None, atol=1e12, 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 rankreduction, the simplification methods make use of the nonzero 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 forantidiag_gauge
'D'
: stands fordiagonal_reduce
'C'
: stands forcolumn_reduce
'R'
: stands forrank_simplify
'S'
: stands forsplit_simplify
'L'
: stands forloop_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 lowrank 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 base10 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:
 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:
 compress_simplify(output_inds=None, atol=1e06, 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]¶
 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.
 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')¶
 class quimb.tensor.optimize.Vectorizer(tree)[source]¶
Object for mapping back and forth between any pytree of mixed real/complex ndimensional 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.
 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 optin tags to optimise.
shared_tags (str, or sequence of str, optional) – Subset of optin 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 optout 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(arrays, tn)[source]¶
Given the list of optimized variables
arrays
and the target tensor network or pytreetn
, 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 hadf
applied to it. Structured raw arrays should implement thetree = get_params()
andset_params(tree)
methods which get or set their underlying data using an arbitrary pytree.
 class quimb.tensor.optimize.TensorFlowHandler(jit_fn=False, autograph=False, experimental_compile=False, device=None)[source]¶
 quimb.tensor.optimize._BACKEND_HANDLERS¶
 class quimb.tensor.optimize.MultiLossHandler(autodiff_backend, executor=None, **backend_opts)[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
.
 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
.
 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
.
 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
.
 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
.
 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'¶
 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='LBFGSB', 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 asloss_constants
andloss_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 (seeexecutor
).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
(unlikeloss_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 ‘optout’ mode is overridden if either
tags
orshared_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 termbyterm 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
ordevice='cpu'
.
 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.
 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:
inject the current optimized vector into the target tensor network,
run it through
norm_fn
,drop any tags used to identify variables.
 Returns:
tn_opt
 Return type:
 optimize(n, tol=None, jac=True, hessp=False, optlib='scipy', **options)[source]¶
Run the optimizer for
n
function evaluations, using by defaultscipy.optimize.minimize()
as the driver for the vectorized computation. Supplying the gradient and hessian vector product is controlled by thejac
andhessp
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:
 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 performsnhop
local optimization each withn
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:
 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, usingnlopt
as the backend library to run the optimization. Whether the gradient is computed depends on whichoptimizer
is selected, see valid options at https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/.The following scipy
optimizer
options are automatically translated to the correspondingnlopt
algorithms: {“lbfgsb”, “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:
 optimize_ipopt(n, tol=None, **options)[source]¶
Run the optimizer for
n
function evaluations, usingipopt
as the backend library to run the optimization via the python packagecyipopt
. Parameters:
n (int) – The maximum number of iterations for the optimizer.
 Returns:
tn_opt
 Return type:
 optimize_nevergrad(n)[source]¶
Run the optimizer for
n
function evaluations, usingnevergrad
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:
 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 xaxis. Default is
"symlog"
, i.e. linear for the first part of the plot, and logarithmic for the rest, changing atxscale_linthresh
.xscale_linthresh (int, optional) – The threshold for the change from linear to logarithmic scale, if
xscale
is"symlog"
. Default is20
.zoom (None or int, optional) – If not
None
, show an inset plot of the lastzoom
iterations.hlines (dict, optional) – A dictionary of horizontal lines to plot. The keys are the labels of the lines, and the values are the yvalues of the lines.
 Returns:
fig (matplotlib.figure.Figure) – The figure object.
ax (matplotlib.axes.Axes) – The axes object.