LegPipe¶
full name: tenpy.linalg.charges.LegPipe
parent module:
tenpy.linalg.charges
type: class
Inheritance Diagram
Methods

Initialize self. 

Convert to LegCharge and call 
Return unique rows of self.charges. 

Return a shallow copy with opposite 

Return a (shallow) copy of self. 


Return a new 
Return a copy with both negative qconj and charges. 


Add the (independent) charges of two or more legs to get larger qnumber. 

Remove a charge from a LegCharge. 

Remove a charge from a LegCharge. 

Load instance from a HDF5 file. 

Create a LegCharge from qdict form. 

Create a LegCharge from qflat form. 

Just a wrapper around self.__init__(), see class docstring for parameters. 

Create trivial (qnumber=0) LegCharge for given len of indices ind_len. 

Return charge 

Find qindex containing a flat index. 

Return the slice selecting the block for given charge values. 

Return slice selecting the block for a given qindex. 
Returns whether self is blocked, i.e. 

Checks whether 

Returns whether self.charges is sorted lexiographically. 


Map (flat) incoming indices to an index in the outgoing pipe. 
Like 


Convert a permutation of qind (acting on self) into a flat permutation. 

Convert flat permutation into qind permutation. 

Convert self to LegCharge and call 

Export self into a HDF5 file. 

Convert to LegCharge and call 

Raises a ValueError if charges are incompatible for contraction with other. 

Test if charges are equal including qconj. 
Sanity check, raises ValueErrors, if something is wrong. 

Convert self to a LegCharge, discarding the information how to split the legs. 

Return charges in qdict form. 

Return charges in qflat form. 

class
tenpy.linalg.charges.
LegPipe
(legs, qconj=1, sort=True, bunch=True)[source]¶ Bases:
tenpy.linalg.charges.LegCharge
A LegPipe combines multiple legs of a tensor to one.
Often, it is necessary to “combine” multiple legs into one: for example to perfom a SVD, the tensor needs to be viewed as a matrix.
This class does exactly this job: it combines multiple LegCharges (‘incoming legs’) into one ‘pipe’ (the ‘outgoing leg’). The pipe itself is a
LegCharge
, with indices running from 0 to the product of the individual legs’ ind_len, corresponding to all possible combinations of input leg indices.(This class is implemented in
tenpy.linalg.charges
but also imported intenpy.linalg.np_conserved
for convenience.) Parameters
legs (list of
LegCharge
) – The legs which are to be combined.qconj ({+1, 1}) – A flag telling whether the charge of the resulting pipe points inwards (+1, default) or outwards (1).
sort (bool) – Whether the outgoing pipe should be sorted. Default
True
; recommended. Note: callingsort()
after initialization converts to a LegCharge.bunch (bool) – Whether the outgoing pipe should be bunched. Default
True
; recommended. Note: callingbunch()
after initialization converts to a LegCharge.

subshape
¶ ind_len for each of the incoming legs.
 Type
tuple of int

subqshape
¶ block_number for each of the incoming legs.
 Type
tuple of int

q_map
¶ Shape (block_number, 3 + nlegs). Rows:
[ b_j, b_{j+1}, I_s, i_1, ..., i_{nlegs}]
, See Notes below for details. Type
array[np.intp, ndim=2]

q_map_slices
¶ Defined such that the row indices of in
range(q_map_slices[I_s], q_map_slices[I_s+1])
haveq_map[:, 2] == I_s
. Type
array[np.intp, ndim=1]

_perm
¶ A permutation such that
q_map[_perm, 3:]
is sorted by i_l. Type
1D array

_strides
¶ Strides for mapping incoming qindices i_l to the index of
q_map[_perm, :]
. Type
1D array
Notes
For np.reshape, taking, for example, \(i,j,... \rightarrow k\) amounted to \(k = s_1*i + s_2*j + ...\) for appropriate strides \(s_1,s_2\).
In the charged case, however, we want to block \(k\) by charge, so we must implicitly permute as well. This reordering is encoded in q_map.
Each qindex combination of the nlegs input legs \((i_1, ..., i_{nlegs})\), will end up getting placed in some slice \(a_j:a_{j+1}\) of the outgoing pipe. Within this slice, the data is simply reshaped in usual rowmajor fashion (‘C’order), i.e., with strides \(s_1 > s_2 > ...\).
It will be a subslice of a new total block labeled by qindex \(I_s\). Because many charge combinations fuse to the same total charge, in general there will be many tuples \((i_1, ..., i_{nlegs})\) belonging to the same \(I_s\). The rows of q_map are precisely the collections of
[b_j, b_{j+1}, I_s, i_1, . . . , i_{nlegs}]
. Here, \(b_j:b_{j+1}\) denotes the slice of this qindex combination within the total block I_s, i.e.,b_j = a_j  self.slices[I_s]
.The rows of q_map are lexsorted first by
I_s
, then thei
. EachI_s
will have multiple rows, and the order in which they are stored in q_map is the order the data is stored in the actual tensor, i.e., it might look like[ ..., [ b_j, b_{j+1}, I_s, i_1, ..., i_{nlegs} ], [ b_{j+1}, b_{j+2}, I_s, i'_1, ..., i'_{nlegs} ], [ 0, b_{j+3}, I_s + 1, i''_1, ..., i''_{nlegs} ], [ b_{j+3}, b_{j+4}, I_s + 1, i'''_1, ..., i'''_{nlegs}], ...]
The charge fusion rule is:
self.charges[Qi]*self.qconj == sum([l.charges[qi_l]*l.qconj for l in self.legs]) mod qmod
Here the qindex
Qi
of the pipe corresponds to qindicesqi_l
on the individual legs.
save_hdf5
(hdf5_saver, h5gr, subpath)[source]¶ Export self into a HDF5 file.
This method saves all the data it needs to reconstruct self with
from_hdf5()
.In addition to the data saved for the
LegCharge
, it just saves thelegs
as subgroup.

classmethod
from_hdf5
(hdf5_loader, h5gr, subpath)[source]¶ Load instance from a HDF5 file.
This method reconstructs a class instance from the data saved with
save_hdf5()
. Parameters
hdf5_loader (
Hdf5Loader
) – Instance of the loading engine.h5gr (
Group
) – HDF5 group which is represent the object to be constructed.subpath (str) – The name of h5gr with a
'/'
in the end.
 Returns
obj – Newly generated class instance containing the required data.
 Return type
cls

to_LegCharge
()[source]¶ Convert self to a LegCharge, discarding the information how to split the legs.
Usually not needed, but called by functions, which are not implemented for a LegPipe.

conj
()[source]¶ Return a shallow copy with opposite
self.qconj
. Returns
conjugated – Shallow copy of self with flipped
qconj
. Whenever we contract two legs, they need to be conjugated to each other. The incoming legs of the pipe are also conjugated. Return type

sort
(*args, **kwargs)[source]¶ Convert to LegCharge and call
LegCharge.sort()
.

bunch
(*args, **kwargs)[source]¶ Convert to LegCharge and call
LegCharge.bunch()
.

project
(*args, **kwargs)[source]¶ Convert self to LegCharge and call
LegCharge.project()
.In general, this could be implemented for a LegPipe, but would make
split_legs()
more complicated, thus we keep it simple. If you really want to project and split afterwards, use the following workaround, which is for example used inexact_diagonalization
:Create the full pipe and save it separetely.
Convert the Pipe to a Leg & project the array with it.
[… do calculations …]
To split the ‘projected pipe’ of A, create and empty array B with the legs of A, but replace the projected leg by the full pipe. Set A as a slice of B. Finally split the pipe.

map_incoming_flat
(incoming_indices)[source]¶ Map (flat) incoming indices to an index in the outgoing pipe.
 Parameters
incoming_indices (iterable of int) – One (flat) index on each of the incoming legs.
 Returns
outgoing_index – The index in the outgoing leg.
 Return type

charge_sectors
()[source]¶ Return unique rows of self.charges.
 Returns
charges – Rows are the rows of self.charges lexsorted and without duplicates.
 Return type
array[QTYPE, ndim=2]

extend
(extra)[source]¶ Return a new
LegCharge
, which extends self with futher charges.This is needed to formally increase the dimension of an Array.
 Parameters
extra (
LegCharge
 int) – By what to extend, i.e. the charges to be appended to self. An int stands for extending the length of the array by a single new block of that size and zero charges. Returns
extended_leg – Copy of self extended by the charge blocks of the extra leg.
 Return type

flip_charges_qconj
()[source]¶ Return a copy with both negative qconj and charges.
 Returns
conj_charges – (Shallow) copy of self with negative qconj and charges, thus representing the very same charges.
test_equal()
of self with conj_charges will not raise an error. Return type

classmethod
from_add_charge
(legs, chargeinfo=None)[source]¶ Add the (independent) charges of two or more legs to get larger qnumber.
 Parameters
legs (iterable of
LegCharge
) – The legs for which the charges are to be combined/added.chargeinfo (
ChargeInfo
) – The ChargeInfo for all charges; create new ifNone
.
 Returns
combined – A LegCharge with the charges of both legs. Is neither sorted nor bunched!
 Return type

classmethod
from_change_charge
(leg, charge, new_qmod, new_name='', chargeinfo=None)[source]¶ Remove a charge from a LegCharge.
 Parameters
leg (
LegCharge
) – The leg from which to drop/remove a charge.charge (int  str) – Number or name of the charge (within chinfo) for which mod is to be changed.
new_qmod (int) – The new mod to be set for charge in the
ChargeInfo
.new_name (str) – The new name for charge.
chargeinfo (
ChargeInfo
) – The ChargeInfo with charge changed; create new ifNone
.
 Returns
leg – A LegCharge with the specified charge changed. Is neither sorted nor bunched!
 Return type

classmethod
from_drop_charge
(leg, charge=None, chargeinfo=None)[source]¶ Remove a charge from a LegCharge.
 Parameters
leg (
LegCharge
) – The leg from which to drop/remove a charge.charge (int  str) – Number or name of the charge (within chinfo) which is to be dropped.
None
means dropping all charges.chargeinfo (
ChargeInfo
) – The ChargeInfo with charge dropped; create new ifNone
.
 Returns
dropped – A LegCharge with the specified charge dropped. Is neither sorted nor bunched!
 Return type

classmethod
from_qdict
(chargeinfo, qdict, qconj=1)[source]¶ Create a LegCharge from qdict form.
 Parameters
chargeinfo (
ChargeInfo
) – The nature of the charge.qdict (dict) – A dictionary mapping a tuple of charges to slices.

classmethod
from_qflat
(chargeinfo, qflat, qconj=1)[source]¶ Create a LegCharge from qflat form.
Does neither bunch nor sort. We recommend to sort (and bunch) afterwards, if you expect that tensors using the LegCharge have entries at all positions compatible with the charges.
 Parameters
chargeinfo (
ChargeInfo
) – The nature of the charge.qflat (array_like (ind_len, qnumber)) – qnumber charges for each index of the leg on entry.
qconj ({1, 1}) – A flag telling whether the charge points inwards (+1) or outwards (1).

classmethod
from_qind
(chargeinfo, slices, charges, qconj=1)[source]¶ Just a wrapper around self.__init__(), see class docstring for parameters.

classmethod
from_trivial
(ind_len, chargeinfo=None, qconj=1)[source]¶ Create trivial (qnumber=0) LegCharge for given len of indices ind_len.

get_qindex
(flat_index)[source]¶ Find qindex containing a flat index.
Given a flat index, to find the corresponding entry in an Array, we need to determine the block it is saved in. For example, if
slices = [[0, 3], [3, 7], [7, 12]]
, the flat index5
corresponds to the second entry,qindex = 1
(since 5 is in [3:7]), and the index within the block would be2 = 5  3
. Parameters
flat_index (int) – A flat index of the leg. Negative index counts from behind.
 Returns
qindex (int) – The qindex, i.e. the index of the block containing flat_index.
index_within_block (int) – The index of flat_index within the block given by qindex.

get_qindex_of_charges
(charges)[source]¶ Return the slice selecting the block for given charge values.
Inverse function of
get_charge()
. Parameters
charges (1D array_like) – Charge values for which the slice of the block is to be determined.
 Returns
slice(i, j) – Slice of the charge values for
 Return type
:raises ValueError : if the answer is not unique (because self is not blocked).:

perm_flat_from_perm_qind
(perm_qind)[source]¶ Convert a permutation of qind (acting on self) into a flat permutation.

perm_qind_from_perm_flat
(perm_flat)[source]¶ Convert flat permutation into qind permutation.
 Parameters
perm_flat (1D array) – A permutation acting on self, which doesn’t mix the blocks of qind.
 Returns
perm_qind – The permutation of self.qind described by perm_flat.
 Return type
1D array
 Raises
ValueError – If perm_flat mixes blocks of different qindex.

test_contractible
(other)[source]¶ Raises a ValueError if charges are incompatible for contraction with other.
 Parameters
other (
LegCharge
) – The LegCharge of the other leg condsidered for contraction. Raises
ValueError – If the charges are incompatible for direct contraction.
Notes
This function checks that two legs are ready for contraction. This is the case, if all of the following conditions are met:
the
ChargeInfo
is equalthe slices are equal
the charges are the same up to opposite signs
qconj
:self.charges * self.qconj =  other.charges * other.qconj
In general, there could also be a change of the total charge, see Charge conservation with np_conserved This special case is not considered here  instead use
gauge_total_charge()
, if a change of the charge is desired.If you are sure that the legs should be contractable, check whether the charges are actually valid or whether
self
andother
are blocked or should be sorted.See also
test_equal()
self.test_contractible(other)
just performsself.test_equal(other.conj())
.

test_equal
(other)[source]¶ Test if charges are equal including qconj.
Check that all of the following conditions are met:
the
ChargeInfo
is equalthe slices are equal
the charges are the same up to the signs
qconj
:self.charges * self.qconj = other.charges * other.qconj
See also
test_contractible()
self.test_equal(other)
is equivalent toself.test_contractible(other.conj())
.