pyblock.tensor¶

pyblock.tensor.tensor¶

Block-sparse tensor and tensor network.

class pyblock.tensor.tensor.SubTensor(q_labels=None, reduced=None, cgs=None)¶

Bases: object

A block in block-sparse tensor.

Attributes:

q_labels : tuple(DirectProdGroup..): Quantum labels for this sub-tensor block. Each element in the tuple corresponds one rank of the tensor.
rank : int: Rank of the tensor. rank == len(q_labels).
ng : int: Number of sub-symmetry groups. ng == q_labels[0].ng.
reduced : numpy.ndarray: Rank-rank dense reduced matrix.
reduced_shape : tuple(int..): Shape of reduced
cgs : list(numpy.ndarray): A list of CG factors of length ng with each element being Rank-rank dense reduced matrix representing CG coefficients for projected quantum numbers in each sub-symmetry group.

T¶: Transpose.

add_noise(noise)¶

Add noise to reduced matrix by random numbers in [-0.5 * noise, 0.5 * noise).

Args:

noise : float: prefactor for the noise.

build_random()¶: Set reduced matrix with random numbers in [0, 1).

build_rank3_cg()¶: Generate cgs for rank-3 tensor.

build_zero()¶: Set reduced matrix to zero.

equal_shape(o)¶

class pyblock.tensor.tensor.Tensor(blocks=None, tags=None, contractor=None)¶

Bases: object

Block-sparse tensor.

Attributes:

blocks : list(SubTensor): A list of (non-zero) blocks.
tags : set(str or int): Tags of the tensor for labeling the type or site index of the tensor.
contractor :: If not None, this is used to perform specialized tensor contraction and diagonalization.

add_noise(noise)¶

Add noise to reduced matrix by random numbers in [-0.5 * noise, 0.5 * noise).

Args:

noise : float: prefactor for the noise.

add_tags(tags)¶: Add the tags, return self for chain notation.

align(o)¶

build_identity()¶: Set the reduced matrix to identity. Not work for general situations.

build_random()¶: Fill the reduced matrix with random numbers in [0, 1).

build_rank3_cg()¶: Generate CG coefficients for rank-3 tensor.

build_zero()¶: Fill the reduced matrix with zero.

static contract(tsa, tsb, idxa, idxb, target_q_labels=None)¶

Contract two Tensor to form a new Tensor.

Args:

tsa : Tensor: Tensor a, as left operand.
tsb : Tensor: Tensor b, as right operand.
idxa : list(int): Indices to be contracted in tensor a.
idxb : list(int): Indices to be contracted in tensor b.
target_q_labels : None or DirectProdGroup or [DirectProdGroup]: If None, this is contraction of states. For all other cases, this is contraction of operators. If DirectProdGroup, the resulting direct product operator will have the specific quantum label. If [DirectProdGroup], the resulting direct product operator will have mixed quantum labels (not very useful).

Returns:

tensor : Tensor: The contracted Tensor.

copy()¶: Shallow copy.

deep_copy()¶: Deep copy.

diag_eigs(k=-1, limit=None)¶

equal_shape(o)¶

fit(o, v)¶

fuse_index(idxl, fused, target=None, equal=None)¶

get_diag_density_matrix(trace_right, noise=0.0)¶

left_canonicalize(mode='reduced')¶

Left canonicalization (using QR factorization).

Returns:

r_blocks : dict((DirectProdGroup, ) -> numpy.ndarray): The R matrix for each right-index quantum label.

left_multiply(mats)¶

Left Multiplication. Currently only used for multiplying R obtained from right-canonicalization.

Args:

mats : dict((DirectProdGroup, ) -> numpy.ndarray): The R matrix for each right-index quantum label.

modify(other)¶: Modify the blocks according to another Tensor’s blocks.

n_blocks¶: Number of (non-zero) blocks.

ng¶: Number of sub-symmetry groups.

norm()¶

static operator_init(basis, repr, op_q_labels)¶

Build tensor for single-site primiary operator. When this is a tensor operator, repr and op_q_labels will contain multiple items. cgs and reduced will be calculated.

Args:

basis : list(DirectProdGroup): Site basis.
repr : list(numpy.ndarray): A list of dense matrices for different op_q_label s.
op_q_labels : list(DirectProdGroup): A list of operator quantum labels.

Returns:

tensor : Tensor: Operator Tensor.

static partial_trace(ts, idx_l, idx_r, target_q_labels=None)¶

Partial trace of a tensor. The indices in idx_l will be combined. The indices in idx_r will also be combined. Then for each tensor block with q_label[idx_l] == q_label[idx_r], the term will be included, with its reduced matrix traced in corresponding indices.

Args:

ts : Tensor: Tensor to be traced.
idx_l : list(int): Left traced indices.
idx_r : list(int): Right traced indices.
target_q_labels : None: Defaults to None. Currently only the default is implemented.

Returns:

tensor : Tensor: The resulting Tensor with indices idx_l and idx_r are traced.

rank¶: Rank of the tensor.

static rank2_init_target(left, right, target)¶

static rank3_init_left(pre, basis, post)¶

Build the MPS rank-3 tensor by coupling states in pre and basis into states in post. cgs and reduced will not be calculated.

Args:

pre : dict(DirectProdGroup -> int): Left basis.
basis : dict(DirectProdGroup -> int): Site basis.
post : dict(DirectProdGroup -> int): Right basis. Right basis should be obtained from truncating the direct product of left and site basis.

Returns:

tensor : Tensor

static rank3_init_right(pre, basis, post)¶

Build the MPS rank-3 tensor by coupling states in pre and basis into states in post. cgs and reduced will not be calculated.

Args:

pre : dict(DirectProdGroup -> int): Right basis.
basis : dict(DirectProdGroup -> int): Site basis.
post : dict(DirectProdGroup -> int): Left basis. Left basis should be obtained from truncating the direct product of right and site basis.

Returns:

tensor : Tensor

right_canonicalize(mode='reduced')¶

Right canonicalization (using LQ factorization).

Returns:

l_blocks : dict((DirectProdGroup, ) -> numpy.ndarray): The L matrix for each left-index quantum label.

right_multiply(mats)¶

Right Multiplication. Currently only used for multiplying L obtained from right-canonicalization.

Args:

mats : dict((DirectProdGroup, ) -> numpy.ndarray): The L matrix for each left-index quantum label.

set_contractor(contractor)¶: Change the contractor, return self for chain notation.

set_tags(tags)¶: Change the tags, return self for chain notation.

sort()¶: Sort non-zero blocks in increasing order of quantum labels.

split(absorb_right, k=-1)¶

Split rank-2 block-diagonal Tensor to two tensors (using SVD).

Args:

absorb_right : bool: If absorb_right is True, singlular values will be multiplied into right Tensor. Otherwise, They will be multiplied into left Tensor.
k : int: Maximal bond length. Defaults to -1 (no truncation).

Returns:

left_tensor : Tensor: Left tensor.
right_tensor : Tensor: Right tensor.
error : float: Sum of Discarded weights.

split_using_density_matrix(dm, absorb_right, k=-1, limit=None)¶

svd(q_label_left, k=-1)¶

Singular Value Decomposition of rank-2 block-diagonal Tensor.

Args:

k : int: Maximal bond length. Defaults to -1 (no truncation).

Returns:

left_tensor : Tensor: Left tensor.
right_tensor : Tensor: Right tensor.
svd_s : list(numpy.ndarray): A list including singular values for each tensor block.
error : float: Sum of Discarded weights (square of singular values).

to_dict(idx)¶

unfuse_index(idx, left, right)¶

zero_copy()¶: A deep copy with zero reduced matrices.

class pyblock.tensor.tensor.TensorNetwork(tensors=None)¶

Bases: object

An inefficient implementation for Quimb TensorNetwork.

Attributes:

tensors : list(Tensor): List of tensors in the network.

add(tn)¶: Add a Tensor or TensorNetwork to the tensor network.

add_tags(tags)¶: Add tags to all tensors in the tensor network.

contract(tags, in_place=False)¶

Contract a sub tensor network specified by tags. If any Tensor in the sub tensor network has a contractor, the specialized contraction will be used. Currently the general contraction is not implemented.

Args:

tags : tuple(str or int..): Tags of sub tensor network.

Kwargs:

in_place : bool: Defaults to False. Indicating whether the current tensor network should be changed.

Returns:

tn : TensorNetwork: The tensor network with selected sub tensor network replaced by its contraction.

copy()¶: Shallow copy.

deep_copy()¶: Deep copy.

remove(tags, which='all', in_place=False)¶

Remove a sub tensor network specified by tags.

Args:

tags : set(str or int): Tags of sub tensor network.

Kwargs:

which : ‘all’ or ‘any’ or ‘exact’: Defaults to ‘all’. Indicating how the tags should be applied for selection.
in_place : bool: Defaults to False. Indicating whether the current tensor network should be changed.

Returns:

tn : TensorNetwork: The remaining tensor network.

remove_tags(tags)¶: Remove tags from all tensors in the tensor network.

replace(tags, tn, which='all')¶

select(tags, which='all', inverse=False)¶

Extract a sub tensor network specified by tags.

Args:

tags : set(str or int): Tags of sub tensor network.

Kwargs:

which : ‘all’ or ‘any’ or ‘exact’: Defaults to ‘all’. Indicating how the tags should be applied for selection.
inverse : bool: Defaults to False. Indicating whether the selection should be inversed.

Returns:

tn : TensorNetwork: The selected tensor network.

set_contractor(contractor)¶: Set contractor for all tensors in the tensor network.

tags¶: Return a list of tags collected from all tensors in the tensor network.

zero_copy()¶: Deep copy with zeros.

exception pyblock.tensor.tensor.TensorNetworkError¶: Bases: Exception