adpeps.utils.nested

Contains utility class that represents a collection of tensors of different types, with operations that can be applied to all contained tensors at once

class Nested(tensors)

This is a helper class for the efficient contraction of variants of tensors, used in the energy evaluation of excited states

A Nested tensor contains the following variants (some may be empty):

• tensors[0]: regular tensor (no B or Bd)

• tensors[1]: (terms with) a single B tensor

• tensors[2]: (terms with) a single Bd tensor

• tensors[3]: (terms with) both a B and a Bd tensor

When two Nested tensors x,y are contracted, all combinations are taken into account and the result is again a Nested tensor, filled with the following variants:

• tensors[0]: x[0] * y[0]

• tensors[1]: x[1] * y[0] + x[0] * y[1]

• tensors[2]: x[2] * y[0] + x[0] * y[2]

• tensors[3]: x[3] * y[0] + x[2] * y[1] + x[1] * y[2] + x[0] * y[3]

By using Nested tensors in a (large) contraction, the many different terms are resummed on the fly, leading to a potentially reduced computational cost

Note

Most implented functions act as wrappers for the corresponding numpy functions on the individual tensors

mult(other, *args)

Parameters

• other (Union[np.ndarray, Nested, EmptyT]) – other tensor-like object to contract with

• *args – arguments to be passed to the contraction method (np.tensordot)

Returns

result of the contraction

Return type

res

Return type

Nested

normalize()

Normalize the contained tensors by the largest value of the first element of self.tensors

transpose(*args)

Applies transpose to each contained tensor

Return type

Nested