TruncationError¶

full name: tenpy.algorithms.truncation.TruncationError
parent module: tenpy.algorithms.truncation
type: class

Inheritance Diagram

Methods

`TruncationError.__init__`([eps, ov])	Initialize self.
`TruncationError.copy`()	Return a copy of self.
`TruncationError.from_S`(S_discarded[, norm_old])	Construct TruncationError from discarded singular values.
`TruncationError.from_norm`(norm_new[, norm_old])	Construct TruncationError from norm after and before the truncation.

Class Attributes and Properties

TruncationError.ov_err

Error 1.-ov of the overlap with the correct state.

class tenpy.algorithms.truncation.TruncationError(eps=0.0, ov=1.0)[source]¶

Bases: object

Class representing a truncation error.

The default initialization represents “no truncation”.

Warning

For imaginary time evolution, this is not the error you are interested in!

Parameters: ov (eps,) – See below.

eps¶

The total sum of all discared Schmidt values squared. Note that if you keep singular values up to 1.e-14 (= a bit more than machine precision for 64bit floats), eps is on the order of 1.e-28 (due to the square)!

Type: float

ov¶

A lower bound for the overlap \(|\langle \psi_{trunc} | \psi_{correct} \rangle|^2\) (assuming normalization of both states). This is probably the quantity you are actually interested in. Takes into account the factor 2 explained in the section on Errors in the TEBD Wikipedia article <https://en.wikipedia.org/wiki/Time-evolving_block_decimation>.

Type: float

Examples

>>> TE = TruncationError()
>>> TE += tebd.time_evolution(...)  # add `eps`, multiply `ov`

copy()[source]¶: Return a copy of self.

classmethod from_norm(norm_new, norm_old=1.0)[source]¶

Construct TruncationError from norm after and before the truncation.

Parameters

norm_new (float) – Norm of Schmidt values kept, \(\sqrt{\sum_{a kept} \lambda_a^2}\) (before re-normalization).
norm_old (float) – Norm of all Schmidt values before truncation, \(\sqrt{\sum_{a} \lambda_a^2}\).

classmethod from_S(S_discarded, norm_old=None)[source]¶

Construct TruncationError from discarded singular values.

Parameters

S_discarded (1D numpy array) – The singular values discarded.
norm_old (float) – Norm of all Schmidt values before truncation, \(\sqrt{\sum_{a} \lambda_a^2}\). Default (None) is 1.

property ov_err¶: Error 1.-ov of the overlap with the correct state.