TruncationError

• full name: tenpy.linalg.truncation.TruncationError

• parent module: tenpy.linalg.truncation

• type: class

Inheritance Diagram

Methods

TruncationError.__init__([eps, ov])
TruncationError.copy()	Return a copy of self.
TruncationError.from_S(S_discarded[, norm_old])	Construct TruncationError from discarded singular values.
TruncationError.from_hdf5(hdf5_loader, h5gr, ...)	Load instance from a HDF5 file.
TruncationError.from_norm(norm_new[, norm_old])	Construct TruncationError from norm after and before the truncation.
TruncationError.save_hdf5(hdf5_saver, h5gr, ...)	Export self into a HDF5 file.

Class Attributes and Properties

TruncationError.ov_err

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

class tenpy.linalg.truncation.TruncationError(eps=0.0, ov=1.0)

Bases: Hdf5Exportable

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:

• eps (float) – See below.

• ov (float) – See below.

eps

The total sum of all discarded 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

copy()

Return a copy of self.

classmethod from_norm(norm_new, norm_old=1.0)

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)

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.

classmethod from_hdf5(hdf5_loader, h5gr, subpath)

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

save_hdf5(hdf5_saver, h5gr, subpath)

Export self into a HDF5 file.

This method saves all the data it needs to reconstruct self with from_hdf5().

This implementation saves the content of __dict__ with save_dict_content(), storing the format under the attribute 'format'.

Parameters:

• hdf5_saver (Hdf5Saver) – Instance of the saving engine.

• h5gr (:class`Group`) – HDF5 group which is supposed to represent self.

• subpath (str) – The name of h5gr with a '/' in the end.