TruncationError¶

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

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

Examples

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

Attributes

ov_err: Error 1.-ov of the overlap with the correct state.
epsfloat: 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)!
ovfloat: 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>.

Methods

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

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

Construct TruncationError from norm after and before the truncation.

Parameters

norm_newfloat: Norm of Schmidt values kept, \(\sqrt{\sum_{a kept} \lambda_a^2}\) (before re-normalization).
norm_oldfloat: 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_discarded1D numpy array: The singular values discarded.
norm_oldfloat: Norm of all Schmidt values before truncation, \(\sqrt{\sum_{a} \lambda_a^2}\). Default (None) is 1.