sisl.mixing.AndersonMixer

class sisl.mixing.AndersonMixer(weight: float | int = 0.2, history: int | History = 0)[source]

Bases: BaseHistoryWeightMixer

Anderson mixing

The Anderson mixing assumes that the mixed input/output are linearly related. Hence

\[|\bar{n}^{m}_{\mathrm{in}/\mathrm{out}\rangle = (1 - \beta)|n^{m}_{\mathrm{in}/\mathrm{out}\rangle + \beta|n^{m-1}_{\mathrm{in}/\mathrm{out}\rangle\]

Here the optimal choice \(\beta\) is calculated as:

\[\begin{split}\boldsymbol\delta_i &= \mathbf f_i^{\mathrm{out}} - \mathbf f_i^{\mathrm{in}} \\ \beta &= \frac{\langle \boldsymbol\delta_i | \boldsymbol\delta_i - \boldsymbol\delta_{i-1}\rangle} {\langle \boldsymbol\delta_i - \boldsymbol\delta_{i-1}| \boldsymbol\delta_i - \boldsymbol\delta_{i-1} \rangle}\end{split}\]

Finally the resulting output becomes:

\[|n^{m+1}\rangle = (1 - \alpha)|\bar n^m_{\mathrm{in}}\rangle + \alpha|\bar n^m_{\mathrm{out}}\rangle\]

See [3] for more details.

Methods

set_history(history)

Replace the current history in the mixer with a new one

set_weight(weight)

Set a new weight for this mixer

history

History object tracked by this mixer

weight

This mixers mixing weight, the weight is the fractional contribution of the derivative
Parameters:

  • weight (TypeWeight)

  • history (TypeArgHistory)

__call__(f: T, df: T, delta: Any | None = None, append: bool = True) → T[source]

Calculate a new variable \(\mathbf f'\) using input and output of the functional

Parameters:

  • f (object) – input variable for the functional

  • df (object) – derivative of the functional

  • delta (Any | None)

  • append (bool)

Return type:

T

__init__(weight: float | int = 0.2, history: int | History = 0)
Parameters:
property history: History

History object tracked by this mixer

set_history(history: int | History) → None

Replace the current history in the mixer with a new one

Parameters:

history (int | History) – if an int a new History object will be created with that number of history elements Otherwise the object will be directly attached to the mixer.

Return type:

None

set_weight(weight: float | int)

Set a new weight for this mixer

Parameters:

weight (float) – the new weight for this mixer, it must be bigger than 0

property weight: float | int

This mixers mixing weight, the weight is the fractional contribution of the derivative