sisl.mixing.AndersonMixer

class sisl.mixing.AndersonMixer(weight=0.2, 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:

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

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

__call__(f, df, delta=None, append=True)[source]

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

Parameters

f (object) – input variable for the functional
df (object) – derivative of the functional

Return type

TypeVar(T)

__init__(weight=0.2, history=0)

property history: History: History object tracked by this mixer

set_history(history)

Replace the current history in the mixer with a new one

Parameters: history (Union[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)

Set a new weight for this mixer

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

property weight: Union[float, int]: This mixers mixing weight, the weight is the fractional contribution of the derivative