sisl.mixing.AndersonMixer

class sisl.mixing.AndersonMixer

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:

$$\begin{array}{rl}{\mathit{\delta }}_i& ={\mathbf{f}}_i^{\mathrm{out}}-{\mathbf{f}}_i^{\mathrm{in}}\\ \beta & =\frac{⟨{\mathit{\delta }}_i|{\mathit{\delta }}_i-{\mathit{\delta }}_{i-1}⟩}{⟨{\mathit{\delta }}_i-{\mathit{\delta }}_{i-1}|{\mathit{\delta }}_i-{\mathit{\delta }}_{i-1}⟩}\end{array}$$

Finally the resulting output becomes:

$$|n^{m+1}⟩=(1-\alpha )|{\overline{n}}_{\mathrm{in}}^m⟩+\alpha |{\overline{n}}_{\mathrm{out}}^m⟩$$

See [5] 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

Attributes

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)

Calculate a new variable ${\mathbf{f}}^{\prime }$ 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

set_history(history)

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)

Set a new weight for this mixer

Parameters:

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

property history: History

History object tracked by this mixer

property weight: float | int

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