netket.symmetry.group.PGSymmetry

class netket.symmetry.group.PGSymmetry

Bases: Element

An abstract group element object to geometrically describe point group symmetries.

Construction: PGSymmetry(W,w) with an orthogonal matrix W and an optional translation vector w returns an object that maps vectors \(\vec x\) to \(W\vec x + \vec w\).

Internally, the transformation is stored as the affine matrix [[W,w],[0,1]], such that matrix inverses and multiplication correspond to inverting and multiplying the transformation itself.

Inheritance

Attributes

affine_matrix

Returns the (d+1) × (d+1) dimensional matrix representing the action of self as an affine transformation.

is_proper

Returns True if self is a proper rotation (det(self.matrix) is +1).

is_symmorphic

Returns True if self leaves the origin in place.

matrix

Returns the d×d dimensional matrix representing the rotational action of self.

ndim

Returns the dimension of vectors self acts on.

translation

Returns the translation vector associated with self.

Methods

__call__(ket)

Call self as a function.

change_origin(origin)

Returns a PGSymmetry representing a pure point-group transformation around origin with transformation matrix self._W.

Return type:

PGSymmetry

Parameters:

origin (ndarray | Array)

k_action(x)

Returns the action of self on the input without the associated translation. This is how the symmetry acts on wave vectors.

preimage(x)

Returns the preimage of x under the transformation (i.e., self @ self.preimage(x) == x up to numerical accuracy.

replace(**updates)

Returns a new object replacing the specified fields with new values.