mt.geond.dilated_isometry

Functions

mt.geond.dilated_isometry.approx_Aff_to_Dliso(obj)

Approximates an Aff instance with a Dliso.

Classes

  • Dliso: Dilated isometry = Isometry following a uniform scaling.

class mt.geond.dilated_isometry.Dliso(offset=array([0., 0.]), scale=1, unitary=array([[1., 0.], [0., 1.]]))

Dilated isometry = Isometry following a uniform scaling.

An isometry is a (Euclidean-)metric-preserving transformation. In other words, it is an affine transformation but the linear part is a unitary matrix.

References

Inheritance

digraph inheritance629cbddbc4 { bgcolor=transparent; rankdir=LR; size="8.0, 12.0"; "Aff" [URL="mt.geond.affine.html#mt.geond.affine.Aff",fillcolor=white,fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",fontsize=10,height=0.25,shape=box,style="setlinewidth(0.5),filled",target="_top",tooltip="A transformer to perform affine transformations using the same transformation matrix in n-dim space."]; "LieTransformer" -> "Aff" [arrowsize=0.5,style="setlinewidth(0.5)"]; "GeometricObject" -> "Aff" [arrowsize=0.5,style="setlinewidth(0.5)"]; "Dliso" [URL="#mt.geond.dilated_isometry.Dliso",fillcolor=white,fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",fontsize=10,height=0.25,shape=box,style="setlinewidth(0.5),filled",target="_top",tooltip="Dilated isometry = Isometry following a uniform scaling."]; "Aff" -> "Dliso" [arrowsize=0.5,style="setlinewidth(0.5)"]; "GeometricObject" [URL="../mt.geo/mt.geo.object.html#mt.geo.object.GeometricObject",fillcolor=white,fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",fontsize=10,height=0.25,shape=box,style="setlinewidth(0.5),filled",target="_top",tooltip="A geometric object which lives in a d-dimensional Euclidean space."]; "InvertibleTransformer" [URL="../mt.geo/mt.geo.transformation.html#mt.geo.transformation.InvertibleTransformer",fillcolor=white,fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",fontsize=10,height=0.25,shape=box,style="setlinewidth(0.5),filled",target="_top",tooltip="A mixin asserting that this is a class of invertible transformers. "]; "Transformer" -> "InvertibleTransformer" [arrowsize=0.5,style="setlinewidth(0.5)"]; "LieTransformer" [URL="../mt.geo/mt.geo.transformation.html#mt.geo.transformation.LieTransformer",fillcolor=white,fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",fontsize=10,height=0.25,shape=box,style="setlinewidth(0.5),filled",target="_top",tooltip="A mixin asserting that this is a class of transformers living in a Lie group, supporting the associative multiplication operator and the inversion operator. "]; "InvertibleTransformer" -> "LieTransformer" [arrowsize=0.5,style="setlinewidth(0.5)"]; "Transformer" [URL="../mt.geo/mt.geo.transformation.html#mt.geo.transformation.Transformer",fillcolor=white,fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",fontsize=10,height=0.25,shape=box,style="setlinewidth(0.5),filled",target="_top",tooltip="A mixin asserting that this is a class of transformers."]; }
__init__(offset=array([0., 0.]), scale=1, unitary=array([[1., 0.], [0., 1.]]))
__repr__()

Return repr(self).

property bias

The bias component of the affine transformation matrix.

property bias_dim

Returns the dimension of the bias vector.

invert()

Lie inverse

property linear

Returns the linear part of the affine transformation matrix of the dilated isometry.

multiply(other)

a*b = Lie operator

property offset

The offset/bias part of the dilated isometry.

property scale

The scale component/scalar of the dilated isometry.

property unitary

The unitary matrix of the dilated isometry.

property weight

The weight/linear component of the affine transformation matrix.

property weight_shape

Returns the shape of the weight matrix.