mt.geond.affine

Affine transformation in ND.

Functions

mt.geond.affine.transform_Aff_on_Moments(aff_tfm, moments)

Transform the Moments using an affine transformation.

Parameters:

  • aff_tfm (Aff) – general affine transformation

  • moments (Moments) – general moments

Returns:

affined-transformed moments

Return type:

Moments

mt.geond.affine.transform_Aff_on_PointList(aff_tfm, point_list)

Transform a point list using an affine transformation.

Parameters:

  • aff_tfm (Aff) – general affine transformation

  • point_list (PointList) – a point list

Returns:

affine-transformed point list

Return type:

PointList

Classes

  • Aff: A transformer to perform affine transformations using the same transformation matrix in n-dim space.

class mt.geond.affine.Aff(weight=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]), bias=array([0., 0., 0.]), check_shapes=True)

A transformer to perform affine transformations using the same transformation matrix in n-dim space.

Examples

>>> from mt import np, geond as gn
>>> a = gn.Aff(weight=np.array([[1,-1],[-2,3]]), bias=np.array([3,4]))
>>> a.bias
array([3, 4])
>>> a.weight
array([[ 1, -1],
       [-2,  3]])
>>> a.matrix
array([[ 1., -1.,  3.],
       [-2.,  3.,  4.],
       [ 0.,  0.,  1.]])
>>> ~a
Aff(weight_diagonal=[3. 1.], bias=[-13. -10.])
>>> a*~a
Aff(weight_diagonal=[1. 1.], bias=[0. 0.])
>>> ~a*a
Aff(weight_diagonal=[1. 1.], bias=[0. 0.])
>>> a/a
Aff(weight_diagonal=[1. 1.], bias=[0. 0.])
>>> a%a
Aff(weight_diagonal=[1. 1.], bias=[0. 0.])
>>> a*a
Aff(weight_diagonal=[ 3 11], bias=[ 2 10])
>>> a*a*a
Aff(weight_diagonal=[11 41], bias=[-5 30])
>>> (a*a)*a
Aff(weight_diagonal=[11 41], bias=[-5 30])
>>> a*(a*a)
Aff(weight_diagonal=[11 41], bias=[-5 30])
>>> b = gn.Aff(weight=np.array([[1,-1],[-3,2]]), bias=np.array([2,1]))
>>> a*b
Aff(weight_diagonal=[4 8], bias=[4 3])
>>> b*a
Aff(weight_diagonal=[3 9], bias=[1 0])
>>> a.conjugate(b)
Aff(weight_diagonal=[ 6. -3.], bias=[-18.  66.])

Inheritance

digraph inheritance255988c9b4 { bgcolor=transparent; rankdir=LR; size="8.0, 12.0"; "Aff" [URL="#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)"]; "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__(weight=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]), bias=array([0., 0., 0.]), check_shapes=True)
__repr__()

Return repr(self).

property bias

The bias component of the affine transformation matrix.

property bias_dim

Returns the dimension of the bias vector.

property det

Returns the determinant of the transformation matrix.

property dim

Returns the dimension of the transformation.

invert()

Lie inverse

property matrix

Returns the transformation matrix.

multiply(other)

a*b = Lie operator

property ndim

Returns the number of dimensions in which the geometric object lives.

property weight

The weight/linear component of the affine transformation matrix.

property weight_shape

Returns the shape of the weight matrix.