transform¶

The transform module.

class nutils.transform.TransformItem(todims, fromdims)¶

Bases: Singleton

Affine transformation.

Base class for transformations of the type \(x ↦ A x + b\).

Parameters:

todims (int) – Dimension of the affine transformation domain.
fromdims (int) – Dimension of the affine transformation range.

class nutils.transform.Matrix(linear, offset)¶

Bases: TransformItem

Affine transformation \(x ↦ A x + b\), with \(A\) an \(n×m\) matrix, \(n≥m\)

Parameters:

linear (numpy.ndarray) – The transformation matrix \(A\).
offset (numpy.ndarray) – The offset \(b\).

class nutils.transform.Square(linear, offset)¶

Bases: Matrix

Affine transformation \(x ↦ A x + b\), with \(A\) square

Parameters:

linear (numpy.ndarray) – The transformation matrix \(A\).
offset (numpy.ndarray) – The offset \(b\).

class nutils.transform.Identity(ndims)¶

Bases: Square

Identity transformation \(x ↦ x\)

Parameters:: ndims (int) – Dimension of \(x\).

class nutils.transform.Index(ndims, index)¶

Bases: Identity

Identity transform with index

This transformation serves as an element-specific or topology-specific index to form the basis of transformation lookups. Otherwise, the transform behaves like an identity.

class nutils.transform.Updim(linear, offset, isflipped)¶

Bases: Matrix

Affine transformation \(x ↦ A x + b\), with \(A\) an \(n×(n-1)\) matrix

Parameters:

linear (numpy.ndarray) – The transformation matrix \(A\).
offset (numpy.ndarray) – The offset \(b\).

class nutils.transform.EvaluableTransformChain(args, todims, fromdims)¶

Bases: Evaluable

The Evaluable equivalent of a transform chain.

todims¶

The to dimension of the transform chain.

Type:: int

fromdims¶

The from dimension of the transform chain.

Type:: int

static empty(_EvaluableTransformChain__dim)¶

Return an empty evaluable transform chain with the given dimension.

Parameters:: dim (int) – The to and from dimensions of the empty transform chain.
Returns:: The empty evaluable transform chain.
Return type:: EvaluableTransformChain

static from_argument(name, todims, fromdims)¶

Return an evaluable transform chain that evaluates to the given argument.

Parameters:

name (str) – The name of the argument.
todims (int) – The to dimension of the transform chain.
fromdims (int) – The from dimension of the transform chain.

Returns:

The transform chain that evaluates to the given argument.

Return type:

EvaluableTransformChain

property linear: Array¶

The linear transformation matrix of the entire transform chain. Shape (todims,fromdims).

Type:: nutils.evaluable.Array

property basis: Array¶

A basis for the root coordinate system such that the first fromdims vectors span the tangent space. Shape (todims,todims).

Type:: nutils.evaluable.Array

apply(self, _EvaluableTransformChain__coords)¶

Apply this transform chain to the last axis given coordinates.

Parameters:: coords (nutils.evaluable.Array) – The coordinates to transform with shape (...,fromdims).
Returns:: The transformed coordinates with shape (...,todims).
Return type:: nutils.evaluable.Array

index_with_tail_in(self, _EvaluableTransformChain__sequence)¶

Return the evaluable index of this transform chain in the given sequence.

Parameters:

sequence (nutils.transformseq.Transforms) – The sequence of transform chains.

Returns:

nutils.evaluable.Array – The index of this transform chain in the given sequence.
EvaluableTransformChain – The tail.