scipy.spatial.transform.RigidTransform.

identity#

static RigidTransform.identity(num=None, *, shape=None)[source]#

Initialize an identity transform.

Composition with the identity transform has no effect, and applying the identity transform to a vector has no effect.

Parameters:
numint, optional

Number of identity transforms to generate. If None (default), then a single transform is generated.

shapeint or tuple of ints, optional

Shape of the identity transforms. If specified, num must be None.

Returns:
transformRigidTransform instance

The identity transform.

Notes

Array API Standard Support

identity has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library

CPU

GPU

NumPy

✅

n/a

CuPy

n/a

✅

PyTorch

✅

✅

JAX

✅

✅

Dask

⛔

n/a

See Support for the array API standard for more information.

Examples

>>> from scipy.spatial.transform import RigidTransform as Tf
>>> from scipy.spatial.transform import Rotation as R
>>> import numpy as np

Creating a single identity transform:

>>> tf = Tf.identity()
>>> tf.as_matrix()
array([[1., 0., 0., 0.],
       [0., 1., 0., 0.],
       [0., 0., 1., 0.],
       [0., 0., 0., 1.]])
>>> tf.single
True

The identity transform can be applied to a vector without effect:

>>> tf.apply([1, 2, 3])
array([1., 2., 3.])

The identity transform when composed with another transform has no effect:

>>> rng = np.random.default_rng()
>>> t = rng.random(3)
>>> r = R.random(rng=rng)
>>> tf = Tf.from_components(t, r)
>>> np.allclose((Tf.identity() * tf).as_matrix(),
...             tf.as_matrix(), atol=1e-12)
True

Multiple identity transforms can be generated at once:

>>> tf = Tf.identity(2)
>>> tf.as_matrix()
array([[[1., 0., 0., 0.],
        [0., 1., 0., 0.],
        [0., 0., 1., 0.],
        [0., 0., 0., 1.]],
       [[1., 0., 0., 0.],
        [0., 1., 0., 0.],
        [0., 0., 1., 0.],
        [0., 0., 0., 1.]]])
>>> tf.single
False
>>> len(tf)
2