scipy.spatial.transform.Rotation.

from_matrix#

static Rotation.from_matrix(matrix, *, assume_valid=False)[source]#

Initialize from rotation matrix.

Rotations in 3 dimensions can be represented with 3 x 3 orthogonal matrices [1]. If the input is not orthogonal, an approximation is created by orthogonalizing the input matrix using the method described in [2], and then converting the orthogonal rotation matrices to quaternions using the algorithm described in [3]. Matrices must be right-handed.

Parameters:
matrixarray_like, shape (…, 3, 3)

A single matrix or an ND array of matrices, where the last two dimensions contain the rotation matrices.

assume_validbool, optional

Must be False unless users can guarantee the input is a valid rotation matrix, i.e. it is orthogonal, rows and columns have unit norm and the determinant is 1. Setting this to True without ensuring these properties is unsafe and will silently lead to incorrect results. If True, normalization steps are skipped, which can improve runtime performance. Default is False.

Returns:
rotationRotation instance

Object containing the rotations represented by the rotation matrices.

Notes

This function was called from_dcm before.

Added in version 1.4.0.

Array API Standard Support

from_matrix 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.

References

[3]

F. Landis Markley, “Unit Quaternion from Rotation Matrix”, Journal of guidance, control, and dynamics vol. 31.2, pp. 440-442, 2008.

Examples

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

Initialize a single rotation:

>>> r = R.from_matrix([
... [0, -1, 0],
... [1, 0, 0],
... [0, 0, 1]])
>>> r.single
True
>>> r.as_matrix().shape
(3, 3)

Initialize multiple rotations in a single object:

>>> r = R.from_matrix([
... [
...     [0, -1, 0],
...     [1, 0, 0],
...     [0, 0, 1],
... ],
... [
...     [1, 0, 0],
...     [0, 0, -1],
...     [0, 1, 0],
... ]])
>>> r.as_matrix().shape
(2, 3, 3)
>>> r.single
False
>>> len(r)
2

If input matrices are not special orthogonal (orthogonal with determinant equal to +1), then a special orthogonal estimate is stored:

>>> a = np.array([
... [0, -0.5, 0],
... [0.5, 0, 0],
... [0, 0, 0.5]])
>>> np.linalg.det(a)
0.125
>>> r = R.from_matrix(a)
>>> matrix = r.as_matrix()
>>> matrix
array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.]])
>>> np.linalg.det(matrix)
1.0

It is also possible to have a stack containing a single rotation:

>>> r = R.from_matrix([[
... [0, -1, 0],
... [1, 0, 0],
... [0, 0, 1]]])
>>> r.as_matrix()
array([[[ 0., -1.,  0.],
        [ 1.,  0.,  0.],
        [ 0.,  0.,  1.]]])
>>> r.as_matrix().shape
(1, 3, 3)

We can also create an N-dimensional array of rotations:

>>> r = R.from_matrix(np.tile(np.eye(3), (2, 3, 1, 1)))
>>> r.shape
(2, 3)
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