`scipy.spatial.transform._rotation:Rotation.from_matrix`

source: /scipy/spatial/transform/_rotation.py :476

Signature

staticmethod

   def     from_matrix (    matrix  :  ArrayLike    ,  * ,     assume_valid  :  bool    =  False     )   →  Rotation

Summary

Initialize from rotation matrix.

Extended Summary

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

matrix : array_like, shape (..., 3, 3): A single matrix or an ND array of matrices, where the last two dimensions contain the rotation matrices.
assume_valid : bool, 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

rotation : `Rotation` instance: Object containing the rotations represented by the rotation matrices.

Notes

This function was called from_dcm before.

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 dev-arrayapi for more information.

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
r.as_matrix().shape

✓

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
r.single
len(r)

✓

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)

✗

r = R.from_matrix(a)
matrix = r.as_matrix()
matrix

✓

np.linalg.det(matrix)

✗

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()
r.as_matrix().shape

✓

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

✓

Aliases

scipy.spatial.transform.Rotation.from_matrix