a ߙfbz@shdZddlmZddlZddlmZddlm Z ddZ d d Z dd d Z ddZ ddZdddZdS)zC Utililies used for constructing and inspecting rotation matrices. )reduceN)units)AnglecGs ttj|S)axMatrix multiply all arguments together. Arguments should have dimension 2 or larger. Larger dimensional objects are interpreted as stacks of matrices residing in the last two dimensions. This function mostly exists for readability: using `~numpy.matmul` directly, one would have ``matmul(matmul(m1, m2), m3)``, etc. For even better readability, one might consider using `~numpy.matrix` for the arguments (so that one could write ``m1 * m2 * m3``), but then it is not possible to handle stacks of matrices. Once only python >=3.5 is supported, this function can be replaced by ``m1 @ m2 @ m3``. )rnpmatmul)ZmatricesrClib/python3.9/site-packages/astropy/coordinates/matrix_utilities.pymatrix_products r cCs |ddS)aQTranspose a matrix or stack of matrices by swapping the last two axes. This function mostly exists for readability; seeing ``.swapaxes(-2, -1)`` it is not that obvious that one does a transpose. Note that one cannot use `~numpy.ndarray.T`, as this transposes all axes and thus does not work for stacks of matrices. )swapaxes)matrixrrr matrix_transposesrzc Cst|tjr|tj}n(|dur.t|}nt|tj |}t |}t |}zd |}Wnt yXt|}|t||jddd}|dtjf|dtjddfd|dtjtjf}tdd D]v}|d||f|7<|d d }|d d }|d||f|d|f|7<|d||f|d|f|8<qYnx0|d d }|d d }tt|d d d}d|d||f<||d||f<||d||f<| |d||f<||d||f<|S)aU Generate matrices for rotation by some angle around some axis. Parameters ---------- angle : angle-like The amount of rotation the matrices should represent. Can be an array. axis : str or array-like Either ``'x'``, ``'y'``, ``'z'``, or a (x,y,z) specifying the axis to rotate about. If ``'x'``, ``'y'``, or ``'z'``, the rotation sense is counterclockwise looking down the + axis (e.g. positive rotations obey left-hand-rule). If given as an array, the last dimension should be 3; it will be broadcast against ``angle``. unit : unit-like, optional If ``angle`` does not have associated units, they are in this unit. If neither are provided, it is assumed to be degrees. Returns ------- rmat : `numpy.matrix` A unitary rotation matrix. NZxyzr T)axiskeepdims.?rrshaperrr) isinstanceuZQuantityZto_valueradianrZdeg2radZUnittoZradZsinZcosindex TypeErrorZasarraysqrtsumZnewaxisrangezerosgetattr) anglerZunitsciRZa1Za2rrr rotation_matrix)s<        "*  r(cCst|}|jdddkr$tdt|jdd}|d|d|d<|d |d |d <|d |d |d<t||jddd}t|d|d|d|dd}t|t j | |fS)av Angle of rotation and rotation axis for a given rotation matrix. Parameters ---------- matrix : array-like A 3 x 3 unitary rotation matrix (or stack of matrices). Returns ------- angle : `~astropy.coordinates.Angle` The angle of rotation. axis : array The (normalized) axis of rotation (with last dimension 3). r Nrzmatrix is not 3x3r ).rr).rr).r).rr).rr).r).rr).rr).rT)r).rr).rr).rrr) rZ asanyarrayr ValueErrorr!rrZarctan2rrr)rmrrr#rrr angle_axishs  r,cCs:t|jd}tjtj||dd|dddd}|S)aCheck whether a matrix is in the length-preserving group O(3). Parameters ---------- matrix : (..., N, N) array-like Must have attribute ``.shape`` and method ``.swapaxes()`` and not error when using `~numpy.isclose`. Returns ------- is_o3 : bool or array of bool If the matrix has more than two axes, the O(3) check is performed on slices along the last two axes -- (M, N, N) => (M, ) bool array. Notes ----- The orthogonal group O(3) preserves lengths, but is not guaranteed to keep orientations. Rotations and reflections are in this group. For more information, see https://en.wikipedia.org/wiki/Orthogonal_group r r gV瞯<)Zatol)r r )r)rZidentityralliscloser )rIis_o3rrr is_O3s r1FcCsDt|}|r(tttj|d}nttj|d}||@S)ahCheck whether a matrix is a rotation, proper or improper. Parameters ---------- matrix : (..., N, N) array-like Must have attribute ``.shape`` and method ``.swapaxes()`` and not error when using `~numpy.isclose` and `~numpy.linalg.det`. allow_improper : bool, optional Whether to restrict check to the SO(3), the group of proper rotations, or also allow improper rotations (with determinant -1). The default (False) is only SO(3). Returns ------- isrot : bool or array of bool If the matrix has more than two axes, the checks are performed on slices along the last two axes -- (M, N, N) => (M, ) bool array. See Also -------- astopy.coordinates.matrix_utilities.is_O3 : For the less restrictive check that a matrix is in the group O(3). Notes ----- The group SO(3) is the rotation group. It is O(3), with determinant 1. Rotations with determinant -1 are improper rotations, combining both a rotation and a reflection. For more information, see https://en.wikipedia.org/wiki/Orthogonal_group r)r1rr.absZlinalgZdet)rZallow_improperr0Zis_det1rrr is_rotations !r3)rN)F)__doc__ functoolsrZnumpyrZastropyrrZanglesrr rr(r,r1r3rrrr s    ?