g@dZddlmZddlZddlZGddZdS)z! A module for using quaternions. ) annotationsNceZdZdZdZdZdZdZdZdZ ddd Z ddZ ddZ e ddZe dd dZdS)! Quaternionz"A class representing a Quaternion.cFtj|t|_dS)Ndtype)npasarrayfloatdata)selfr s T/granary/edev/quantum/lib/python3.11/site-packages/qiskit/quantum_info/quaternion.py__init__zQuaternion.__init__sJt5111 c|j|SN)r )r idxs r__call__zQuaternion.__call__sy~rc4tj|jSrr array_strr r s r__repr__zQuaternion.__repr__|DI&&&rc4tj|jSrrrs r__str__zQuaternion.__str__!rrct|tr|}tjdt}|d|dz|d|dzz |d|dzz |d|dzz |d<|d|dz|d|dzz|d|dzz |d|dzz|d<|d|dz|d|dzz|d|dzz|d|dzz |d<|d|dz|d|dzz |d|dzz|d|dzz|d<t|St S)Nrr) isinstancerr zerosr NotImplemented)r rqout_datas r__mul__zQuaternion.__mul__$s a $ $ "Ax///H!A$$1+!qqtt 3aaddQQqTTkAAAaDD11Q44KOHQK!A$$1+!qqtt 3aaddQQqTTkAAAaDD11Q44KOHQK!A$$1+!qqtt 3aaddQQqTTkAAAaDD11Q44KOHQK!A$$1+!qqtt 3aaddQQqTTkAAAaDD11Q44KOHQKh'' '! !rcBddlm}||jS)zNorm of quaternion.rN) scipy.linalglinalgnormr )r las rr,zQuaternion.norm0s(!!!!!!wwty!!!rFinplaceboolreturnc|r&|}|xj|zc_dS|}tj|jd}||z}t |S)zNormalizes a Quaternion to unit length so that it represents a valid rotation. Args: inplace (bool): Do an inplace normalization. Returns: Quaternion: Normalized quaternion. NT)copy)r,r r arrayr)r r.nrm data_copys r normalizezQuaternion.normalize6si  ))++C II II4iikkHTYT222 S )$$$r np.ndarrayc |j\}}}}tjdd|dzzz d|dzzz d|z|zd|z|zz d|z|zd|z|zzgd|z|zd|z|zzdd|dzzz d|dzzz d|z|zd|z|zz gd|z|zd|z|zz d|z|zd|z|zzdd|dzzz d|dzzz ggt}|S)zxConverts a unit-length quaternion to a rotation matrix. Returns: ndarray: Rotation matrix. rr r)r6r r r3r )r wxyzmats r to_matrixzQuaternion.to_matrixIs3 ^^%%* 1ahQAXAqD(!a%!)a!eai*?QQQRUUVYAVWQQUQY&A1H q1a4x(?QQQRUUVYAVWQQUQY&A AEAI(=q1q!t8|aRSUVRVh?VW       rc|}tjdt}|ddkr|ddkrgt j|d|d|d<t j|d|d<t j|d |d  |d <nYt j|d |d  |d<tj|d<n$t j|d |d |d<|S)zConverts a unit-length quaternion to a sequence of ZYZ Euler angles. Returns: ndarray: Array of Euler angles. r!r)r r r)rr )rr r)r r)r rr )rr)rr)r>r r#r mathatan2acospi)r r=eulers rto_zyzzQuaternion.to_zyzZsnn%((( t9q==4y2~~:c$iT;;a9SY//a:c$i#d)<<a Js4y#d)<<<a5az#d)SY77E!H rangler axisstrctjdt}|dkrd|d<n'|dkrd|d<n|dkrd|d<ntd |t j|d z z}t j|d z |d <||S) a$Return quaternion for rotation about given axis. Args: angle (float): Angle in radians. axis (str): Axis for rotation Returns: Quaternion: Quaternion for axis rotation. Raises: ValueError: Invalid input axis. rrr:rr;r r<r!zInvalid axis input.g@r)r r#r ValueErrorrAsincos)clsrGrHouts rfrom_axis_rotationzQuaternion.from_axis_rotationoshq&&& 3;;CFF S[[CFF S[[CFF233 3 tx $$$%#+&&As3xxryzyangleslist | np.ndarrayorderc8tj|t}||d|d||d|dz||d|dz}|d|S)aGenerate a quaternion from a set of Euler angles. Args: angles (array_like): Array of Euler angles. order (str): Order of Euler rotations. 'yzy' is default. Returns: Quaternion: Quaternion representation of Euler rotation. rrrr T)r.)r r r rPr6)rNrRrTquats r from_eulerzQuaternion.from_eulersF%000  " "6!9eAh 7 7$$VAYa99 :$$VAYa99 : t$$$ rN)F)r.r/r0r)r0r7)rGr rHrIr0r)rQ)rRrSrTrIr0r)__name__ __module__ __qualname____doc__rrrrr(r,r6r>rF classmethodrPrWrrrrs,,222'''''' " " """" %%%%%&"*[4[rr)r[ __future__rrAnumpyr rr]rrr`st#""""" GGGGGGGGGGr