z i8SrSSKJr SSKrSSKr"SS5rg)z! A module for using quaternions. ) annotationsNc\rSrSrSrSrSrSrSrSr Sr SSS jjr SS jr SS jr \SS j5r\SSS jj5rSrg) Quaternionz"A class representing a Quaternion.c@[R"U[S9Ulg)Ndtype)npasarrayfloatdata)selfr s X/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/quantum_info/quaternion.py__init__Quaternion.__init__sJJt51 c URU$Nr )ridxs r__call__Quaternion.__call__syy~rcB[R"UR5$rr array_strr rs r__repr__Quaternion.__repr__||DII&&rcB[R"UR5$rrrs r__str__Quaternion.__str__!rrc[U[5(GaNUn[R"S[S9nU"S5U"S5-U"S5U"S5-- U"S5U"S5-- U"S5U"S5-- US'U"S5U"S5-U"S5U"S5--U"S5U"S5-- U"S5U"S5--US'U"S5U"S5-U"S5U"S5--U"S5U"S5--U"S5U"S5-- US'U"S5U"S5-U"S5U"S5-- U"S5U"S5--U"S5U"S5--US'[U5$[ $)Nrr) isinstancerr zerosr NotImplemented)rrqout_datas r__mul__Quaternion.__mul__$sU a $ $Axx/HA$1+!qt 3adQqTkAAaD1Q4KOHQKA$1+!qt 3adQqTkAAaD1Q4KOHQKA$1+!qt 3adQqTkAAaD1Q4KOHQKA$1+!qt 3adQqTkAAaD1Q4KOHQKh' '! !rcDSSKJn URUR5$)zNorm of quaternion.rN) scipy.linalglinalgnormr )rlas rr3Quaternion.norm0s!wwtyy!!rcU(a&UR5nU=RU-slgUR5n[R"URSS9nX2-n[ U5$)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)r3r r arrayr)rinplacenrm data_copys r normalizeQuaternion.normalize6sU ))+C II IiikHHTYYT2  )$$rc UR5Rupp4[R"SSUS--- SUS--- SU-U-SU-U-- SU-U-SU-U--/SU-U-SU-U--SSUS--- SUS--- SU-U-SU-U-- /SU-U-SU-U-- SU-U-SU-U--SSUS--- SUS--- //[S9nU$)z`Converts a unit-length quaternion to a rotation matrix. Returns: ndarray: Rotation matrix. r%r&r)r<r r r8r )rwxyzmats r to_matrixQuaternion.to_matrixIs' ^^%** ahhQAXAqD(!a%!)a!eai*?QQQRUUVYAVWQQUQY&A1H q1a4x(?QQQRUUVYAVWQQUQY&A AEAI(=q1q!t8|aRSUVRVh?VW     rcUR5n[R"S[S9nUSS:aUSS:a_[R "USUS5US'[R "US5US'[R "US US *5US 'U$[R "US US 5*US'[RUS'U$[R "US US 5US'U$)zsConverts a unit-length quaternion to a sequence of ZYZ Euler angles. Returns: ndarray: Array of Euler angles. r'r)r&r&r%)r%r&)rr&r)r&r%)r&rr&)r%r)r%r%)rDr r)r mathatan2acospi)rrCeulers rto_zyzQuaternion.to_zyzZsnn%( t9q=4y2~::c$iT;a99SY/a::c$i#d)<a  !JJs4y#d)<<a55a zz#d)SY7E!H rc[R"S[S9nUS:XaSUS'O#US:XaSUS'OUS:XaSUS'O [S 5eU[R "US - 5-n[R "US - 5US 'U"U5$) zReturn quaternion for rotation about given axis. Args: angle (float): Angle in radians. axis (str): Axis for rotation Returns: Quaternion: Quaternion for axis rotation. Raises: ValueError: Invalid input axis. r$rr@r%rAr&rBr'zInvalid axis input.g@r)r r)r ValueErrorrHsincos)clsangleaxisouts rfrom_axis_rotationQuaternion.from_axis_rotationoshhq& 3;CF S[CF S[CF23 3 txx $$%#+&A3xrc[R"U[S9nURUSUS5URUSUS5-URUSUS5-nUR SS9 U$)zGenerate 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. rrr%r&T)r9)r r r rWr<)rSanglesorderquats r from_eulerQuaternion.from_eulersF%0  " "6!9eAh 7$$VAYa9 :$$VAYa9 : t$ rrN)F)r9boolreturnr)r`z np.ndarray)rTr rUstrr`r)yzy)rZzlist | np.ndarrayr[rar`r)__name__ __module__ __qualname____firstlineno____doc__rrrr!r.r3r<rDrM classmethodrWr]__static_attributes__rrrrsZ,2'' "" %&"*4rr)rg __future__rrHnumpyr rrjrrrms!# GGr