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Quellcode für qiskit.quantum_info.synthesis.quaternion

# This code is part of Qiskit.
#
# (C) Copyright IBM 2017.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.

"""
A module for using quaternions.
"""
import math
import numpy as np


[Doku]class Quaternion: """A class representing a Quaternion.""" def __init__(self, data): self.data = np.asarray(data, dtype=float) def __call__(self, idx): return self.data[idx] def __repr__(self): return np.array_str(self.data) def __str__(self): return np.array_str(self.data) def __mul__(self, r): if isinstance(r, Quaternion): q = self out_data = np.zeros(4, dtype=float) out_data[0] = r(0) * q(0) - r(1) * q(1) - r(2) * q(2) - r(3) * q(3) out_data[1] = r(0) * q(1) + r(1) * q(0) - r(2) * q(3) + r(3) * q(2) out_data[2] = r(0) * q(2) + r(1) * q(3) + r(2) * q(0) - r(3) * q(1) out_data[3] = r(0) * q(3) - r(1) * q(2) + r(2) * q(1) + r(3) * q(0) return Quaternion(out_data) else: raise Exception("Multiplication by other not supported.")
[Doku] def norm(self): """Norm of quaternion.""" import scipy.linalg as la return la.norm(self.data)
[Doku] def normalize(self, inplace=False): """Normalizes a Quaternion to unit length so that it represents a valid rotation. Args: inplace (bool): Do an inplace normalization. Returns: Quaternion: Normalized quaternion. """ if inplace: nrm = self.norm() self.data /= nrm return None nrm = self.norm() data_copy = np.array(self.data, copy=True) data_copy /= nrm return Quaternion(data_copy)
[Doku] def to_matrix(self): """Converts a unit-length quaternion to a rotation matrix. Returns: ndarray: Rotation matrix. """ w, x, y, z = self.normalize().data mat = np.array( [ [1 - 2 * y**2 - 2 * z**2, 2 * x * y - 2 * z * w, 2 * x * z + 2 * y * w], [2 * x * y + 2 * z * w, 1 - 2 * x**2 - 2 * z**2, 2 * y * z - 2 * x * w], [2 * x * z - 2 * y * w, 2 * y * z + 2 * x * w, 1 - 2 * x**2 - 2 * y**2], ], dtype=float, ) return mat
[Doku] def to_zyz(self): """Converts a unit-length quaternion to a sequence of ZYZ Euler angles. Returns: ndarray: Array of Euler angles. """ mat = self.to_matrix() euler = np.zeros(3, dtype=float) if mat[2, 2] < 1: if mat[2, 2] > -1: euler[0] = math.atan2(mat[1, 2], mat[0, 2]) euler[1] = math.acos(mat[2, 2]) euler[2] = math.atan2(mat[2, 1], -mat[2, 0]) else: euler[0] = -math.atan2(mat[1, 0], mat[1, 1]) euler[1] = np.pi else: euler[0] = math.atan2(mat[1, 0], mat[1, 1]) return euler
[Doku] @classmethod def from_axis_rotation(cls, angle, axis): """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. """ out = np.zeros(4, dtype=float) if axis == "x": out[1] = 1 elif axis == "y": out[2] = 1 elif axis == "z": out[3] = 1 else: raise ValueError("Invalid axis input.") out *= math.sin(angle / 2.0) out[0] = math.cos(angle / 2.0) return cls(out)
[Doku] @classmethod def from_euler(cls, angles, order="yzy"): """Generate 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. """ angles = np.asarray(angles, dtype=float) quat = ( cls.from_axis_rotation(angles[0], order[0]) * cls.from_axis_rotation(angles[1], order[1]) * cls.from_axis_rotation(angles[2], order[2]) ) quat.normalize(inplace=True) return quat