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qiskit.quantum_info.operators.quaternion의 소스 코드

# 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 warnings
import math
import numpy as np
import scipy.linalg as la


[문서]class Quaternion: """A class representing a Quaternion. """
[문서] 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.')
[문서] def norm(self): """ Norm of quaternion. """ return la.norm(self.data)
[문서] 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)
[문서] 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
[문서] 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
[문서] @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)
[문서] @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
def quaternion_from_axis_rotation(angle, axis): """DEPRECATED - 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. """ warnings.warn("quaternion_from_axis_rotation is deprecated. " "Use Quaternion.from_axis_rotation() class method instead", DeprecationWarning) return Quaternion.from_axis_rotation(angle, axis) def quaternion_from_euler(angles, order='yzy'): """DEPRECATED - 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. """ warnings.warn("quaternion_from_euler is deprecated. " "Use Quaternion.from_euler() class method instead", DeprecationWarning) return Quaternion.from_euler(angles, order)

© Copyright 2020, Qiskit Development Team. 최종 업데이트: 2021/01/17

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