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137 lines
4.1 KiB
Python
137 lines
4.1 KiB
Python
"""
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Define the super Signal class
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"""
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import numpy as np
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class Signal():
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"""
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An arbitrary signal that can be translated to another position and time.
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Note that position can be of any length.
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Super object, cannot be used directly.
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"""
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def __init__(self, t_0 = 0, x_0 = 0, velocity=None, t_f = None, x_f = None):
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"""
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Parameters
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----------
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t_0 : float, optional
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Time that this signal is sent out.
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x_0 : float, optional
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Location that this signal is sent out from.
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velocity : float, optional
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Defaults to the speed of light in m/s.
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t_f : float, optional
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Default time that this signal is received.
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x_f : float, optional
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Default Location that this signal is received.
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"""
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if t_0 is None:
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raise ValueError("t_0 cannot be None")
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if x_0 is None:
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raise ValueError("x_0 cannot be None")
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self.x_0 = np.asarray(x_0) # m
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self.t_0 = np.asarray(t_0) # s
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self.velocity = 299792458 if velocity is None else velocity # m / s
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# Default final positions
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t_f = np.asarray(t_f) if t_f is not None else None
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x_f = np.asarray(x_f) if x_f is not None else None
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self.x_f = x_f
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self.t_f = t_f
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def __call__(self, t_f = None, x_f = None, **kwargs):
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"""
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Allow this class to be used as a function.
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"""
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return self._translate(t_f, x_f, **kwargs)[0]
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def _translate(self, t_f = None, x_f = None, t_0 = None, x_0 = None, velocity = None):
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"""
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Translate the signal from (t_0, x_0) to (t_f, x_f) with optional velocity.
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Returns the signal at (t_f, x_f)
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"""
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raise NotImplementedError
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def spatial_time_offset(self, x_f=None, x_0=None, velocity=None):
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"""
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Calculate the time offset caused by a spatial distance.
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"""
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if velocity is None:
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velocity = self.velocity
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if x_0 is None:
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x_0 = self.x_0
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if x_f is None:
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x_f = self.x_f
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## make sure they are arrays
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x_0 = np.asarray(x_0) if x_0 is not None else None
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x_f = np.asarray(x_f) if x_f is not None else None
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return np.sqrt( np.sum((x_f - x_0)**2, axis=-1) )/velocity
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def temporal_time_offset(self, t_f=None, t_0=None):
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"""
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Calculate the time offset caused by a temporal distance.
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"""
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if t_0 is None:
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t_0 = self.t_0
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if t_f is None:
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t_f = self.t_f
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## make sure they are arrays
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t_0 = np.asarray(t_0) if t_0 is not None else None
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t_f = np.asarray(t_f) if t_f is not None else None
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return t_f - t_0
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def total_time_offset(self, t_f = None, x_f = None, t_0 = None, x_0 = None, velocity = None):
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"""
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Calculate how much time shifting is needed to go from (t_0, x_0) to (t_f, x_f).
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Convention:
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(t_0, x_0) < (t_f, x_0) gives a positive time shift,
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(t_0, x_0) != (t_0, x_f) gives a negative time shift
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Returns:
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the time shift
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"""
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# Get default values
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## starting point
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if t_0 is None:
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t_0 = self.t_0
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if x_0 is None:
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x_0 = self.x_0
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## final point
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if x_f is None:
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x_f = self.x_f
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if t_f is None:
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t_f = self.t_f
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## make sure they are arrays
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t_0 = np.asarray(t_0) if t_0 is not None else None
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x_0 = np.asarray(x_0) if x_0 is not None else None
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t_f = np.asarray(t_f) if t_f is not None else None
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x_f = np.asarray(x_f) if x_f is not None else None
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# spatial offset
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if x_f is None:
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spatial_time_offset = 0
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else:
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spatial_time_offset = self.spatial_time_offset(x_f, x_0=x_0, velocity=velocity)
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# temporal offset
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if t_f is None:
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temporal_time_offset = 0
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else:
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temporal_time_offset = self.temporal_time_offset(t_f, t_0=t_0)
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return temporal_time_offset - spatial_time_offset
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