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figure: 4antennasetup + iter clock fix
Also showcases how to remove time offsets iteratively
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figures/beacon/src/four_antenna_setup.py
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figures/beacon/src/four_antenna_setup.py
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#!/usr/bin/env python3
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__doc__ = \
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"""
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Create a figure showing the timing and geometry of 3+1 antennas,
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and the triangles between them.
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The additional antenna is to show that baselines are shared between
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triangles.
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In code (and on stdout), the antennas have time offsets which can be determined iteratively up to an overall offset.
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"""
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import matplotlib.pyplot as plt
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import numpy as np
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from itertools import combinations
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c_light = 3e8 # m/s
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def distance(x1, x2):
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"""
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Calculate the Euclidean distance between two locations x1 and x2
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"""
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assert type(x1) in [Antenna]
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x1 = np.array([x1.x, x1.y, x1.z])
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assert type(x2) in [Antenna]
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x2 = np.array([x2.x, x2.y, x2.z])
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return np.sqrt( np.sum( (x1-x2)**2 ) )
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def phase_mod(phase, low=np.pi):
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"""
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Modulo phase such that it falls within the
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interval $[-low, 2\pi - low)$.
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"""
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return (phase + low) % (2*np.pi) - low
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class Antenna:
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"""
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Simple Antenna class
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"""
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def __init__(self,x=0,y=0,z=0,t0=0,name=""):
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self.x = x
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self.y = y
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self.z = z
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self.t0 = t0
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self.name = name
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self.offsets = []
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def __repr__(self):
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cls = self.__class__.__name__
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return f'{cls}(x={self.x!r},y={self.y!r},z={self.z!r},t0={self.t0!r},name={self.name!r})'
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def antenna_triangles(antennas):
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return combinations(antennas, 3)
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def antenna_baselines(antennas):
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return combinations(antennas, 2)
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def plot_four_antenna_geometry(tx, ants, extra_ant=None, ax=None, line_kwargs={}, scatter_kwargs={}, scatter_zorder=5):
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default_line_kwargs = dict( color='grey', lw=3, alpha=0.7)
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default_scatter_kwargs = dict( color='grey', s=200)
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if ax is None:
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ax = plt.gca()
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ax.set_aspect('equal')
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ax.set_xlabel("x")
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ax.set_ylabel("y")
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line_kwargs = {**default_line_kwargs, **line_kwargs}
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scatter_kwargs = {**default_scatter_kwargs, **scatter_kwargs}
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# Plot Antennas + Tx
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for i, ant in enumerate([tx] + ants + [extra_ant]):
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ax.scatter(ant.x, ant.y, zorder=scatter_zorder, **scatter_kwargs)
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ax.annotate(ant.name, (ant.x, ant.y), ha='center', va='center',zorder=scatter_zorder)
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# Lines connecting Tx and ants
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tmp_line_kwargs = line_kwargs
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for ant in ants:
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ax.plot([tx.x, ant.x], [tx.y, ant.y], **tmp_line_kwargs)
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# Lines due to all Antennas (including extra_ant)
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line_offset = 0.08*np.array([1,1])
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for i, ant_triangle in enumerate(antenna_triangles(ants + [extra_ant])):
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tmp_line_kwargs['color'] = None
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tmp_line_kwargs['linestyle'] = '--'
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tmp_line_kwargs['alpha'] = 0.4
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for j, ant in enumerate(antenna_baselines(ant_triangle)):
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a, b = ant[0], ant[1]
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if j == 1: # fix ordering
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a, b == b, a
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dx, dy = (i-1)*line_offset
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l = ax.plot([ a.x+dx, b.x+dx], [a.y+dy, b.y+dy], **tmp_line_kwargs)
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line_kwargs['color'] = l[0].get_color()
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# Lines internal to ants triangle
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tmp_line_kwargs = line_kwargs
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tmp_line_kwargs['color'] = 'green'
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tmp_line_kwargs['alpha'] = 0.7
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for j, ant_pair in enumerate(combinations(ants,2)):
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a, b = ant_pair[0], ant_pair[1]
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if j == 1: # fix ordering
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a, b = b, a
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ax.plot([ a.x, b.x], [a.y, b.y], **tmp_line_kwargs)
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return ax
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if __name__ == "__main__":
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use_phase = False
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correct_time = True
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tx = Antenna(name="T", x=-8, y=2, t0=0)
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ants = [
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Antenna(name='1', x=0, y= 0, t0=1 ),
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Antenna(name='2', x=2, y=-3, t0=4 ),
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Antenna(name='3', x=1, y= 3, t0=10 ),
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]
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extra_ant = Antenna(name='4', x=4, y=-1, t0=-6)
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if False:#correct_time: # taken from the output of this script
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"""
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Antenna Triangle(1,2,3)
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j=0: 1,2
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j=1: 3,1
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j=2: 2,3
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sigmas: [-2.99999999 9. -6.00000001]
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sigmas sum: -8.881784197001252e-16
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(Antenna(x=0,y=0,z=0,t0=1,name='1'), Antenna(x=2,y=-3,z=0,t0=4,name='2'), Antenna(x=1,y=3,z=0,t0=10,name='3')) : [0. 2.99999999 9. ]
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Antenna Triangle(1,2,4)
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sigmas: [-2.99999999 -7.00000001 10. ]
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sigmas sum: 0.0
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(Antenna(x=0,y=0,z=0,t0=1,name='1'), Antenna(x=2,y=-3,z=0,t0=4,name='2'), Antenna(x=4,y=-1,z=0,t0=-6,name='4')) : [ 0. 2.99999999 -7.00000001]
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Antenna Triangle(1,3,4)
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sigmas: [-9. -7.00000001 16.00000001]
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sigmas sum: 0.0
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(Antenna(x=0,y=0,z=0,t0=1,name='1'), Antenna(x=1,y=3,z=0,t0=10,name='3'), Antenna(x=4,y=-1,z=0,t0=-6,name='4')) : [ 0. 9. -7.00000001]
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Antenna Triangle(2,3,4)
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sigmas: [ -6.00000001 -10. 16.00000001]
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sigmas sum: 0.0
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(Antenna(x=2,y=-3,z=0,t0=4,name='2'), Antenna(x=1,y=3,z=0,t0=10,name='3'), Antenna(x=4,y=-1,z=0,t0=-6,name='4')) : [ 0. 6.00000001 -10.
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"""
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print("Running with pre-corrected times")
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ants[1].t0 -= 2.99999999
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ants[2].t0 -= 9
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extra_ant.t0 -= -7
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ax = plot_four_antenna_geometry(tx, ants, extra_ant=extra_ant)
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fig = ax.get_figure()
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### Lol, show my calculations are right
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for i, triangle in enumerate(antenna_triangles(ants + [extra_ant])):
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print("Antenna Triangle({},{},{})".format(*[ant.name for ant in triangle]))
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sigma = np.zeros((3))
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for j, ant_pair in enumerate(antenna_baselines(triangle)):
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a, b = ant_pair[0], ant_pair[1]
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if j == 1: # fix ordering
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a, b = b, a
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if i == 0: # print sigma pairing for first triangle
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print('j={}: {},{}'.format(j, a.name, b.name))
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phys_Dt = (distance(tx, a) - distance(tx, b))/c_light
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meas_Dt = a.t0 - b.t0
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if use_phase:
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f_beacon = 50e6 # Hz
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to_phase = lambda t: phase_mod(2*np.pi*f_beacon*t)
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phys_Dt = to_phase(phys_Dt)
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meas_Dt = to_phase(meas_Dt)
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sigma[j] = meas_Dt - phys_Dt
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if False:
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print(
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"Dt'_{},{} = ".format(a.name, b.name)
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+ "{}".format(meas_Dt)
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+ " = {} - {}".format(a.t0, b.t0)
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)
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print(
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"Dt_{},{} = ".format(a.name, b.name)
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+ "{}".format(phys_Dt)
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+ " = {} - {}".format(distance(tx, a), distance(tx, b))
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)
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print(
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"sigma_{},{} = ".format(a.name, b.name)
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+ "{}".format(sigma[j])
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)
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print("sigmas:", sigma)
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if use_phase:
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print("sigmas sum:", phase_mod(np.sum(sigma)))
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else:
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print("sigmas sum:", np.sum(sigma))
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# Take the first antenna as reference
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ref_idx = 0
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ref_sigma = sigma[ref_idx]
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sigma = sigma - ref_sigma
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ant_sigma = 1/3*np.array([0, sigma[1] + sigma[2], 2*sigma[1] - sigma[2]])
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for i in [1,2]:
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triangle[i].offsets.append(-ant_sigma[i])
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if correct_time:
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triangle[i].backup_t0 = triangle[i].t0
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triangle[i].t0 += -ant_sigma[i]
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if correct_time:
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print(ants + [extra_ant])
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for i, ant in enumerate(ants + [extra_ant]):
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print(i, ant.name, ant.offsets)
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plt.show()
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