Created
October 4, 2020 12:50
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import matplotlib.pyplot as plt | |
import numpy as np | |
trip_distance = 6.0 # km | |
trip_duration = 12.0 # minutes | |
trip_avg_speed = 30.0 # km/h | |
# trip duration in minutes | |
def duration(distance, speed): | |
return distance * 1/speed * 60.0 | |
def speed_error(speed): | |
dur = duration(trip_distance, speed) | |
return trip_duration - dur | |
# Approximate diff using limit definition | |
def speed_error_num_diff(speed, delta=1e-3): | |
return (speed_error(speed+delta)**2 - speed_error(speed)**2) / delta | |
# Compute diff using exact formula | |
def speed_error_diff(speed, delta=1e-3): | |
return 2 * trip_distance*60.0/speed**2 * speed_error(speed) | |
speeds = np.linspace(20, 50) | |
error = np.vectorize(speed_error)(speeds) | |
squared_error = error**2 | |
fig, ax = plt.subplots() | |
ax.grid(True, which='both') | |
ax.plot(speeds, squared_error, label='Squared error wrt to speed param') | |
v_avg = 35 | |
for i in range(0,7): | |
diff = speed_error_diff(v_avg) | |
tangente = speed_error(v_avg)**2 + diff * (np.linspace(20, 50) - v_avg) | |
ax.scatter([trip_avg_speed, v_avg], [0, speed_error(v_avg)**2]) | |
ax.plot(np.linspace(20, 50), tangente, label=f'Tangent {v_avg}') | |
v_avg = v_avg - diff * 2.0 | |
print('new avg: ', v_avg) | |
plt.xlabel('average speed') | |
plt.legend() | |
plt.show() |
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