descent_dp.py

import matplotlib.pyplot as plt
import numpy as np

from forward_autodiff import DualFloat

trip_distance = DualFloat(6.0) # km
trip_duration = DualFloat(12.0) # minutes
trip_avg_speed = DualFloat(30.0) # km/h

# trip duration in minutes
def duration(distance, speed):
    return DualFloat(60.0, 0) * distance / speed

def speed_error(speed):
    dur = duration(trip_distance, speed)
    return trip_duration - dur

speeds = np.vectorize(DualFloat)(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(np.vectorize(float)(speeds),
        np.vectorize(float)(squared_error),
        label='Squared error wrt to speed param')
v_avg = DualFloat(35, 1.0)
for i in range(0,7):
    error = speed_error(v_avg)**2
    diff = error.derivative()
    tangente = (speeds - v_avg) * diff + speed_error(v_avg)**2
    ax.scatter([trip_avg_speed, v_avg], [0, speed_error(v_avg)**2])
    ax.plot(np.vectorize(float)(speeds),
            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()