kayhman

import matplotlib.pyplot as plt

for alpha in np.linspace(0.1, 0.9, 5):
    x = np.array(range(-10, 11))
    y = np.where(x > 0, alpha * x, (alpha - 1) * x)
    plt.plot(x, y, label=f'Q = {alpha}')
plt.legend(loc='upper left')
plt.show()

kayhman

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(-20, 20, 200)
y = np.abs(x)
alpha = 0.2
y_Q = np.where(x > 0, alpha * x, (alpha - 1) * x)
y_logcosh = np.where(x > 0, alpha * np.log(np.cosh(x)), (1 - alpha) * np.log(np.cosh(x)))
plt.plot(x, y_Q, label=f'Q = 0.2')
plt.plot(x, y_logcosh, label=f'Smooth Q=0.2 regression using log_cosh')

kayhman

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

kayhman

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

kayhman

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

kayhman

from forward_autodiff import DualFloat

def simple_polynome(a, b):
    return lambda x : x**2 * a + b

def squared_polynome(a, b, c):
    return lambda x : x**2 * a + x * b + c

def squared_polynome_check(a, b, c):
    return lambda x : 2*x * a + b

kayhman

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

kayhman

import numpy as np

def linear_predictions(weights, inputs):
    # y = weights[0] inputs[0] + weights[1] * inputs[1]
    # where inputs[0] = 1.0
    return np.dot(inputs, weights) * 60.0 # minutes

v_avg = 30 # km/h
startup_time = 2 /60.0 # hours

kayhman

import numpy as np

def linear_predictions(weights, inputs):
    # y = weights[0] inputs[0] + weights[1] * inputs[1]
    # where inputs[0] = 1.0
    return np.dot(inputs, weights) * 60.0

def squared_loss(weights, inputs, targets):
    # Training loss is the negative squared loss
    preds = linear_predictions(weights, inputs)

kayhman

from functools import reduce
import numpy as np
import jax.numpy as jnp


class LagrangianPolynome:
    def __init__(self, Ts, Xs):
        self.Ts = Ts
        self.Xs = Xs