"""
Warm-up: numpy
--------------
A third order polynomial, trained to predict :math:`y=\sin(x)` from :math:`-\pi`
to :math:`pi` by minimizing squared Euclidean distance.
This implementation uses numpy to manually compute the forward pass, loss, and
backward pass.
A numpy array is a generic n-dimensional array; it does not know anything about
deep learning or gradients or computational graphs, and is just a way to perform
generic numeric computations.
"""
import numpy as np
import math
x = np.linspace(-math.pi, math.pi, 2000)
y = np.sin(x)
a = np.random.randn()
b = np.random.randn()
c = np.random.randn()
d = np.random.randn()
learning_rate = 1e-6
for t in range(2000):
y_pred = a + b * x + c * x ** 2 + d * x ** 3
loss = np.square(y_pred - y).sum()
if t % 100 == 99:
print(t, loss)
grad_y_pred = 2.0 * (y_pred - y)
grad_a = grad_y_pred.sum()
grad_b = (grad_y_pred * x).sum()
grad_c = (grad_y_pred * x ** 2).sum()
grad_d = (grad_y_pred * x ** 3).sum()
a -= learning_rate * grad_a
b -= learning_rate * grad_b
c -= learning_rate * grad_c
d -= learning_rate * grad_d
print(f'Result: y = {a} + {b} x + {c} x^2 + {d} x^3')