def test_extended_inputs():
inputs = np.array([[3]])
assert np.all(utils.extended_inputs(inputs) == np.array([[1, 3]]))
inputs = np.array([[3], [4]])
assert np.all(utils.extended_inputs(inputs) == np.array([[1, 3], [1, 4]]))
inputs = np.array([[3, 4, 5], [6, 7, 8]])
assert np.all(
utils.extended_inputs(inputs) == np.array([[1, 3, 4, 5], [1, 6, 7, 8]
]))
def normal_equation(inputs, outputs):
X = utils.extended_inputs(inputs)
theta = np.linalg.inv(X.T @ X) @ X.T @ outputs
return theta
def linear_model(theta, inputs):
inputs_extended = utils.extended_inputs(inputs)
return inputs_extended @ theta
def jacobien_rms(theta, inputs, outputs, model):
n_samples = outputs.shape[0]
return 1 / n_samples * (
(model(theta, inputs) - outputs) @ utils.extended_inputs(inputs))
def logistic_model(theta, inputs):
inputs_extended = utils.extended_inputs(inputs)
return sigmoid(inputs_extended @ theta)