def fit(self, x, t):
self.w = np.zeros([x.shape[1]*t.shape[1]])
if self.solver == 'gradient':
solver.gradient_descent(self, x, t, self.alpha, self.e, self.verbose)
elif self.solver == 'newton':
solver.newton(self, x, t, self.e, self.verbose)
def find_oscillator_eigenvalue(e0):
"""Finding the eigenvalue for harmonic oscillator potential by iterative gradient descent method.
Author
------
Paweł Czyż, Date: 01/05/2018
Parameters
----------
e0 : float
positive number being an initial guess of the eigenvalue
Returns
-------
float
the eigenvalue near the initial guess of the system with harmonic oscillator
Example
-------
>>> print(find_oscillator_eigenvalue(1.2))
0.98
>>> print(find_oscillator_eigenvalue(3.4))
3.0
"""
n = int(0.5 * (e0 - 1))
def loss(et):
x, y = solve_numerical_method(0.05, 5, n, et)
return (y[-1] / 100)**2
e_found, _ = gradient_descent(loss, e0, step=2e-5, dx=0.05, n_steps=200)
return e_found
def test_basic(self):
"""Test if a minimum of a square function is found."""
xm, vm = gradient_descent(self.loss, 0.2)
with self.subTest("Point"):
self.assertLess(abs(xm), 0.05)
with self.subTest("Value"):
self.assertEqual(vm, self.loss(xm))
def fit(self, y, X):
"""
Finds weights to fit the data to the model
:param y: answers
:param X: data
"""
# dimensions
n, d = X.shape
# initial weight vector
self.w = np.zeros(d)
# fit weights
self.w, f = solver.gradient_descent(self.function_object, self.w, self.max_evaluations,
self.verbose, y, X)
def test_right_minimum(self):
x, _ = gradient_descent(self.loss, 8, step=0.001, n_steps=40)
self.assertLess(abs(x - 10), 0.05)
def test_left_minimum(self):
x, _ = gradient_descent(self.loss, 2, step=0.001, n_steps=50)
self.assertLess(abs(x), 0.05)
def test_far_away(self):
"""Start from value lying very far from the global maximum."""
xm, _ = gradient_descent(self.loss, 200, n_steps=40)
with self.subTest("Point"):
self.assertLess(abs(xm), 0.05)