def test_exact_polynomial_approximation_1d(self):
data = helper.load_test_npz('train_points_10_2.npz')
X = data['X']
X_1d = X[:, 0].copy()
f_1d = 2 + 5 * X_1d
pr = rs.PolynomialRegression(N=1)
pr.train(X_1d, f_1d)
data = helper.load_test_npz('test_points_10_2.npz')
X = data['X']
X_1d_test = X[:, 0].copy()
f, df, v = pr.predict(X_1d_test, compgrad=True, compvar=True)
np.testing.assert_almost_equal(f,
2 + 5 * X_1d_test.reshape((10, 1)),
decimal=10)
np.testing.assert_almost_equal(df, 5 * np.ones((10, 1)), decimal=10)
f_1d = 2 - 3 * X_1d + 5 * X_1d * X_1d
pr = rs.PolynomialRegression(N=2)
pr.train(X_1d, f_1d)
data = helper.load_test_npz('test_points_10_2.npz')
X = data['X']
X_1d_test = X[:, 0].copy()
f, df, v = pr.predict(X_1d_test, compgrad=True, compvar=True)
f_test = 2 - 3 * X_1d_test + 5 * X_1d_test * X_1d_test
df_test = -3 + 10 * X_1d_test
np.testing.assert_almost_equal(f, f_test.reshape((10, 1)), decimal=10)
np.testing.assert_almost_equal(df,
df_test.reshape((10, 1)),
decimal=10)
def test_poly_order_2d(self):
data = helper.load_test_npz('test_points_uniform_50_2.npz')
X = data['X']
X_test = X.copy()
xx = np.linspace(-1.0, 1.0, 21)
X1, X2 = np.meshgrid(xx, xx)
X_train = np.hstack((X1.reshape((441, 1)), X2.reshape((441, 1))))
f_train = np.sin(np.pi * X1.reshape(
(441, 1))) * np.cos(np.pi * X2.reshape((441, 1)))
print '\nPOLY 2D ORDER CONVERGENCE\n'
for N in range(3, 10):
pr = rs.PolynomialRegression(N=N)
pr.train(X_train, f_train)
f, df, v = pr.predict(X_test, compgrad=True, compvar=True)
f_true = np.sin(np.pi * X[:, 0].reshape(
(50, 1))) * np.cos(np.pi * X[:, 1].reshape((50, 1)))
df1_true = np.cos(np.pi * X[:, 1].reshape(
(50, 1))) * np.pi * np.cos(np.pi * X[:, 0].reshape((50, 1)))
df2_true = -np.sin(np.pi * X[:, 0].reshape(
(50, 1))) * np.pi * np.sin(np.pi * X[:, 1].reshape((50, 1)))
err_f = np.linalg.norm(f - f_true) / np.linalg.norm(f_true)
err_df1 = np.linalg.norm(df[:, 0].reshape((50, 1)) -
df1_true) / np.linalg.norm(df1_true)
err_df2 = np.linalg.norm(df[:, 1].reshape((50, 1)) -
df2_true) / np.linalg.norm(df2_true)
print 'Order: %d, Error in f: %6.4e, Error in df1: %6.4e, Error in df2: %6.4e' % (
N, err_f, err_df1, err_df2)
def test_polynomial_grad_2d(self):
data = helper.load_test_npz('train_points_200_2.npz')
X = data['X']
X_train = X.copy()
ff0 = np.cos(X_train[:, 0]).reshape((200, 1))
ff1 = np.sin(X_train[:, 1]).reshape((200, 1))
f_2d = ff0 * ff1
pr = rs.PolynomialRegression(N=5)
pr.train(X_train, f_2d)
data = helper.load_test_npz('test_points_10_2.npz')
X = data['X']
X_test = X.copy()
f0, df0, v0 = pr.predict(X_test, compgrad=True, compvar=True)
e = 1e-6
X_testp = X_test.copy()
X_testp[:, 0] += e
f1 = pr.predict(X_testp)[0]
df1_fd = (f1 - f0) / e
np.testing.assert_almost_equal(df0[:, 0].reshape((10, 1)),
df1_fd,
decimal=5)
X_testp = X_test.copy()
X_testp[:, 1] += e
f1 = pr.predict(X_testp)[0]
df2_fd = (f1 - f0) / e
np.testing.assert_almost_equal(df0[:, 1].reshape((10, 1)),
df2_fd,
decimal=5)
def test_exact_polynomial_approximation_2d(self):
data = helper.load_test_npz('train_points_10_2.npz')
X = data['X']
X_train = X.copy()
f_2d = 2 + 5 * X_train[:, 0] - 4 * X_train[:, 1]
pr = rs.PolynomialRegression(N=1)
pr.train(X_train, f_2d)
data = helper.load_test_npz('test_points_10_2.npz')
X = data['X']
X_test = X.copy()
f, df, v = pr.predict(X_test, compgrad=True, compvar=True)
f_test = 2 + 5 * X_test[:, 0] - 4 * X_test[:, 1]
np.testing.assert_almost_equal(f, f_test.reshape((10, 1)), decimal=10)
np.testing.assert_almost_equal(df[:, 0].reshape((10, 1)),
5 * np.ones((10, 1)),
decimal=10)
np.testing.assert_almost_equal(df[:, 1].reshape((10, 1)),
-4 * np.ones((10, 1)),
decimal=10)
f_2d = 2 - 3 * X_train[:, 1] + 5 * X_train[:, 0] * X_train[:, 1]
pr = rs.PolynomialRegression(N=2)
pr.train(X_train, f_2d)
data = helper.load_test_npz('test_points_10_2.npz')
X = data['X']
X_test = X.copy()
f, df, v = pr.predict(X_test, compgrad=True, compvar=True)
f_test = 2 - 3 * X_test[:, 1] + 5 * X_test[:, 0] * X_test[:, 1]
df1_test = 5 * X_test[:, 1]
df2_test = -3 + 5 * X_test[:, 0]
np.testing.assert_almost_equal(f, f_test.reshape((10, 1)), decimal=10)
np.testing.assert_almost_equal(df[:, 0].reshape((10, 1)),
df1_test.reshape((10, 1)),
decimal=10)
np.testing.assert_almost_equal(df[:, 1].reshape((10, 1)),
df2_test.reshape((10, 1)),
decimal=10)
def test_polynomial_grad_1d(self):
data = helper.load_test_npz('train_points_10_2.npz')
X = data['X']
X_1d = X[:, 0].copy()
f_1d = np.cos(X_1d)
pr = rs.PolynomialRegression(N=7)
pr.train(X_1d, f_1d)
data = helper.load_test_npz('test_points_10_2.npz')
X = data['X']
X_1d_test = X[:, 0].copy()
f0, df0, v0 = pr.predict(X_1d_test, compgrad=True, compvar=True)
e = 1e-6
X_1d_testp = X_1d_test.copy() + e
f1 = pr.predict(X_1d_testp)[0]
df0_fd = (f1 - f0) / e
np.testing.assert_almost_equal(df0, df0_fd, decimal=5)
def test_poly_order_1d(self):
data = helper.load_test_npz('test_points_uniform_50_2.npz')
X = data['X']
X_1d_test = X[:, 0].copy().reshape((50, 1))
X_train = np.linspace(-1.0, 1.0, 201).reshape((201, 1))
f_train = np.sin(np.pi * X_train)
print '\nPOLY 1D ORDER CONVERGENCE\n'
for N in range(3, 10):
pr = rs.PolynomialRegression(N=N)
pr.train(X_train, f_train)
f, df, v = pr.predict(X_1d_test, compgrad=True, compvar=True)
f_true = np.sin(np.pi * X_1d_test)
err_f = np.linalg.norm(f - f_true) / np.linalg.norm(f_true)
df_true = np.pi * np.cos(np.pi * X_1d_test)
err_df = np.linalg.norm(df - df_true) / np.linalg.norm(df_true)
print 'Order: %d, Error in f: %6.4e, Error in df: %6.4e' % (
N, err_f, err_df)