def test_exact_rbf_approximation_1d(self):
np.random.seed(42)
X = np.random.normal(size=(10, 2))
M = X.shape[0]
X_1d = X[:, 0].copy().reshape((M, 1))
f_1d = 2 + 5 * X_1d
gp = rs.RadialBasisApproximation(N=1)
gp.train(X_1d, f_1d)
print 'Rsqr: {:6.4f}'.format(gp.Rsqr)
np.random.seed(42)
X = np.random.normal(size=(10, 2))
M = X.shape[0]
X_1d_test = X[:, 0].copy().reshape((M, 1))
f, df = gp.predict(X_1d_test, compgrad=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
gp = rs.RadialBasisApproximation(N=2)
gp.train(X_1d, f_1d)
print 'Rsqr: {:6.4f}'.format(gp.Rsqr)
np.random.seed(42)
X = np.random.normal(size=(10, 2))
M = X.shape[0]
X_1d_test = X[:, 0].copy().reshape((M, 1))
f, df = gp.predict(X_1d_test, compgrad=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_exact_rbf_approximation_2d(self):
np.random.seed(42)
X = np.random.normal(size=(10,2))
X_train = X.copy()
f_2d = 2 + 5*X_train[:,0] - 4*X_train[:,1]
gp = rs.RadialBasisApproximation(N=1)
gp.train(X_train, f_2d.reshape((f_2d.size,1)))
print(('Rsqr: {:6.4f}'.format(gp.Rsqr)))
X = np.random.normal(size=(10,2))
X_test = X.copy()
f, df = gp.predict(X_test, compgrad=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]
gp = rs.RadialBasisApproximation(N=2)
gp.train(X_train, f_2d.reshape((f_2d.size,1)))
print(('Rsqr: {:6.4f}'.format(gp.Rsqr)))
X = np.random.normal(size=(10,2))
X_test = X.copy()
f, df = gp.predict(X_test, compgrad=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_rbf_points_2d(self):
np.random.seed(42)
X = np.random.uniform(-1.0, 1.0, size=(50, 2))
X_test = X.copy()
print '\nRBF 2D POINT CONVERGENCE\n'
for N in range(1, 5):
xx = np.linspace(-1.0, 1.0, 2**N + 1)
X1, X2 = np.meshgrid(xx, xx)
X_train = np.hstack((X1.reshape(
((2**N + 1)**2, 1)), X2.reshape(((2**N + 1)**2, 1))))
f_train = np.sin(np.pi * X1.reshape(
((2**N + 1)**2, 1))) * np.cos(np.pi * X2.reshape(
((2**N + 1)**2, 1)))
gp = rs.RadialBasisApproximation(N=2)
gp.train(X_train, f_train)
f, df = gp.predict(X_test, compgrad=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 'Points: %d, Error in f: %6.4e, Error in df1: %6.4e, Error in df2: %6.4e' % (
(2**N + 1)**2, err_f, err_df1, err_df2)
def test_rbf_grad_2d(self):
np.random.seed(42)
X = np.random.normal(size=(200, 2))
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
gp = rs.RadialBasisApproximation(N=5)
gp.train(X_train, f_2d)
X = np.random.normal(size=(10, 2))
X_test = X.copy()
f0, df0 = gp.predict(X_test, compgrad=True)
e = 1e-6
X_testp = X_test.copy()
X_testp[:, 0] += e
f1 = gp.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 = gp.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_rbf_as(self):
np.random.seed(42)
X_test = np.random.uniform(-1.0,1.0,size=(50,2))
np.random.seed(42)
X_train = np.random.uniform(-1.0,1.0,size=(200,2))
f_train = 2 + 5*X_train[:,0] - 4*X_train[:,1] +2*X_train[:,0]*X_train[:,1]
gp = rs.RadialBasisApproximation(N=1)
e = np.array([1.0, 0.5, 0.1, 0.05, 0.01])
gp.train(X_train, f_train.reshape((f_train.size,1)), e=e)
f, df = gp.predict(X_test, compgrad=True)
v = 0.0001*np.ones(f_train.shape)
gp.train(X_train, f_train.reshape((f_train.size,1)), e=e, v=v)
f, df = gp.predict(X_test, compgrad=True)
def test_rbf_grad_1d(self):
np.random.seed(42)
X = np.random.normal(size=(10, 2))
M = X.shape[0]
X_1d = X[:, 0].copy().reshape((M, 1))
f_1d = np.cos(X_1d)
gp = rs.RadialBasisApproximation(N=0)
gp.train(X_1d, f_1d)
X = np.random.normal(size=(10, 2))
M = X.shape[0]
X_1d_test = X[:, 0].copy().reshape((M, 1))
f0, df0 = gp.predict(X_1d_test, compgrad=True)
e = 1e-6
X_1d_testp = X_1d_test.copy() + e
f1 = gp.predict(X_1d_testp)[0]
df0_fd = (f1 - f0) / e
np.testing.assert_almost_equal(df0, df0_fd, decimal=5)
def test_rbf_points_1d(self):
np.random.seed(42)
X = np.random.uniform(-1.0,1.0,size=(50,2))
X_1d_test = X[:,0].copy().reshape((50,1))
print('\nRBF 1D POINT CONVERGENCE\n')
for N in range(1,9):
X_train = np.linspace(-1.0, 1.0, 2**N+1).reshape((2**N+1,1))
f_train = np.sin(np.pi*X_train)
gp = rs.RadialBasisApproximation(N=0)
#pdb.set_trace()
gp.train(X_train, f_train)
f, df = gp.predict(X_1d_test, compgrad=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(('Points: %d, Error in f: %6.4e, Error in df: %6.4e' % (2**N+1, err_f, err_df)))
