def test_exact_polynomial_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
pr = rs.PolynomialApproximation(N=1)
pr.train(X_1d, f_1d)
print(('Rsqr: {:6.4f}'.format(pr.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 = pr.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
pr = rs.PolynomialApproximation(N=2)
pr.train(X_1d, f_1d)
print(('Rsqr: {:6.4f}'.format(pr.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 = pr.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_polynomial_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]
pr = rs.PolynomialApproximation(N=1)
pr.train(X_train, f_2d.reshape((f_2d.size,1)))
print(('Rsqr: {:6.4f}'.format(pr.Rsqr)))
X = np.random.normal(size=(10,2))
X_test = X.copy()
f, df = pr.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]
pr = rs.PolynomialApproximation(N=2)
pr.train(X_train, f_2d.reshape((f_2d.size,1)))
print(('Rsqr: {:6.4f}'.format(pr.Rsqr)))
X = np.random.normal(size=(10,2))
X_test = X.copy()
f, df = pr.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_poly_order_2d(self):
np.random.seed(42)
X = np.random.uniform(-1.0, 1.0, size=(50, 2))
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.PolynomialApproximation(N=N)
pr.train(X_train, f_train)
f, df = pr.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 '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):
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
pr = rs.PolynomialApproximation(N=5)
pr.train(X_train, f_2d)
X = np.random.normal(size=(10, 2))
X_test = X.copy()
f0, df0 = pr.predict(X_test, compgrad=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_3d(self):
np.random.seed(42)
X = np.random.normal(size=(20, 3))
X_train = X.copy()
f_3d = 2 + 5 * X_train[:, 0] - 4 * X_train[:, 1] + 2 * X_train[:, 2]
pr = rs.PolynomialApproximation(N=3)
pr.train(X_train, f_3d.reshape((f_3d.size, 1)))
def test_rs_data_train_pr_bnd(self):
np.random.seed(42)
X0 = np.random.uniform(-1.0, 1.0, size=(50, 3))
f0 = np.random.normal(size=(50, 1))
df0 = np.random.normal(size=(50, 3))
sub = ss.Subspaces()
sub.compute(df=df0)
avd = dom.BoundedActiveVariableDomain(sub)
avm = dom.BoundedActiveVariableMap(avd)
pr = rs.PolynomialApproximation()
asrs = asm.ActiveSubspaceResponseSurface(avm, pr)
asrs.train_with_data(X0, f0)
XX = np.random.uniform(-1.0, 1.0, size=(10, 3))
ff, dff = asrs.predict(XX, compgrad=True)
def test_rs_fun_train_pr_ubnd_2d(self):
np.random.seed(42)
X0 = np.random.normal(size=(50, 3))
f0 = np.random.normal(size=(50, 1))
df0 = np.random.normal(size=(50, 3))
sub = ss.Subspaces()
sub.compute(df=df0)
sub.partition(2)
avd = dom.UnboundedActiveVariableDomain(sub)
avm = dom.UnboundedActiveVariableMap(avd)
pr = rs.PolynomialApproximation()
asrs = asm.ActiveSubspaceResponseSurface(avm, pr)
asrs.train_with_interface(self.quad_fun, 10)
XX = np.random.normal(size=(10, 3))
ff, dff = asrs.predict(XX, compgrad=True)
def test_poly_order_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))
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.PolynomialApproximation(N=N)
pr.train(X_train, f_train)
f, df = pr.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 'Order: %d, Error in f: %6.4e, Error in df: %6.4e' % (
N, err_f, err_df)
def test_polynomial_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)
pr = rs.PolynomialApproximation(N=7)
pr.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 = pr.predict(X_1d_test, compgrad=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)
