def test_LLbar(self):
x, y = sp.symbols('x y')
Identity = lambda k: k
A = lambda k: k.diff(x)
A_bar = lambda k: k.diff(y)
sigma = 0.1
k = sp.exp(-(x - y)**2 / (2 * sigma**2))
ops = [A, Identity]
ops_bar = [A_bar, Identity]
oc = bpdes.operator_compilation.compile_sympy(ops,
ops_bar,
k, [[x], [y]],
mode='cython')
pts = np.linspace(0, 1, 11)
interior = pts[1:-1, None]
bdy = pts[[0, -1], None]
print(interior.shape, bdy.shape)
obs = [(interior, None), (bdy, None)]
llbar = bpdes.collocation.calc_LLbar(ops, ops_bar, obs, oc)
top_left = llbar[:len(interior), :len(interior)]
compare_top_left = pairwise.apply(k_x_x_prime, interior, interior,
np.array([sigma]))
true_np.testing.assert_almost_equal(top_left, compare_top_left)
bottom_right = llbar[len(interior):, len(interior):]
compare_bottom_right = pairwise.apply(k_autograd, bdy, bdy,
np.array([sigma]))
true_np.testing.assert_almost_equal(bottom_right, compare_bottom_right)
top_right = llbar[:len(interior), len(interior):]
compare_top_right = pairwise.apply(k_x, interior, bdy,
np.array([sigma]))
true_np.testing.assert_almost_equal(top_right, compare_top_right)
bottom_left = llbar[len(interior):, :len(interior)]
compare_bottom_left = pairwise.apply(k_x_prime, bdy, interior,
np.array([sigma]))
true_np.testing.assert_almost_equal(bottom_left, compare_bottom_left)
def test_pairwise_2d(self):
def __fun(a, b):
assert a.shape == b.shape == (2,)
return np.sum(a*b)
A = np.array([[0., 1.], [1., 2.]])
B = np.array([[1., 0.], [1., 2.]])
res = pairwise.apply(__fun, A, B)
expected = np.array([[0., 2.], [1., 5.]])
np.testing.assert_array_equal(res, expected)
def test_pairwise_1d(self):
def __fun(a, b):
assert a.shape == b.shape == (1,)
return a * b
A = np.array([[0., 1.]]).T
B = np.array([[-1., 1.]]).T
res = pairwise.apply(__fun, A, B)
expected = np.array([[0, 0], [-1, 1]])
np.testing.assert_array_equal(res, expected)
def test_timing(self):
def __fun(a, b):
return np.sum(a*b)
A,B = np.mgrid[0:1:100j, 0:1:100j]
cython_timing = timeit(lambda: pairwise.apply(__fun, A, B), number=10)
print cython_timing
python_timing = timeit(lambda: manual_pairwise(__fun, A, B), number=10)
print python_timing
self.assertLess(cython_timing, python_timing)
def test_LLbar(self):
x, y = sp.symbols("x y")
Identity = lambda k: k
A = lambda k: k.diff(x)
A_bar = lambda k: k.diff(y)
sigma = 0.1
k = sp.exp(-(x - y) ** 2 / (2 * sigma ** 2))
ops = [A, Identity]
ops_bar = [A_bar, Identity]
oc = bpdes.operator_compilation.compile_sympy(ops, ops_bar, k, [[x], [y]], mode="cython")
pts = np.linspace(0, 1, 11)
interior = pts[1:-1, None]
bdy = pts[[0, -1], None]
print(interior.shape, bdy.shape)
obs = [(interior, None), (bdy, None)]
llbar = bpdes.collocation.calc_LLbar(ops, ops_bar, obs, oc)
top_left = llbar[: len(interior), : len(interior)]
compare_top_left = pairwise.apply(k_x_x_prime, interior, interior, np.array([sigma]))
true_np.testing.assert_almost_equal(top_left, compare_top_left)
bottom_right = llbar[len(interior) :, len(interior) :]
compare_bottom_right = pairwise.apply(k_autograd, bdy, bdy, np.array([sigma]))
true_np.testing.assert_almost_equal(bottom_right, compare_bottom_right)
top_right = llbar[: len(interior), len(interior) :]
compare_top_right = pairwise.apply(k_x, interior, bdy, np.array([sigma]))
true_np.testing.assert_almost_equal(top_right, compare_top_right)
bottom_left = llbar[len(interior) :, : len(interior)]
compare_bottom_left = pairwise.apply(k_x_prime, bdy, interior, np.array([sigma]))
true_np.testing.assert_almost_equal(bottom_left, compare_bottom_left)
def __return(x_1, x_2, fun_args=None):
return pairwise.apply(function, x_1, x_2)
def __return(x_1, x_2, fun_args=None):
return pairwise.apply(function, x_1, x_2)
def __ret_function(a, b, extra=None):
return pairwise.apply(sympy_fun, a, b, extra)
