def test_simplex_inside():
# assert inside simplex identical
for i in range(100):
x = np.random.rand(100)
x = x / np.sum(x)
x_proj, d_0, theta = simplex_proj(x)
assert_almost_equal(x, x_proj, decimal=8)
assert d_0 == l0_norm(x_proj)
def test_ball_inside():
# assert inside B(z) identical
for i in range(100):
radius = 10
x = np.random.rand(100)
x = x / np.sum(np.abs(x)) * radius
x_proj, d_0, theta = l1_ball_proj(x, radius)
assert_almost_equal(x, x_proj, decimal=8)
assert 100 == l0_norm(x_proj)
def test_ball_correct_x():
x = np.array([1.1, 0.0])
x_proj, d_0, theta = l1_ball_proj(x, 1)
assert_almost_equal(np.array([1.0, 0.0]), x_proj, decimal=8)
assert d_0 == l0_norm(x_proj)
def test_norm_zeros():
# norm_0(0) == 0
x = np.zeros(3)
norm = l0_norm(x)
assert norm == 0.0
def test_simplex_correct_endpoint_x():
x = np.array([1.1, 0.0])
x_proj, d_0, theta = simplex_proj(x)
assert_almost_equal(np.array([1.0, 0.0]), x_proj, decimal=8)
assert d_0 == l0_norm(x_proj)
def test_simplex_exterior_to_frontier():
# exterior point projects to frontier
x = np.array([0.6, 1.1])
x_proj, d_0, theta = simplex_proj(x)
assert_almost_equal(np.sum(x_proj), 1.0, decimal=8)
assert d_0 == l0_norm(x_proj)
def test_simplex_norm_0():
x = np.array([1.1, 0.6])
x_proj, d_0, theta = simplex_proj(x)
assert d_0 == l0_norm(x_proj)
def test_norm_small():
# norm_0(eps*1) == len(1)
x = 1e-12 * np.ones(3)
norm = l0_norm(x)
assert norm == len(x)
def test_norm_rand():
# norm_0(rand(3)) == 3 (a.s.)
x = np.random.rand(3)
norm = l0_norm(x)
assert norm == len(x)
def test_norm_ones():
# norm_0(1) == len(1)
x = np.ones(3)
norm = l0_norm(x)
assert norm == len(x)