def test_constructor_linear(self):
s = Segment()
self.assertTrue((s.nodes() == np.array([-1., 1.])).all())
# 1D
s = Segment(-5, 5)
self.assertTrue((s.nodes() == np.array([-5., 5.])).all())
s = Segment([-5, 5])
self.assertTrue((s.nodes() == np.array([-5., 5.])).all())
s = Segment([[-5], [5]])
self.assertTrue((s.nodes() == np.array([-5., 5.])).all())
# 2D
s = Segment([-5, 4], [5, -4])
self.assertTrue((s.nodes() == np.array([[-5, 4], [5, -4]])).all())
s = Segment([[-5, 4], [5, -4]])
self.assertTrue((s.nodes() == np.array([[-5, 4], [5, -4]])).all())
# 3D
s = Segment([-5, 4, 1], [5, -4, 1])
self.assertTrue((s.nodes() == np.array([[-5, 4, 1], [5, -4,
1]])).all())
s = Segment([[-5, 4, 1], [5, -4, 1]])
self.assertTrue((s.nodes() == np.array([[-5, 4, 1], [5, -4,
1]])).all())
def test_constructor_quadratic(self):
s = Segment(Caribou.Quadratic)
self.assertTrue((s.nodes() == np.array([-1., 1., 0.])).all())
# 1D
s = Segment(-5, 5, 0)
self.assertTrue((s.nodes() == np.array([-5., 5., 0])).all())
s = Segment([-5, 5, 0])
self.assertTrue((s.nodes() == np.array([-5., 5., 0])).all())
s = Segment([[-5], [5], [0]])
self.assertTrue((s.nodes() == np.array([-5., 5., 0])).all())
# 2D
s = Segment([-5, 5], [5, -5], [0, 0])
self.assertTrue((s.nodes() == np.array([[-5, 5], [5, -5], [0,
0]])).all())
s = Segment([[-5, 5], [5, -5], [0, 0]])
self.assertTrue((s.nodes() == np.array([[-5, 5], [5, -5], [0,
0]])).all())
# 3D
s = Segment([-5, 4, 1], [5, -4, 1], [0, 0, 1])
self.assertTrue((s.nodes() == np.array([[-5, 4, 1], [5, -4, 1],
[0, 0, 1]])).all())
s = Segment([[-5, 4, 1], [5, -4, 1], [0, 0, 1]])
self.assertTrue((s.nodes() == np.array([[-5, 4, 1], [5, -4, 1],
[0, 0, 1]])).all())
def test_linear_1D(self):
# Shape functions
s = Segment()
self.assertTrue((s.nodes() == np.array([-1., 1.])).all())
self.assertTrue((s.L([-1]) == [1, 0]).all())
self.assertTrue((s.L([+1]) == [0, 1]).all())
s = Segment(-5.5, 1.1)
# Center
self.assertEqual(s.center()[0], -2.2)
# Inverse transformation
for gauss_node in s.gauss_nodes():
self.assertMatrixEqual(
gauss_node.position,
s.local_coordinates(s.world_coordinates(gauss_node.position)))
# Contains point
s.contains_local(s.local_coordinates(s.center()))
# Integration
numerical_solution = 0.
for gauss_node in s.gauss_nodes():
x = gauss_node.position
w = gauss_node.weight
detJ = s.jacobian(x)[0]
numerical_solution += p1(s.world_coordinates(x)) * w * detJ
analytic_solution = (5 * 1.1 + (1.1 * 1.1)) - (-5.5 * 5 + (-5.5) *
(-5.5))
self.assertAlmostEqual(numerical_solution,
analytic_solution,
delta=1e-10)