def test_make_trapezoid_rule():
"""
Testing creation of quadrature formula on equally distributed points of order 1.
"""
p, w = lagrange_polynomial.make_quadrature_formula(
1, lagrange_polynomial.PointDistributionType.EQUALLY_DISTRIBUTED)
np_test.assert_array_almost_equal(p, [0.0, 1.0])
np_test.assert_array_almost_equal(w, [0.5, 0.5])
def test_make_gauss_lobatto_order2():
"""
Testing creation of gauss-lobatto quadrature formula of order 2.
"""
p, w = lagrange_polynomial.make_quadrature_formula(
2, lagrange_polynomial.PointDistributionType.GAUSS_LOBATTO)
np_test.assert_array_almost_equal(p, [0.0, 0.5, 1.0])
np_test.assert_array_almost_equal(w, [1.0 / 6.0, 2.0 / 3.0, 1.0 / 6.0])
def test_make_simpson_1_3_rule():
"""
Testing creation of quadrature formula on equally distributed points of order 2.
"""
p, w = lagrange_polynomial.make_quadrature_formula(
2, lagrange_polynomial.PointDistributionType.EQUALLY_DISTRIBUTED)
np_test.assert_array_almost_equal(p, [0.0, 0.5, 1.0])
np_test.assert_array_almost_equal(w, [1.0 / 6.0, 2.0 / 3.0, 1.0 / 6.0])
def test_make_gauss_lobatto_order3():
"""
Testing creation of gauss-lobatto quadrature formula of order 3.
"""
p, w = lagrange_polynomial.make_quadrature_formula(
3, lagrange_polynomial.PointDistributionType.GAUSS_LOBATTO)
np_test.assert_array_almost_equal(p, [0.0, 0.276393202, 0.723606798, 1.0])
np_test.assert_array_almost_equal(
w, [0.0833333333, 0.4166666667, 0.4166666667, 0.0833333333])
def test_make_boole_villarceau():
"""
Testing creation of quadrature formula on equally distributed points of order 4.
"""
p, w = lagrange_polynomial.make_quadrature_formula(
4, lagrange_polynomial.PointDistributionType.EQUALLY_DISTRIBUTED)
np_test.assert_array_almost_equal(p, [0.0, 0.25, 0.50, 0.75, 1.0])
np_test.assert_array_almost_equal(
w, [7.0 / 90.0, 32.0 / 90.0, 12.0 / 90.0, 32.0 / 90.0, 7.0 / 90.0])
def test_get_quadrature_weight():
"""
Testing extractin of quadrature weights.
"""
fe_space = fe_sp.FiniteElementSpace(mesh.Mesh([0.0, 1.0]),
fe_order=3,
quad_order=4)
_, w = lag_poly.make_quadrature_formula(
4, lag_poly.PointDistributionType.GAUSS_LOBATTO)
for iq in range(len(w)):
np_test.assert_almost_equal(fe_space.get_quadrature_weight(iq), w[iq])
def test_eval_at_quadrature_pnts():
"""
Testing evaluation of callable at quadrature points.
"""
fe_space = fe_sp.FiniteElementSpace(
mesh.Mesh([0.0, -1.0, -4.0]),
quad_order=3,
quad_type=lag_poly.PointDistributionType.EQUALLY_DISTRIBUTED)
# Testing quadrature point indexes.
np_test.assert_array_equal(
fe_space.eval_at_quadrature_pnts(lambda k, s: k), [0, 1, 2, 3])
# Testing quadrature points coordinates.
p, _ = lag_poly.make_quadrature_formula(
3, lag_poly.PointDistributionType.EQUALLY_DISTRIBUTED)
np_test.assert_array_equal(
fe_space.eval_at_quadrature_pnts(lambda k, s: s), p)