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examples_test.py
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examples_test.py
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import numpy
import quadpy
def test_u2():
scheme = quadpy.u2.schemes["krylov"](3)
scheme.integrate(lambda x: numpy.exp(x[0]), numpy.array([0.0, 0.3]), 0.7)
scheme = quadpy.u2.schemes["krylov"](5)
scheme.integrate(
lambda x: [numpy.exp(x[0]), numpy.exp(x[0])],
numpy.array([[1.0, 1.0], [0.0, 0.3], [2.0, 2.0]]),
[1.0, 0.7, 0.333],
)
def test_s2():
scheme = quadpy.s2.get_good_scheme(5)
scheme.integrate(lambda x: numpy.exp(x[0]), numpy.array([0.0, 0.3]), 0.7)
scheme = quadpy.s2.get_good_scheme(6)
scheme.integrate(
lambda x: [numpy.exp(x[0]), numpy.exp(x[1])],
numpy.array([[1.0, 1.0], [0.0, 0.3], [2.0, 2.0]]),
[1.0, 0.7, 0.333],
)
def test_c3():
scheme = quadpy.c3.product(quadpy.c1.newton_cotes_closed(3))
val = scheme.integrate(
lambda x: numpy.exp(x[0]),
quadpy.c3.cube_points([0.0, 1.0], [0.0, 1.0], [0.0, 1.0]),
)
scheme = quadpy.c3.product(quadpy.c1.newton_cotes_closed(3))
val = scheme.integrate(
lambda x: [numpy.exp(x[0]), numpy.exp(x[1])],
numpy.stack(
[
quadpy.c3.cube_points([0, 1], [0, 1], [0, 1]),
quadpy.c3.cube_points([0, 1], [0, 1], [0, 1]),
quadpy.c3.cube_points([0, 1], [0, 1], [0, 1]),
quadpy.c3.cube_points([0, 1], [0, 1], [0, 1]),
quadpy.c3.cube_points([0, 1], [0, 1], [0, 1]),
],
axis=-2,
),
)
assert val.shape == (2, 5)
def test_c1():
quadpy.c1.newton_cotes_closed(4).integrate(numpy.exp, [0.0, 1.0])
quadpy.c1.newton_cotes_closed(4).integrate(numpy.exp, numpy.array([[0.0], [1.0]]))
quadpy.c1.newton_cotes_closed(4).integrate(
lambda x: [numpy.exp(x), numpy.sin(x), numpy.cos(x)],
numpy.array([[0.0, 1.0], [1.0, 2.0]]),
)
def test_p3():
scheme = quadpy.p3.felippa_3()
scheme.integrate(
lambda x: numpy.exp(x[0]),
numpy.array([[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0], [0, 0, 1]]),
)
scheme = quadpy.p3.felippa_5()
scheme.integrate(
lambda x: [numpy.exp(x[0]), numpy.exp(x[1])],
numpy.array(
[
[[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]],
[[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0]],
[[1, 1, 0], [1, 1, 0], [1, 1, 0], [1, 1, 0], [1, 1, 0]],
[[0, 1, 0], [0, 1, 0], [0, 1, 0], [0, 1, 0], [0, 1, 0]],
[[0, 0, 1], [0, 0, 1], [0, 0, 1], [0, 0, 1], [0, 0, 1]],
]
),
)
def test_c2():
quadpy.c2.schemes["stroud_c2_5_4"]().integrate(
lambda x: numpy.exp(x[0]),
quadpy.c2.rectangle_points([0.0, 1.0], [0.0, 1.0]),
)
val = quadpy.c2.schemes["stroud_c2_3_1"]().integrate(
lambda x: [numpy.exp(x[0]), numpy.exp(x[1])],
numpy.stack(
[
quadpy.c2.rectangle_points([0.0, 1.0], [0.0, 1.0]),
quadpy.c2.rectangle_points([0.0, 1.0], [0.0, 1.0]),
quadpy.c2.rectangle_points([0.0, 1.0], [0.0, 1.0]),
quadpy.c2.rectangle_points([0.0, 1.0], [0.0, 1.0]),
quadpy.c2.rectangle_points([0.0, 1.0], [0.0, 1.0]),
],
axis=-2,
),
)
assert val.shape == (2, 5)
def test_e2r2():
scheme = quadpy.e2r2.get_good_scheme(3)
scheme.integrate(lambda x: numpy.exp(x[0]))
def test_e2r():
scheme = quadpy.e2r.get_good_scheme(5)
scheme.integrate(lambda x: numpy.exp(x[0]))
def test_u3():
quadpy.u3.schemes["lebedev_003a"]().integrate(
lambda x: numpy.exp(1j * x[0]) + 1j * x[0] ** 2,
numpy.array([0.0, 0.3, 0.0]),
0.7,
)
# quadpy.u3.lebedev_003a().integrate(
# lambda x: [numpy.exp(x[0]), numpy.exp(x[1])],
# numpy.array([[1.0, 1.0, 0.0], [0.0, 0.3, 0.0], [2.0, 2.0, 0.0]]),
# [1.0, 0.7, 0.333],
# )
def test_s3():
scheme = quadpy.s3.get_good_scheme(3)
scheme.integrate(lambda x: numpy.exp(x[0]), [0.0, 0.0, 0.0], 1.0)
scheme = quadpy.s3.get_good_scheme(5)
scheme.integrate(
lambda x: [numpy.exp(x[0]), numpy.exp(x[1])],
[[1.0, 1.0, 0.0], [0.0, 0.3, 0.0], [2.0, 2.0, 0.0]],
[1.0, 0.7, 0.333],
)
def test_t3():
scheme = quadpy.t3.get_good_scheme(4)
scheme.integrate(
lambda x: numpy.exp(x[0]),
numpy.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]], dtype=float),
)
scheme.integrate(
lambda x: [numpy.exp(x[0]), numpy.exp(x[1])],
numpy.stack(
[
[[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0], [0.0, 0, 1]],
[[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0], [0.0, 0, 1]],
[[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0], [0.0, 0, 1]],
[[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0], [0.0, 0, 1]],
],
axis=-2,
),
)
def test_t2():
quadpy.t2.schemes["cubtri"]().integrate(
lambda x: numpy.exp(x[0]), numpy.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]])
)
val = quadpy.t2.schemes["cubtri"]().integrate(
lambda x: [numpy.exp(x[0]), numpy.exp(x[1])],
numpy.stack(
[
[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]],
[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]],
[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]],
[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]],
[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]],
],
axis=-2,
),
)
assert val.shape == (2, 5)
def test_w3():
quadpy.w3.felippa_4().integrate(
lambda x: numpy.exp(x[0]),
numpy.array(
[[[0, 0, 0], [1, 0, 0], [0, 1, 0]], [[0, 0, 1], [1, 0, 1], [0, 1, 1]]]
),
)
val = quadpy.w3.felippa_4().integrate(
lambda x: [numpy.exp(x[0]), numpy.exp(x[1])],
numpy.stack(
[
[[[0, 0, 0], [1, 0, 0], [0, 1, 0]], [[0, 0, 1], [1, 0, 1], [0, 1, 1]]],
[[[0, 0, 0], [1, 0, 0], [0, 1, 0]], [[0, 0, 1], [1, 0, 1], [0, 1, 1]]],
[[[0, 0, 0], [1, 0, 0], [0, 1, 0]], [[0, 0, 1], [1, 0, 1], [0, 1, 1]]],
],
axis=-2,
),
)
assert val.shape == (2, 3)
def test_tn():
dim = 4
quadpy.tn.grundmann_moeller(dim, 3).integrate(
lambda x: numpy.exp(x[0]),
numpy.array(
[
[0.0, 0.0, 0.0, 0.0],
[1.0, 2.0, 0.0, 0.0],
[0.0, 1.0, 0.0, 0.0],
[0.0, 3.0, 1.0, 0.0],
[0.0, 0.0, 4.0, 1.0],
]
),
)
def test_sn():
dim = 4
quadpy.sn.dobrodeev_1970(dim).integrate(
lambda x: numpy.exp(x[0]), numpy.zeros(4), 1.0
)
def test_cn():
dim = 4
quadpy.cn.stroud_cn_3_3(dim).integrate(
lambda x: numpy.exp(x[0]),
quadpy.cn.ncube_points([0.0, 1.0], [0.1, 0.9], [-1.0, 1.0], [-1.0, -0.5]),
)
def test_un():
dim = 4
quadpy.un.dobrodeev_1978(dim).integrate(
lambda x: numpy.exp(x[0]), numpy.zeros(dim), 1.0
)
def test_enr2():
dim = 4
quadpy.enr2.stroud_enr2_5_2(dim).integrate(lambda x: numpy.exp(x[0]))
def test_e1r():
scheme = quadpy.e1r.gauss_laguerre(5)
scheme.integrate(lambda x: x[0] ** 2)
def test_e3r():
quadpy.e3r.get_good_scheme(5).integrate(lambda x: numpy.exp(x[0]))
def test_e1r2():
scheme = quadpy.e1r2.gauss_hermite(5)
scheme.integrate(lambda x: x[0] ** 2)
if __name__ == "__main__":
test_u3()