def test_recursive_quad():
x, w = recursive_quad(modified_moments(rl1, 9, 0.5, 0.5))
exact = [2.69982, 0.475878, 0.826076, 0.238427, 0.470906,
0.153639, 0.325999, 0.112006, 0.248412, 0.0877162]
for i in range(10):
est = np.sum(w * x ** i)
np.testing.assert_almost_equal(exact[i], est, 5)
def test_small_order_recursive_quad():
for N in range(2, 4):
moments = modified_moments(rl1, N - 1, 0.5, 0.5)
x, w = recursive_quad(moments)
exact = [2.69982, 0.475878]
for i in range(len(exact)):
est = np.sum(w * x**i)
np.testing.assert_almost_equal(exact[i], est, 5)
def test_small_order_recursive_quad():
for N in range(2, 4):
moments = modified_moments(rl1, N - 1, 0.5, 0.5)
x, w = recursive_quad(moments)
exact = [2.69982, 0.475878]
for i in range(len(exact)):
est = np.sum(w * x ** i)
np.testing.assert_almost_equal(exact[i], est, 5)
def test_recursive_quad():
x, w = recursive_quad(modified_moments(rl1, 9, 0.5, 0.5))
exact = [
2.69982, 0.475878, 0.826076, 0.238427, 0.470906, 0.153639, 0.325999,
0.112006, 0.248412, 0.0877162
]
for i in range(10):
est = np.sum(w * x**i)
np.testing.assert_almost_equal(exact[i], est, 5)
def test_recursive_quad2():
x, w = recursive_quad(modified_moments(rl1, 9, 0.5, 2.5))
exact = [
0.7675150090814903, 0.01779131391448664, 0.2514125580305381,
0.01042604118726131, 0.1497329916946964, 0.007351040226216374,
0.1065156992309334, 0.005670755078910097, 0.08263150653792486,
0.004613594538086503
]
for i in range(10):
est = np.sum(w * x**i)
np.testing.assert_almost_equal(exact[i], est, 11)
def test_high_order_recursive_quad():
N = 100
x, w = recursive_quad(modified_moments(rl1, N - 1, 0.5, 0.5))
exact = dict()
# I get 10 digits at N = 100
exact[100] = 0.007920933265917480
# I get 5 digits at N = 110
exact[110] = 0.007192320886184629
exact[121] = 0.01703712555375862
exact[150] = 0.005257679877042412
exact[200] = 0.003934647991362962
est = np.sum(w * x**(N - 1))
np.testing.assert_almost_equal(exact[N], est, 9)
def test_high_order_recursive_quad():
N = 100
x, w = recursive_quad(modified_moments(rl1, N - 1, 0.5, 0.5))
exact = dict()
# I get 10 digits at N = 100
exact[100] = 0.007920933265917480
# I get 5 digits at N = 110
exact[110] = 0.007192320886184629
exact[121] = 0.01703712555375862
exact[150] = 0.005257679877042412
exact[200] = 0.003934647991362962
est = np.sum(w * x ** (N - 1))
np.testing.assert_almost_equal(exact[N], est, 9)
def test_recursive_quad2():
x, w = recursive_quad(modified_moments(rl1, 9, 0.5, 2.5))
exact = [0.7675150090814903,
0.01779131391448664,
0.2514125580305381,
0.01042604118726131,
0.1497329916946964,
0.007351040226216374,
0.1065156992309334,
0.005670755078910097,
0.08263150653792486,
0.004613594538086503]
for i in range(10):
est = np.sum(w * x ** i)
np.testing.assert_almost_equal(exact[i], est, 11)
def test_mapped_recursive_quad2():
mapped_ay = map_singular_pt(0.2, 0.0, 1.0)
mapped_by = map_distance_to_interval(0.3, 0.0, 1.0)
moments = modified_moments(rl1, 10, mapped_ay, mapped_by)
x, w = recursive_quad(moments)
x, w = map_pts_wts(x, w, 0.0, 1.0)
w = map_weights_by_inv_power(w, 1.0, 0.0, 1.0)
exact = [2.332556553293539,
0.9603565576440610,
0.5636909785950152, \
0.3894662160471265,
0.2949533988361775,
0.2365588120191993, \
0.1971850086215070,
0.1689379319389373,
0.1477219765628722, \
0.1312177383160300]
for i in range(len(exact)):
est = np.sum(w * x**i)
np.testing.assert_almost_equal(exact[i], est, 9)
def test_mapped_recursive_quad2():
mapped_ay = map_singular_pt(0.2, 0.0, 1.0)
mapped_by = map_distance_to_interval(0.3, 0.0, 1.0)
moments = modified_moments(rl1, 10, mapped_ay, mapped_by)
x, w = recursive_quad(moments)
x, w = map_pts_wts(x, w, 0.0, 1.0)
w = map_weights_by_inv_power(w, 1.0, 0.0, 1.0)
exact = [2.332556553293539,
0.9603565576440610,
0.5636909785950152, \
0.3894662160471265,
0.2949533988361775,
0.2365588120191993, \
0.1971850086215070,
0.1689379319389373,
0.1477219765628722, \
0.1312177383160300]
for i in range(len(exact)):
est = np.sum(w * x ** i)
np.testing.assert_almost_equal(exact[i], est, 9)
def test_mapped_recursive_quad():
mapped_ay = map_singular_pt(0.5, 1.0, 2.0)
mapped_by = map_distance_to_interval(0.5, 1.0, 2.0)
moments = modified_moments(rl1, 10, mapped_ay, mapped_by)
x, w = recursive_quad(moments)
x, w = map_pts_wts(x, w, 1.0, 2.0)
w = map_weights_by_inv_power(w, 1.0, 1.0, 2.0)
exact = [0.9370728722124352,
1.342568485003826,
2.000243585190683, \
3.091829672374373,
4.940760583752816,
8.128175556459884, \
13.70706664710914,
23.59959784014733,
41.33761425072659, \
73.44841816566141]
for i in range(10):
est = np.sum(w * x**i)
np.testing.assert_almost_equal(exact[i], est, 10)
def test_mapped_recursive_quad():
mapped_ay = map_singular_pt(0.5, 1.0, 2.0)
mapped_by = map_distance_to_interval(0.5, 1.0, 2.0)
moments = modified_moments(rl1, 10, mapped_ay, mapped_by)
x, w = recursive_quad(moments)
x, w = map_pts_wts(x, w, 1.0, 2.0)
w = map_weights_by_inv_power(w, 1.0, 1.0, 2.0)
exact = [0.9370728722124352,
1.342568485003826,
2.000243585190683, \
3.091829672374373,
4.940760583752816,
8.128175556459884, \
13.70706664710914,
23.59959784014733,
41.33761425072659, \
73.44841816566141]
for i in range(10):
est = np.sum(w * x ** i)
np.testing.assert_almost_equal(exact[i], est, 10)