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test_cubature.py
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test_cubature.py
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import pytest
import cubature._test_integrands as ti
from cubature import cubature
import numpy as np
import math
# test that the Genz oscillatory exact formula actually agrees at an
# even and odd dimension
def test_genz_oscillatory_exact_d3():
exact = 4 * np.cos(1056 + np.pi/7)*np.sin(12)*np.sin(306)*np.sin(738)/6273
calculated = ti.genz_oscillatory_exact(12, np.array([2, 123, 51]), 1/14)
assert np.allclose([exact], [calculated])
def test_genz_oscillatory_exact_d4():
exact = np.sin(29988 - 7*np.pi/34) * \
np.sin(51)*np.sin(2601/2)*np.sin(6273/2)*np.sin(25500) / \
784125
calculated = ti.genz_oscillatory_exact(51, np.array([2, 123, 51, 1000]),
11/17)
assert np.allclose([exact], [calculated])
def test_genz_oscillatory_d2():
x = np.array([17, 201], dtype=float)
a = np.array([41, 1/11], dtype=float)
u = 1/51
exact = np.cos(7868/11 + 2*np.pi/51)
calculated = ti.genz_oscillatory(x, a, u)
assert np.allclose([exact], [calculated])
def test_genz_oscillatory_c_d2():
x = np.array([17, 201], dtype=float)
a = np.array([41, 1/11], dtype=float)
u = 1/51
exact = np.cos(7868/11 + 2*np.pi/51)
calculated = ti.genz_oscillatory(x, a, u)
calculated_2 = ti.genz_oscillatory_c(x, a, u)
assert np.allclose([exact], [calculated_2])
assert np.allclose([calculated], [calculated_2])
def test_hcubature_genz_oscillatory_d2():
u = 2*np.pi*15/609
a = np.array([15.51, 2], dtype=float)
n = 3
xmin = np.zeros((2,))
xmax = np.ones((2,)) * n
exact = ti.genz_oscillatory_exact(n, a, u)
# check that integrand is callable
ti.genz_oscillatory(np.ones((2,), dtype=float), a, u)
val, err = cubature(ti.genz_oscillatory, 2, 1, xmin, xmax, args=(a, u),
adaptive='h')
assert np.allclose(exact, val)
def test_cubature_zero_exact():
d = 1
xmin = np.zeros((d,), dtype=float)
xmax = np.ones((d,), dtype=float)*np.pi/2
assert np.allclose(0., ti.cubature_zero_exact(xmin))
assert np.allclose(1., ti.cubature_zero_exact(xmax))
d = 3
xmin = np.zeros((d,), dtype=float)
assert np.allclose(0., ti.cubature_zero_exact(xmin))
assert np.allclose(1., ti.cubature_zero_exact(xmax))
d = 4
xmin = np.zeros((d,), dtype=float)
assert np.allclose(0., ti.cubature_zero_exact(xmin))
assert np.allclose(1., ti.cubature_zero_exact(xmax))
def test_cubature_zero():
d = 5
k = 2/np.sqrt(np.pi)
x = np.ones((d,), dtype=float)
expected = k**d
assert np.allclose(ti.cubature_one(x), expected)
def test_hcubature_cubature_zero():
xmin = np.zeros((4,))
xmax = np.array([12, 4, 0.25, 1], dtype=float)
# check that it is possible to run
ti.cubature_zero(xmax)
exact = ti.cubature_zero_exact(xmax)
val, err = cubature(ti.cubature_zero, xmax.shape[0], 1, xmin, xmax)
assert np.allclose([exact], [val])
def test_hcubature_cubature_one():
d = 3
xmax = np.ones((d,), dtype=float)
xmin = np.zeros_like(xmax)
ti.cubature_one(xmin)
exact = ti.cubature_one_exact(xmax)
val, err = cubature(ti.cubature_one, d, 1, xmin, xmax)
assert np.allclose([exact], [val])
def test_cubature_two_exact():
radius = 1.
d = 1
exact = 2
val = ti.cubature_two_exact(d, radius)
assert np.allclose([exact], [val])
d = 2
exact = np.pi
val = ti.cubature_two_exact(d, radius)
assert np.allclose([exact], [val])
d = 3
exact = 4/3*np.pi
val = ti.cubature_two_exact(d, radius)
assert np.allclose([exact], [val])
@pytest.mark.slow
def test_hcubature_cubature_two():
radius = 0.68244456511919859846
d = 2
xmin = -np.ones((d,))
xmax = np.ones((d,))
exact = ti.cubature_two_exact(d, radius)
val, err = cubature(ti.cubature_two, d, 1, xmin, xmax, args=(radius,),
abserr=1e-4, relerr=1e-4, maxEval=1000000)
true_error = np.abs(val - exact)
assert true_error < 1e-4
def test_cubature_three_exact():
d = 8
xmin = -np.ones((d,))
xmax = np.ones((d,))
val = ti.cubature_three_exact(xmin, xmax)
assert np.abs(val) < 1e-14
xmin = np.zeros((d,))
xmax = np.ones((d,))
val = ti.cubature_three_exact(xmin, xmax)
assert np.abs(val - 1) < 1e-14
def test_hcubature_cubature_three():
d = 8
xmin = np.zeros((d,))
xmax = np.ones((d,))
exact = ti.cubature_three_exact(xmin, xmax)
val, err = cubature(ti.cubature_three, d, 1, xmin, xmax)
assert np.allclose([exact], [val])
def test_genz_gaussian_exact():
u = np.array([1, 21, 2], dtype=float)
a = np.array([1/10, 1/100, 1/500], dtype=float)
val = ti.genz_gaussian_exact(u, a)
exact = 62500*pow(np.pi, 3/2)*math.erf(1/10)*(math.erf(1/250) -
math.erf(1/500))*(math.erf(21/100) - math.erf(1/5))
assert np.allclose([val], [exact])
def test_hcubature_genz_gaussian():
u = np.array([1, 21, 2], dtype=float)
a = np.array([1/10, 1/100, 1/500], dtype=float)
xmin = np.zeros_like(u)
xmax = np.ones_like(u)
exact = ti.genz_gaussian_exact(u, a)
val, err = cubature(ti.genz_gaussian, u.shape[0], 1, xmin, xmax, args=(u, a),
adaptive='h')
assert np.allclose([exact], [val])
def test_hcubature_cubature_five():
d = 3
xmin = -np.ones((d,))
xmax = np.ones((d,))
exact = 1.
val, err = cubature(ti.cubature_five, d, 1, xmin, xmax)
assert np.allclose([exact], [val])
def test_hcubature_cubature_six():
d = 3
xmin = np.zeros((d,))
xmax = np.ones((d,))
exact = 1.
val, err = cubature(ti.cubature_six, d, 1, xmin, xmax)
assert np.allclose([exact], [val])
def test_hcubature_cubature_seven():
d = 4
xmin = np.zeros((d,))
xmax = np.ones((d,))
exact = 1.
val, err = cubature(ti.cubature_seven, d, 1, xmin, xmax)
assert np.allclose([exact], [val])