def test_square_aliased_ranges_and_opts(self):
def f(y, x):
return 1.0
r = [-1, 1]
opt = {}
assert_quad(nquad(f, [r, r], opts=[opt, opt]), 4.0)
def test_matching_dblquad(self):
def func2d(x0, x1):
return x0**2 + x1**3 - x0 * x1 + 1
res, reserr = dblquad(func2d, -2, 2, lambda x: -3, lambda x: 3)
res2, reserr2 = nquad(func2d, [[-3, 3], (-2, 2)])
assert_almost_equal(res, res2)
assert_almost_equal(reserr, reserr2)
def test_matching_quad(self):
def func(x):
return x**2 + 1
res, reserr = quad(func, 0, 4)
res2, reserr2 = nquad(func, ranges=[[0, 4]])
assert_almost_equal(res, res2)
assert_almost_equal(reserr, reserr2)
def test_matching_tplquad(self):
def func3d(x0, x1, x2, c0, c1):
return x0**2 + c0 * x1**3 - x0 * x1 + 1 + c1 * np.sin(x2)
res = tplquad(func3d, -1, 2, lambda x: -2, lambda x: 2,
lambda x, y: -np.pi, lambda x, y: np.pi,
args=(2, 3))
res2 = nquad(func3d, [[-np.pi, np.pi], [-2, 2], (-1, 2)], args=(2, 3))
assert_almost_equal(res, res2)
def test_square_aliased_fn_ranges_and_opts(self):
def f(y, x):
return 1.0
def fn_range(*args):
return (-1, 1)
def fn_opt(*args):
return {}
ranges = [fn_range, fn_range]
opts = [fn_opt, fn_opt]
assert_quad(nquad(f, ranges, opts=opts), 4.0)
def test_fixed_limits(self):
def func1(x0, x1, x2, x3):
val = (x0**2 + x1*x2 - x3**3 + np.sin(x0) +
(1 if (x0 - 0.2*x3 - 0.5 - 0.25*x1 > 0) else 0))
return val
def opts_basic(*args):
return {'points': [0.2*args[2] + 0.5 + 0.25*args[0]]}
res = nquad(func1, [[0, 1], [-1, 1], [.13, .8], [-.15, 1]],
opts=[opts_basic, {}, {}, {}], full_output=True)
assert_quad(res[:-1], 1.5267454070738635)
assert_(res[-1]['neval'] > 0 and res[-1]['neval'] < 4e5)
def test_square_separate_fn_ranges_and_opts(self):
def f(y, x):
return 1.0
def fn_range0(*args):
return (-1, 1)
def fn_range1(*args):
return (-1, 1)
def fn_opt0(*args):
return {}
def fn_opt1(*args):
return {}
ranges = [fn_range0, fn_range1]
opts = [fn_opt0, fn_opt1]
assert_quad(nquad(f, ranges, opts=opts), 4.0)
def test_variable_limits(self):
scale = .1
def func2(x0, x1, x2, x3, t0, t1):
val = (x0*x1*x3**2 + np.sin(x2) + 1 +
(1 if x0 + t1*x1 - t0 > 0 else 0))
return val
def lim0(x1, x2, x3, t0, t1):
return [scale * (x1**2 + x2 + np.cos(x3)*t0*t1 + 1) - 1,
scale * (x1**2 + x2 + np.cos(x3)*t0*t1 + 1) + 1]
def lim1(x2, x3, t0, t1):
return [scale * (t0*x2 + t1*x3) - 1,
scale * (t0*x2 + t1*x3) + 1]
def lim2(x3, t0, t1):
return [scale * (x3 + t0**2*t1**3) - 1,
scale * (x3 + t0**2*t1**3) + 1]
def lim3(t0, t1):
return [scale * (t0 + t1) - 1, scale * (t0 + t1) + 1]
def opts0(x1, x2, x3, t0, t1):
return {'points': [t0 - t1*x1]}
def opts1(x2, x3, t0, t1):
return {}
def opts2(x3, t0, t1):
return {}
def opts3(t0, t1):
return {}
res = nquad(func2, [lim0, lim1, lim2, lim3], args=(0, 0),
opts=[opts0, opts1, opts2, opts3])
assert_quad(res, 25.066666666666663)
def test_dict_as_opts(self):
try:
out = nquad(lambda x, y: x * y, [[0, 1], [0, 1]], opts={'epsrel': 0.0001})
except(TypeError):
assert False
def test_square_separate_ranges_and_opts(self):
def f(y, x):
return 1.0
assert_quad(nquad(f, [[-1, 1], [-1, 1]], opts=[{}, {}]), 4.0)